Investigation of magnetic order in nickel - 5d transition metal …uu.diva-portal.org/smash/get/diva2:1314127/FULLTEXT01.pdf · 2019-05-07 · Muon Spin Rotation/Relaxation and Resonance

Investigation of magnetic order in nickel- 5d transition metal systems

Konstantinos Papadopoulos

Department of Physics and AstronomyUppsala University

This dissertation is submitted for the degree ofMaster of Physics

Uppsala University April 2019

To my parents

Abstract

Double perovskite materials exhibit alterations in magnetic order through manipulation oftheir crystal structure. Certain ultra thin metallic bilayers can create an exotic magnetic stateof confined spin textures called skyrmions. In both cases, new atomic arrangements leadto new electrical and magnetic properties. The following work comprises two studies, bothof which examine the magnetic properties of transition metals in either powder or thin filmsamples.

The first part is dedicated to a series of muon spin rotation and relaxation (muSR)experiments on a LaSrNiReO6, double perovskite, powder sample. In the muSR technique, aspin polarized muon beam is focused onto a powder envelope in low pressure and temperatureconditions. The spins of the implanted muons evolve depending on the intrinsic or externallyapplied magnetic field according to Larmor precession. The measurement is based onthe detection of decay positrons that carry this precession information on their preferreddecay directions. Measurements that were realized in wTF, ZF and LF setups, reveal asecond transition to magnetic order at Tc ≃ 22K, below a transition that was observed at T =

261K from magnetic susceptibility measurements. The experimental results point to threemagnetic phases, paramagnetic for T > 261K, dilute ferrimagnetic for 22 < T < 261K and amagnetically ordered state for T < 22K, that may implicate ferro- and antiferromagnetismfrom Ni sublattices and Ni-Re interactions.

The second part follows an attempt to produce and characterize ultra thin bilayer filmsfor the observation of interfacial chiral structures and skyrmions. Co/Fe/MgO (100) andW/Ni/Cu (100) bilayers were grown with magnetron sputter deposition in various layerthicknesses and their structure was determined by X-ray reflectometry (XRR). The XRRscans presented a relatively thick-layered Co/Fe/MgO film, while extremely thin and roughW/Ni/Cu bilayers, for the purposes of studying films with broken interfacial inversionsymmetry. This study was concluded with indicative magneto-transport measurements thatalso point to the reconfiguration of the growth procedure.

Table of contents

List of figures ix

List of tables xi

1 Introduction 1

2 Muon Spin Rotation/Relaxation and Resonance 52.1 Basic principles of muSR . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.2 muSR setup and the TRIUMF M20 beam-line . . . . . . . . . . . . . . . . 92.3 Double Perovskites and magnetic interactions . . . . . . . . . . . . . . . . 132.4 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.4.1 Weak Transverse Field measurements . . . . . . . . . . . . . . . . 142.4.2 Zero Field measurements . . . . . . . . . . . . . . . . . . . . . . . 162.4.3 Longitudinal Field measurements . . . . . . . . . . . . . . . . . . 202.4.4 DC and AC magnetic susceptibility . . . . . . . . . . . . . . . . . 222.4.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3 Skyrmions in transition metal bilayers 253.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253.2 Sample preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3.2.1 The Molecular Beam Epitaxy and sputter deposition methods . . . 283.2.2 Sample growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

3.3 Experimental Techniques and discussion . . . . . . . . . . . . . . . . . . . 353.3.1 XRR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353.3.2 Transport measurements . . . . . . . . . . . . . . . . . . . . . . . 40

4 Summary and future prospects 43

5 Svensk Sammanfatting 45

viii Table of contents

References 49

List of figures

2.1 Muon spin precession and positron emission . . . . . . . . . . . . . . . . . 72.2 Depolarization function evolution . . . . . . . . . . . . . . . . . . . . . . 92.3 LF, ZF and TF setups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.4 Meson Hall at TRIUMF . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.5 M20 end station and sample photos . . . . . . . . . . . . . . . . . . . . . . 122.6 Single and double perovskite structure . . . . . . . . . . . . . . . . . . . . 132.7 wTF asymmetry vs time . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.8 wTF components vs temperature . . . . . . . . . . . . . . . . . . . . . . . 162.9 ZF asymmetry vs time . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.10 ZF perpendicular components vs temperature . . . . . . . . . . . . . . . . 182.11 ZF frequency vs temperature . . . . . . . . . . . . . . . . . . . . . . . . . 192.12 ZF parallel components vs temperature . . . . . . . . . . . . . . . . . . . . 202.13 LF asymmetry vs time . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212.14 LF depolarization rate vs field . . . . . . . . . . . . . . . . . . . . . . . . 222.15 FC and ZFC DC susceptibility vs temperature . . . . . . . . . . . . . . . . 232.16 AC susceptibility components vs temperature . . . . . . . . . . . . . . . . 23

3.1 Skyrmion lattice and phase diagram . . . . . . . . . . . . . . . . . . . . . 263.2 HM/FM bilayer interfacial spin chirality . . . . . . . . . . . . . . . . . . . 273.3 Sputtering and MBE system schematics . . . . . . . . . . . . . . . . . . . 293.4 Sputtering and MBE instrument photo . . . . . . . . . . . . . . . . . . . . 303.5 XRR scan and resistivity measurement of the Pd/Si film . . . . . . . . . . . 313.6 AFM scan of Pd/Si and Co/Fe/MgO films . . . . . . . . . . . . . . . . . . 333.7 RHEED pattern of Cu substrate . . . . . . . . . . . . . . . . . . . . . . . . 333.8 Growth rates for Ni and W on Si substrates . . . . . . . . . . . . . . . . . 343.9 Specular XRR setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353.10 XRR scan of the Co/Fe/MgO sample . . . . . . . . . . . . . . . . . . . . . 373.11 XRR scan of the W/Ni/Cu samples . . . . . . . . . . . . . . . . . . . . . . 39

x List of figures

3.12 VSM system photos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403.13 Co/Fe/MgO resistivity vs temperature vs field . . . . . . . . . . . . . . . . 413.14 W/Ni/Cu magnetization vs field vs temperature . . . . . . . . . . . . . . . 42

List of tables

2.1 Positive muon properties. . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

3.1 Sample growth details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323.2 Resistivity vs temperature fit parameters . . . . . . . . . . . . . . . . . . . 41

Chapter 1

Introduction

From magnetite, to Earth’s magnetic field and the compass, to Faraday’s law of inductionand the modern age, magnetism is one of the most complex and fascinating phenomenain fundamental science while at the same time definitive in most modern technologicalapplications.

Magnetism is the result of uncoupled spin and orbital angular momenta of unpairedelectrons. The exchange interaction between two electron spins s1 and s2 , one in thevicinity of the other so that their wave functions overlap, can be described by the exchangehamiltonian:

H = Js1 · s2 (1.1)

where J the exchange constant. From this interaction arise a singlet ground state and tripletexcited states with energy difference J. The two spins will orientate parallel or antiparalleldepending on the sign of J. In a system of many interacting spins, the ground state can beextracted from Hund’s rules [1]:

(i) The orbital angular momenta configuration must maximize the L quantum number.

(ii) The spin configuration must maximize the S quantum number.

(iii) The total angular momentum quantum number will be J = |L−S| for less than halffilled subshells and J = |L+S| for more than half filled subshells.

The spin-orbit coupling interaction is given by:

HLS =−µs ·Bl = A∑i

Si ·Li (1.2)

2 Introduction

where µs is the spin magnetic moment and Bl the effective magnetic field generated bythe orbiting electrons. Additionally to the spin-orbit coupling, an ion interacts with theelectrostatic environment of the neighbouring ligands. The sum of these interactions isformulated as a crystal field:

V (r) =∫

ρ(r′)|r− r′|

dr′ (1.3)

at the position of the ion r, where ρ(r′) is the charge density of the surrounding electrons.The single electron hamiltonian term of the crystal field interaction is represented as:

HLS =−e∑i

V(r)i (1.4)

where i is the number of electrons of an incomplete shell. The competition between thosetwo interactions will determine the ground state. If the spin-orbit coupling (SOC) is largerthan the crystal field (CF) then Hund’s rules are valid and J is a good quantum number.However, if SOC is smaller than CF, then Hund’s rules can not produce the ground stateand the time average of the orbital component L is zero, a phenomenon known as orbitalquenching. This is the case for 3d transition metals. For example, in the case of Ni+2,the electronic configuration of nickel becomes [Ar]3d8. Hence, the ground state quantumnumbers become S = J = 2 (since we assume L = 0) and its total magnetic moment ism = gµb

√J(J+1) = 4.89µB where g is the Lande factor and µB the Bohr magneton.

In an ensemble of atoms the magnetic part of the hamiltonian is given by H =−∑Ji j(si · s j

)over nearest neighbours. However, if one assumes chemical bonds between magnetic ionsand interstitial ligands, the length and the angle of the bonds give rise to the so-called super-exchange interaction, described by Kramers [2] and later by Anderson [3]. Based on thiswork, the Goodenough-Kanamori-Anderson rules [4] suggest a strong antiferromagneticinteraction between two ions with unfilled orbitals and overlapping wave functions, con-nected through an interstitial ligand with filled or empty orbitals, at an 180 angle. A typicalexample is the MnO antiferromagnet. Alternatively, a weak ferromagnetic interaction ispredicted if ions with half-filled orbitals overlap with an empty/filled orbital of an interstitialligand at 90, that is the case for chloride compounds NiCl2, MnCl2, CrCl3 etc [4, 5].

In the second chapter, we present a study on a LaSrNiReO6 double perovskite’s magneticphases, that are theoretically predicted by the Goodenough-Kanamori rules. A series ofmuon spin rotation and relaxation experiments, as well as ac and dc susceptibility measure-ments have been realized, in order to map the sample’s magnetization at both high and lowtemperature range.

3

The most dramatic result of particle interactions is the creation of new macroscopic phasesfrom energetically favourable states. The properties of these states can be deduced from thefree energy of the partition function. At a phase transition various physical quantities undergosubstantial changes, which lead to singularities in the free energy. A singular behaviour,close to a critical point, is described by a set of critical exponents. The order parameter is astatistical function that changes values at each phase. In magnetism, the corresponding orderparameter is the magnetization:

m(T ) =1V

limh→0

M(h,T ) (1.5)

For T < Tc the magnetization can be described by m(T,h = 0) ∝ ((Tc −T )/Tc) and m(T =

Tc,h) ∝ h1/δ , where β and δ the critical exponents along the coexistence line and the criticalisotherm respectively.

Intrinsic magnetic properties can be significantly different, when the dimensions of amagnetic system are reduced from the bulk to the nanometre scale of 1-100nm. Phasetransitions may be shifted along the temperature and magnetic field axis or phases may alter.The characteristic length scales, e.g the domain wall length, become comparable with thestructure dimensions. Various magnetic interactions and anisotropies can be enhanced orscreened out.

The third chapter consists of the growth and characterization process of Co/Fe/MgO(100) and W/Ni/Cu (100) transition metal bilayers. The aim of this process is to study thetransition to the helical and conical spin order phase, as well as the introduction of spin chiralstructures in the bilayer interface.

Chapter 2

Muon Spin Rotation/Relaxation andResonance

2.1 Basic principles of muSR

The acronym muSR stands for muon spin rotation, relaxation and resonance. It is particlephysics probing technique, that is used to investigate intrinsic magnetic properties of materials.In the following experiment, we use positive muons which are neither captured nor attractedto the nuclei, but implanted in the electron cloud, our area of interest. Consequently, themuSR experiment is based on the interaction between the muon spin and the local magneticfield of its environment.

Muons belong to the lepton family with a rest mass of two hundred electron masses orone ninth of a proton mass and spin S = 1/2. Due to its spin, the muon has a magneticmoment, which is about three times as large as the proton magnetic moment (table 2.1).Muons were discovered to be the major constituent of cosmic rays, arriving at ground levelat ∼ 1µ/m ·cm2 with GeV −TeV energies. However, for the purpose of a muSR experiment,higher fluxes of about 104 −105µ/s · cm2 with lower 10−100 MeV energies are required[6].

charge spin magn.moment γ/2π lifetime mass

+e 1/2 3.18µp 13.5kHzG−1 2.197µs 206.768me= 0.1124mp= 105.7MeV

Table 2.1 Positive muon properties.

6 Muon Spin Rotation/Relaxation and Resonance

The process of creating positive muons is the following. A high energy proton beam isdirected into a graphite or beryllium target. As a result, positively charged, spinless pions areproduced:

p+ p → π++ p+n (2.1)

which decay with a very short life time of 26.033 ns to positive muons:

π+ → µ

++νµ (2.2)

In the weak decay of the pion, the spin angular momentum of the nearly massless muonneutrino νµ is antiparallel to its orbital angular momentum (left handed), while the spin of theantineutrino νµ is always parallel (right handed). For pions at rest, the angular momentumof the muon and its neutrino must be zero. This means that the positive muon must alsobe left handed. This allows us to produce an almost perfectly spin polarized muon beam,which is driven into the sample. After implantation, their spin polarization evolves in thelocal magnetic field until they decay with probability exp(−t/τµ) where τµ = 2.2 µs is themuon lifetime. The products of their decay are a positron, an electron neutrino and a muonantineutrino:

µ+ → e++νe + νµ (2.3)

Since the positive muon is at rest at an interstitial site of the sample structure, its orbitalangular momentum is zero, and the total angular momentum is equal to the muon spin. Thetotal angular momentum of the positron and the two neutrinos must also be zero. The totalspin of the neutrino and antineutrino is zero too. These conditions allow the positron tobe either right handed with an angular momentum in the direction of the muon spin, orleft handed with angular momentum in the opposite direction. Due to conservation of totalangular momentum and parity violation, the positron is preferably emitted in the direction ofthe muon spin (forward direction), thus creating the so called forward-backward asymmetryof the positron emission. The probability distribution of the emitted positrons as a functionof the angle θ between the emitted positron direction and the muon spin is given by:

N(θ) ∝ 1+A(E)cosθ (2.4)

where A(E) is the asymmetry parameter that depends on the energy of the emitted positronand is unity for E = Emax [7]. In figure 2.1 the cardiod shows the angular distribution

2.1 Basic principles of muSR 7

for the maximun asymmetry where the length of each radial segment is proportional tothe probability of emission in that direction. The average asymmetry over all energies isAavg(E) = 0.33 which is represented by the blue area.

Since positrons are the only particles that can be systematically detected, and theiremission is asymmetric, by collecting millions of emitted positrons, we can construct thedepolarization function of the muon spin ensemble in the local fields. For the radioactive

Fig. 2.1 Left:The cardioid represents the angular distribution N(θ) of the emission directionof the most energetically emitted positrons relative to the muon spin (bold arrow). Right:TheLarmor precession of a muon’s spin around a local magnetic field. Reproduced from [7].

muon decay, the number of events at a forward and backward detector around the sample(corresponding to the forward/backward spin-momentum asymmetry) as a function of time,must be described by an exponential decay:

NF |B = N0e−t/τµ

[1±α

Pµ(t)Pmax

](2.5)

The normalized depolarization function can then be calculated as:

αPµ(t)Pmax

=NB(t)−NF(t)NB(t)+NF(t)

(2.6)

where N0 is a normalization constant, α the initial asymmetry and Pmax(≈ 0.25) the maximumasymmetry [6].


If the sample creates an intrinsic magnetic field then the muon magnetic moment willprecess around it as a result of a torque:

τ =dSdt

= γ S× Blocal (2.7)

known as Larmor precession (figure 2.1). The angular precession evolves with Larmorfrequency ω = dϕ/dt = γµBlocal where γµ the gyromagnetic ratio of the muon (table 2.1).If the local field is the same for all implanted muons, the Larmor equation results to apolarization evolution:

αPµ,norm(t) = cos2θ + sin2

θ cos(ωµt) (2.8)

If the local field varies in different regions of the material, the depolarization functiondepends on the spatial distribution and the temporal fluctuations of the local field. For aspatially random magnetic field, an average over all directions results to:

αPµ,norm(t) =13+

23

cos(ωµt) (2.9)

The oscillating part describes the sample’s magnetic order (figure 2.2). The muon’s largemagnetic moment allows it to probe magnetic fields down to 10−5T . The field distribution ateach muon site is an interplay of individual magnetic fields (applied, dipolar, demagnetization,hyperfine field). In equation (2.9), the constant component remains also in polycrystallinesamples, since only one type of muon site with identical Blocal is assumed [8]. For a magnet,the local field is a result of the nuclear and electronic magnetic moments. If the magnetis disordered, Blocal variations lead to damping of the oscillations [8]. In a more realisticdescription the muons interact with a local magnetic field distribution rather than a particularfield. The local field contribution can be described by a gaussian (or a lorentzian) distributionwith width ∆/γµ around zero, then equation (2.9) averages to:

αPµ,norm(t) =13+

23(1−∆

2t2)e(−∆ 2t2/2) (2.10)

which is known as the Kubo-Toyabe (KT) function [9]. Falling from unity as expected, aminimum is located at t =

√3/∆ and depending on ∆ the function obtains an average value

1/3 (figure 2.2, right). This depolarization function describes the experimental data when thecontributing local fields are random and the average field at the muon site is zero [6, 9]. Ingeneral the depolarization depends on static distribution of local fields, as well as fluctuation

2.2 muSR setup and the TRIUMF M20 beam-line 9

of fields in time, and can be described by a variety of functions, each one weighted with anasymmetry parameter

αPµ,norm(t) = A1 f1(t)+A2 f2(t)+ ...+An fn(t) (2.11)

in order to describe the relaxation and possible oscillations of the muon spins with time.

Fig. 2.2 Left:Time evolution of the depolarization function (equation 2.9) for various mag-netic field amplitudes. Right:Time evolution of the field averaged Kubo-Toyabe depolariza-tion function (equation 2.10).

Since muons are implanted uniformly in the sample structure, each decay event signalstrength is proportional to its volumic fraction. Therefore partly ordered and multiple phasespace systems can be studied [6]. Muons lose energy quickly in their path inside the material,being energetic enough only to propagate and rest at an interstitial site. Phonon activatedmuon or atom hopping, quantum diffusion, impurities and defects also contribute to fieldfluctuations [6, 8]. Consequently, the local environment of the muon together with thesample’s intrinsic magnetic properties determine the spin relaxation of the muon ensemble.

2.2 muSR setup and the TRIUMF M20 beam-line

The muSR technique consists of three different types of measurements, namely transversefield (TF), longitudinal field (LF) and zero field (ZF). Each of these measurements requiresa partly different setup and studies the spin relaxation of muons for a particular externallyapplied magnetic field or no magnetic field [10, 11].


For the LF and ZF experiments, a magnetic field Bext,z is applied parallel to the initialmuon polarization direction or no field is applied respectively. The positron detectors areplaced in the forward (FD) and backward (BD) direction with respect to the muon momentum(figure 2.3a).

Fig. 2.3 Schematics of a muSR experiment for the longitudinal (or zero) and transverse fieldsetup. The arrival time t0 of each incoming muon of the conntinuous beam is given by adetector. Following the muon’s decay in the sample, the emitted positron is collected by thedetectors (arrival time t1) which are placed a) parallel and b) perpendicular to the externalfield Bext in the LF-ZF and TF setups, respectively. Reproduced from [10].

The polarization of spin sµ and momentum pµ direction of the muons are antiparallel. Thepositron is predominantly emitted in the sµ direction. In the ZF case, for no depolarization ofthe muon beam, most of the positrons will be collected at the backward detector. However, ifthe sample has an intrinsic magnetic structure, muons precess under the internal magnetic

2.2 muSR setup and the TRIUMF M20 beam-line 11

fields. The difference in positron yield from the backward and forward detector will result toa depolarization function.

In the LF case, since the muon spin is parallel to the applied field, it relaxes about itsoriginal direction. For increasing applied fields, the saturated asymmetry value will increaseuntil it reaches unity. This method allows us to distinguish between static distributions oflocal fields and fluctuating fields of nuclear and electronic nature, that may appear the samein ZF.

For the weak TF experiment, the magnetic field Bext,z is applied perpendicular to the muonspin. The detectors are placed with their normal perpendicular to applied field (figure 2.3b).The spin precesses about this transverse field with a frequency fµ = γµBµ/2π proportionalto the local field at the muon site. If there exists an intrinsic local field distribution, theoscillations created by the transverse applied field will dephase.

Fig. 2.4 The BL1A beamline at the TRIUMF accelerator facilities. This experiment wasrealised at the M20 muon beamline. Reproduced from [12].

In our set of experiments we use a continuous muon beam, which means that muonsarrive at the sample constantly. In order to be able to match each muon to the correspondingemitted positron, the setup allows only one muon decay at a time. As the muon enters fromthe left (figure 2.3), it is detected by a muon detector which triggers a clock. Until that muondecays, all other events are either disregarded, or muons are not permitted in the sample.


After the decay and its corresponding positron being collected by one of the detectors, theclock is stopped.

A continuous beam resolution is only limited by the detector hardware in comparisonto a pulsed beam facility. For a pulsed beam, the temporal width of the pulse constrainsthe resolution. An advantage of the latter is the use of total muon intensity, resulting tobetter statistics and increasing the probability to measure long-lived muons. Since there isno continuous muon events, but a muon batch arrives simultaneously, there is also lowerbackground due to coincidences of incoming muons and decaying positrons [11].

Our experiments took place in TRIUMF accelerator facilities [13]. The BL1A beam-line(figure 2.4) is the source of high energy protons produced in a cyclotron. The protons arefired in the T2 target to produce pions which then decay into spin polarized muons, driventowards the M20 end-station (figure 2.5).

Fig. 2.5 Left:The end-station of M20 beam-line. The electromagnets and the detectors inthe centre and centre-right are clearly visible.Right: Detail of the sample holder with themounted powder sample in an Al-coated Mylar tape envelope.

Our sample is a LaSrNiReO6 powdered compound with a double-perovskite structure.Approximately one gram of powder is enclosed in an envelope with 1×1 cm2 area, made ofAl-coated Mylar tape and fixed on the sample holder (figure 2.5). The sample holder is theninserted into the cryostat in vacuum in the middle of the electromagnets and the detectors.Both muons and positrons have sufficient kinetic energy to pass through the walls of thecryostat, however the silver may add an additional background signal. Measurements ofincoming positrons are taken on the backward and forward detector for 3-15 million countsat a preset magnetic field and sample temperature.

2.3 Double Perovskites and magnetic interactions 13

2.3 Double Perovskites and magnetic interactions

Perovskites are a class of materials with structures based on calcium titanate CaTiO3. Thegeneral perovskite has the stoichiometry ABX3 where A and B are cations of different sizesthat both bond to an X anion. Perovskite oxides ABO3 are the most versatile and well-studiedspecies because of their high tolerance to substitutions in both the cationic sites [14].

The ideal perovskite oxide has a cubic crystal structure with the larger, 12-fold coordi-nated, A cations placed at the center and the smaller, 6-fold coordinated, B cations at thecorner positions. The structure is typically visualized as a 3D system of adjoining BO6octahedra (figure 2.6). The structure is often distorted from tilting of the octahedra, cationdisplacements or the Jahn-Teller effect. These distortions can significantly alter the physicalproperties of the perovskite [15].

Because of the high tolerance of the perovskite structure, both A and B sublattices canform superstructures by adopting cations with different oxidation states and sizes. Doping ofa second B’ cation at the B sites may create an ordered arrangement in the crystal, leadingto a new stoichiometry A2BB′O6, termed as a double perovskite (figure 2.6). The 1:1 B-cation ratio provides a staggered ordering of small B′O6 and big BO6 edge-sharing octahedracontaining cations in different oxidation states [16]. In the majority of double perovskites,the B and B’ cations are ordered according to the cation and anion positions in the rock salt,which is the most symmetric ordering [14].

Fig. 2.6 Left: A typical cubic structure of a perovskite oxide with distortion. Right: TheB-site, rock salt type crystal structure of an A2BB′O6 double perovskite.

Double perovskites, where A is an alkaline earth and B/B’ are 3d, 4d or 5d transitionmetals, exhibit interesting magnetic and electronic properties, such as superconductivity [17],colossal magnetoresistance [18], ferroelectricity [19], piezoelectricity [20] etc, related to aninterplay between structure, charge and spin ordering [21, 22]. Their possible applications in


magnetoelectronics and spintronics are however constrained, since their physical propertiesare sensitive to structure distortions and oxygen concentration changes, leaving room formore fundamental research.

In our experiments, we study the magnetic properties of a LaSrNiReO6 double perovskitepowder sample, which was prepared by Dr. Somnath Jana [23], in the Molecular andCondensed Matter Physics Division of Uppsala University. The Ni and Re cations charge andradii are sufficiently large to create a rock-salt ordering. In ionic crystals, the magnetic ions arealways separated by non-magnetic anions, thus both the direct ferromagnetic exchange andthe kinetic antiferromagnetic exchange interactions become too small. The main interactionin these systems is a result of electron hopping from a magnetic cation to anion to the nextcation, known as superexchange interaction. Magnetic and magneto-transport propertiesdepend on the length of the bond B−O and the ∠B−O−B′ bond angle [16, 24]. Accordingto ligand field theory and Goodenough-Kanamori rules, there is a strong antiferromagneticexchange interaction if half-filled orbitals of two cations overlap with the same empty or filledorbital of intervening anion at 180o, while there is a weak ferromagnetic exchange interactionif half-filled orbitals overlap with orthogonal orbitals of anions. However, if the orbitals arein contact but do not overlap, as is the case for t2g and eg in a ∠eg(B)−O− t2g(B′) = 180o

position, there will be a weak ferromagnetic interaction between the half filled eg orbitals ofNi2+ and partially filled t2g orbitals of Re5+. In the case of lattice distortion, increasing bondlength reduces hopping which weakens the interaction [25, 26]. In the case of a deviation from180o there will be an overlap of orbitals which will favour an antiferromagnetic interaction.This is expected of LaSr1−xCaxNiReO6 where Ca2+ cations replace Sr2+ and as a resultaffect the bond angles and lattice parameters of the structure. In the following experimentsonly the LaSrNiReO6 system has been studied.

2.4 Experimental Results

For this experiment wTF, ZF and LF measurements were performed for various temperatures(2-300K) and magnetic fields in order to investigate the magnetic ground state and itstemperature dependence.

2.4.1 Weak Transverse Field measurements

When the implanted muons are taking part to a magnetic interaction with the sample, theirpolarization becomes time dependent. The polarization of the muon ensemble is derivedfrom the positron count distribution on the backward and forward detectors, as a function

2.4 Experimental Results 15

of time intervals between the muon implantation and detection of the emitted positron. Thecount rate of backward/forward detector translates to the asymmetry of the muon decay. Theweak TF measurements took place in a 50 Gauss field, perpendicular to the initial muon spinpolarization. In figure 2.7 the depolarization function time spectrum for temperatures in threedifferent orders of magnitude is presented. In the wTF case, the muons interact also with theapplied magnetic field. With the increase of temperature, a volume fraction of the sampleundergoes a transition from a magnetic to a paramagnetic phase, where the weak externalfield can drive the muon depolarization. The signature of the external field taking control ofthe muon depolarization is an oscillatory depolarization function dominating along the timespectrum. The maximum asymmetry, in this case, is not reached until T > 250K.

Fig. 2.7 Weak Transverse Field depolarization function versus time for various temperatures.

The wTF depolarization function was fitted using an oscillatory component with anexponential decay:


A0PwT F(t) = AwT F cos(2πνt +ϕ)e−λwT F t +Ainte−λintt (2.12)

where A0 the initial asymmetry, PwT F(t) the wTF muon depolarization function, AwT F ,ν ,φ ,λ

the asymmetry, frequency, relative phase and depolarization rate due to the external magneticfield and Aint ,λint the asymmetry and depolarization rate due to the intrinsic field [27]. Themaximum asymmetry is estimated to be A0 = 0.24 from a preliminary wTF measurementon Ag sample. The AwT F asymmetry is plotted as a function of temperature with a blue lineshape as a guide for the eye (figure 2.8). The observed transition consists of two steps, indi-cating a transition from a complex magnetic phase to the paramagnetic phase of maximumasymmetry above 250K. Therefore we employ a simple linear fit for the transition at lowT, which results to a critical temperature Tc = 30.77±0.36K. In the T ≃ 1.7K regime, theasymmetry seems to become constant at AwT F ≃ 0.025 suggesting that ∼ 8% of the sampleis in a paramagnetic state, which is a background added by the envelope.

Fig. 2.8 Left: Weak Transverse Field asymmetry versus temperature. The transition is fittedwith a linear fit : y = 0.00321x−0.00569. Right: Depolarization rate versus temperature.

Near the transition temperature, the relaxation time of the asymmetry should becomevery small. This critical slowing down is exhibited by the depolarization rate λ (figure 2.8)while λ → 0 in the motional narrowing limit at high temperatures.

2.4.2 Zero Field measurements

At the ZF measurements, the implanted muons may interact and depolarize due to thesample’s intrinsic magnetic field. Figure 2.9 shows the depolarization at the short and longtime domain, for various temperatures around transition.


For the fast part, a damped oscillation takes place while for the slow part, an exponentialdecay is expected. The fitting function that was selected is therefore

A0PZF(t) = A f astJ0(2πνt +ϕ)e−(λ f t)β f+Aslowe−(λst)βs (2.13)

where A0 the forementioned maximum asymmetry, and PZF(t) the ZF muon depo-larization function and J0 a Bessel function of zeroth order. Since A f ast/A0 ≃ 0.65 andAslow/A0 ≃ 0.35, according to the KT 1/3 tail, the decaying part components Aslow,λs,βs canbe attributed to the parallel field components [28, 29]. Then the oscillatory part componentsA f ast ,ν ,λ f ,β f can be connected to the internal field components which are perpendicular tothe initial muon spin polarization [30].

Fig. 2.9 Zero Field depolarization function versus short (left) and long (right) time domainabove and below transition temperature.

A single oscillation frequency is manifested in the depolarization spectra at each temper-ature, adding to the fast depolarization component evidence towards a single muon site. Acosine fitting function was initially used for the oscillatory part. A single cosine however didnot give a satisfactory fit in the transition region and the Bessel function J0(ωt) was selectedinstead, that is a negative

π

4phase shift of a cosine function [31]. A Bessel function typically

applies to incommensurate magnetic structures or spin density waves (sine-waves, helimag-netic structures, etc). In this case, the internal field at the muon site varies sinusoidally sincethere is a sinusoidal modulation of spin density at this position in the unit cell. A distributionof local fields leads to a muon relaxation that is described by the Bessel function [32, 33]. Incase of incommensurate spin density wave (SDW) order, the Bessel frequency would linkto an internal field near to the maximum SDW amplitude. According to this scenario, theNi and Re moments in a volume fraction order with an incommensurate SDW amplitude


modulation and a maximum frequency, while non-magnetic regions account for the zero-fieldsite signals [34]. One must treat this assumption with caution though. An incommensurateSDW structure may lead to a Bessel type oscillation, however conversely, a Bessel functionfit does not identify this specific structure. A complex magnetic structure or a superpositionof oscillations from magnetically and/or structurally inequivalent muon sites may as wellresult to a Bessel depolarization function [35].

The perpendicular components at the short time domain below and above the transitionare displayed in figures 2.10 and 2.11. A blue line shape is drawn as a guide for the eye. Theasymmetry component illustrates a disordered to an ordered magnetic state transition around20K. The fast depolarization component behaves similarly for the asymmetry and frequency,suggesting magnetically equivalent muon stopping sites. The depolarization rate rises withtemperature to a maximum in the transition region. This behaviour indicates an increase ofdynamics and a broadening in case of an internal field distribution.

Fig. 2.10 Asymmetry, depolarization rate and critical exponent versus temperature for theperpendicular components.


The fast critical exponent is rather constant below the transition temperature and dropsabove it. Its value ranges β ≃ [1.4,2], that is from an exponential to gaussian depolarizationmode. A gaussian function would suggest that muons interact with a static magnetic fieldwhile an exponential would mean that the magnetic state changes dynamically. Thus a value1 < β < 2 is indicative of a intermediately dynamic/quasi-static magnetic state [36]. Thefrequency-temperature relation was fitted with the phenomenological power law [28, 37]:

ν(T ) = ν0[1− (T/Tc)α ]β (2.14)

The depolarization frequency is proportional to the internal field at the muon site. Thiswas verified in the wTF measurements where γµv = B, with B being the 50G appliedmagnetic field. The power law function fits the data fairly well within the error. The criticalexponent α corresponds to the low temperature properties T ≪ Tc, v0 − v(T ) ∝ T α thatare governed by magnon excitations while β determines the asymptotic behaviour of thezero-field magnetization near the transition temperature T ≃ Tc, v(T ) ∝ (T −Tc)

β .

Fig. 2.11 Zero Field precession frequency versus temperature. The transition is fitted withthe phenomenological function y = 44.37[1− (x/22.63)1.4]0.21 .

The extracted values are α = 1.4 and β = 0.21, while the β value for the 2D-Isingmodel ≃ 0.125 and for the 3D-Ising model ≃ 0.33 [29, 37, 38]. The critical temperature iscalculated from the power law to be Tc = 22.63±0.0036K.

The parallel components of the long time domain below transition are presented in figure2.12. The slow asymmetry component follows a reverse behaviour in comparison to the fastone since the two asymmetries must add up to the total initial asymmetry. An increase aroundthe transition temperature is demonstrated, an indication of breaking of the magnetic order.


The depolarization rate λ∥ exhibits a critical behaviour around Tc while reaching zero forT → 0 and above transition, up to room temperature. These trends comply with an increaseof dynamics and a static behaviour respectively. The critical exponent β∥ varies aroundthe 1

3 value with an upward trend towards the lowest T while in high temperatures it variesaround 2

3 pointing to a dilute magnetic system. These β∥ < 1 values suggest inhomogeneousdynamics with multiple magnetic components [36].

Fig. 2.12 Asymmetry, depolarization rate and critical exponent versus temperature of theparallel components.

2.4.3 Longitudinal Field measurements

To better understand whether the nature of local magnetic fields which appear at low temper-atures, is static or dynamic, we perform measurements with an applied field BLF parallel tothe initial muon spin Sµ(0).


Let us consider a polycrystaline sample with static internal field Blocal and its magneticmoments randomly oriented. The total local field at a muon site Btot is set at an angle θ tothe initial muon spin Sµ(0). As already described, the parallel component Sµ(0) cosθ will notprecess, while the perpendicular component Sµ(0) sinθ will precess with angular frequencyω = γµBµ . The LF signal is given by the projection of the longitudinal, non-precessingcomponent, onto Sµ(0).

The perpendicular component contribution relaxes with a rate λ⊥ that is dominatedby a static field contribution while longitudinal relaxation rate λ∥ comes from low energyspin fluctuations. If a longitudinal external field is applied, the resultant Btot = Blocal +

BLF , if BLF > Blocal , will decouple from the local field and become parallel to the initialmuon polarization direction [39]. This will increase the average contribution of the parallelcomponent ⟨cos2 θ⟩ and enhance the parallel signal at the slow time domain[30, 40].

Fig. 2.13 Left: LF depolarization versus time spectrum for zero and 43G longitudinal fieldRight: LF depolarization versus time spectrum for various longitudinal magnetic fields.

The depolarization functions for various longitudinal applied fields 0 < BLF < 4000G atT = 22.9K are presented in figure 2.13. A single exponential would not fit the data properly,meaning that our sample is not 100% paramagnetic directly above transition. Instead twostretched exponentials for the fast and the slow component were used:

A0PLF(t) = A f aste−(λ f t)β f+Aslowe−(λst)βs (2.15)

The upward shift in the slow component between the zero field and the small BLF = 43Gconfirms that the sample state lies above transition since BLF > Blocal . A field of 4 ·103 Gaussdoes not completely decouple the muon spin and relaxation is still observed. This behaviourshows that at 23K, the local field that muons see, includes not only fluctuating fields but also


a static field distribution is present. Possible short range order and paramagnetic fractionswould fit this behaviour. Muons in the short range order fraction will perform a staticor quasi-static relaxation and muons in the paramagnetic fraction will relax dynamically[30]. The LF decoupling reveals that the static magnetic phase persists above transition inagreement to the wTF measured transition.

Fig. 2.14 Fast depolarization rate versus external magnetic field at T=22.9K. The curve isfitted with the Redfield formula.

The depolarization rate for the fast component is decreasing with increased appliedLF field (figure 2.14). This behaviour indicates the gradual decoupling of the muon spinpolarization from the internal fields while the polarization relaxes with the external field [41].The relaxation rate - LF field relation can be described with the Redfield function:

λLF =2γ2(µHlocal)

2τc

1+(γµHLFτc)2 (2.16)

where γ the muon gyromagnetic ratio (13.533kHz/G), τc the correlation time and µHlocal =

Blocal the local field distribution width [40, 42]. This will be a Lorentzian function withwidth at half maximum equal to (τcγ)−1 [43]. The fitted values do not coincide with theformula in intermediate fields. The fit results to a local field of Blocal = 48.39±1.046G anda correlation time τc = 98.8±4.99µs or a 10kHz fluctuation frequency.

2.4.4 DC and AC magnetic susceptibility

Additionally to the muSR, magneto-transport measurements were carried out at low andhigh temperatures [23]. The DC magnetic susceptibility was measured in field cooled (FC)and zero field cooled (ZFC) cycles down to 5K (figure 2.15). The sample undergoes a


ferromagnetic transition at Tc ≃ 252K visible through a bifurcation of the susceptibilitycurves when a 200Oe field is applied. The FC susceptibility saturates below 20K. A second,as discussed, transition takes place around Tc ≃ 30K in the ZFC measurement and appears tobe of an antiferromagnetic nature.

Fig. 2.15 DC susceptibility versus temperature for a field cooled and zero field cooled sample.

In order to comment on the dynamics of the magnetic system, AC magnetic susceptibilitymeasurements were also realized, since the ac measurement is sensitive to the slope ofM(H) and not its absolute value. The real and imaginary part of the susceptibility at hightemperatures are presented in figure 2.16. The inset with the temperature derivative of thereal part, pinpoints the high temperature transition at T = 261K [44].

Fig. 2.16 Real (left) and imaginary (right) part of AC susceptibility versus temperaturefor various operating frequencies. Inset: The temperature derivative of χ ′ as a function oftemperature.

Both real and imaginary part are dependent on the frequency (1.7, 17, 170Hz) of thedrive field. Around the transition the curves are depressed with a higher frequency but


do not exhibit any shift in temperature as it is a typical behaviour of frustrated magneticsystems [45]. The observed transition points to a dilute ferrimagnetic where the paramagnetto ferrimagnet transition is not an immediate one but a relaxation process that requires somemagnetic moment modulation [44].

2.4.5 Conclusions

The musr and susceptibility measurements reveal three magnetic states of the LaSrNiReO6double perovskite compound. These states are, paramagnetic for T > 261K, dilute ferri-magnetic for 22 < T < 261K and a magnetically ordered state for T < 22K. Such a dilutemagnetic system can change its magnetic properties depending on the Ni-O and Ni-O-Rebonds, magnetic element (Ni, Re) sublattices and lattice distortions.

A bifurcation between the ZFC and FC dc susceptibility indicates a transition at Tc,high =

261K. Considering also the ac susceptibility frequency dependence, a transition from aparamagnetic to a dilute ferrimagnetic state is suggested.

The musr ZF depolarization data at low T could not be fitted with a Kubo-Toyabefunction until above Tc,high, a fact that excludes a 100% paramagnetic or spin-glass system.The oscillatory part was fitted with a Bessel function, typical for incommensurate magneticstructures. The perpendicular components expose a transition from a dilute magnetic to anintermediately dynamic/quasi-static state at Tc,low = 22.63K. The fitted parallel exponentβ∥ and depolarization rate λ∥ suggest an inhomogeneous field distribution system withmultiple magnetic components. The LF measurements just above transition present anincomplete decoupling of static fields at high field, backing up the wTF results of a persistingmagnetic phase above transition. These results, combined with the ac susceptibility frequencydependence, point to an incommensurate short range ordered system transitioning to a diluteferrimagnetic state before becoming a paramagnet. Neutron powder diffraction for thissample supports the short range order case, since no magnetic Bragg peaks were foundbetween diffraction patterns above and below transition [23]. In order to investigate furtherthe magnetic state and dynamics at low T, more LF measurements at various fields andtemperatures below transition can be realised.

The theoretical Goodenough-Kanamori rules suggest a weak ferromagnetic interactionbetween Ni and Re ions. Indeed a single oscillation frequency is observed, however themusr ZF data were not fitted with a single cosine but a Bessel oscillation. A ferromagneticcontribution , would most likely originate from the Ni sublattice since the Ni-Re interactioncould change from ferro- to antiferromagnetic with a distortion of the Ni-O-Re bonds.The β∥ ≃ 0.3 values could also be justified by a possible incommensurate order with anantiferromagnetic spin-wave ground state.

Chapter 3

Skyrmions in transition metal bilayers

3.1 Introduction

Competition between dipolar, exchange interactions and magnetic anisotropies can formnon-collinear or non-coplanar spin textures in bulk or nanoscale structures. Amongst them,magnetic skyrmions, particle-like stable structures of topological nature, promise anotherlevel of electric control of magnetism, able to store information in their spin arrangementwhile being spatially driven.

These structures were originally proposed in the high energy physics field by TonySkyrme. In condensed matter physics, as localized spin textures, they exhibit topologicalstability on condition that there is a break of inversion symmetry in the spatial distributionof magnetic moments (figure 3.1). This breaking of symmetry leads to the Dzyaloshinskii-Moriya (DM) interaction, which plays a leading role in the formation of swirling spin texturesthat minimize the magnetic energy of the system [46].

Different mechanisms lead to a variety of spin textures and skyrmion structures. Here,the case of skyrmions, created in inversion asymmetric chiral lattices in the interface betweenferromagnet and heavy metal layers, is presented. The Heisenberg ferromagnetic interactionleads to parallel or antiparallel spin configurations while the DM interaction enforces perpen-dicular alignment of the magnetic moments. With the addition of an applied magnetic field,the winded spin texture of skyrmions is formed. The corresponding hamiltonian forms as:

H =− ∑⟨i, j⟩

Ji j(si · s j

)+ ∑

⟨i, j⟩Di j ·

(si × s j

)−∑

iKi

(si · ki

)2 −∑i

gµBH · si (3.1)

where the four terms are the Heisenberg interaction Ji j, DM interaction Di j, uniaxialanisotropy Ki and interaction of the spins with the applied field H respectively [46, 47].

26 Skyrmions in transition metal bilayers

Depending on the D/J ratio and their signs, different spin states and skyrmion structures canappear in each layer. Five magnetic states arise depending on temperature and magnetic fieldas illustrated in the phase diagram of cubic chiral helimagnets in figure 3.1 (right).

A helical phase appears below Tc in low external magnetic fields. In this phase the spinsrotate around the propagation direction of the spin spirals. In higher magnetic fields a conicalphase appears with a net magnetic moment in the field’s direction, while above Hc the spinsare completely polarized along the field lines. Close to Tc and at fields where the conicalphase exists, a phase transition takes place, which results to the skyrmion lattice [48].

Fig. 3.1 Left: The Néel skyrmion spin configuration with topological charge Q = 1 and itsstereographic projection on the unit sphere [49]. Right: Typical magnetic phase diagram ofcubic chiral helimagnets as a function of temperature, presenting five possible spin states.Reproduced from [50].

The textures created from the distribution of spins can be described by topological classes,each characterized by an integer number Q known as the topological charge or skyrmionnumber. This parameter is defined as:

Q =1

4π

∫n ·

(∂ n∂x

× ∂ n∂y

)dxdy (3.2)

an integral of solid angles that sums the number of times the spin unit vector n wrapsaround the unit sphere [51]. The skyrmion number is a topological invariant and can beused to describe different spin textures. An example is illustrated in figure 3.1 where a Néelskyrmion with Q = 1 is presented. If we observe the spin chain along a diameter, a chiralstructure with the centre as a mirror point is evident.

Aside from bulk materials, it has been discovered that chiral magnetic textures alsoarise at the interface of transition metal bilayers [52, 53]. Especially in a ferromagnet-5d

3.1 Introduction 27

heavy metal (FM/HM) bilayer thin films with interfacial inversion asymmetry, a strong spin-orbit coupling from the high transition metal has been found to add a large DM interactioncontribution [54]. The D vector lies in the film plane, normal to the distance vector of twoneighbouring spins. This promotes the creation of chiral Néel type domain wall or skyrmiontextures as displayed in figure 3.2.

Fig. 3.2 Non-collinear spin chiral structure due to DM interaction at the interface of a FM/HMbilayer with broken inversion symmetry. Reproduced from [55].

The thickness of the layers is crucial since for relatively thick films with an in-planemagnetic anisotropy, spins are aligned along the easy magnetization axis. In these in-planemagnetized systems neither Bloch nor Néel type domain walls will assume any chiralconfiguration. In the case of FM/HM bilayers, the HM layer also creates a perpendicular spincurrent into the FM layer due to its large spin-Hall effect. This current induces spin-orbittorques that can be used to electrically control the motion of skyrmions. Therefore theFM/HM systems gain further attention concerning possible technological applications inmagnetic "racetrack" memories [46, 56].


3.2 Sample preparation

A series of FM/FM and FM/HM bilayer thin films have been prepared in order to study theirinterfacial magnetic configurations. The growth techniques in use are introduced in the firstsection, followed by a full account on the growth procedure of all samples. The collectiveinformation of sample growth can be found in the summary table 3.1.

3.2.1 The Molecular Beam Epitaxy and sputter deposition methods

MBE

Molecular beam epitaxy (MBE) is a thin film growth technique that produces epitaxial layerswith clean, abrupt interfaces and composition altering in a highly controlled environment.

The MBE chamber environment is maintained in ultra high vacuum (p < 10−9Torr)which ensures low contamination of the produced samples. A number of material targetsare located in effusion furnaces (also known as effusion cells), where they are thermallyevaporated, producing atomic or molecular beams of the constituent elements or theircompounds (figure 3.3). These beams can travel in nearly collision-free paths to reachand condense on the substrate surface of the selected base material. The beam pressureis sufficiently low so the molecular flow regime is preserved and the incident beam fluxescan be controlled mechanically or pneumatically through shutters or needle valves. Thisfeature allows low deposition rates (a few Å/s) and abrupt changes in the composition of thecollective incoming molecular beams. As result, one can produce systematically elementalor complex crystals even in one atomic layer at a time, with well defined interfaces [57, 58].

The growth chamber contains also the substrate rotating holder and heater, a coolingsystem of liquid nitrogen and the reflection high-energy electron diffraction (RHEED) system.The in situ RHEED is an important element to the high-end growth quality of MBE. It is usedto inspect the crystallinity of the surface, visualize the layer by layer growth and calibrategrowth rates. The RHEED electron gun emits electrons which hit the sample surface atgrazing angles. The reflected electrons off the surface layers impinge on a phosphor screenforming a RHEED pattern that consists of the specular reflection and diffraction patternswhich indicate the surface crystalline structure [58, 59].

The MBE system used in this thesis consists of three chambers, the load lock, the bufferand the growth chamber, in order to maintain the ultra high vacuum (UHV) environment.Different vacuum systems are used in each stage (rotary, diffusion, tubro and ion pumps) inorder to achieve these pressure conditions. The substrates are inserted/retrieved into/from the

3.2 Sample preparation 29

vacuum environment at the load lock (∼ 10−6Torr) as shown in figure 3.4 (point a). Fromthere, the sample can pass to the buffer chamber (point c) -with the use of a transfer rod (pointb)- and be placed on a storage carousel with multiple holder pockets. There the substrate canbe sputtered with Argon and annealed with a heating coil in order to destroy, reconstruct andthus clean the surface [60]. Another transfer rod can then carry the sample holder from thecarousel to the growth chamber (point d) where the deposition will take place (point e).

Fig. 3.3 Schematics of the sputtering (left) and MBE (right) chambers.

Sputter deposition

The sputtering process configuration is a planar diode consisting of an anode, a cathodeand an intermediate ionized inert gas. In this case, the atoms of a target are not thermallyevaporated off the material but "sputtered" off by bombarding its surface with energetic ions.

A system of evacuated chambers is also used in the sputtering method. A substrate isinserted at the load lock and when evacuation is complete, it is transferred to the sputteringchamber and placed on a heated, rotating base, which serves as the grounded anode of thesystem. Opposite to the anode there is a cathode were the target material is placed. Afterfurther evacuation, an inert gas (typically argon) is inserted in the chamber and negativecharge is applied to the target from a DC power supply (figure 3.3). The anode-target systemhas a water-cooled backing plate to dissipate the heat created from ion bombardment. Thisprevents outgassing or melting of the target material. Free electrons flow from the negativelycharged target and collide with the argon atom’s outer electronic shell creating and sustaininga plasma state in the chamber. Once the plasma is ignited, the positive argon ions areattracted to the target where they collide with and extract atoms from the target material


through momentum transfer. Providing that these "sputtered" atoms obtain kinetic energieshigher than their thermalization energy, they fly through the ionized gas and deposit on thesubstrate surface [59].

Fig. 3.4 The sputtering (left) and MBE (right) chambers of the growth instrument in theMaterial Physics division of Uppsala University.

The sputter yield depends on the working gas pressure, the power of the generated current,the ion’s angle to the target, their relative mass to the target atoms, the target’s surface bindingenergy etc. The applied electric field can also drive secondary electrons, negative ions ordesorbed impurities to the substrate. In total, the active environment of the electrodes and theionized gas create conditions that are harder to control than in MBE. Typically, pressures upto 100mTorr and voltages of several kV are applied. For a low working gas pressure, ionsare produced away from the target and may not reach and sputter atoms, therefore the flow oftarget atoms decreases. For low voltage, the sputtered atoms will not carry enough kineticenergy and ultimately thermalize during their flight through the plasma. With no directedflight they will diffuse backward or forward, depositing to the closest, target or substrate.This process will lower the deposition rate, compromise the uniformity of the sputtered filmand impede the composition process [59, 60].

In order to achieve higher deposition rate while allowing lower operating pressures andvoltages a magnetron is utilized. Permanent magnets are arranged on the back of the targetmaterial in alternating N and S poles (figure 3.3). This array of magnets creates a magnetic


field tunnel in front of the target which (together with the E field) forces electrons that flyoff into a cycloidal motion, confining them in the cathode area. This leads to a denser andconfined generated plasma near the target which increases the sputter rate and reduces gasscattering for the atoms in flight [58].

3.2.2 Sample growth

A series of transition metal thin-film samples were prepared in order to familiarize ourselveswith the growth techniques and test the properties of different systems.

The MBE instrument (figure 3.4) was used for a single layer Pd test-sample on a Si(111) substrate. The growth took place in an ultra high vacuum chamber at 1.2 ·10−10Torrbase pressure. The substrate was degassed at 300°C and the Pd layer was grown at roomtemperature, in a 10−8Torr atmosphere as presented in table 3.1. The Pd/Si sample was thenscanned using X-ray reflectometry (XRR) and atomic force microscopy (AFM) in order toestimate the layer thickness and surface roughness. The experimental results are presented infigures 3.5 and 3.6 respectively. The XRR fit, presented in figure 3.5 (left), does not followthe oscillation amplitude and the superimposed slope precisely. However, the thickness of thelayer is determined by the period of oscillations (see section 3.3.1) which is fitted sufficiently.Taking this into consideration, the thickness of the Pd layer was simulated to be dPd ≃ 15nm.

Fig. 3.5 XRR intensity versus 2theta angle (left) and longitudinal resistivity versus tempera-ture (right) for the Pd/Si thin films.

The mean roughness (the average of the absolute values of the surface height deviationsmeasured from the mean plane) is calculated from the AFM NanoScope-Analysis program tobe Ra = 1.76Å. In a resistivity measurement down to 10K and at zero magnetic field (figure3.5) the sample exhibited a typical metallic behaviour with a constant value below 14K. This


measurement took place in a VSM, using the Van der Pauw method as described in section3.3.2.

Film Method Thickness Reciperate:0.4Å/s, Tdeg = 300°C

Pd/Si MBE Pd:15nm pb ≃ 10−10Torr, pdep = 10−8TorrTdep: r.t, e-beam: 6.5kV, 0.13A

Tf l = 1000°C, Tan = 320°CCo/Fe/MgO Sputtering Co:8nm Fe:3.9nm pb ≃ 10−10Torr, pAr = 5mTorr

PFe/PCo = 60/65W , rate ≃ 0.25Å/s#1 W:1.25nm Ni:1.4nm pAr = 1mTorr(5.5ml/min)

W/Ni/Cu (x3) Sputtering #2 W:0.74nm Ni:1.7nm pb ≃ 10−7Torr, P = 10W#3 W:0.9nm Ni:1.5nm Tan ≃ 375°C

Table 3.1 Sample growth details.

The other samples were prepared with sputter deposition in two sputtering systems. ForCo/Fe/MgO, in the same UHV system as for MBE, an MgO (100) substrate was loaded in themagnetron sputtering instrument (figure 3.4) and flashed to 1000°C for one minute in orderto remove any humidity since magnesium oxide has a tendency to absorb water easily [61].The substrate was then heated up to 320°C and a Fe layer was deposited under Ar pressurepAr = 5mTorr with I = 0.17A current. The growth is not expected to be epitaxial, howeveriron can grow epitaxially on MgO [62]. The temperature was then lowered below 150°Cand a layer of Co was grown with I = 0.16A on iron. The film was allowed to cool downbefore being removed from the vacuum chambers. This sample was also scanned with XRRand AFM. The thickness of each layer is presented in table 3.1 while the mean roughnessof the surface was calculated to be Ra = 1.13Å. In figure 3.6 the 3D images for the heightprofile of the Pd/Si and Co/Fe/MgO samples are presented. Both surface layers are expectedto be a thin oxide of the top metal layer. The iron-cobalt sputtered bilayer appeared to havea smoother surface than the Pd monolayer on Si grown with MBE at about the same totalthickness. This was expected since high growth rate enables island growth and in our casethe MBE growth rate was double the sputtering one.

The MBE instrument was not used further due to the limited time for the thesis’s ex-periments. Problems in the vacuum system and shortage of the required targets wouldprolong substantially the growth sessions in the thesis plan. However, since the MBE methodcan produce extremely thin films with clean/flat interfaces, properties that are essential forthe investigation on interfacial skyrmion lattices, it is still in our future plans for thin filmfabrication.


Fig. 3.6 AFM height profile scan for the Pd/Si (left) and Co/Fe/MgO (right) thin films.

A set of Ni/W bilayers was prepared at a different sputtering instrument in the SolidState Physics division of Uppsala University. The bilayers were prepared in high vacuum(HV) pressure pb ≃ 10−7Torr with copper (100) single crystal being the selected substrate.A RHEED scan of the copper substrate was performed in the MBE chamber at 12kV/1.5A.The substrate was annealed up to 750°C giving 10−7Torr pressure which means that oxygenor other contaminants existed on the surface. After annealing the RHEED pattern exhibitedhigher surface crystallinity (figure 3.7).

Fig. 3.7 The RHEED pattern of a monocrystalline Cu substrate on the phosphor screen at theMBE chamber (left) before and (right) after annealing.


Although nickel has a small lattice mismatch to copper and therefore can grow epitaxially[53], the XRR results point to excessively rough layers, meaning predominantly islandgrowth instead of layering. The sputtering method does not allow easily an epitaxial growth.However this was also the result of the low argon pressure (1mTorr) and driving current (10-40mA), values that are well below the typical sputtering conditions, as well as an incompletetreatment of the copper surface [59]. The surface was not cleaned with an argon gun andprobably not completely degassed.

Prior to the bilayer, a series of nickel and tungsten monolayers were grown on silicon(111) substrates. These sample thicknesses were measured using an ellipsometer in order toestimate the deposition rate of the sputtering targets for the given configuration. The deposi-tion time range differs for Ni and W because the tungsten target was depleted. Additionally,W is a heavier element than Ni therefore the same working gas is less efficient in sputteringoff tungsten. The Nickel growth rate deviates from both a linear and polynomial behaviour.For these quick sputtering periods that are required, a very low Argon pressure does not givea consistent sputtering.

For the final bilayers, the copper substrate was heated up to Tan ≃ 375C approximatelyand then was allowed to reach equilibrium for 15 minutes. Each layer was then grown at Tan

, P = 10Watts and pAr = 1mTorr while the current at the tungsten was lower (0.01A) than atthe nickel deposition (0.04A).

Fig. 3.8 Growth rates for Ni (left) and W (right) on silicon substrates according to spectro-scopic ellipsometry measurements performed in the Solid State Physics division of UppsalaUniversity.

The samples were let to cool down to room temperature for 20 minutes before removingthem from the load-lock chamber. Three samples of various tungsten and nickel layer

3.3 Experimental Techniques and discussion 35

thickness were produced in the same conditions and scanned with XRR as described in thefollowing section.

3.3 Experimental Techniques and discussion

Following the sample growth, a series of XRR measurements were realized in order to struc-turally identify the Co/Fe/MgO and W/Ni/Cu bilayers. The basic, principles, experimentalprocedure and results of the XRR scans are presented in the following section. Additionally,a first approach to the magnetic and electrical properties of the films, consisting of resistivityand magnetization measurements, concludes the sample characterization.

3.3.1 XRR

Introduction

X-ray reflectometry is a non-destructive method that allows us to determine the density,thickness and roughness of layers in a thin-film with angstrom resolution. The XRR systemconsists of an X-ray source (X), which irradiates the sample (S) with a beam at a grazingangle θ . The grazing angle is scanned by rotating the x-y plane about the z axis. The X-raydetector (D), which records the reflected beam intensity, is rotated through a 2θ angle (twicethe speed of rotating sample) to retain its position at specular angle with respect to the filmsurface, thus a "θ −2θ scan" is performed (figure 3.9).

Fig. 3.9 Schematic (left) and photo (right) of specular XRR experimental setup in theMaterial Physics division of Uppsala University.


Total reflection of the X-ray beam occurs below a critical angle θc. Above θc the reflectionintensity reduces rapidly from the interference of refracted beams off different interfacesin the sample. The measured value is the relative, reflected to incident, beam intensity asa function of the scattering vector Q = ki − k f where ki,k f the incident and reflected wavevectors. For a specular measurement, the incident and reflected angles are equal and thescattering vector is normal to the sample surface Q = Qz. At small Qz, one probes out ofplane length scales larger than atomic dimensions, and the reflectivity can be described withthe optical Fresnel law.

According to Snell’s law for incident and refracted waves between two media:

cosθi

cosθr=

n2

n1(3.3)

The reflection and transmission coefficients are given by the Fresnel equations. For the X-rayregion, the index of refraction can be calculated from the classical dispersion theory and is acomplex number:

n = 1−δ − iβ (3.4)

where β is related to X-ray absorption β = λ µ/4π and δ gives the critical angle θc =√

2δ .The reflectivity can then be calculated as:

RF(QZ) = r2 =QZ −Q′

ZQZ +Q′

Z≃(

2QQC

)−4

(3.5)

where QZ = Q = 2k sinθ , QC = 2k sinθC and Q′ =√

Q2 −Q2C. Equation 3.5, as derived

from Fresnel formalization, gives the reflectivity for an ideal surface [63]. This functiondecreases as Q−4 above θc. Since the indices δ ,β are related to the electron density of thematerial, Als-Nielsen [64] proposed the reflectivity formula:

R(Q) =

(2QQC

)−4 ∣∣∣∣∫ ρ′(z)eiQzdz

∣∣∣∣2 (3.6)

where ρ ′(z) the electron density gradient perpendicular to the surface which describes thedeviations from RF . For more than one interface, the interference of the waves reflected offthem cause oscillations (figure 3.10), called thickness fringes, of period:

∆Q =2π

d(3.7)


where d is the thickness of each layer. The amplitude of the oscillations depends on thedensity difference between the two layers. Taking also into consideration the roughness ofthe interfaces, there will be a rise in diffuse scattering leading to lower reflected intensity.According to Nèvot and Croce, the layer thickness can be assumed as a gaussian distributionwith a mean d and a standard deviation σ that corresponds to the interface roughness [65]:

R(Q) = RF(Q)e−Q2σ2(3.8)

which is indicated by the negative slope on the intensity versus angle graph, meaning that forrough interfaces the intensity will decrease rapidly.

Measurements

The XRR measurements were performed with X-ray beam wavelength λ = 1.5418Å(Cu-Ka),anode current 40mA and acceleration voltage 40kV. The reflectivity data were analysed andfitted using the GenX reflectivity software [66].

Fig. 3.10 XRR intensity versus 2theta angle for the Co/Fe/MgO sample.

For the Co/Fe/MgO sample we execute a 90min scan with a 0.01 degrees scan-step ata range up to 6.5 degrees. The generated plot and fitted function are presented in figure3.10. The simulations were executed for material densities and instrument setup detailslocked as constant fit parameters. For given densities (Fe : 7.874g/cm3,Co : 8.9g/cm3,CoO :6.44g/cm3,MgO : 3.6g/cm3) the density, as scattering atoms per unit volume, is calculatedby:


ρ

[atomA3

]=

ρ

[g

cm3

]1.66054 · f

(3.9)

where f the scattering length, calculated from the atomic weights. In the model sample,CoO was added as the surface layer, with thickness dCoO = 1.6nm (16.6% of the total cobaltlayer thickness) and roughness σCoO = 0.6nm. The roughness of the cobalt, iron and substrateinterface, are calculated to be 0.6, 0.5 and 0.3 nm respectively. The layer thicknesses arepresented in table 3.1.

The W/Ni/Cu bilayers are scanned for 90min with 0.02 scan-step for up to 8 degreesangle of incidence. In the model sample, a tungsten oxide WO3 and a copper oxide Cu2Owas also added on the surface and substrate-nickel interface respectively. This modelproduces a satisfactory fit for all three samples. The generated plots are presented in figure3.11. The data were also fitted for given instrument settings and material densities (WO3 :7.16g/cm3,W : 19.25g/cm3,Ni : 8.908g/cm3,Cu2O : 6g/cm3,Cu : 8.96g/cm3). From theshape of the reflectivity curve it is evident that very thin and rough layers were producedsince the periodicity of the fringes is large and the intensity decreases fast. The tungsten isoxidized up to 36%, 5.4% and 27.6% of its thickness for samples #1,#2,#3 respectively. Thecopper oxide appears to have the same thickness on each substrate, approximately 1.5Å. Allsample surfaces are given a 1.5nm roughness while the transition metal interfaces are givenvarious high roughnesses, comparable to each layer thickness. These XRR curves, due tohigh roughness and thin layers, do not contain definite information about the model, howeverthis model’s results are a most possible scenario, fit the data well and are reproducible foreach one of the samples.


Fig. 3.11 XRR intensity versus 2theta angle for the W/Ni/Cu #1, #2 and #3 sample.


3.3.2 Transport measurements

The Co/Fe/MgO bilayer dc-resistivity was measured at a vibrating sample magnetometer(VSM) using the four-probe Van der Pauw method in a commercial cryostat system PPMS(Quantum Design) of the Solid State Physics division of Uppsala University. The thin filmwas placed in the sample holder and capped with a four probe connector on its surface, in asquare arrangement (figure 3.12). The resistance is measured by passing current betweentwo probes and measuring the voltage between the other two [67].

Fig. 3.12 Left:The four-probe connector cap of the VSM sample holder. Right: The VSMliquid helium cryostat.

The longitudinal resistivity ρxx (parallel to B) was measured at zero field and for smallperpendicular fields of 10,30,50 and 100Oe while the sample was cooled to 5K (figure 3.13).The observed resistivity versus temperature is the typical behaviour of many metals, whichcan be predicted at low and high temperatures with a power law and a linear fit respectively:

low T : ρ(T ) = ρ0 +AT 2 +BT 5 , high T : ρ(T ) = a+bx (3.10)

where, for low T, the second order term typically describes conduction electron scattering offspin-waves or scattering between s and d orbital electrons and the fifth order term describesscattering from phonons.


Fig. 3.13 Left:Longitudinal resistivity versus temperature at 0,10,30,50,100 Oe appliedmagnetic field. Inset: Minor resistivity shift at B ≃ 10Oe. Right: Resistivity versus appliedmagnetic field at various temperatures.

At high T, metal resistivity is generally described with a linear dependence to temperature,mainly created by electron scattering from lattice vibrations [68]. The parameter values foreach applied magnetic field strength are presented in table 3.2. A small shift (∆ρ ≃ 10−5) inresistivity is observed from 10 to 30Oe, also presented in the inset detail at figure 3.13 (left).

B (Oe) r0(10−3Ωm) A(10−9Ωm/K2) B(10−14Ωm/K5) a(10−3Ωm) b(10−6Ωm/K)

0 1.47 9.38 4.14 1.22 4.6010 1.48 8.88 4.35 1.23 4.6030 1.48 9.29 4.17 1.23 4.6050 1.48 9.20 4.28 1.23 4.59

100 1.48 9.59 4.14 1.24 4.59

Table 3.2 Resistivity versus temperature fit parameters for the linear and polynomial fits.

The field dependence of resistivity ratio ρ(B)/ρ(0) at various temperatures is alsopresented in figure 3.13 (right). A small positive magnetoresistance (MR) is observed, thatreaches a value of 0.6%. The magnetoresistance appears to increase with lower temperaturesand to reach a saturation value above 50Oe [69]. This behaviour has to be explored further,at higher magnetic fields, for possible changes in the magnetoresistance sign or contributionsfrom a helical magnetic phase or a skyrmion lattice [70].

For the ultra-thin films of W/Ni/Cu bilayers, the magnetic transition critical temperatureof nickel is expected to decrease rapidly below ten monolayers [71]. This together with the


fact that all copper substrate surfaces were not properly cleaned, led us to investigate whetherthe nickel layer is magnetic or not.

Fig. 3.14 Magnetization versus field for T 300,100K.

All samples were measured in a longitudinal MOKE setup at room temperature wherethey did not produce any hysteresis loop for fields up to 700mT . The W/Ni/Cu #3 sample wassuccessively measured in a SQUID magnetometer at T = 300,100K in the longitudinal modefor up to 4kOe applied magnetic field. The results are presented in figure 3.14. Theoreticalcalculations for nickel in the given layer dimensions result to a magnetization which isone order of magnitude lower than the observed one at room temperature. The tungstencontribution is much lower and copper is diamagnetic, however a paramagnetic Cu-CuOsystem could explain the contribution to the film’s magnetization [72]. Although we aimfor ultra-thin transition metal layers which increase the DM interaction and minimize theproperties of the bulk, it has been established that the best strategy should be a series ofsamples of various thicknesses, starting well above 10ML for single layer thickness, at thebetter controlled environment of MBE growth technique in UHV conditions.

Chapter 4

Summary and future prospects

In this work, a double perovskite powder and thin film bilayer samples were used to investi-gate the structure and magnetic order in nickel-5d transition metal systems, with a series ofexperimental techniques.

Concerning the LaSrNiReO6 double perovskite, an muSR experiment was carried out inorder to determine the nature of magnetic phases at high and low temperatures, indicatedby dc and ac susceptibility measurements. Weak transverse, longitudinal and zero fieldmeasurements were realized in a temperature range of 2−300K. The fitting components ofthe time-variant muSR signals correspond to a first transition from a paramagnetic to diluteferrimagnetic state at T = 261K, and a second transition from the latter to an incommensurateshort range order state at T = 22.6K.

The second part of this thesis included both the fabrication and characterization of thinfilms. Our aim was the growth of ultra-thin transition metal bilayers with clean and smoothinterfaces, that allow the formation of interfacial skyrmion lattices. Five samples werefabricated in total, Pd/Si, Co/Fe/MgO and a set of three W/Ni/Cu bilayers with differentthicknesses. The samples were grown using the MBE and sputtering methods. Consequentlytheir structural characteristics were probed with AFM and XRR scans. The experiments wereconcluded with indicative measurements of their electric and magnetic properties at a VSMand a SQUID instrument. The scan results point to rough interfaces. Moreover, the layerthickness, the substrate selection and the growth recipes must be reassessed in order to moveon with the creation and study of chiral structures and skyrmion lattices.

This film growth process and characterization was a first approach to ultra-thin transitionmetal bilayers. Its purpose was mainly an introduction to methods and instrumentation.The MBE and sputtering techniques will be used in future work for systematic thin filmfabrication towards the creation and manipulation of interfacial skyrmions. Recent advancesin muSR technique allows the characterization of thin films. Another area of interest, which

44 Summary and future prospects

also employs muSR, is superconductivity. Together with scanning probe microscopy (SPM),x-ray diffraction/reflectometry and transport measurement techniques, we form an arsenalof methods that will be used in the investigation of magnetic ordering in condensed mattersystems.

Chapter 5

Svensk Sammanfatting

Magnetism är, flera hundra år efter att egenskapen upptäcktes, en av de mest intressanta, kom-plexa och teknologiskt viktiga egenskaperna hos material. Datorer, generatorer, medicinskainstrument, forskningsanläggningar och många andra dagligen använda produkter användermagneter. Material består av en struktur av specifikt ordnade atomer, magnetism uppstårfrån denna ordning och interaktionen mellan dessa atomer och deras elektroner. Mångatyper av magnetisk ordning existerar i material. Dessa uppkommer efter övergångar frånicke-magnetiska till magnetiska faser och beror både på temperatur och pålagt magnetfält.Ämnet i denna uppsats är studier av magnetiska faser i en serie material. Dessa materialbestår bland annat av magnetiska metaller och är i formen av pulver eller tunna filmer.

Denna uppsats är uppdelad i två studier. I den första studien studeras ett material i formav pulver bestående av en komplex struktur av magnetiska metaller och and atomslag. Dennastruktur kallas perovskit och är en stor materialfamilj med många intressanta magnetiskaoch elektriska egenskaper som kan manipuleras genom att ändra materialets kemiska sam-mansättning. En partikelaccelerator användes för att skapa och accelerera sönderfallandesubatomära partiklar, kallade myoner, in i proven. Dessa partiklar används sedan som ettslags magnetisk sond som interagerar med det lokala magnetiska fältet inuti materialetsatomära struktur. Från denna interaktion kan sedan den magnetiska strukturen hos materialetbestämmas vid olika temperaturer. Två magnetiska fasövergångar hittas i provet när detkyls ner. Den första vid -12,15°C från en icke-magnetisk till en magnetisk fas och denandra vid -250,55°C från en magnetisk ordning till en annan. Förändringar i den kemiskasammansättningen och strukturen kan ändras mellan dessa olika tillstånd. Dessa experimentskapar en ökad förståelse om dessa material och möjliggör förbättringar för att anpassa dessegenskaper och funktion i framtida applikationer.

Den andra studien fokuserar på tillverkningen nanometertjocka metalliska tunnfilmer.En nanometer är en miljarddel av en meter, och i denna storleksskala kan material uppvisa

46 Svensk Sammanfatting

helt nya egenskaper. Målet med dessa prover är att skapa specifika exotiska kvasi-partiklari materialens elektronstruktur. En kvasi-partikel är ett kollektivt exciterat och i rymdenbegränsat tillstånd av atomer och deras elektroner inuti ett material. Dessa agerar sedantillsammans som en partikel. I detta fall är det skyrmioner som undersöks. De är magnetiska,nanometerstora kvasi-partiklar som kan förflyttas utan att de sönderfaller, de kan alltsåanvändas för att skapa en ström eller för att spara information (ettor och nollor) genomatt manipulera deras magnetiseringsriktning. På detta sätt kan skyrmioner användas sombitar av information i nya data-lagringsenheter, så kallade racerbans minnen (race-trackmemories). Denna uppsats täcker ett första tillvägagångssätt för tillverkning av tunnaskiktade filmer som möjliggör uppkomsten av skyrmioner i gränsskikten mellan dessa lager.Filmerna tillverkades i vakuumkammare där grundmaterialen varierades och deponeradesatom för atom ovanpå ett grundmaterial så att önskad skiktstruktur erhölls. För att bestämmaskikttjockleken användes röntgenljusbaserade tekniker samt för att bestämma filmytansgrovhet fördes atomärt tunna spetsar fram och tillbaka över ytan. Filmernas resistivitet ochmagnetiseringsförmåga testades också. Dessa test användes för att bestämma kvaliteten påproverna samt för att ge återkoppling för att kunna tillverka nya prov som kan användas föratt skapa, och studera skyrmioner.

Acknowledgements

At this point, I would like to express my gratitude towards all who contributed to my masterthesis project and the course of my studies in Uppsala university the past two years.

First of all I would like to thank my supervisor Yasmine Sassa, who has given me theopportunity not only to work on this project but also to take part, collaborate and take initiativein a broad range of experiments. Through this process not only did I gain experimentalexperience and deeper insight on the physics of magnetism but also developed my skills inreaching out to and working together with many scientists. Her support and patience allowedme to go through this period in good shape and gave me the drive to keep digging.

For the muSR experiment I’d like to send a big thank you to Martin Månsson, OlaKenji Forslund and Elisabetta Nocerino for their advice, the teamwork, their relaxed and funcompany during experiments and through every day life in our visit to Vancouver.

Here, in Ångström Laboratory, Vassilis Kapaklis who introduced me to the sample growthand characterization instruments and together with Petra Jönsson for their guidance along thispath. Andreas Mattsson, for taking the time to arrange and assist me in sample growth. PeterSvedlindh and Daniel Hedlund for their participation and advice in sample characterization.

All my friends that I met along the way here in Sweden, for the endless fika, ourdiscussions, games, music, food and drink inside and outside the university. Without themand support from my family none of this would be possible, thank you all.

References

[1] F. Hund, Linienspektren: Und Periodisches System der Elemente. Springer-Verlag,2013, vol. 4.

[2] H. Kramers, “L’interaction entre les atomes magnétogènes dans un cristal paramagné-tique,” Physica, vol. 1, no. 1-6, pp. 182–192, 1934.

[3] P. W. Anderson, “New approach to the theory of superexchange interactions,” PhysicalReview, vol. 115, no. 1, p. 2, 1959.

[4] J. B. Goodenough, Magnetism and chemical bond. Interscience Publ., 1963, vol. 1.

[5] J. Kanamori, “Superexchange interaction and symmetry properties of electron orbitals,”Journal of Physics and Chemistry of Solids, vol. 10, no. 2-3, pp. 87–98, 1959.

[6] S. Blundell, “Spin-polarized muons in condensed matter physics,” ContemporaryPhysics, vol. 40, no. 3, pp. 175–192, 1999.

[7] D. Andreica, “Muon spin rotation.”

[8] P. D. De Reotier and A. Yaouanc, “Muon spin rotation and relaxation in magneticmaterials,” Journal of Physics: Condensed Matter, vol. 9, no. 43, p. 9113, 1997.

[9] R. Kubo and T. Toyabe, “Magnetic resonance and relaxation: Proc. 14th coll,” Ampere(Ljubljana, 1966) ed R Blinc (Amsterdam: North-Holland) p, vol. 810, 1967.

[10] J. Sonier, “Muon spin rotation/relaxation/resonance (µsr),” µSr Studies Of Vortex StateIn Type-Ii Superconductors, Rev. Mod. Physics, vol. 72, p. 769, 2000.

[11] J. H. Brewer, “µsr howto,” Hyperfine Interactions, vol. 230, no. 1-3, pp. 35–55, 2015.

[12] “Beamlines & experimental facilities,” https://www.triumf.ca/home/contact-us/maps-triumf/building-maps, accessed: 2019-02-26.

[13] G. M. Marshall, “Muon beams and facilities at triumf,” in The Future of Muon Physics.Springer, 1992, pp. 226–231.

[14] G. King and P. M. Woodward, “Cation ordering in perovskites,” Journal of MaterialsChemistry, vol. 20, no. 28, pp. 5785–5796, 2010.

[15] M. Borowski, Perovskites: structure, properties, and uses. Nova Science PublishersHauppauge, NY, 2010.

https://www.triumf.ca/home/contact-us/maps-triumf/building-maps

https://www.triumf.ca/home/contact-us/maps-triumf/building-maps

50 References

[16] M. Singh, K. Truong, S. Jandl, and P. Fournier, “Multiferroic double perovskites:Opportunities, issues, and challenges,” Journal of Applied Physics, vol. 107, no. 9, p.09D917, 2010.

[17] D. Marx, P. Radaelli, J. Jorgensen, R. Hitterman, D. Hinks, S. Pei, and B. Dabrowski,“Metastable behavior of the superconducting phase in the babi 1- x pb x o 3 system,”Physical Review B, vol. 46, no. 2, p. 1144, 1992.

[18] K.-I. Kobayashi, T. Kimura, H. Sawada, K. Terakura, and Y. Tokura, “Room-temperature magnetoresistance in an oxide material with an ordered double-perovskitestructure,” Nature, vol. 395, no. 6703, p. 677, 1998.

[19] B. Stojanovic, C. Jovalekic, V. Vukotic, A. Simoes, and J. A. Varela, “Ferroelectricproperties of mechanically synthesized nanosized barium titanate,” Ferroelectrics, vol.319, no. 1, pp. 65–73, 2005.

[20] P. Muralt, R. Polcawich, and S. Trolier-McKinstry, “Piezoelectric thin films for sensors,actuators, and energy harvesting,” MRS bulletin, vol. 34, no. 9, pp. 658–664, 2009.

[21] D. Serrate, “D. serrate, jm de teresa, and mr ibarra, j. phys.: Condens. matter 19, 023201(2007).” J. Phys.: Condens. Matter, vol. 19, p. 023201, 2007.

[22] J. Blasco, C. Ritter, L. Morellon, P. Algarabel, J. De Teresa, D. Serrate, J. Garcıa, andM. Ibarra, “Structural, magnetic and transport properties of sr2fe1- xcrxmoo6- y,” Solidstate sciences, vol. 4, no. 5, pp. 651–660, 2002.

[23] S. Jana, P. Aich, P. A. Kumar, O. Forslund, E. Nocerino, V. Pomjakushin, M. Mans-son, Y. Sassa, P. Svedlindh, O. Karis et al., “Revisiting goodenough-kanamori rulesin a new series of double perovskites lasr _1− x ca _x nireo _6,” arXiv preprintarXiv:1810.10995, 2018.

[24] Y. Hou, H. Xiang, and X. Gong, “Understanding the magnetic puzzles of doubleperovskites a2feoso6 (a= ca, sr),” arXiv preprint arXiv:1410.4280, 2014.

[25] Y. Shimakawa, M. Azuma, and N. Ichikawa, “Multiferroic compounds with double-perovskite structures,” Materials, vol. 4, no. 1, pp. 153–168, 2011.

[26] M. Suzuki and I. S. Suzuki, “Lecture note on solid state physics superexchange interac-tion,” Binghamton, New York, pp. 13 902–16 000, 2009.

[27] M. Månsson, H. Nozaki, J. Wikberg, K. Prša, Y. Sassa, M. Dahbi, K. Kamazawa,K. Sedlak, I. Watanabe, and J. Sugiyama, “Lithium diffusion & magnetism in batterycathode material lixni1/3co1/3mn1/3o2,” in Journal of Physics: Conference Series, vol.551, no. 1. IOP Publishing, 2014, p. 012037.

[28] C. Thompson, J. Carlo, R. Flacau, T. Aharen, I. Leahy, J. Pollichemi, T. Munsie,T. Medina, G. Luke, J. Munevar et al., “Long-range magnetic order in the 5d2 doubleperovskite ba2caoso6: comparison with spin-disordered ba2yreo6,” Journal of Physics:Condensed Matter, vol. 26, no. 30, p. 306003, 2014.

References 51

[29] I. Franke, P. Baker, S. Blundell, T. Lancaster, W. Hayes, F. Pratt, and G. Cao, “Measure-ment of the internal magnetic field in the correlated iridates ca 4 iro 6, ca 5 ir 3 o 12, sr3 ir 2 o 7 and sr 2 iro 4,” Physical Review B, vol. 83, no. 9, p. 094416, 2011.

[30] G. Kalvius, O. Hartmann, R. Wäppling, A. Günther, A. Krimmel, A. Loidl,D. MacLaughlin, O. Bernal, G. Nieuwenhuys, M. Aronson et al., “Magnetism ofpd 1- x ni x alloys near the critical concentration for ferromagnetism,” Physical ReviewB, vol. 89, no. 6, p. 064418, 2014.

[31] A. J. Steele, “Quantum magnetism probed with muon-spin relaxation,” Ph.D. disserta-tion, Oxford University, UK, 2011.

[32] J. CARLO, Y. UEMURA, T. GOKO, G. MACDOUGALL, J. RODRIGUEZ, W. YU,G. LUKE, D. PENGCHENG, N. SHANNON, S. MIYASAKA et al., “Static magneticorder and superfluid density of rfeas (o, f)(r,” Physical review letters, vol. 102, no. 8,2009.

[33] A. Aczel, E. Baggio-Saitovitch, S. Budko, P. Canfield, J. Carlo, G. Chen, P. Dai,T. Goko, W. Hu, G. Luke et al., “Muon-spin-relaxation studies of magnetic order andsuperfluid density in antiferromagnetic ndfeaso, bafe 2 as 2, and superconducting ba 1-x k x fe 2 as 2,” Physical Review B, vol. 78, no. 21, p. 214503, 2008.

[34] A. Savici, Y. Fudamoto, I. Gat, T. Ito, M. Larkin, Y. Uemura, G. Luke, K. Kojima,Y. Lee, M. Kastner et al., “Muon spin relaxation studies of incommensurate magnetismand superconductivity in stage-4 la 2 cuo 4.11 and la 1.88 sr 0.12 cuo 4,” PhysicalReview B, vol. 66, no. 1, p. 014524, 2002.

[35] M. C. Thede, “Low-dimensional quantum magnets studied by musr,” Ph.D. dissertation,ETH Zurich, 2015.

[36] H. Takeya, K. Ishida, K. Kitagawa, Y. Ihara, K. Onuma, Y. Maeno, Y. Nambu, S. Nakat-suji, D. E. MacLaughlin, A. Koda et al., “Spin dynamics and spin freezing behaviorin the two-dimensional antiferromagnet ni ga 2 s 4 revealed by ga-nmr, nqr and µ srmeasurements,” Physical Review B, vol. 77, no. 5, p. 054429, 2008.

[37] A. Yaouanc and P. D. De Reotier, Muon spin rotation, relaxation, and resonance:applications to condensed matter. Oxford University Press, 2011, vol. 147.

[38] P. Hendriksen, S. Linderoth, and P.-A. Lindgard, “Magnetic properties of heisenbergclusters,” Journal of Physics: Condensed Matter, vol. 5, no. 31, p. 5675, 1993.

[39] P. K. Biswas, Z. Salman, T. Neupert, E. Morenzoni, E. Pomjakushina, F. von Rohr,K. Conder, G. Balakrishnan, M. C. Hatnean, M. R. Lees et al., “Low-temperaturemagnetic fluctuations in the kondo insulator smb 6,” Physical Review B, vol. 89, no. 16,p. 161107, 2014.

[40] J. Larsen, N. B. Christensen, C. Niedermayer, and T. Vegge, “Quantum phase transitionsin cocl2 salts, and the nature of the co-existance of magnetism and superconductivity iny9co7 and la2-xsrxcuo4+ y,” 2013.

52 References

[41] N. Gauthier, B. Prévost, A. Amato, C. Baines, V. Pomjakushin, A. Bianchi, R. Cava,and M. Kenzelmann, “Evidence for spin liquid ground state in srdy2o4 frustratedmagnet probed by µsr,” in Journal of Physics: Conference Series, vol. 828, no. 1. IOPPublishing, 2017, p. 012014.

[42] W. MacFarlane, O. Ofer, K. Chow, M. Hossain, T. Parolin, H. Saadaoui, Q. Song,D. Wang, D. Arseneau, B. Hitti et al., “Longitudinal field muon spin rotation study ofmagnetic freezing in fe rich fese0. 25te0. 75,” Physics Procedia, vol. 30, pp. 254–257,2012.

[43] J. Xu, C. Balz, C. Baines, H. Luetkens, and B. Lake, “Spin dynamics of the ordereddipolar-octupolar pseudospin-1 2 pyrochlore nd 2 zr 2 o 7 probed by muon spinrelaxation,” Physical Review B, vol. 94, no. 6, p. 064425, 2016.

[44] M. Balanda, “Ac susceptibility studies of phase transitions and magnetic relaxation:conventional, molecular and low-dimensional magnets,” Acta Phys. Pol. A, vol. 124,no. 6, pp. 964–976, 2013.

[45] A. Haldar, K. Suresh, and A. Nigam, “Observation of re-entrant spin glass behavior in(ce1-xerx) fe2 compounds,” EPL (Europhysics Letters), vol. 91, no. 6, p. 67006, 2010.

[46] S. Seki and M. Mochizuki, Skyrmions in magnetic materials. Springer, 2016.

[47] J. P. Liu, Z. Zhang, and G. Zhao, Skyrmions: topological structures, properties, andapplications. CRC Press, 2016.

[48] L. Pierobon, C. Moutafis, Y. Li, J. F. Löffler, and M. Charilaou, “Skyrmion lat-tice collapse and defect-induced melting in chiral magnetic films,” arXiv preprintarXiv:1805.10230, 2018.

[49] A. Fert, N. Reyren, and V. Cros, “Advances in the physics of magnetic skyrmions andperspective for technology,” arXiv preprint arXiv:1712.07236, 2017.

[50] T. Schwarze, J. Waizner, M. Garst, A. Bauer, I. Stasinopoulos, H. Berger, C. Pfleiderer,and D. Grundler, “Universal helimagnon and skyrmion excitations in metallic, semi-conducting and insulating chiral magnets,” Nature materials, vol. 14, no. 5, p. 478,2015.

[51] N. Nagaosa and Y. Tokura, “Topological properties and dynamics of magneticskyrmions,” Nature nanotechnology, vol. 8, no. 12, p. 899, 2013.

[52] M. Bode, M. Heide, K. Von Bergmann, P. Ferriani, S. Heinze, G. Bihlmayer, A. Kubet-zka, O. Pietzsch, S. Blügel, and R. Wiesendanger, “Chiral magnetic order at surfacesdriven by inversion asymmetry,” Nature, vol. 447, no. 7141, p. 190, 2007.

[53] G. Chen, J. Zhu, A. Quesada, J. Li, A. N’Diaye, Y. Huo, T. Ma, Y. Chen, H. Kwon,C. Won et al., “Novel chiral magnetic domain wall structure in fe/ni/cu (001) films,”Physical review letters, vol. 110, no. 17, p. 177204, 2013.

[54] A. Hrabec, N. Porter, A. Wells, M. Benitez, G. Burnell, S. McVitie, D. McGrouther,T. Moore, and C. Marrows, “Measuring and tailoring the dzyaloshinskii-moriya inter-action in perpendicularly magnetized thin films,” Physical Review B, vol. 90, no. 2, p.020402, 2014.

References 53

[55] A. Fert, V. Cros, and J. Sampaio, “Skyrmions on the track,” Nature nanotechnology,vol. 8, no. 3, p. 152, 2013.

[56] W. Jiang, G. Chen, K. Liu, J. Zang, S. G. te Velthuis, and A. Hoffmann, “Skyrmions inmagnetic multilayers,” Physics Reports, vol. 704, pp. 1–49, 2017.

[57] J. R. Arthur, “Molecular beam epitaxy,” Surface science, vol. 500, no. 1-3, pp. 189–217,2002.

[58] W. Kern, Thin film processes II. Elsevier, 2012, vol. 2.

[59] M. Ohring, Materials science of thin films. Elsevier, 2001.

[60] D. L. Smith, Thin-film deposition: principles and practice. McGraw-hill New Yorketc, 1995, vol. 108.

[61] J. Günster, S. Krischok, J. Stultz, and D. Goodman, “Interaction of na with multilayerwater on mgo (100),” The Journal of Physical Chemistry B, vol. 104, no. 33, pp.7977–7980, 2000.

[62] Y. V. Goryunov, I. Garifullin, T. Mühge, and H. Zabel, “Magnetic anisotropy of epi-taxial iron films on single-crystal mgo (001) and al2 o3 (1120) substrates,” Journal ofExperimental and Theoretical Physics, vol. 88, no. 2, pp. 377–384, 1999.

[63] E. Chason and T. Mayer, “Thin film and surface characterization by specular x-rayreflectivity,” Critical Reviews in Solid State and Material Sciences, vol. 22, no. 1, pp.1–67, 1997.

[64] J. A. Nielsen, Structure and Dynamics of Surfaces II: Phenomena, Models, and Methods.Springer-Verlag, 1987.

[65] L. Nevot and P. Croce, “Characterization of surfaces by grazing x-ray reflection–application to the study of polishing of some silicate glasses,” Revue de PhysiqueApplique, vol. 15, no. 3, pp. 761–80, 1980.

[66] M. Björck, “M. björck and g. andersson, j. appl. crystallogr. 40, 1174 (2007).” J. Appl.Crystallogr., vol. 40, p. 1174, 2007.

[67] R. Chwang, B. Smith, and C. Crowell, “Contact size effects on the van der pauw methodfor resistivity and hall coefficient measurement,” Solid-State Electronics, vol. 17, no. 12,pp. 1217–1227, 1974.

[68] K. A. Rogers, “The behavoir of the resistivity of metals at low and high temperatures.”

[69] M. Gruyters, “Anisotropic magnetoresistance in coo/co and coo/fe bilayers in the biasedand unbiased state,” Journal of applied physics, vol. 95, no. 5, pp. 2587–2592, 2004.

[70] R. Ritz, M. Halder, C. Franz, A. Bauer, M. Wagner, R. Bamler, A. Rosch, and C. Pflei-derer, “Giant generic topological hall resistivity of mnsi under pressure,” PhysicalReview B, vol. 87, no. 13, p. 134424, 2013.

54 References

[71] R. Zhang and R. F. Willis, “Thickness-dependent curie temperatures of ultrathin mag-netic films: effect of the range of spin-spin interactions,” Physical review letters, vol. 86,no. 12, p. 2665, 2001.

[72] A. Samokhvalov, T. Arbusova, N. Viglin, S. Naumov, V. Galakhov, D. Zatsepin, Y. A.Kotov, O. Samatov, and D. Kleshchev, “Paramagnetism in copper monoxide systems,”Physics of the Solid State, vol. 40, no. 2, pp. 268–271, 1998.

Documents

Investigation of magnetic order in nickel - 5d transition metal …uu.diva-portal.org/smash/get/diva2:1314127/FULLTEXT01.pdf · 2019-05-07 · Muon Spin Rotation/Relaxation and Resonance