on the spin orientation 1. qualitative rules for predicting preferred spin orientations? 2. spin...
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On the spin orientation
1. Qualitative rules for predicting preferred spin orientations?
2. Spin orientations of Sr3NiIrO6, Sr2IrO4, Ba2NaOsO6: Implications on the magnetism of Jeff=1/2 ions
M.-H. WhangboDepartment of ChemistryNorth Carolina State UniversityNC 27695-8204, USA
E. E. Gordon: Chemistry, NCSUJ. W. Kim, S.-W. Cheong: Physics, Rutgers UniversityH. J. Xiang: Physics, Fudan University
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Energy Mapping Analysis
"SA"
)SS(D
SSJ
2izi i
jiji ij
jiji ij
3. Broken-Symmetry Spin States
4. DEspin-H DEDFT
1. Model Hamiltonian: Parameters
2. DFT calculations
Qualitative prediction?
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Spin orientation spin-orbit coupling (SOC)
Large SOCTopological insulatorsRashba-Dresselhaus effectsValleytronicsSpin-textured bandsJeff=1/2 states
Coupling between spin and orbital momentsweak L-S couplingstrong j-j coupling
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Magnetic insulator of 5d oxides Strong SOC + weak correlationPRB 75, 052407 (2007)
Ba2NaOsO6: Os7+ (5d1, S = 1/2)
qCW -10 KFM below TC 7 KPRB 84, 144416 (2011)
DFT+U
DFT+SOC
DFT+U+SOC
Os7+ (5d1, S = 1/2) in Ba2NaOsO6 No preferred spin orientation
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Sr2IrO4: low-spin Ir4+ (5d5, S = 1/2) (t2g)5
Corner-sharing IrO6 IrO4 layer, Axially-elongated IrO6
Magnetic insulatorStrong SOC + weak correlation split of Jeff=1/2
PRL 101, 076402 (2008)Science 323, 1329 (2009)
xy
xz yz
Excitation different orbital states
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PRB 87, 140406(R) (2013)
Low-spin Ir4+ (5d5, S = 1/2) ion in Sr2IrO4
Weakly anisotropic, preferred spin orientation: Ir-Oax
ESR study of Sr2IrO4
Isotropic Heisenberg interactions between Ir4+ spins PRB 89, 180401(R) (2014)
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Ni
Irc
Sr3NiIrO6: low-spin Ir4+ (5d5, S = 1/2), high-spin Ni2+ (3d8, S = 1)
Strongly anisotropicM-H hysteresis FM? Ferrimagnetic?PRB 89, 180401(R) (2014)PRL, under review
1/3 B/FU
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Ni2+ and Ir4+ spinsboth ||cnn AFM Ferrimagnetic
PRB 90, 014408 (2014) arXiv:1501.05735 [cond-mat.str-el]
Partially disordered AFM (PDA) 1/3 B/FU
Low-spin Ir4+ (5d5, S = 1/2) in Sr3NiIrO6
Strongly anisotropic
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Weak single-ion isotropy: SOC from a trace orbital moment
x
y
z
z'
)sineL2
1sineL
2
1cosL(S
H LSH
iizz
0SOSO
(x, y, z) for orbital, (x’, y’, z’) for spin
uo
2
u0SOo
SOC ee
HE
Most important,
between the HO and the LU statesDalton Trans. 42, 823 (2013)
= 0: easy-axis anisotropy = 90: easy-plane anisotropyJ. Comput. Chem. 29, 2187 (2008)
L
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z2
xy
xz, yz
x2-y2
U
Spin-polarized d-states
Selection rules for SOC
)sineL2
1sineL
2
1cosL(S ii
zz
3z2-r2
xy, x2-y2
xz, yz
|DLz|=2
|DLz|=1
|DLz|=1
|DLz|=0 |DLz|=0
plane-easy 1L LsinLL
plane-easy 1L LsinLL
axis-easy 0L LcosLL
zzz
zzz
zzzz
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High-spin Mn3+ in TbMnO3 & Ag2MnO2
Axially-elongated MnO6 octahedron
(xy)1 < (z2)1 < (x2-y2)0
||z, easy-axis anisotropyPRL 101, 037209 (2008)PRB 81, 094421 (2010)
x2-y2
z2
xy
xz yz
z
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Concluding remarks The preferred spin orientations of magnetic ions, predicted by uniaxial magnetism, or weak single-ion anisotropy.