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Magnetic OxidesGerald F. Dionne
Department of Materials Science and EngineeringMassachusetts Institute of Technology
Spins in Solids Summer SchoolUniversity of Virginia
Charlottesville, VA21 June 2006
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Lecture Outline
• Magnetic oxide overview
• Transition-metal ions and lattice sites (crystal fields)
• Electronic ground states (Hund vs Pauli)
• Spin-orbit-lattice effects (Jahn-Teller, λL·S, T1)
• Magnetic order in oxide systems (superexchange)
• Signal propagation (RF and IR)
• Spin transport phenomena (polarons for CMR, HTS)
• Other magnetic oxides (orthoferrites, ferroics, dilute systems)
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Technology Overview
Permanent magnetsMagnetic recordingAC magnetsRF control devicesMicrowave absorbersEPR and FMR (medical)Fiber opticsSuperconductorsMagnetoresistanceSpintronics
Refractory (Tmelt → 2000 C)Chemically stablePhysically ruggedFilm (not so) friendlyFrequency tunable by ε and µBroad range 4πMs (102 - 104 G)Curie TC → 1000 KResistivity ρ < 10−4 Ω-cmWell-studied
ApplicationsProperties
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Periodic Table
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Transition Element Models
3dn 4fn
Active 3d shellActive 3d shell Inert 4f shellInert 4f shell
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Hund’s Rule − 3dn Series
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Oxygen Lattice Sites
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Octahedral-Site Distortions
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d Orbitals in Octahedral Site
eg
t2g
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Low-Spin State of Mn3+ (3d4)
HighHigh--spin configurations (spin configurations (Hund’sHund’s rule) that arise fromrule) that arise fromInternal repulsion correspond to ferromagnetism inInternal repulsion correspond to ferromagnetism inmolecular molecular antibondingantibonding states.states.
LowLow--spin configurations (spin configurations (PauliPauli principle) correspondprinciple) correspondto the condensation of to the condensation of antiferromagnicantiferromagnic spinsspinsin molecular bonding states. in molecular bonding states.
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One-Electron Models (Octahedral)
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Jahn-Teller / Spin-Orbit Stabilizations
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Jahn-Teller / Spin-Orbit (cont’d)
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Exchange Diagrams
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Bond Types
IonicIonic(bound electrons)(bound electrons)
MetallicMetallic(collective electrons)(collective electrons)
MetalMetal--OxideOxide(occupied hybrid (occupied hybrid orbitalsorbitals))
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Bonding and Spin Alignment
Magnetic MetalsMagnetic Metals
Collective (delocalized) d spinsCollective (delocalized) d spins High density: High density: ∑∑ee22/r/rij ij repulsion, repulsion, antibondingantibonding ((Hund’sHund’s rule): rule): FMFM Low density: nuclear attraction, bonding ( Low density: nuclear attraction, bonding (PauliPauli pairing): pairing): AFMAFM Direct exchange; band models Direct exchange; band models
Magnetic OxidesMagnetic Oxides
Localized d spins in bonding statesLocalized d spins in bonding states ∑∑ee22/r/rij ij ~ 0~ 0 Electron Electron--nuclear attraction, (nuclear attraction, (PauliPauli pairing): pairing): AFMAFM SuperexchangeSuperexchange; Anderson, ; Anderson, GoodenoughGoodenough, , BallhausenBallhausen
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Combined Exchange Constant
∑>
⋅∆ji
jiij SSJE 2– = ex
e + =
e +e
e–
e–
e
– e
– ) + (m2
– =
12
2
1
2
12
2
1
2
2
22
2
1
222
2
0
r
rZZ
rrZ
rZ
rZ
rZ
ba
ab
ba
b
b
a
a
b
b
a
aba
HHH
H
+
+
∇∇
h
( )∑ ++−n
nij
nij
nijij J JJ = J doubledirectupers
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Molecular Orbital Theory
( )
± +±+=
=
−−
−−
ϕϕ=
ϕϕ=
−=
≈=
++=
2ML
2MLLM2
1
LMLML
MLMLM
LMML
LMML
LMML
LM,LM,LM,LM,
2LM
bUEEE
0EEEb
EbEE
b transfer
overlap
EEU LE+IPE where
/e
SS
H
S
H
~HHH 01 ijr
( )
( ) LLMM221
LMML221
cc
cc
2ML
2ML
ϕϕϕ
ϕϕϕ
+=
−=
++
−−
S
S
bondingbonding
antibondingantibonding
OneOne--Electron Perturbation ModelElectron Perturbation Model EnergyEnergy--Level Occupancy (Level Occupancy (AufbauAufbau))
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Bonding – Antibonding States
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Goodenough-Kanamori Rules (180°)
VIRTUAL TRANSFER (two unpaired spins)Half-filled ↔ half-filled orbitals
Correlation superexchange, J < 0 ANTIFERROMAGNETISM
REAL TRANSFER (one spin)Filled ↔ half-filled ↔ empty orbitalsHund’s rule exchange Uex > 0
Delocalization superexchange, J > 0 FERROMAGNETISM
SPIN TRANSPORT (special case of mixed-valence)Filled ↔ half-filled ↔ empty orbitalsPolaron trap activation energy Up << bp
Double exchange J > 0 FERROMAGNETISM (ITINERANT)TRANSPORT BY:
A) THERMAL ACTIVATED MOBILITY (Verwey hopping, random) B) COVALENT TUNNELING (Holstein polarons, coherent)
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G-K Diagrams
Correlation AFMCorrelation AFM
Delocalization FMDelocalization FM
Polaron (double) FMPolaron (double) FM
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G-K Table (180° bonds)
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Magnetic Sublattices
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Ferrite Thermomagnetism
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Spinel Ferrites
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Rare-Earth Garnets
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Diluted Y3Fe5O12 (YIG)
octahedraloctahedral--sitesite dilutiondilutiontetrahedraltetrahedral--sitesite dilutiondilution
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Circular Polarization
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Faraday Rotation
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Dipole Transitions
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Resonance Line Shapes
PermeabilityPermeability PermittivityPermittivity
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Bismuth Iron Garnet
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Faraday Rotation Isolators
HighHigh--Power MicrowavesPower Microwaves FiberFiber--Optic InfraredOptic Infrared
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G-K Diagrams
Correlation AFMCorrelation AFM
Delocalization FMDelocalization FM
Polaron (double) FMPolaron (double) FM
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Brillouin-Weiss vs Applied H
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Brillouin Function H Sensitivity
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Perovskite Cells
B siteB site A siteA site
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Charge Transfer in J-T Ions
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CMR Theory
[ ]),(– 1 + = Sexhop
0hophop HTEEE B
1
eff kee
–
TDn = ρ
′
( ) ( )( )[ ] T/E–– + T/E–n = n SSe k1kexp hop0hopffeff BB′
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CMR Curves vs T,H
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CMR Data Fitting
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Metallic Perovskites
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Polaron Rings
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3d8 Low-Spin State
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d8 S = 0 Stabilization vs Axial Field
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Spin Frustration by S = 0 Cu3+ Ions
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Polaron Tunneling vs Hopping
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Polaron Mobility
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Zero-Spin Transfer Combinations
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Tc,TN = 0 Condition
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Tc Fitting of Theory to Data
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Tc vs x, β Predictions
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Unconventional Magnetic Oxides
Magnetic Perovskites (Orthoferrties): (RE)3+Fe3+O3 → 0.5-degree canted AFM sublattices produce net 4πM ~102 G, TC > 550 K
Double Perovskite Ferrites: A3+2Fe(3+n)+M(3–n)+O6 → charge-ordered cation form
magnetically unbalanced sublattices and produce higher 4πM, TC > 300 K. Polarized spin transport can be expected
Double Perovskite Ferromagnet: A3+2Mn4+Ni2+O6 → charge-ordered
ferromagnetism by delocalization exchange produces ferromagnetism with semiconducting properties near 300 K. Classic example of Goodenough-Kanamori rules.
Magnetoelectric (Piezomagnetic) Perovskite: Bi3+Fe3+O3 films offer basis for combined ferroelectric/piezoelectric/ferromagnetic properties at T > 600 K
Dilute Magnetic Oxides: Substitutional combinations of Fe and Cu in In2O3films produce both ferromagnetism and n-type semiconduction at T → 600 K