Spintronics and Magnetic Properties of Materials

1. Spintronics and Magnetic Properties of Materials Natia L. Frank Department of Chemistry University of Washington Seattle, WA 98117

2. The Earth’s Magnetic Field Glatzmaier (Los Alamos) Alerstam, Nature 2001

3. Navigating the Earth’s Magnetic Field • Magnetoreception: • How organisms use magnetic information to control and direct their behavior • Magnetotaxis: movement along field lines: alignment • Menotaxis (Kuhn) compass orientation with respect to external field

4. Early Magnetism Origin of the name “magnetism”: Magnesia (Thessaly, Greece) Greeks: Lodestone FeO-Fe2O3 “leading stone or compass” “The magnet’s name the observing Grecians drew From the magnetick region where it grew”- Lucretius Carus 100B.C. “The nails of whose shoes and the tip of whose staff stuck fast in a magnetick field while he pastured his flocks”-Pliny the Elder(Magnus) Greek Writings: Lodestone appeared as early as 800 B.C.

5. Gilbert: The Father of Magnetism 1600. William Gilbert: “ Father of Magnetism “ b. 1544. London physician, physics by hobby. Queen Elizabeth’s personal physician. d. 1603 plague. “ it is easy for men of acute intellect to slip and err”. Treatise “ On the Magnet: Magnetic Bodies Also, and On the Great Magnet the Earth; a New Physiology, Demonstrated by Many Arguments and Experiments”

6. Magnetic Field Vector H The density of lines is proportional to the magnitude of the magnetic field vector.

7. Quantum Mechanical Basis of Spin Rotation of the charge of an electron produces current loops with a magnetic moment directed along the rotation axis:spin angular momentum. Origin of magnetic moment: orbital angular momentum(a) and spin angular momentum(b). Bohr Magneton (mB or b) = eh/4pmc = 9.27 x 10-21 erg/Oe

8. Magnetization (M) and Induction(B)Vectors Magnetic dipole moment:m: m = 1 when a force of 1 dyne is experienced in a field of 1 oersted. Magnetic Induction, B = H + DH measured in gauss (G) and H in oersted (Oe) Intensity of magnetization (magnetic dipole moment / unit volume) = M (emu/cm3) In cgs units, DH = 4pM, therefore,B = H + 4pM. The magnetic induction is equal to the external field corrected for the magnetization of the substance.

9. Magnetic Susceptibility and Permeability When the vectors B, H and M are parallel, it is useful to define the magnetic permeability(m) and magnetic susceptibility(c) of a substance: Define M/H = cV where cV is the volume magnetic susceptibility and is dimensionless. Gram Susceptibility, cg = cV/ r (cm3 g-1) wherer is the density Molar Susceptibility,cM = cg*molecular weight and is in units of (emu/cm3•G•mol) The magnetic susceptibility and permeability characterize the type of magnetism observed: diamagnetism, paramagnetism, ferromagnetism, or antiferromagnetism

10. Types of Magnetism (a) Diamagnetism:  < 0, 10-6 emu,  independent of H, origin field induced, paired electron circulation. (b) Paramagnetism  > 0, 0 to10-4 emu,  independent of H, origin angular momentum of electron. No interactions between spins. (c) Ferromagnetism  > 0, 10-4 to 10-2 emu,  dependent on H, spin alignment from dipole-dipole interaction of moments or intramolecular exchange coupling. high spin ground state. (d) Antiferromagnetism  > 0, 0 to10-4 emu,  dependent on H, origin field induced, spin pairing from dipole-dipole interaction or intramolecular exchange coupling. low spin ground state. (e) Ferrimagnetism  > 0, 10-4 to 10-2 emu,  dependent on H, origin field induced, spin pairing (antiferromagnetic coupling) of two species with different magnetic moments from dipole-dipole interaction or intramolecular exchange coupling. leads to net magnetization Unpaired e- Paired e- (b) (c) (d) (e) (a)

11. Diamagnetism Theory of Diamagnetism: Langevin (1905) • Paired electrons produce a current loop that repels an external magnetic field. • Diamagnetic susceptibilities are negative (c < 0), independent of field and temperature. • Must be taken into account in the measurement of paramagnetic susceptibilities: c= p + cdia • Diamagnetic corrections can be calculated using Pascal’s constants and are always negative. (Classical Langevin result) Nijmegen High Field Magnet Laboratory, Netherlands

12. Superconductors: The Perfect Diamagnet Superconductivity: 1911: Heike K. Onnes noted that the resistance of a frozen mercury rod suddenly dropped to zero when cooled to the boiling point of helium (4.2 Kelvin). The conductivity occurs with zero resistance, and probably involves the formation of “Cooper pairs”. The mechanism of cooper pair formation is still under investigation. Meissner effect: Magnetic fields are excluded from superconductors below their Tc Levitation at T<Tc YBa2Cu3O7 (YBCO) YBa2Cu3O6 Images cortesy of ILL-France

13. Paramagnetism Theory of Paramagnetism: Curie (1907) • Unpaired electrons produce an induced field that attracts an external magnetic field. • Paramagnetic susceptibilities are positive (c > 0), dependent on field and temperature. Random alignment of spins Partial alignment of spins: c increases

14. Paramagnetism: gbH vs. kT Alignment of spins with field Randomization of spins m =-gbS DE = -2 gbSH = 2 m 

15. Fundamental Law in Magnetism: Van Vleck • No angular momentum and no coupling between ground and excited state: • magnetic moment= -gbH • interacting with magnetic field:Hamiltonian: = -gbH S • operate Hamiltonian on spin wavefunction: two eigenvalues are obtained: E=msgbH (microscopic magnetization) Macroscopic magnetization: Application of Boltzmann distribution M=f (NgbkT) For ms=1/2: • Valid for H / kT<<1 • H large, T low: Msat = N gb S • H moderate, T moderate: Curie Law

16. Paramagnetism: Curie Law The dependence of the magnetic susceptibility with temperature for spin only systems is governed by the Curie Law. Before quantum mechanics:(Curie, 1900) After quantum mechanics: (Van Vleck, 1931) c = C/T, where C = Curie Constant c = Ng2b2 S(S+1) / 3kT Magnetic Moment Susceptibility [Cu(H20)6](SO4)2 S = 1/2 [Ni(H20)6](SO4)2 S = 1 [Mn(H20)6](SO4)2 S = 5/2  (emu•K/cm3•G•mol) c (emu/cm3•G•mol) T(K) T(K)

17. Diamagnetism vs. Paramagnetism

18. Paramagnetic Susceptibility of Conduction Electrons Pauli paramagnetism: Only the fraction T/TF contribute to the susceptibility.

19. Field dependence of the Magnetization Brillouin Function M = NgJmBBJ(x) Assumptions made: x<<1 ( gJmBB << kBT) W. E. Henry

20. “Spin-only” Magnetism Spin only magnetism refers to systems in which there is no orbital angular momentum, and no exchange interactions (No spin orbit coupling, g-anisotropy, zero field splittings, exchange interactions)

21. Deviations from “Ideal behavior”:The Curie-Weiss Law Deviations from Curie Law behavior may be due to internal electronic structure ( g-anisotropy, ZFS, spin-orbit coupling) or magnetic exchange interactions which lead to an additional mean field, causing a different distribution of spin states. If the mean field is small relative to the splitting of original states, the magnetic susceptibility follows the Curie Weiss Law: where  is essentially a mean field parameter.

22. Magnetic Exchange Interactions Magnetic exchange interactions between two spin containing units depends to a first approximation on the orbital overlap either directly through space (direct exchange) or through bond (spin delocalization, spin polarization or superexchange). Ferromagnetic exchange Antiferromagnetic exchange 2J = interaction between unpaired spins

23. What is Exchange??? Exchange interaction: spin dependent coulomb energy Exchange energy ( Exchange Field): If two atoms i and j have spin angular momentum Sih/2p and Sjh/2p, respectively, then the exchange energy between them can be described in terms of the exchange integral Jex. Kinetic energy term (antiferromagnetic) and potential energy term (ferromagnetic):

24. Dimer Model for Magnetic Exchange Hamiltonian: Summing over states: isotropic Heisenberg Hamiltonian J = E (S=0) - E (S=1) which is the isotropic interaction parameter. In this case, J < 0 is antiferromagnetic coupling, while J > 0 is ferromagnetic coupling. Bleaney Bowers (1952)

25. Types of Magnetism Diamagnetic

26. Magnetic Ordering T < Tc:Ferromagnet T < Tc: Antiferromagnet T > Tc: paramagnet Fe (Tc = 1043K) Ni (Tc = 631K) Cr (Tc = 313K) Mn (Tc = 95K) CrO2 (Tc = 387K) CrBr3 (Tc = 33K) NiO (Tc = 523K) MnO (Tc = 120K)

27. Long Range Order: Antiferromagnetism

28. Long Range Order: Ferromagnetism Large magnetization energies associated with ferromagnetism give rise to formation of domain walls. Driving force? Magnetostatic energy.

29. Hysteresis: Hard and Soft Magnets

30. Single Domain Particles First postulated in 1930 by Frenkel and Dorfman Single domain particles cannot be demagnetized (no domain walls), their magnetization can only be reversed by rotation.

31. single domain multidomain Hc Super- paramagnetic D Dc Magnetic Nanoparticles Behavior of nanoparticles is a function of structure, size, and interactions in the material.

32. Spintronics Spintronics: Spin-polarized charge transport Spin orientation of conduction electrons has is a slow process (ns), compared to the rate of electron momentum decay (fs). Applications: quantum computing, (each spin corresponds to a bit “qubit”) magnetic information storage(GMR) magnetic hard drives M-RAM (GMR-RAM) nonvolatile programmable logic(AND, OR, NAND and NOR gates) NY Times, (IBM) 2001 Nature June 2000

33. Magnetoresistance Prinz(1998)

34. Spin Valves A general magnetic field sensor made of GMR multilayers (iron-nickel with silver) (Institute of Physics)

35. Dilute Magnetic Semiconductors (DMS) Can spin polarized transport be realized in semiconductor structures? semiconductor quantum dots, atoms, or molecules quantum bits (qubits) for quantum computing and quantum communication. ferromagnetic semiconductors = charge transport and magnetic storage. Challenges: ferromagnetic material ( with high Tc) effective spin-injection (100% ideally) resistivity comparable to that of a semiconductor for effective band matching. Mn-based zinc-blende III-V and II-VI magnetic semiconductors: hole-mediated exchange based on the Zener model (double exchange) correctly predicts the magnetic exchange in these systems.

36. RKKY Theory The phenomenon of magnetic exchange in electron-delocalized solid state materials was described for magnetically dilute semiconductors by Kondo, Heeger and Ruderman and Kittel, Kasuya, and Yosida. Indirect exchange interaction between the two magnetic ions that occurs through electron scattering and hyperfine interactions between the scattered electron and magnetic nucleus. The conduction gas is magnetized in the vicinity of the magnetic ion; the second ion perceives the magnetization of the first, leading to an interaction between them, known as the Friedel or RKKY interaction.

37. Kondo Effect The Kondo Effect is a minimum in the electrical resistivity-temperature curve of dilute magnetic alloys at low temperatures. Anomalously high scattering probability: dynamic nature of the scattering of the exchange coupling, and of the sharpness of the Fermi surface at low temperatures. The spin dependent contribution to the resistivity is dependent on the exchange energy, nearest neighbors, and strength of exchange scattering. (Experiment: MacDonald) 0.090 0.200 (Theory:Kondo) Au(Fe) 0.08%Fe Resistance() 0.006%Fe minimum 0.074 0.184 T(K)

38. Kondo effect in single-atom transistors Park, Pasupathy Nature 2002