Systematic Studies of the Surface Structural and

Physical Properties in Ca2-xSrxRuO4( 20 ≤≤ x )

and Sr3(Ru1-yMny)2O7( 10 <≤ y )

Submitted to the University of Tennessee

Comprehensive Exam: Proposal for the Original Research

Biao Hu

Sep 24 2007

Abstract

Transition metal oxides (TMOs) attract extensive attention due to the strong

coupling between charge, lattice, orbital, and spin, which results in a variety of exotic

phenomena. The Ruddlesden-Popper (RP) (Sr,Ca)n+1RunO3n+1 series are proto-type of

strong correlated systems. Due to their layered structures, crystals can be cleaved to

create a surface, ideal for studying surface physics. The breaking of the symmetry at

the surface will trigger distinct surface phases due to the lattice distortions at the

surface. This project will focus on the surface structural and physical properties of

Ca2-xSrxRuO4 and Sr3(Ru1-yMny)2O7 while the surface structure can be determined by

Low Energy Electron Diffraction (LEED). The surface phonon modes will be probed

by High Resolution Electron Energy Loss Spectroscopy (HREELS). Scanning

Tunneling Microscopy (STM) and Spectroscopy (STS) will allow us to study the

topography and spectroscopy versus temperature and doping level. The doping

dependence of the surface structural and physical properties of Ca2-xSrxRuO4 and

Sr3(Ru1-yMny)2O7 will be systematically investigated.

Page 1 of 18

§1. Introduction

Ruthenium-based oxides are known to exhibit a variety of unexpected physical

properties. Both Sr2RuO4 and Sr3Ru2O7 are members of the Ruddlesden-Popper (RP)

series (Sr,Ca)n+1RunO3n+1, as shown in Fig.1 [1]. The main difference between the

structures is the number (n) of Ru-O planes interlinked by sharing apical oxygens

prior to the separation by Sr-O planes. This difference leads to different physical

properties among the family. Sr2RuO4 (n=1) is the only-known superconducting

compound with p-wave pairing symmetry while Sr3Ru2O7 (n=2) is a paramagnetic

metal with strong antiferromagnetic correlation [2, 3]. The bulk and surface properties

of Ca2-xSrxRuO4 system has been widely investigated by different techniques [4, 5, 6,

7].

Fig.1 Ruddlesden-Popper series (Sr,Ca)n+1RunO3n+1. Crystal structures for various n. T site is occupied by Ru. Ref. [1]

§1.1 Ca2-xSrxRuO4 ( ) 20 ≤≤ x

Single layered Sr2RuO4 forms a tetragonal crystal structure. When smaller Ca

partially replaces the Sr, its structure varies from a p-wave superconductor Sr2RuO4 to

an antiferromagnetic insulator Ca2RuO4. As shown in Fig.2, its physical properties

change drastically [4].

Page 2 of 18

Fig.2 Phase diagram of Ca2-xSrxRuO4: Ref. [4] P-I: Paramagnetic insulator; CAF-I: Canted Antiferromagnetic insulator; M-M: Metamagnetic; P-M: Paramagnetic metal; SC: Superconductor; Tp: Peak temperature of the susceptibility for the [001] component; TM/NM: Metal/nonmetal transition temperature

Due to the smaller radius, the substitution of Sr by Ca will distort the structure of

Ca2-xSrxRuO4, which causes a rotation of the RuO6 octahedron around the long axis

with an angle φ and a tilt around an axis lying in the RuO2 plane with an angle θ

[5]. Fig.3 demonstrates two kinds of tilt angle: ( )1O−θ representing the angle

between the octahedron basal planes and the a-b planes; ( )2O−θ representing the

angle between the Ru-O(2) bond and the long axis [6]. The rotation and tilt of the

octahedron reflects a zone-boundary 3∑ mode (rotational mode) and mode (tilt

mode), respectively, as shown in Fig.4. The inelastic neutron scattering data reveals

that in pure Sr

4∑

2RuO4 the branch ends at the (0.5 0.5 0) zone boundary and

exhibits a sharp drop near the zone boundary, which clearly indicates a rotational

instability [7].

3∑

Fig.3 RuO6 rotation angle φ and tilt

angle θ . Ref. [6]

Fig.4 Low-frequency part of the phonon dispersion along [110]. The lines denotes the frequencies calculation by a shell model. Ref.[7]

Page 3 of 18

Raman scattering experiment identified three symmetry-allowed phonon modes

in bulk Sr2RuO4 crystal at room temperature [8]. The lower-energy A1g mode at

197cm-1(24.5meV) is a vibration due to Sr and the higher one at 540cm-1(67.0meV)

due to apical oxygen along the c-axis. The Eg mode at 247cm-1(30.62meV) is the

vibration of apical oxygen along a-axis. As displayed in Fig.5 and Table I, three

surface optical phonons, which has the energy at 30.0meV (A1g(2) or A2u(3)),

50.0meV (A2u(2)), and 75.0meV (A1g(1)) with a shoulder appearing at 67.5meV, were

observed in the Sr2RuO4 surface by high-resolution electron energy loss spectroscopy

(HREELS) [9]. As seen from Table I, the observed surface phonons have noticeably

higher energies than these associated bulk modes. Such differences are intimately

related to the structural changes due to lattice relaxation at the surface and maybe

result from an inward contraction of the topmost Sr plane [6]. Specifically, the Ca/Sr

ions in the Ca1.5Sr0.5RuO4(001) surface display a large inward displacement

(0.13± 0.03)o

A [10].

Fig.5 HREELS spectra from Sr2RuO4 surface along the [100] direction at T=80K. Ref. [9]

The intuitive structural and physi

surface in Ca2-xSrxRuO4 is shown in Fig

low temperature and for decreasing Sr

I4/mmm region in pure Sr2RuO4 to a sim

Sr content, near x=0.5, there is a com

Table I. Optical phonons of Sr2RuO4 in the bulk and surface (80K) at the center ( ) of Simplified Brillouin Zone. Ref. [9]

Γ

cal properties difference between bulk and

. 8(a) [11] and Fig. 8(b) [6]. For the bulk, at

content, one passes from the space group

ple rotation I41/acd region. In much smaller

bination of rotation and small tilt. Further

Page 4 of 18

decreasing of Sr content leads finally to the combination of the rotation and the large

tilt in the Pbca phase. At the surface case, as Ca replaces for Sr, the surface structure

starts from a metallic region with a p4gm plane to a pm region, finally enters an

insulating region with a pg plane group at low temperatures [6].

Fig.8(a) Bulk structural phase diagram of Ca2-xSrxRuO4. Ref. [11]

Fig. 8(b) Surface structural phase diagram of Ca2-xSrxRuO4. Solid lines denote structural phase transitions; Dashed line indicates onset of tilt instability; Light orange and green regions are projections based on current trends; Light red region indicates insulating phases. Ref. [6]

§1.2 Sr3(Ru1-yMny)2O7( 10 <≤ y )

Different from the superconductivity in Sr2RuO4, the bilayered Sr3Ru2O7 is a

paramagnetic metal, critically close to magnetic order [3]. Sr3Ru2O7 shows

metamagnetism for magnetic fields oriented both in the ab plane below 10K, centered

at a field of approximately 5.5T, and along c axis with a well-defined transition at

approximately 7.7T [12]. However, there has a controversy in the bulk structure of

Sr3Ru2O7. From neutron powder diffraction Shaked et al. found that at room

temperature Sr3Ru2O7 has the symmetry of orthorhombic space group Bbcb, with an

octahedral rotation of 6.8o about the c axis [13]. A 000 22 caa •• supercell is

identified from the superlattice reflections (SLR) in the diffraction pattern, as

displayed in Fig. 9.

Page 5 of 18

Fig.9 The structure of supercell corresponding lattice parameters:

02aa = Ref. [13]

Different from the Bbcb space group, Huang

Fig. 10] is formed by stacking two blocks of

axis, interleaved with SrO layers, belonging

295K [14]. There is a rotation with respect

corner-sharing octahedra in each double pero

RuO2 planes is about 165。, rather than 180。.

Moreover, Iliev et al. investigated the po

All observed Raman modes corresponds to A

vibrations in the simplification of tetragona

contain only one double RuO6 layer per u

distortion. As shown in Fig. 12, five lines of

xx and zz spectra at 118, 165, 212, 395, and

observed in the xy spectra at 306 and 377 cm

seen in the zx(zy) spectra where are allowe

lattice dynamics calculation (LDC) for the Pb

Fig.10 Symmetry of two neighboringblocks in the structure of Sr3Ru2O7.Ref. [14]

et al. considered that the structure [see

distorted SrRuO3 perovskite along the c

to the symmetry of space group Pban at

to each other between the neighboring

viskite block. The Ru-O-Ru angle in the

larized Raman spectra of Sr3Ru2O7 [15].

g or B1g symmetry for particular atomic

l P4/nbm structure [See Fig. 11], which

nit cell and account for the rotational

Ag symmetry are clearly indicated in the

577cm-1; two lines of B1g symmetry are -1, but no lines of detectable intensity are

d the modes of B2g(B3g) symmetry. The

an structure predicts that the Ag modes

Page 6 of 18

Fig. 11 Simplified distorted structure (P4/nbm) of Sr3Ru2O7 with unit cell containing one double Ru-O layer. The distortion-activated Ag and B1g modes are also shown. Ref. [15]

Fig.12 Polarized Raman spectra of Sr3Ru2O7, obtained at room temperature with 633, 515, and 488nm excitation. Some curves are shifted vertically for clarity. Ref. [15]

below 250cm-1 are strongly mixed, each involving vibrations along z of Ru and Sr2 as

well as RuO6 rotations around z. The two high-frequency Ag modes, confirmed by

LDC, correspond to out-of-plane in-phase vibrations of O3 (395cm-1) and stretching

vibrations of O2 (577cm-1). The two B1g modes of the distorted P4/nbm structure

indicate the out-of-phase vibrations along z of O3 (306cm-1) and “scissors-like”

bending of O3 parallel to the xy plane (377cm-1).

Furthermore, Mathieu et al. found that a small amount substitution of Ru by Mn

in Sr3Ru2O7 can restore the RuO6 octahedra distortion in the symmetry of space group

Pban to the (Ru1-yMny)O6 octahedra with the space group I4/mmm because the ion

radius of Mn (0.60o

A ) is smaller than that of Ru (0.67o

A ) [16]. A doping level of 5%

Ru by Mn in Sr3Ru2O7 can change the ground state from a paramagnetic metal to an

antiferromagnetic insulator with a Mott-like gap [16]. A schematic electronic phase

diagram, shown in Fig.13, is obtained from the measurement of the temperature

dependence of various physical properties of Sr3(Ru1-yMny)2O7 ( ). The 2.00 ≤≤ y

Page 7 of 18

diagram defines the phase boundary between the paramagnetic metal (PM) and the

antiferromagnetic insulator (AFI).

Fig.13 The electronic phase diagram of Sr3(Ru1-yMny)2O7 for different Mn doping y. Ref. [16]

A metal-insulator transition occurs in a vicinity of 180K in the larger amount

substitution Ru by Mn in Sr3(Ru0.77Mn0.23)2O7. As demonstrated in Fig. 14,

dTd abρ and dTd cρ change sign relatively abruptly at TMIT, where abρ and cρ

are in-plane and c-axis electronical resistivities, respectively [17].

Fig. 14 In-plane ( abρ ) and out-of-plane

resisitivity ( cρ ) vs temperature T in a

logarithmic scale. Inset: In-plane resistivity

)(Tabρ in the vicinity of the metal-insulator

transition, in linear scale. Ref. [17]

Although the structural, magnetic and transport properties in the bulk Sr3Ru2O7

have been widely studied, the surface structural and physical properties in both pure

and Mn doped cases are still unknown.

§2. Proposed work

§2.1 Quantum critical behavior at the surface of Ca2-xSrxRuO4 and Sr3Ru2O7

In addition to the properties mentioned above, the Ruddlesden-Popper

(Sr,Ca)n+1RunO3n+1 series are ideal systems for observing quantum critical phenomena

near quantum critical point. Quantum critical point is defined as zero-temperature

Page 8 of 18

second-order phase transition. A driving force exerted by external change, such as

chemical doping, pressure or magnetic field, will affect the unstable equilibrium

around the instability point. The quantum critical point is approached through

chemical doping in Ca2-xSrxRuO4. As shown in Fig. 15, the critical increase of

low-temperature susceptibility at x≈0.5 indicates a dramatic change of the ground

state to a nearly ferromagnetic region [4]. Neutron powder diffraction measurement

shows a high temperature tetragonal-to-lower temperature orthorhombic (HTT-LTO)

phase transition occurring at x ≈ 0.5 [18]. However, the surface studies revealed

modified surface phase diagram, suggesting that the QCP is altered on the surface [6].

We will probe the surface electronic properties using STM/STS in the vicinity of

xc=0.5, searching for QCP at the surface.

Fig. 15 ( )0χ : the susceptibility at 2.0 K

against the Sr concentration x in the metallic regions II and III. I: AF insulating ground state; II: Magnettic metallic region III: Paramagnetic metal Ref. [18]

Similarly, a quantum criticality has been found at the metamagnetic transition in

Sr3Ru2O7. As shown in Fig. 16, non-Fermi liquid behavior was observed [19]. The

experimental data are analyzed using a general expression ( ) αρρ ATT res += , where ρ

is the electrical resistivity, resρ is the residual resistivity at T=0, A is a

temperature-independent coefficient related to a quasi-particle effective mass, and the

exponent α contains valuable information about the nature of the metallic state. The

variance of the exponent α reflects the coupling extent between charge, lattice,

orbital, and spin freedom in the TMOs. The Fermi liquid theory predicts that α =2 as

T 0. But a characteristic signature of non-Fermi liquid metals has been the

observation of

→

2<α in this limit. At low field, the quadratic temperature

dependence expected in a Fermi liquid is seen below 10K. Near the metamagnetic

Page 9 of 18

field of ~7.8T, a power close to 1 persist down to 4.5K, before rising again as the field

is increased. It is evident that the properties of Sr3Ru2O7 are affected by a QCP

associated with the metamagnetic transition.

Fig.16 Summary of the high-temperature resistivity, ρ , near the metamagnetic transition in Sr3Ru2O7, for magnetic field applied parallel to the c axis. Ref. [19]

This critical behavior will be investigated by STM/STS. Although the dI/dV

spectra in the latest STS experiment do not display any evident anomaly at the critical

field [20], unlike in the bulk [19], we can investigate the non-Fermi liquid behavior

near QCP under applied external magnetic field. We will observe the resistibility as a

function of temperature and magnetic field. Namely try to understand the non-Fermi

liquid behavior in the complex strong correlated system Sr3Ru2O7.

§2.2 Surface phase of Sr3(Ru1-yMny)2O7

Creating a surface drives the 3-dimensional (3D) symmetry in bulk into the

2-dimensional (2D) symmetry in surface. In Sr2RuO4 the LEED-I(V) analysis shows

that the surface structure has a reconstruction o45)22( R× , belonging to a p4gm

plane group symmetry [21]. The surface indicates a glide-line symmetry in the [110]

direction. The surface layer also shows a lattice distortion characterized by rigid RuO6

octahedra rotation of around the surface-normal direction, which is not

present in the bulk [22]. But in the bulk of Sr

oo 5.25.8 ±

3Ru2O7, the octahedra are already rotated

by [14, 15]. The latest research via STM by K. Iwaya et al. demonstrates a

superstructure in the surface, as shown in Fig. 17 [20]. The LEED-I(V)

o8~

( 22×c )

Page 10 of 18

analysis will be applied to quantitatively analyze the surface structure of Sr3Ru2O7. As

mentioned previously, the small Mn substitution for Ru can restore Sr3Ru2O7 from the

distortional structure (octahedra rotation) to the undistortional K2NiF4-type in

Sr3(Ru1-yMny)2O7. The LEED pattern and the structure refinement within a LEED-I(V)

analysis can reflect the variety of the intrinsic surface structure when doped Mn into

Sr3Ru2O7.

Fig. 17 Crystal structure of Sr3Ru2O7 in ab plane. Both 1st (SrO plane) and 2nd layer (RuO2 plane) after cleavage are shown. The c(2x2) unit cell is shown as a dashed square. Ref. [20]

Besides the study of the bulk and surface structural properties in the Sr3Ru2O7,

the study of lattice dynamics, which represents the strong coupling between electronic,

lattice, orbital, and spin degrees of freedom, also attracts an attention. The spectra in

HREELS reflect the surface dielectric responses through quasi-particle excitations

including phonons and low-energy electron excitations. Three surface optical phonons,

which have higher energies than their corresponding bulk modes, were observed in

Sr2RuO4 by HREELS [9]. The comparison between the bulk and surface phonon

mode in Sr3Ru2O7 is an important subject in the project. As HREELS is sensitive to

the dipole-active mode, referring to dynamic dipole moments perpendicular to the

surface. So these Ag modes in the bulk Sr3Ru2O7, involving atomic vibrations along z,

are expected to observed in the surface optical phonons.

§2.3 Metal-insulator transition in Sr3(Ru1-xMnx)2O7

In the layered perovskite Ca1.9Sr0.1RuO4, the bulk MIT occurs at TC = 154 K as

shown by the abrupt change of the bulk electrical resistivity while the surface

transition occurs at TC,S = 130 K as indicated by the opening of the energy gap up

to measured by scanning tunneling spectroscopy (STS), as shown in eV1.04.0 ±

Page 11 of 18

Fig.18 (a) and (b) [23]. It is evident that a shift of the MIT to lower temperature

occurs at the surface of Ca1.9Sr0.1RuO4 single crystal. The MIT in both bulk and

surface is a first-order transition. On the contrary, a second-order MIT occurs in Mn

Fig. 18(a) Signature of the MIT in the bulk (Tc=154K; red line) and at the [001] surface (Tc,s=130K; blue line) of Ca1.9Sr0.1RuO4 single crystal. Ref. [23]

Fig. 18(b) The measured T-dependence of STS spectra in Ca1.9Sr0.1RuO4. Ref.[23]

doped Sr3Ru2O7, as illustrated in Fig.13 and 14. A T-dependence of the energy gap in

Sr3(Ru1-yMny)2O7 will be determined by the STS spectra. The shift of MIT

temperature between bulk and surface will be discussed. The difference of first-order

MIT in Ca1.9Sr0.1RuO4 and second-order MIT in Sr3(Ru1-yMny)2O7 also attract our

interests. In sum, the goal of the project is to obtain the topography and spectroscopy

versus temperature both in pure and doped Sr3Ru2O7 by STM & STS.

§3. Experimental techniques

§3.1 High Resolution Electron Energy Loss Spectroscopy

HREELS is a highly surface sensitive technique to investigate the surface lattice

dynamics by analyzing inelastically scattered electrons. It has been widely utilized to

investigate lattice vibrations (phonons), surface plasmons, and interband electronic

transitions on the surface [24]. If considering a monoenergetic beam of electrons with

energy Ei and momentum ki incident on the sample surface at an angle iθ , the electron

can be inelastically backscattered into the vaccum with energy Es, momentum ks at an

Page 12 of 18

angle sθ as shown in Fig. 19 [6].

Fig. (19) HREELS scattering geometryRef. [6]

Then we can get a general energy conservation equation (1) under the inelastic

conditions:

( ) ( ) ( )//qkEkE iiss νωh−= (1)

where ωh=∆E is the energy of the surface excitation and is the momentum

transfer parallel to the surface satisfying the momentum conservation law:

//q

khis Gqkk ,////// ±−= (2)

Where is a two-dimensional reciprocal lattice vector parallel to the surface. The

energy of excitation is usually in the range of tens of millivolts, thus requiring a

highly monochromatic incident beam with meV energy resolution. Typically, if the

incident and scattered electrons are restricted in a plane, we only measure the

momentum transfer parallel to the surface. Consequently, we have a more simple

equation (3):

khG ,

( ) khsiiie

II GEEm

q ,sinsin2

±−−= θωθ νhh

(3)

where iϑ and sθ is incident angle and scattering angle, respectively.

A typical HREELS raw data in Ca1.9Sr0.1RuO4 is shown in Fig. 20.

Page 13 of 18

Fig. 20 HREELS raw data about phonon mode at T=200K. Ref. [6]

§3.2 Low Energy Electron Diffraction

Low Energy Electron Diffraction (LEED) is another sensitive technique to

determine the surface structure. Low energy electron beams can be used as a kind of

incident wave whose wavelength is shorter than the lattice constant but whose

penetration depth in the solid in the range of severalo

A . From the de Broglie relation

the wavelength of the electrons is given by:

ph=λ (4)

where h is the Planck’s constant and p is the electron momentum. If the electrons are

accelerated by a voltage V, the kinetic energy of electrons is eV, the electron

wavelength is determined by:

( ) ( ) 2121 /4.1502 VmeVh ==λ (5)

where e is the electron charge, and m is the mass of electron. In Eq. (5), the unit of V

is volt, and λ is in o

A .

From LEED experiment we can directly get an I-V curve, which is the intensity

of a certain diffraction beam as a function of the incident electron beam energy.

Retarding Field Analyzer (RFA ) is the main part in LEED apparatus (see Fig. 21(a)),

Fig. 21(b) is a scheme of I(V) curves collection [26].

Page 14 of 18

al results. It usually

analysis is to set up a model surface

nt with the symmetry of the LEED pattern. As

-scattering theory produce theoretical I-V

requires a process

f v ructural

ar der to minimize the differences between

calc

The first step in the procedure of LEED

structure, which is chosen to be consiste

a second step, calculations applying multiple

curves, which are compared to the experiment

o refinement: the model needs to ha

ameters systematically varied in or

e several structural and non-st

p

ulated and experimental spectra. Generally, the imaginary part of the

optical-potential, which attenuates the electrons, and the Debye temperature of the

model surface are two non-structural parameters of the model until satisfactory

agreement is obtained. So the surface structure is finally determined when the set of

theoretical and experimental curves “match” [26]. In LEED, the so called reliability

factor (Rp-factor) is used to quantitatively evaluate the goodness of fit between the

theoretical and experimental I-V. If Rp=0 there is perfect correlation between the

theoretical and experimental I-V curves. Rp=1 means that theory and experiment are

completely uncorrelated. The lower Rp factor acquired, the better is surface structural

determination. Usually, it is confident if 3.0≤pR [10].

Scanning tunneling microscopy (STM) is one of the most powerful, versatile, and

easy to use techniques for surface characterization. Specifically, in my focused

surface area, STM is more favorable to

§3.3 Scanning Tunneling Microscopy

investigate the topography at the cleave

surface of layered perovskite in transition metal oxides. A simplified working

Fig.21 (a) Retarding Field Analyzer-RFA Ref. [26]

(b) I(V) curves collection. Ref. [26]

Page 15 of 18

principle of STM is shown in Fig. 22 [27]. STM can image the electronic structure of

a surface with atomic resolution.

Scanning tunneling spectroscopy (STS) is the study of the dependence of an STM

signal upon the local electronic structure of the surface. In ST nsity of

states (LDOS) at the sample surface is related to the local conductance of the

tip-sample configuration. Under small bias voltage V, the tunneling current of STM in

the first approximation can be expressed by

S, the local de

( ) ( ) ( )dEVETEVI ,∫≈ ρ (8)

where ( )Eρ is the LDOS near the sample surface, ( )VET , is a transfer matrix, and

integration is taken from the Fermi level Ef to Ef+V. So, in a very simple but realistic

model, the differential conductance dI/dV reflects directly the LDOS. The method of

measuring STS ramps the bias voltage with the tip positioned over a feature of interest

whilst recording the tunneling current. This results in current versus voltage (I-V)

lectronic structure at a ample curves characterizing the e specific x, y location on the s

surface. For measuring the differential conductan igh-frequency sinusoidal

modulation amplifier, ( )

ce, a h

dVVdI curves can be collected directly.

§4. Summary

We will focus on quantum critical behavior at the surface of Ca2-xSrxRuO4 and

Sr3(Ru1-yMny)2O7. The power-law behavior in pure Sr3Ru2O7 and the expectant gap

opening in MIT in Mn doped Sr3Ru2O7 will be systematically studied by STM/STS.

Fig. 22 A simplified working principle of STM. Ref. [27]

Page 16 of 18

The topography in STM and spectroscopy in STS versus temperature and doping level

are expected. A surface diagram of Sr3(Ru1-yMny)2O7 will be determined by LEED.

he surface phonon modes of Sr3Ru2O7 can obtain by HREELS. The study of surface

nd doped Sr3Ru2O7 will facilitate the understanding of surface

phy

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