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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