Magnets without Direction Collin Broholm

Johns Hopkins University and NIST Center for Neutron Research

Introduction

Moment Free Magnetism in one dimension

Higher dimensional MFM

Frustrated origins of MFM

Interesting aspects of MFM

Conclusions

G. AeppliP. BischerY. ChenJ. F. DiTusaD. V. FerrarisC. D. FrostT. ItoT. Lectka K. Oka

Acknow

ledgements

Ack

now

ledg

emen

ts R. PaulD. H. ReichJ. RittnerM. B. StoneH. TakagiM. TreacyG. XuH. YardimciI. Zaliznyak

NIST Center for Neutron ResearchISIS Facility, Rutherford Appleton LaboratoryNational Science Foundation DMR 0074571Civilian Research and Development Foundation

Rutgers 10/17/01

Many electrons, few magnetic materials

Filled shell in solid:

Ti V Cr Mn Fe Co Ni Cu

Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm

U Np Pu Am Cm

Partially filled shell in solid:

Rutgers 10/17/01

Magnetization of Solid with unfilled Shells

Susceptibility data for paramagnetic salt

j jBg SHH

j jBg SHH

HSM j j

B

V

g HSM j j

B

V

g

Tk

SSg

B

B

3

)1(2

H

Mχ

Tk

SSg

B

B

3

)1(2

H

Mχ

Spin susceptibility diverges as T 0Spin susceptibility diverges as T 0

FeBr(C44H28N4)Dilute Fe in organic matrix

FeBr(C44H28N4)Dilute Fe in organic matrix

Rutgers 10/17/01

S=1/2S=1/2 S=1/2

Coulomb + Pauli = Heisenberg

Coulomb interactions plus Pauli principle split 4-fold spin degeneracy

jiJ SS H jiJ SS H

The level scheme is reproduced by Heisenberg Exchange Hamiltonian

|J|1totS

0totS

S=1/2

|J|0totS

1totS

Singlet gnd. State: J > 0

Triplet gnd. State: J < 0

Rutgers 10/17/01

Interactions orient moments

1

Ferromagnetic EuOFerromagnetic EuO

1

Antiferromagnetic KNiF3Antiferromagnetic KNiF3

CWNT

Rutgers 10/17/01

Unconventional magnetism in NENP

K91CWK91CW

Negative Curie Weiss temperature indicates AFM interactions No phase transition and

Negative Curie Weiss temperature indicates AFM interactions No phase transition and 0for small T

1

Rutgers 10/17/01

A can of magnetic worms

Magnetic interactionslink spins in chains

Magnetic interactionslink spins in chains

Ensemble of Quasi-one-dimensionalAntiferromagnets chains

Ensemble of Quasi-one-dimensionalAntiferromagnets chains

NENP=Ni(C2H8N2)2NO2ClO4

Rutgers 10/17/01

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

When is the Neel state unstable?

Q

QQR RR

g

v

d

SSS

NSS

BZ

3

2

11

2

1

S

S 0Q

SS

A putative D=1 Neel state has soft planes and so is unstableA putative D=1 Neel state has soft planes and so is unstable

Moment Free Magnetism averts infrared catastrophe

Y2BaNiO5

Ajiro et al. (1989)

Bg

Rutgers 10/17/01

Unconventional magnetism in PHCC

K15CWK15CW

Negative Curie Weiss temperature indicates AFM interactions No phase transition and

Negative Curie Weiss temperature indicates AFM interactions No phase transition and 0for 0 T

1

Rutgers 10/17/01

b

c

Structure is “consistent” with spin chains

PHCC = C4H12N2Cu2Cl6

a

cCu

ClC

N

Rutgers 10/17/01

Magnetic Neutron Scattering

fi kkQ

fi EE

ik fk

Q

2

The scattering cross section is proportional to the Fourier transformed dynamic spin correlation function

''R

)'( )0(S)(S1

2

1),(

RRR

RRQiti teN

edtQ

S

Rutgers 10/17/01SPINS cold neutron triple axis spectrometer at NCNR

Rutgers 10/17/01

Dispersion along c axisDispersion along c axis

Could be spin chainCould be spin chain

No dispersion along b No dispersion along b

Is PHCC quasi-one-dimensional?PHCC is quasi-two-dimensional

Dispersion to “chains”Dispersion to “chains”

Not chains but planesNot chains but planes

Rutgers 10/17/01

Unconventional magnetism in CuHpCl

Negative CW indicates AFM interactions No phase transition and Spin ladder model consistent with (T)

Negative CW indicates AFM interactions No phase transition and Spin ladder model consistent with (T)

0for 0 T

Putative S

pin ladder model for C

uHpC

l

Rutgers 10/17/01 CuHpCl hydrogenous single crystals

Rutgers 10/17/01

….But there is dispersion to “ladder”Q // to chain Q to chain

….and there are two modes when ladder gives only one….and there are two modes when ladder gives only one

Rutgers 10/17/01

Other means of destabilizing Neel order

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

Frustrated

Weak connectivity: Order in one part of lattice does notconstrain surrounding spins

Rutgers 10/17/01

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

A Frustrated Route to Moment Free Magnetism?

Q

QQR RR

g

v

d

SSS

NSS

BZ

3

2

11

2

1

S

S 0Q

SS

Frustration can produce local soft modes that destabilize Neel order

Frustration can produce local soft modes that destabilize Neel order

Rutgers 10/17/01

Neutrons can reveal frustration

dQSSQ drrrd

d cos11

3

1),(2 J

Nd S

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

For a powder sample we know only Q=|Q|

Qd

QdJ

NQd

sin1

1

3

1),(2

drrrd

d SS S

high Qd plateau measures ground state energy

negative terms are “frustrated bonds”bond energies are small if small drrd SSand/or J

Magnetic scattering from CuHpCl powder

Rutgers 10/17/01

Neutrons reveal frustration in CuHpCl

Peak to plateau ratio 217.1sin

1max

x

x

Mixed signs for bond energiesMixed signs for bond energies FrustrationFrustration

Rutgers 10/17/01

Structure of CuHpClCuHpCl is hydrogen bonded crystal of Cu2(C5H12N2)2Cl4

Molecules possess approximate centro symmetryExchange interaction within molecule |J|<1 meV

Two lattices from H-bond exchange

b

Rutgers 10/17/01

Building an enigma

Dispersion throughout a-c plane Dispersion throughout a-c plane

Spin liquid on 3-dimensional latticeSpin liquid on 3-dimensional lattice

Rutgers 10/17/01

Detailed bond energy distribution

a*

c* (101)

(100)

(001)

Point size First moment

Rutgers 10/17/01

Frustrated three dimensional spin liquid

Significance of findings so far

Neutron scattering required to classify quantum spin liquids

Systems thought to be one dimensional may

represent a richer class of materials

Experimental realizations of spin liquids were

sought, not found, in symmetric frustrated magnets

Spin liquids may be more abundant in complex

geometrically frustrated lattices

Rutgers 10/17/01

Field induced T=0 phase transition

PHCC

Rutgers 10/17/01

Reentrant behavior close to critical point

3 D long range order3 D long range order

Moment freeMoment free

Rutgers 10/17/01

Holes dressed by spin polarons

Y3+

Ni

O

FM

Ca2+

Xu et al. Science (2000).

Rutgers 10/17/01

Transport in Ca doped Y2BaNiO5

T. Ito et al. Submitted to PRL (2001)

Charge Transfer excitationCharge Transfer excitation

Charge polaronCharge polaron

1D conductivity, no Charge ordering1D conductivity, no Charge ordering

Rutgers 10/17/01

Holes in a quantum spin liquid

Some organic materials can be doped and conduct in Field Effect Transistors [Schon et al. Science (2000)]

Moment free organo-metallic systems should have interesting transport properties if they can conduct.

PHCC

ConclusionsSpin systems with a gap can be mistaken for being

quasi-one-dimensional Two and three dimensional moment free

magnetism found in PHCC and CuHpClNeutron scattering reveals frustrated bonds in the

corner-sharing triangular clusters of these materialsHypothesis: Moment free magnetism may be a

common state of interacting spin systems with triangular motif and weak connectivity

Idea: Novel strongly correlated transport may occur if the materials can be doped