Collin Broholm- Magnetic Surprises on a Triangular Lattice

8/3/2019 Collin Broholm- Magnetic Surprises on a Triangular Lattice

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Magnetic Surprises on a Triangular Lattice

Collin BroholmJohns Hopkins University & NIST

Introduction Frustration

Neutron Scattering Triangular Lattice AFM

Theoretical Status Experimental Status

Triangular lattice systems Neel (RbFe(MoO4)2) Glassy (NiGa2S4)

Conclusions


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11/15/05 Rutgers Seminar 2

Collaborators

RbFe(MoO4)2G. GasparovicM. KenzelmannS. ParkA. SmirnovL. N. Demianets

A. Ya. ShapiroG. LawesA. P. Ramirez

NiGa2S4S. NakatsujiY. NambuH. TonomuraO. SakaiC. Stock

S. JonasY. QiuY. MaenoJ. Chung

La4Cu3MoO12Y. Qiu

S. IshiwataM. AzumaM. TakanoR. BewleyW. J. L. Buyers


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Frustrated Condensed Matter

Lattice symmetry established by chemical bonding (large energyscales) can frustrate weaker magnetic interactions

Frustrated

Frustration produces classically degenerate states of matter witha potential for emergent quantum properties

Satisfied


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11/15/05 Rutgers Seminar 4MACS spectrometer under construction at NIST

MACS spectrometerunder construction at NIST

pi pf

Q

"!

RR'RR

RRQ

Q )(S)0(

1

2

1

),( ''

tSeNedt

iti FE[EF

T[ JS


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z=3/4 CuMoO plane

La4Cu3MoO12: A lattice of spin-1/2 trimers

Magnetic susceptibility Crystal Structure

(Azuma et. al., PRB 62 R3588)


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Frustrated quantum spin triangles

133221 SSSSSS ! JH

J

J J

J2

3

J2

3

133322211 SSSSSS ! JJJH

J1

J3

J2

22

3 J

J

H

2

132

322

2121 JJJJJJJ !H

JH

YimingQiu etal. PRB 2005


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Spectroscopy of spin trimers

Transition to quartet


70 K

10 K

0.0

0.1

0.0

0.1

0.2

JH


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Magnetic Ordering of Composite spin-1/2

002

1!Q


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Strongly fluctuating spin trimer AFM



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Neutron Scattering

Exact two-spinon

cross-section

Stoneetal. (2003).

Karbach etal. 2000


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Frustrated Linkage of Triangles

Triangular lattice Kagome lattice


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A brief status of Triangular lattice research

Theory RVB state proposed (Anderson 1973) Classical Heisenberg model has 120o LRO at T=0

(Huse, Rutenberg) S=1/2 model has LRO for T=0 (Huse, Singh)

Finite temperature KT transition (Kawa

mura

&Miyashita) RVB state in Ising model (Moessner and Sondhi)

Experiments Spin-1/2 insulators generally have some form of

dimerization and no LRO Spin-1/2 (ET)2Cu2(CN)3 close to MIT shows no spin

order. It superconducts under pressure Spin-1/2 anisotropic system has de-confined

excitations in a field (Cs2CuCl4)


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RbFe(MoO4)2: spin-5/2 triangular AFM

J

J1

J2J

Kenzelmann, Gasparovic etal. (2005)


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Field Dependent Long Range Order

120o structure Field dependent

Incommensurate

stacking Spins in

triangular plane Moment reduced

to 75(1)% Incommensurate

state isferroelectric!

Kenzelmann, Gasparovic etal. (2005)


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NiGa2S4 : Spin-1 Triangular Lattice AFM

J11 x 97o2 x 2.42

J22 x 100o2 x 2.42 1 x 3.21

J32 x 138.5o

2 x 2.421 x 3.63

Nakatsuji et

al. Science (2005)


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No phase transition as T/5CW 0

5CW=80 K so AFM Cusp in G for T7 K

No conventionalphase transition

Two maxima in C/T Finite T entropy

plateau

Nakatsuji etal. (2005)


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Spin freezing without C(T) anomaly

Single crystal



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Short range magnetic correlations

2 * 22

2

0 22 2

/ 1 2 cos2

d g Ar F Q N

d

W O TE

O

! ; s

q q

m Q m Q c

Q q

Surprises:

1

2 120oQ Q}

1 25(3)O !



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Single crystals confirm 2D Incom. SRO

0.155(1)L !1 16(1)O

! FM inter-plane correlationsPlanar spin structure

1 16 6 1

C. Stock etal. (2005)


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Excitations from low T state

Early dispersion relation

What is clear so far:

Spin wave like modes at low T

A slow low E mode throughout zone

+ A highly dispersive mode


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Frozen spin structure

120o structure on 2asuper-lattice (colors)

Incommensuratemodulation

Spins in triangularplane Moment reduced to

75(8)% Weak ferromagnetic

inter-plane correlations



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J1-J3 model on triangular lattice?

0LL!Q J1=0

J1=-0.2J3

Accounts for no peak incommensurability

Plausible given likelyexchange paths

Further confirmationneeded

1 13 3 0


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Thought on quantum glassy phase

Not conventional disordered glass: Coherent wave propagation No forward scattering

Impurities involved but unlikely todefine short length scale

Puddles of AFM around impurities inisolated singlet ground state system

Gapped triplet sector gapless singletsector pinned by impurities


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Conclusions Glassy phases endemic to real spin systems near quantum

critical point Distinguishing characteristics of glassy phase

Coherent modes despite short range spin-correlations Absence of forward scattering Gapless triplet spectrum

RbFe(MoO4)2 120o structure for sufficient inter-plane coupling Competing interplane interactions yield incommensurate

ferroelectric phase NiGa2S4

spin-1 system with potential for J1-J3 model Glassy incommensurate phase at low T suggest weakinterlayer coupling and weak or absent 2D Neel order

Double peak structure in C(T) indicates a gapped phasemay be present in this problem

e


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Future plans

RbFe(MoO4)2 Explore multiferroic properties in particular electricfield induced handedness of magnetic state

Establish exchange constants through spin wavemeasurements

NiGa2S

4 Carrier doping may be possible. Effects of uni-axial stress and pressure Spin wave measurements to determine hamiltonian Increase disorder (Zn, S)

Theoretical issues: Spin-1 triangular lattice AFM: spin liquid? J1-J3 triangular lattice model: entropy plateau? Phenomenology of glassy quantum magnetism

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Collin Broholm- Magnetic Surprises on a Triangular Lattice