Collin BroholmJohns Hopkins University and NIST Center for Neutron Research

Quantum Phase Transition in a Quasi-two-dimensional Frustrated Magnet

M. A. Adams ISIS Y. Chen JHUD. V. Ferraris JHUN. Harrison LANLT. Lectka JHUD. H. Reich JHUJ. Rittner JHUM. B. Stone JHUGuangyong Xu U. ChicagoH. Yardimci JHUI. Zaliznyak BNL

* Work at JHU Supported by the National Science Foundation

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Outline of Seminar

A simple D=1 quantum magnet: Copper Nitrate

A not so simple D=2 quantum magnet: PHCC

Frustration in PHCC

Field induced phase transition in PHCC

Conclusions

Some results published in M. Stone et al., PRB 64, 144405 (2001)See also paper on CuHpCl M. Stone et al., Cond-Mat/0103023

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Spin Hamiltonian of magnetic dielectric

Chemistry determines dimensionality, connectivity Vary H with pressure, magnetic field

H is affected by any lattice distortions

lllB

llll

ll

g

J

SH

SS

''

'H Exchange interaction

Dipole in magnetic field

H = n

nnnnJ 22121221 SSSS

27.0

meV 44.01

J

bH

bH ||

Singlet Ground State in Cu-Nitrate

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A spin-1/2 pair with AFM exchange has a singlet - triplet gap:

Simple description of alternating spin chain

J0totS

1totS

Inter-dimer coupling allows coherent triplet propagation and

produces well defined dispersion relation

Triplets can also be produced in pairs with total Stot=1

432

21

21

totJ

J

S

SSH

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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

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Triplet waves in copper nitrate

JTkB

Xu et al PRL (2000)

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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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b

c

Structure is “consistent” with spin chains

PHCC = C4H12N2Cu2Cl6

a

cCu

ClC

N

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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

(

meV

)

2D dispersion relation

(

meV

)

0

1 0

1

h

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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

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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

A Frustrated Route to Cooperative Singlet?

QQQ

R 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

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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”

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

drrd SSand/or J

1d2d

3d4d

drrrd

d SS J21H

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Measuring Bond Energies

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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

Results in zero field

Systems thought to be one dimensional may represent a richer class of quantum spin liquids.

Neutron scattering required to classify these.

Experimental realizations of spin liquids were

sought, not found, in symmetric frustrated magnets.

Hypothesis: Spin liquids may be more abundant in

complex geometrically frustrated lattices.

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Spin Pair in Magnetic Field

ztotBtot HSg

J 2

2SH

J1totS

ztotS

0

1

H

H

BC g

JH

0totS

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Zeeman splitting of cooperative triplet

PHCC T=60 mK

GS-level crossing for H8 TGS-level crossing for H8 T

Quantum phase transition Quantum phase transition

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Non-linear Magnetization Curve

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H-T Phase Diagram from Magnetization

Field-induced AFM Order

),0,( 21 Q

H=14.5 T T=1.77 K

Inte

nsity

c

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Frustrated bonds parallel spins

ca

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Gapless paramagnetic phase

Gap closesGap closes Onset of 3D LROOnset of 3D LRO

Gap

less

par

amag

net?

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H-T phase diagram

PHCC2D Gapped FM

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Temperature Driven Criticality

T=0.4 (1)

Bra

gg I

nten

sity

M

2

Compare to =0.355 for 3D X-Y modelCompare to =0.355 for 3D X-Y model

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H-T phase diagram

PHCC

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Reentrant low T transition?

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Extracting the critical field

K635.1T

Fit range

H

C

C

H

HHIHI

2

0)(

H

C

C

H

HHIHI

2

0)(

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Reentrant behavior close to critical point

3 D long range order3 D long range order

Spin gapSpin gap

gaplessgapless

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Reentrant behavior in other frustrated magnet

P. Schiffer et al., PRL (1994).Y. K. Tsui et al., PRL (1999).

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Magneto-elastic effects in frustrated magnets?

Lee et al., PRL (2000).

ZnCr2O4 frustrated spinel AFM

ConclusionsQuasi-2D singlet ground state in PHCCNeutron scattering reveals frustrated bonds that

may be instrumental in suppressing Neel orderOrdered state consistent with bond energies derived

from inelastic scattering at H=0Phase diagram features a cross-over to gapless

paramagnetic phaseAnomalous low T reentrant behavior may result

from magnetoelastic effects close to QC point