Magnetic Oxides. Gerald F. Dionne. Department of Materials Science and Engineering Massachusetts Institute of Technology

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1 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

2 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

3 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 ( 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

4 Periodic Table 4

5 Transition Element Models 3d n 4f n Active 3d shell Inert 4f shell 5

6 Hund s Rule 3d n Series 6

7 Oxygen Lattice Sites 7

8 Octahedral-Site Distortions 8

9 d Orbitals in Octahedral Site e g t 2g 9

10 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

11 One-Electron Models (Octahedral) 11

12 Jahn-Teller / Spin-Orbit Stabilizations 12

13 Jahn-Teller / Spin-Orbit (cont d) 13

14 Exchange Diagrams 14

15 Bond Types Ionic (bound electrons) Metallic (collective electrons) Metal-Oxide (occupied hybrid orbitals) 15

16 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 17 Combined Exchange Constant > j i j i ij S S J E 2 = ex e + = e + e e e e e ) + ( 2m = 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

18 Molecular Orbital Theory One-Electron Perturbation Model = E = E = = 2 ( e / r ~ ) H = H + H 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 S 2 ML 2 ML ( ) c L ( ) c M ϕ ϕ M M c + c M L ϕ ϕ L L 18

19 Bonding Antibonding States 19

20 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

21 G-K Diagrams Correlation AFM Delocalization FM Polaron (double) FM 21

22 G-K Table (180 bonds) 22

23 Magnetic Sublattices 23

24 Ferrite Thermomagnetism 24

25 Spinel Ferrites 25

26 Rare-Earth Garnets 26

27 Diluted Y 3 Fe 5 O 12 (YIG) tetrahedral-site dilution octahedral-site dilution 27

28 Circular Polarization 28

29 Faraday Rotation 29

30 Dipole Transitions 30

31 Resonance Line Shapes Permeability Permittivity 31

32 Bismuth Iron Garnet 32

33 Faraday Rotation Isolators High-Power Microwaves Fiber-Optic Infrared 33

34 G-K Diagrams Correlation AFM Delocalization FM Polaron (double) FM 34

35 Brillouin-Weiss vs Applied H 35

36 Brillouin Function H Sensitivity 36

37 Perovskite Cells B site A site 37

38 Charge Transfer in J-T Ions 38

39 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

40 CMR Curves vs T,H 40

41 CMR Data Fitting 41

42 Metallic Perovskites 42

43 Polaron Rings 43

44 3d 8 Low-Spin State 44

45 d 8 S = 0 Stabilization vs Axial Field 45

46 Spin Frustration by S = 0 Cu 3+ Ions 46

47 Polaron Tunneling vs Hopping 47

48 Polaron Mobility 48

49 Zero-Spin Transfer Combinations 49

50 T c,t N = 0 Condition 50

51 T c Fitting of Theory to Data 51

52 T c vs x, β Predictions 52

53 Unconventional Magnetic Oxides Magnetic Perovskites (Orthoferrties): (RE) 3+ Fe 3+ O 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

Contents. Acknowledgments

Contents. Acknowledgments MAGNETIC MATERIALS Fundamentals and Applications Second edition NICOLA A. SPALDIN University of California, Santa Barbara CAMBRIDGE UNIVERSITY PRESS Contents Acknowledgments page xiii I Basics 1 Review