Magnetism and Magnetic Switching

Transcription

1 Magnetism and Magnetic Switching Robert Stamps SUPA-School of Physics and Astronomy University of Glasgow

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3 A story from modern magnetism: The Incredible Shrinking Disk Instead of this: (1980)

4 A story from modern magnetism: The Incredible Shrinking Disk We have this: (10 3 greater capacity)

5 Size and Sensitivity Nobel Prize 2007 The physics of GMR sensors allow 10 to 100 times sensitivity over previous sensors. Greater sensitivity means ability to read data at higher densities.

6 Devices for Tomorrow Magnetic RAM Racetrack Memory Nanomagnetic Logic U. Twente U. Sheffield IBM Almaden Reversal involves precessional magnetic rotation, domain wall formation and domain wall motion

7 Spin Torque Transfer & Spin Currents current of unpolarized electrons Ferromagnet 1 Ferromagnet 2 Spin accumulation and torque transfer Optical analogy: polarising filter measurement filter incident beam of unpolarized light

8 Magnonics Control GHz properties with patterned magnetic films: Spinwave based logic:

9 Outline: Starting points: Magnetic moment and exchange - Electrostatics and exchange energy - Magnetic ordering and mechanisms for exchange Magnetisation dynamics - Torque equations and effective fields - Precessional dynamics - Switching Spin waves - Correlated precession

10 Starting Point 1: Magnetic Moment Spin and orbital angular momentum: ħ J =ħ(s+l) µ=γ(ħ J ) Gyromagnetic ratio γ : γ= g µ B ħ Energy and precession: U= µ B Γ= d dt L=µ B L=L o +l e iω L t l B Larmor precession ω L = µ B ħ B

11 Concept: Exchange Energy Pauli exclusion separates like spins: Can be energetically favourable: suppose parallel alignment results in a small change in average separation. Then if: r a 0.3 nm r p 0.31nm r p e ev r a e eV r p r a E E =0.05 ev (580 K) equivalent field: E E µ B =870T

12 Example: Direct Exchange Electrons on two neighbouring atoms: H= p 2 1 2m + p 2 2 2m + e2 R a R b e2 r 1 r a e2 r 2 r b + e2 r 1 r 2 core-core intra-atomic inter-atomic Assume know solutions for isolated orbitals with energy E on atoms a and b. Solve two electron problem with combination of product orbitals Ψ I =ϕ a (r 1 )ϕ b (r 2 ) ψ=c I Ψ I +c II Ψ II Ψ II =ϕ a (r 2 )ϕ b (r 1 )

13 Example: Direct Exchange Solution involves several overlap integrals: 2( 2 V= d r 1 d r 2 Ψ I, II e R ab r 12 r ab r 1a r 2b) U= d r 1 d r 2 Ψ I * Ψ II e 2( 1 R ab + 1 r 12 1 r ab 1 r 1a 1 r 2b) l= d rϕ a * (r)ϕ b (r) Two electron wavefunctions: space symmetric space anti-symmetric c I =c II c I = c II E + =2 E+ V +U E 1+l 2 =2 E+ V U 1 l 2

14 Example: Direct Exchange For Pauli exclusion require ψ s ψ a (space symmetric)(spin antisymmetric) (space antisymmetric)(spin symmetric) ψ s 1 2 ( ) ψ a ( ) 1 ( + ) ( ) 2 spin 0 spin -1, 0, 1 Energy difference determines whether spins prefer parallel or antiparallel alignment: J=E E + U l 2 V Heitler & London (1927)

15 Examples of Magnetic Ordering Ferromagnetic: Antiferromagnetic: Ferrimagnetic: Helical:

16 Summary I Bohr and Pauli Study Angular Momentum Angular momentum & magnetic moment: Defines energy, torque and precession Exchange: electrostatic repulsion & Pauli exclusion: Determines long range order and phase transitions

17 Starting Point 2: Phenomenology Relevant energy scales (P. W. Anderson, 1953): 1 10 ev Atomic Coulomb integrals Hund's rule exchange energy Electronic band widths Energy/state at ε f spin waves ordering ev Exchange energy splitting ev Spin-orbit coupling 10-4 ev Magnetic spin-spin coupling Interaction of a spin with 10 kg field ev Hyperfine electron-nuclear coupling

18 Dynamics & Effective Field Magnetic parameters describe energy & torques: E= m(r,t) H eff (r,t) t m r = m r H eff H eff H eff =H a +K(m(r))+A 2 m(r) h dip applied field anisotropy exchange

19 Magnetisation & Exchange Parameters Basic idea: define magnetisation density M(r)=gµ B j δ(r r j ) σ j Exchange energy must be compatible with symmetry of local atomic environment: E ex = α k l C kl m α (r) r k Example: isotropic medium m α (r) r l E ex =A[( m x ) 2 +( m y ) 2 +( m z ) 2 ]

20 Magnetic Anisotropy Parameter Local atomic environment affects spin orientation: [Kittel, Introduction to Solid State] Spin orbit interaction and crystal field effects Anisotropy energy and symmetries: Uniaxial: E ani (m z )=E ani ( m z ) E ani = K u (1) m z 2 K u (2) m z Cubic: E ani (m x, m y, m z )=E ani ( m x,m y,m z ), etc. E ani =K 4 (m x 2 m y 2 +m x 2 m z 2 +m y 2 m z 2 )+...

21 h dip (r ij )= 1 2 g 2 µ B 2 Dipolar Interactions Magnetic moments are point dipoles: ij( m(r i) m(r j ) 3 [r ij m(r i )][r ij m(r j )] 3 r ij r ij 5 ) wondermagnet.com θ All moments interact throughout sample. Sample shape contributes to anisotropy. For an ellipsoid: E ani = M 2 V 2µ o (N x sin 2 θ cos 2 ϕ+n y sin 2 θsin 2 ϕ+n z cos 2 θ) Easy direction Hard direction

22 Dissipation Damping: additional torques Gilbert damping: Rayleigh dissipation form t m(r)=γ m(r) H m(r) eff α m(r) t

23 Magnetic Switching

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25 Fast Reversal of Single Particles Switching involves precession + dissipation: Experiment: Apply pulse, drive reversal H bias h pulse Thirion, et al., Nat. Materials 2003

26 Reversal: Nonlinearities Bauer, Hillebrands, Stamps, Phys. Rev. B 2000

27 Sensitivity To Pulse Orientation pulse pulse

28 Bauer, Hillebrands, Stamps, Phys. Rev. B 2000 Reversal: Nonlinear Dynamics Anisotropy creates windows for precessional reversal Pulse: 0.25 ns Ellipsoidal particle Polar plot: field pulse orientation and strength Bright = switched Dark = not switched

29 Thermal Activation: H<H c Climbing to the top: fluctuations Energy transfer between spin system and heat bath Torque equation of motion: thermal fluctuation field t m(r)=γ m(r) H eff α m(r) m(r) +h t f random thermal driving torque

30 Single Particle Switching: Stoner- Wohlfarth Model Approximate reversal as pure relaxation: H θ E=V H M cos K sin 2 =V K [ H M 2K ]2 ɛ Rate depends on activation energy and attempt frequency = 1 = f o exp / k B T [Kramers, 1940; Langer, 1969; Büttiker, 1981]

31 Switching in Elements Attempt frequency ~ energy landscape curvatures

32 Spin Waves

33 Fluctuations in Magnetic Density Energy to reverse one spin in chain: 2 J H = J ij S i S j ij Superposition of ways to flip one spin: n = 1 = + + +K Spin wave excitation (boson)

34 Classical Picture: Correlated Precession Ground state magnetic orderings: 1) Magnetic moments 2) Exchange coupling Excitations: Precession dynamics H eff slide courtesy J-V Kim

35 Dispersion: Spinwaves Contribution from exchange: m x, m y ~exp i t k r H ex ~A 2 m r H ex ~ A k 2 m r 2 2 = H a A k 2 H a 2 K M s A k 2 resonance at k=0 field + anisotropy k

36 Dispersion: Dipole Exchange Modes Dipolar: long range nonlocal term Dynamics: compete with exchange at long wavelengths h dip (r)= g(r r ')m(r ')d r ' Shape anisotropies: create effective K terms

37 Thermal Reduction of Magnetisation M s (0) M s (T) k n k T 3/2 Linear spin waves Large amplitude fluctuations [Weiss & Forrer]

38 Summary II 'Macroscopic' models of magnetic configurations & dynamics Effective fields: magnetic parameters Reversal processes: Thermal activation and precession Spin waves: Fluctuations of magnetisation density walyou.co m

39 The End

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