10/24/01 PPHMF-IV 1

Spinons, Solitons, and Breathers

in Quasi-one-dimensional Magnets

Frustrated Magnetism & Heavy Fermions

Collin BroholmJohns Hopkins University &NIST Center for Neutron Research

SCES 2004 Karlsruhe, Germany 7/29/2004

SCES04 7/29/04

Overview

Introduction

Frustrated magnetism in insulators– Order from competing interactions– Near critical systems– Quantum liquids

Metals with frustrated magnetism– Spinel vanadates– Spinels with rare earth ions– Frustration in heavy fermions?

Conclusions

SCES04 7/29/04

Ni3V2O8

G. Lawes, M. Kenzelmann, N. Rogado, K. H. Kim, G. A. Jorge, R. J. Cava, A. Aharony, O. Entin-Wohlman, A. B. Harris, T. Yildirim, Q. Z. Huang, S. Park, and A. P. Ramirez

ZnCr2O4

S.-H. Lee, W. Ratcliff II, S.-W. Cheong, T. H. Kim, Q. Huang, and G. Gasparovic

PHCCM. B. Stone, I. A. Zaliznyak, Daniel H. Reich

PrxBi2-xRu2O7

J. van Duijn, K.H. Kim, N. Hur, D. T. Adroja, M. Adams, Q. Z. Huang, S.-W. Cheong, and T.G. Perring

V2O3

Wei Bao, G. Aeppli, C.D. Frost, T. G. Pering, P. Metcalf, J. M. Honig

Acknowledgements

SCES04 7/29/04

Destabilizing Static LRO

Frustration: All spin pairs cannot simultaneously be in their lowest energy configuration

Frustrated

Weak connectivity: Order in one part of lattice does notconstrain surroundings

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1. Assume Neel order, derive spin wave dispersion relation2. Calculate the reduction in staggered magnetization due to quantum fluctuations3. If then Neel order is an inconsistent assumption

diverges if on planes in Q-space

Effective low dimensionality from frustration

QQQ

R RR

g

v

d

SSS

NSS

BZ

3

2

11

2

1

S

S 0Q

SS

Frustration + weak connectivity can produce local soft modes that destabilize Neel order

Frustration + weak connectivity can produce local soft modes that destabilize Neel order

T/J

H, P, x, 1/S…

0i S0i SR

en

orm

aliz

ed

C

lass

ical

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Magnetism on a kagome’ Staircase

c

a b

— S=½ spinons above small gap— S=∞ No order or spin glass— Ising no phase transition — XY Critical at T=0

Ni3V2O8Ni3V2O8

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Order from kagome’ critical state

0 6 12Temperature (K)

0

2

4

6

80

2

4

6

80

2

4

6

8

LTI HTI

HTILTI

LTI

C

C

C

H║a

H║b

TPHTHLTLCTCC’

C’

C’

C’

P

P

H(T

)

(a)

(b)

(c)

HTI P

H║c

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Non-collinear order from competition

T<9 KT<6.5KT<2.1 K

Spine ANNNI modelSpiral reduces

Amplitude modulation Anisotropy overpowers

NNN interaction

Kenzelmann et al. (2004)

SCES04 7/29/04

From quasi-elastic to local resonance

T=30 KT=1.5 K

T/J

H, P, x, 1/S…

0i S0i S

Near

Quantu

m

Cri

tica

l?

Ren

orm

aliz

ed

C

lass

ical

Frustration and short range correlations

CW

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TN<T<|CW| : Short range correlations

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TN<T<|CW| : Dynamic Short Range Order

S.-H. Lee et al. PRL (2000)

Points of interest:

• 2/Qr0=1.4

⇒ nn. AFM correlations

• No scattering at low Q

⇒ satisfied tetrahedra

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T<TN : Resonant mode and spin waves

S.-H. Lee et al. PRL (2000)

Points of interest:

• 2/Qr0=1.4

⇒ nn. AFM correlations

• No scattering at low Q

⇒ satisfied tetrahedra

• Resonance for ħ≈ J

• Low energy spin waves

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Average form factor for AFM hexagons

S.-H. Lee et al. Nature (2002) Tchernyshyov et al. PRL (2001)

++

++

++

▬▬

▬▬

▬▬

2

2

2

2

111ˆˆ

2cos

2cos

2sin

2cos

2cos

2sin

2cos

2cos

2sin

khl

hlk

lkh

FI

nn QQ

n̂

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Sensitivity to impurities near quantum criticality

Ratcliff et al. PRB (2002)

TN

Tf

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Low T spectrum sensitive to bond disorder

Q (Å-1)

0 0.5 1.0 1.5 2.0 2.5

5% Cd

T/J

H, P, x, 1/S…

0i S0i S

Near

Quantu

m

Cri

tica

l?

Quantu

m

Para

mag

net

0i S

SCES04 7/29/04

Singlet Ground state in PHCC

Daoud et al., PRB (1986).

J1=12.5 K=0.6

J1=12.5 K=0.6

1JT

/ m

ax

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2D dispersion relation

(

meV

)

0

1 0

1

h

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Neutrons can reveal frustration

2 1 1( , ) 1 cos

3d J

N d r r d

rd

Q S S Q d S

The first -moment of scattering cross section equals “Fourier transform of bond energies”

bond energies are small if small Positive terms correspond to “frustrated bonds”

drrd SSand/or J

1d2d

3d4d

drrrd

d SS J21H

SCES04 7/29/04

Frustrated bonds in PHCC

Green colored bonds increase ground state energy The corresponding interactions are frustrated

Green colored bonds increase ground state energy The corresponding interactions are frustrated

T/J

H, P, x, 1/S…

0i S0i S

Near

Quantu

m

Cri

tica

l?

SCES04 7/29/04

Colossal T-linear C(T) in PrxBi2-

xRu2O7K

. H. K

im et

al.

SCES04 7/29/04

“Resilient” non-dispersive spectrum

T=1.5 K

T=30 K

T=90 K

J. Van Duijn et al. (2004)

ħ

meV

Q (Å-1)

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Properties of disordered two-level system

2( ) tanh ( ) ( )2

2

0

( ) ( ) " (| |) tanh2

d

21 1 e

S

duue

ueuTBukTBkBkpc

02)1(

2)()(

Generalized susceptibility for two level system, :

Generalized susceptibility with distributed splitting, :

How to derive the distribution function from “scattering law”

How to derive specific heat from distribution function:

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Identify Scaling form for S()

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Colossal “” from inhomogeneously split doublet

What is the role of frustration? — It allows high DOS without order far above percolation

What do we learn from this? — Be aware of non-kramers doublets in alloys— There may be interesting magneto-elastic effects associated with frustrated non-kramers systems

Metal Insulator transition in V2O3 Hole dopingHole doping Increase U/WIncrease U/W

Mott

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Short Range order in Paramagnetic Insulator

B.Z.

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Spin wave dispersion Exchange constants

0.6 meV-22 m

eV -22

meV

Bao et al. Unpublished

Orbital occupancy order

Magnetic order T<TC

Orbital fluctuations

Magnetic SRO T>TC

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Orbital frustration in V2O3?

An interesting possibility:

•Bonds occupy kagome’ lattice

•Ising model on kagome’ lattice has no phase transition whence the low TC

•Orbital occupational order eventually occurs because it enables lower energy spin state

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Competing Interactions in URu2Si2?T=22 KT=22 K

Broholm et al. (1991)

Wie

be e

t al.

(200

4)

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Effective low dimensionality of CeCu6

H.v. Lohneysen et al. (2000)

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Conclusions

Frustration is a central aspect of SCES

Frustrated insulators display– Reduced TN with complex phase diagrams– Composite spin degrees of freedom– Magneto-elastic effects close to criticality– Hypersensitivity to quenched disorder– Singlet ground state phases are common when

symmetry low

Metals with Frustrated magnetism– Large “” from quenched disorder in frustrated non-

kramers doublet systems– Orbital frustration may help to expose MIT in V2O3

– A possible role of frustration in U and Ce based HF systems