Magnetic Oxides Gerald F. Dionne Department of Materials Science and Engineering Massachusetts Institute of Technology Spins in Solids Summer School University of Virginia Charlottesville, VA 21 June 2006 1
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, T 1 ) 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) 2
Technology Overview Properties Applications Refractory (T melt 2000 C) Chemically stable Physically rugged Film (not so) friendly Frequency tunable by ε and µ Broad range 4πM s (10 2-10 4 G) Curie T C 1000 K Resistivity ρ < 10 4 Ω-cm Well-studied Permanent magnets Magnetic recording AC magnets RF control devices Microwave absorbers EPR and FMR (medical) Fiber optics Superconductors Magnetoresistance Spintronics 3
Periodic Table 4
Transition Element Models 3d n 4f n Active 3d shell Inert 4f shell 5
Hund s Rule 3d n Series 6
Oxygen Lattice Sites 7
Octahedral-Site Distortions 8
d Orbitals in Octahedral Site e g t 2g 9
Low-Spin State of Mn 3+ (3d 4 ) High-spin configurations (Hund s( rule) that arise from Internal repulsion correspond to ferromagnetism in molecular antibonding states. Low-spin configurations (Pauli( principle) correspond to the condensation of antiferromagnic spins in molecular bonding states. 10
One-Electron Models (Octahedral) 11
Jahn-Teller / Spin-Orbit Stabilizations 12
Jahn-Teller / Spin-Orbit (cont d) 13
Exchange Diagrams 14
Bond Types Ionic (bound electrons) Metallic (collective electrons) Metal-Oxide (occupied hybrid orbitals) 15
Bonding and Spin Alignment Magnetic Metals Collective (delocalized) d spins High density: e 2 /r ij repulsion, antibonding (Hund s rule): FM Low density: nuclear attraction, bonding (Pauli( pairing): AFM Direct exchange; band models Magnetic Oxides Localized d spins in bonding states e 2 /r ij ~ 0 Electron-nuclear nuclear attraction, (Pauli( pairing): AFM Superexchange; ; Anderson, Goodenough, Ballhausen 16
17 Combined Exchange Constant > j i j i ij S S J E 2 = ex e + = e + e e e e e ) + ( 2m = 12 2 1 2 12 2 1 2 2 2 2 2 1 2 2 2 2 0 r r Z Z r r Z r Z r Z r Z b a ab b a b b a a b b a a b a H H H H + + h ( ) + + n n ij n ij n ij ij J J J = J double direct super
Molecular Orbital Theory One-Electron Perturbation Model = E = E = = 2 ( e / r ~ ) H = H + H + 0 1 M L ij where overlap transfer H U S M,L b ML ML ML ϕ M,L M ϕ M IP E M ϕ L L H M,L ϕ L + LE M,L Energy-Level Occupancy (Aufbau( Aufbau) antibonding b E ML M E E S ML b E S E E ML L ML = 0 bonding E 1 2 ± = E M + E L ± U ML + 2 b 2 ML ϕ ϕ + = = 1 2 2S 1 2+ 2S 2 ML 2 ML ( ) c L ( ) c M ϕ ϕ M M c + c M L ϕ ϕ L L 18
Bonding Antibonding States 19
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 orbitals Hund s rule exchange U ex > 0 Delocalization superexchange, J > 0 FERROMAGNETISM SPIN TRANSPORT (special case of mixed-valence) Filled half-filled empty orbitals Polaron trap activation energy U p << b p Double exchange J > 0 FERROMAGNETISM (ITINERANT) TRANSPORT BY: A) THERMAL ACTIVATED MOBILITY (Verwey hopping, random) B) COVALENT TUNNELING (Holstein polarons, coherent) 20
G-K Diagrams Correlation AFM Delocalization FM Polaron (double) FM 21
G-K Table (180 bonds) 22
Magnetic Sublattices 23
Ferrite Thermomagnetism 24
Spinel Ferrites 25
Rare-Earth Garnets 26
Diluted Y 3 Fe 5 O 12 (YIG) tetrahedral-site dilution octahedral-site dilution 27
Circular Polarization 28
Faraday Rotation 29
Dipole Transitions 30
Resonance Line Shapes Permeability Permittivity 31
Bismuth Iron Garnet 32
Faraday Rotation Isolators High-Power Microwaves Fiber-Optic Infrared 33
G-K Diagrams Correlation AFM Delocalization FM Polaron (double) FM 34
Brillouin-Weiss vs Applied H 35
Brillouin Function H Sensitivity 36
Perovskite Cells B site A site 37
Charge Transfer in J-T Ions 38
CMR Theory ρ = n eff e ed kt 1 n eff = n eff [ ( 0 B exp E / kt ) + ( 1 B )( E / kt )] S hop S hop E hop 0 hop ex hop = E + E S [ 1 B ( T, H )] 39
CMR Curves vs T,H 40
CMR Data Fitting 41
Metallic Perovskites 42
Polaron Rings 43
3d 8 Low-Spin State 44
d 8 S = 0 Stabilization vs Axial Field 45
Spin Frustration by S = 0 Cu 3+ Ions 46
Polaron Tunneling vs Hopping 47
Polaron Mobility 48
Zero-Spin Transfer Combinations 49
T c,t N = 0 Condition 50
T c Fitting of Theory to Data 51
T c vs x, β Predictions 52
Unconventional Magnetic Oxides Magnetic Perovskites (Orthoferrties): (RE) 3+ Fe 3+ O 3 0.5-degree canted AFM sublattices produce net 4πM ~10 2 G, T C > 550 K Double Perovskite Ferrites: A 3+ 2 Fe(3+n)+ M (3 n)+ O 6 charge-ordered cation form magnetically unbalanced sublattices and produce higher 4πM, T C > 300 K. Polarized spin transport can be expected Double Perovskite Ferromagnet: A 3+ 2 Mn4+ Ni 2+ O 6 charge-ordered ferromagnetism by delocalization exchange produces ferromagnetism with semiconducting properties near 300 K. Classic example of Goodenough- Kanamori rules. Magnetoelectric (Piezomagnetic) Perovskite: Bi 3+ Fe 3+ O 3 films offer basis for combined ferroelectric/piezoelectric/ferromagnetic properties at T > 600 K Dilute Magnetic Oxides: Substitutional combinations of Fe and Cu in In 2 O 3 films produce both ferromagnetism and n-type semiconduction at T 600 K 53