Geometrically Frustrated Antiferromagnets Spins on corner-sharing tetrahedra Paramagnetic phase Long Range Ordered phase (ZnCr 2 O 4 ) Spin-glass phase (Y 2 Mo 2 O 7 ) Concluding phase Collin Broholm Hopkins University and NIST Center for Neutron Rese Supported by the NSF through DMR-9453362
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Neutron Scattering from Geometrically Frustrated Antiferromagnets Spins on corner-sharing tetrahedra Paramagnetic phase Long Range Ordered phase (ZnCr.
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Neutron Scattering from Geometrically Frustrated
Antiferromagnets
Spins on corner-sharing tetrahedra
Paramagnetic phase Long Range Ordered phase (ZnCr2O4) Spin-glass phase (Y2Mo2O7) Concluding phase
Collin BroholmJohns Hopkins University and NIST Center for Neutron Research
Supported by the NSF through DMR-9453362
Collaborators
S.-H. Lee NIST and University of MDS.-W. Cheong Bell Labs and Rutgers Univ.T. H. Kim Rutgers UniversityW. Ratcliff III Rutgers UniversityJ. Gardner Chalk River Nuclear LabB. D. Gaulin McMaster UniversityN. P. Raju McMaster UniversityJ. E. Greedan McMaster University
Experiments performed at NIST center for Neutron Research
Theory of spins with AFM interactions on corner-sharing
tetrahedra
SPIN TYPE SPINVALUE
LOW TPHASE
METHOD REFERENCE
Isotropic S=1/2 Spin Liquid Exact Diag. Canals and LacroixPRL'98
Isotropic S= Spin Liquid MC sim. Reimers PRB'92Moessner, ChalkerPRL'98
Anisotropic S= Neel order MC sim. Bramwell, Gingras,ReimersJ. Appl. Phys. '94
What is special about this lattice and this spin system?• Low coordination number• Triangular motif• Infinite set of mean field ground states with zero net spin on all tetrahedra• No barriers between mean field ground states• Q-space degeneracy for spin waves
Some non-disordered cubic insulators
with spins on corner sharing tetrahedra
Material spintype
spinvalue
CW
(K)Tc
(K)Low T phase Ref.
MgV2O4 isotrop. 1 -750 45 LRO Baltzer et al '66ZnV2O4 isotrop. 1 -600 40 LRO Ueda et al '97CdCr2O4 isotrop. 3/2 -83 9 LRO Baltzer et al '66MgCr2O4 isotrop. 3/2 -350 15 LRO Blasse and Fast '63ZnCr2O4 isotrop. 3/2 -392 12.5 LRO S.-H. Lee et al '99FeF3 isotrop. 5/2 -230 20 LRO Ferey et al. '86Y2Mo2O7 isotrop. 1 -200 22.5 spin glass Gingras et al. '97Y2Mn2O7 isotrop. 3/2 17 spin glass Reimers et al '91Tb2Mo2O7 anisotr. 6 and 1 25 spin glass Greedan et al '91Gd2Ti2O7 isotrop. 7/2 -10 1 LRO Radu et al '99Er2Ti2O7 anisotr. -25 1.25 LRO Ramirez et al '99Tb2Ti2O7 anisotr. -19 spin liquid? Gardner et al '99Yb2Ti2O7 anisotr. 0 0.21 LRO Ramirez et al '99Dy2Ti2O7 Ising 7.5 1/2 0.5 1.2 spin ice Ramirez et al '99Ho2Ti2O7 Ising 8 1/2 1.9 spin ice Harris et al ''97
B-s
pin
el
Pyro
chlo
re
Subjects of this talk
Magnetic Neutron Scattering
fi kkQ
fi EE
The scattering cross section is proportional to the Fourier transformed dynamic spin correlation function
ik fk
Q
2
''R
)'( )0(S)(S1
2
1),(
RRR
RRQiti teN
edtQ
S
Fluctuation dissipation theorem:
,1," 2 QegQ B S
AFM correlations in Y2Mo2O7 for T<|CW|=200 K
ZnCr2O4: short range dynamic correlations for
|T/CW|<<1
0 0.5 1.0 1.5 2 2.5 Q (A-1)
h
(meV
)
Points of interest:
• 2/Qr0=1.4 => nn. AFM correlations
• No scattering at low Q => satisfied tetrahedra
• Relaxation rate of order kBT => quantum critical
Spin Fluctuations in Paramagnetic phase of
ZnCr2O4
22),("
Q
QQQ
Lorentzian relaxation spectrum:
Near Quantum Criticalspin system:
TkT
TTkCT
B
QQ
BQ
1
1
3)(
)(
2
1
6.0
8.0
C
meV76.0Bk
No indication of finite T cross over or phase transition in cubic phase
h
(meV
)
Spin resonance for T<TC
T=TC+:
kBT is theenergy scale
T<TC :
Spin resonanceat
J
Low T excitations in ZnCr2O4:
Magnetic DOS Q-dep. of E-integ. intensity
C
A
B
B
C
A
A: Bragg peaksB: Spin wavesC: ResonanceD: Upper band
D
First order phase transition in ZnCr2O4
Dynamics:• Low energy paramag. Fluctuations form a resonance at 4.5 meV