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Magnetic Interactions andOrder-out-of-disorderin Insulating Oxides
Ora Entin-Wohlman, A. Brooks Harris, Taner Yildirim
Robert J. Birgeneau, Marc A. Kastner, Koichi Katsumata
R. Ramirez, C. Broholm, J. W. Lynn
TAU, BGU, U Penn, NIST, MIT, RIKEN, Lucent, JHU
Les Houches summer school on Quantum Magnetism, June 2006
Amnon Aharony
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Lecture 3:
Vanadates:
Competing nn and nnn interactions yieldIncommensurate order
Competing anisotropies yield complex field dependent phase diagrams
Ni and Co have very different magnetic structures
Theoretical tools introduced in pervious lectures suffice to explain most features
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General outline:
Cuprates
VanadatesLecture 3
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823 OVCoBuckled Kagome
823 OVNiS=1 S=3/2
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823 OVCo
Buckled Kagome
823 OVNi
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Crystal Structure of Ni3V2O8
c
a
b
Cross-tie Spine
Only magnetic (S=1) Ni ions are shown
Cross-tie is
FRUSTRATED
?
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823 OVNi
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0
5
0
5
0
5
Ma
gn
etic
Fie
ld (
T)
0 2 4 6 8 10
Temperature (K)
H || a
H || b
H || c
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Specific heat
Neutron scattering intensities in C, LTI and HTI
Incommensurate wave vector
Weak ferromagnetism in C phase
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CAF’ = Incommensurate?
Paramagnetic
HTI = High TemperatureIncommensurate Phase
LTI = Low TemperatureIncommensurate Phase
CAF = Antiferromagnetic + weakly ferromagnetic
MAGNETIC PHASE DIAGRAM OF Ni3V2O8
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MAGNETIC PHASE DIAGRAM OF Ni3V2O8
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Theory
Step I: Main interactions along spines:
Superexchange, Ni—O—Ni and Ni—O—O--Ni
AHSSJSSJH )()( 312211
O
Ni Ni
O O
Ni Ni
Explain HTI, LTI, CAF
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Incommensurability? -- simplest model:
AHSSJSSJH )()( 312211
)0),sin(),cos(cos((
)0,0),cos((
21
qnaSqnaSS
qnaSS
n
nHTI
LTI
)4/()cos( 21 JJqa
At low T, anisotropy wins again CAF
(q locked in)
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Step II: Anisotropy comes from spin orbit interactions
Spin-orbit interaction generates Antiferromagnetic bond-dependent
spin anisotropy
Also Dzyaloshinskii-Moria antisymmetric exchange
Ni Ni
O
Oxygen tilted along z D along y, AFM along x FM along z
Bilinear coupling between staggered Moment along a and ferromagneticMoment along c
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xy
I1 I2
II
xy
I1 I2
II
Step III: spin on cross-tie NI? Pseudodipolar interactions
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More recent results: Multiferroic behavior
Ferroelectric moment alongb, only in LTI phase!
Can switch ferroelectric moment with magnetic field!
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PHASE DIAGRAM SPONTANEOUS POLARIZATION
Ma
gn
etic
Fie
ld (
T)
0
5
0
5
0
5
0 2 4 6 8 10Temperature (K)
ab
P( C
/m2 )
T=5K
P || b
H || c
T=4K
H || a
H || c
0 0.5 1 1.5 2 2.5 3 3.5
Magnetic Field (T)
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LANDAU THEORY WITH TWO ORDER PARAMETERS
4242)()( PdPTTcMbMTTaF PM
THIS DOES NOT WORK!!
WE DO NOT BELIEVE IN ACCIDENTALDEGENERACY (TP = TM). ALSO BOTHM AND P DEPEND STRONGLY ON H, SO
xMPPbMTTaF M
22)(
THEN, WHEN WE MINIMIZE WITH RESPECT TO P, P APPEARS ONLY WHEN M IS NONZERO:
xMP const
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MAGNETOELECTRIC COUPLING
PqqaH yxxy
yx
)()(,,
where x,y are LTI or HTI and = x,y,z
In the HTI phase we have a single order parameterwhich has a node at some lattice site. About thissite there will be inversion symmetry. So
I )q( = )-q( = )q(* I = inversion operator
q) = (-q)* is an order parameter
PqaH |)(| 2 = 0 ) IH = H(
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MANETOELECTRIC INTERACTION
Thus the trilinear magnetoelectricinteraction is of the form
H = HTI LTI P + d P2
So, after we minimize with respect to P:
P = const HTI LTI = const LTI
This qualitatively explains the dependence of P on T and H
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Confirm mean field trilinear term from microscopic Hamiltonian
Can arise from DM and PD interactions
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B2u-phononsMode Number: 64Mode Energy: 69.24 meV (experimental value is about 80 meV!)
Mode Description: Two oxygen atoms connected to cross-tie Ni moves along b-axis, significantly effecting the Ni-O-Ni bond angle for the spine spins (see the animations; side and top views).
Dipole Moment: 0.4612 (One of the largest dipole moment!)
b-axis
Spine-spins (a-axis)
Cross-tieConnected to V
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25 Phys. Rev. B, in press
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26 (Spins along spine parallel to each other)
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FM, =0
AFM, =1/2
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Theory
x(J3)
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Quartic terms
Higher harmonics
Lock-in
Lock-in
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Dielecric constant
Ferroelectricity???
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Conclusions:
Vanadates are almost frustrated; interesting phase diagrams
Can explain incommensurate phases by competing interactions
Multiferroics!
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THE END