collin broholm johns hopkins university and nist center for neutron research quantum phase...
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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
FSU 12/14/01
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
FSU 12/14/01
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
FSU 12/14/01
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
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