Magnetization dynamics for the layman: Experimental Jacques Miltat - PowerPoint PPT Presentation

Magnetization dynamics for the layman: Experimental Jacques Miltat Université Paris-Sud & CNRS, Orsay With the most generous help of Burkard Hillebrands (Symposium SY3, ICM-Rome, July 2003 École de Magnétisme Brasov, Rumania, September 2003

Magnetization dynamics (classical description) Landau-Lifshitz-Gilbert equation of magnetization motion γ 0 : gyromagnetic ratio   ] + α d M M × d M [ dt = −γ 0 M × H eff H eff : acting effective magnetic field     M s dt (embedding the pulsed field) α : Gilbert damping parameter α = 0 d dt M 2 t ( ) = 0 α ≠ 0 d [ ] = 0 ( ) ⋅ H dt M t

Magnetization dynamics (Cont'd) Landau-Lifshitz equation with damping ] −αγ 0 ( ) d M [ [ ] { } 1 +α 2 dt = −γ 0 M × H eff M × M × H eff M s Bloch-Bloembergen Equation dM x , y ] x , y − M x , y [ = −γ 0 M × H eff dt T 2 dM z z − M z [ ] = −γ 0 M × H eff dt T 1 T 1 : Longitudinal relaxation time T 2 : Transverse relaxation time

Magnetization dynamics (Cont'd) Spin waves formalism : kinetic equations (valid for exchange dominated spin waves) M = M s −γ 0 h n ' ( ) M z = M s −γ 0 h n 0 + n ' n 0 k = 0 : Number of magnons with (infinite wavelength) n ' : Number of all other magnons Consider the following rate equations as an example (˜ " TWO Magnons Model" ): Where, dn 0 ( ) n 0 dt = − λ 0 k + λ 0 σ λ 0 k k = 0 is the probability of destruction of a k ≠ 0 magnon with the production of a magnon, dn ' λ 0 σ λ k σ and are the probability of dt = λ 0 k n 0 − λ k σ n ' k = 0 k ≠ 0 disappearance of and magnons, respectively

Magnetization dynamics (Cont'd) Combining : dn 0 ( ) n 0 dt = − λ 0 k + λ 0 σ M = M s −γ 0 h n ' ( ) and M z = M s −γ 0 h n 0 + n ' dn ' dt = λ 0 k n 0 − λ k σ n ' One gets for the sole damping term : dM ( ) + λ k σ M s − M ( ) dt = −λ 0 k M − M z dM z ( ) + λ k σ M s − M ( ) = +λ 0 σ M − M z dt

Magnetization dynamics (Cont'd) I. Thus, depending on the formalism, one may define ONE, TWO or MORE parameters defining damping processes ..... II. This problem remains a yet unsolved issue of spin dynamics

Small Excitations I. FMR in inhomogeneous films : a numerical experiment II. Local dynamics III. Spin waves quantization and localization IV. Magnetic noise spectra

FMR in inhomogeneous films A ferrromagnetic resonance experiment measures both a resonance frequency and a line width. The latter reflects the effects of both damping AND inhomogeneity. In the absence of inhomogeneities , the damping parameter is, within the LLG formalism, related to the derivative of the absorbed power through: α = 3 γ 0 ∆ H pp /2 ω r For weak inhomogeneities treated as perturbations, the two-magnon model has been considered valid [ ? ], whereas for large inhomogeneities the linewidth may be considered as a superposition of linewidths from independently resonating regions.

α ? (schematic) "Disordered" "Ordered" • α directly correlated to electron scattering S. Ingvarsson et al. CondMat 0208207 See also: S. Mizukami et al. Jap. J. Appl. Phys. 40 (2001) 580

Multimode damping in inhomogeneous films Dealing with inhomogeneities: Calculation of eigenmodes in films taking defects into account Precession frequencies of 3001 spin waves with resonant frequencies closest to the uniform resonance mode R.D. McMichael, D.J. Twisselmann, A. Kunz, PRL 90 , 227601 (2003)

Multimode damping in inhomogeneous films I. FMR signals are simulated by replacing each eigenmode spike with a Lorentzian peak with FWHM given by the LLG linewidth for α =0.01. II. This process makes use of a single damping coefficient R.D. McMichael, D.J. Twisselmann, A. Kunz, PRL 90 , 227601 (2003)

Multimode damping in inhomogeneous films I. Results exhibit a clear transition from a "TWO-Magnon" type behaviour to a "LOCAL Resonance" mode II. No comparison to experimental results, yet R.D. McMichael, D.J. Twisselmann, A. Kunz, PRL 90 , 227601 (2003)

Local dynamics in square Py elements Quantized magnetostatic modes under high frequency drive field Spatially resolved FMR-Kerr-Microscopy: Synchronization of laser pulses with microwave source Response at the center of a 50*50 µm2 Py square, 100 nm thick @ 7.04 GHz Amplitude (top) and phase (bottom) response vs position for P1-P5 @ 7.04 GHz S. Tamaru, J.A. Bain et al., J. Appl. Phys. 91 , 8034 (2002) theory: K. Guslienko, R. Chantrell, A.N. Slavin, PRB, in press

Spin dynamics in closure domains Polar Kerr Simulations: response vs Top: position and Fourier Unconvolved Transforms in Bottom : 5 µm*5 µm Py platelets Convolved Average of the frequency power spectrum averaged over the whole sample J.P. Park et al., Phys. Rev. B. 67 , 020403(R) (2003) See also J. P. Park et al., PRL 89 (2002) 277201 (spin-wave modes in wires)

Spatially resolved spin-wave modes in magnetic wires Left: Time-domain images: 5 µm Polar Kerr rotation vs position in width Py wires 5 µm width, 18 nm thick Py wires Right: Frequency domain (BWVMS geometry) Note the absence of edge mode in the DE geometry Comparison between J.P. Park et al., experiments and LLG simulations Note the tendency towards a PRL 89 , 277201 (2002) uniform mode at low field

Localized thermal spin-waves in magnetic wires BLS spectrum, q=0.47 10 5 cm, H e =800 Oe PSSW: thickness mode 300 Frequency (arb. units) 250 Internal field (Oe) 200 150 H z 100 50 Stripe 1 µ m wide C. Bayer et al., Appl. Phys. Lett. 82, 0 607 (2003) -0,50 -0,25 0,00 0,25 0,50 z/w

Quantized spin waves in wires: BLS studies 35 mm NiFe wires 1.75/0.3 µm q-DE PSSW 16 q || = 0 d = 40 nm Spin wave frequency (GHz) 5 cm -1 0.21·10 14 0.42 12 0.63 Intensity (arb. units) film 10 0.83 1.03 8 1.22 6 1.40 0,0 0,5 1,0 1,5 2,0 2,5 5 cm -1 ) q || (10 1.57 1.72 localized dispersionless modes 1.87 2.00 5 cm -1 2.11·10 S.O. Demokritov, B. Hillebrands, in: „Spin dynamics in confined magnetic -25 -20 -15 -10 -5 0 structures“, Topics in Applied Frequency shift (GHz) Physics 83 (2003), Springer

A common idea in all these studies : ?

A common idea in all these studies : The internal field is not homogeneous

Spin wave propagation magnetic field configuration plane of light incidence Z H stat Y a) b) X [mm] = ν 0 = 0.83 GHz 0.7 X ν k = 1.05 GHz H (t) pulse 0.6 X [mm] = 0.5 0.7 0.6 0.4 0.5 0.3 0.4 0.2 H pulse = 1 Oe, 3 ns FFT signal 0.3 MO signal v group = 6.6 cm/µs H stat = 40 Oe 0.1 0.2 0.0 0.1 -0.1 BiLuIG 2.80 6.10 0.0 1.8 mm ≈ T pulse 3 ns -0.2 -0.1 t [ns] 3.2 mm -0.3 -0.2 0.00 3.25 6.60 -0.3 -0.4 -0.4 -0.5 -0.5 -0.6 0.40 3.75 7.05 -0.6 -0.7 -0.7 -1 0 1 2 3 4 5 6 7 8 9 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 0.85 4.20 7.55 time [ns] frequency [GHz] 1.35 4.70 8.00 ν 0 : uniform mode x: distance to stripeline, x=0 ν k : propagating spin wave group velocity 1.85 5.15 8.50 J. Fassbender, in: „Spin dynamics in 2.30 5.65 9.00 confined magnetic structures II“, Topics in Applied Physics 87 (2003), Springer

Magnetic noise spectrum in GMR device k B T " f ( ) = I ∆ R ( ) χ t V n f 2 V 2 π f µ 0 M s NiFe/CoFe/Cu/CoFe/Ru/CoFe/IrMn- spin valve device 1 * 3 µm 2 Good fit by single-domain noise model with noise power proportional to ima- ginary part of dynamic susceptibility N. Stutzke, S.L. Burkett, S.E. Russek, Appl. Phys. Lett. 82 , 91 (2003); J. Vac. Soc. Tech. A 21, 1167 (2003) Resonant behaviour of the noise voltage

Large excitations, Switching I. Conventional switching II. Precessional switching III. rf assisted switching IV. wall motion in nano-wires

Early Experiments: Pulsed field along the easy axis EXPERIMENTS SIMULATIONS Switching mechanisms dominated by wall motion, domain expansion and nucleation, leading to an overall complexity B. C. Choi et al., J. Appl. Phys. 89 (2001) 7171

Time resolved Kerr microscopy: a different kind of excitation 6 µm Co disk, excited with current pulse in microfabricated loop, magneto-optic Kerr microscopy Y. Acremann et al., Science 290 , 495 (2000)

Precessional switching 0.2 0.1 0.0 M z -0.1 1.0 1.0 0.5 0.5 0.0 0.0 M -0.5 x -0.5 M y -1.0 -1.0 Simultaneously demonstrated at MMM Seattle in fall 2001 by: • Nijmegen group: pulse shaping by two fs laser pulses Th. Gerrits et al., Nature 418 , 509 (2002) • NIST Boulder group: MR measurement S. Kaka and S.E. Russek, Appl. Phys. Lett. 80, 2958 (2002) • Orsay group: MR measurement, multiple switching H.W. Schumacher et al., Phys. Rev. Lett. 90 , 017201 (2003)

Precessional switching : principle A two-step process particularly well suited to thin films: 1) The initial torque moves the magnetization out of plane 2) The torque due to the demagnetizing field allows for magnetization rotation along a trajectory that remains close to the plane of the film

Experimental Method H.W. Schumacher et al., APL 2002 Pulse line pulse generator (100 ps – 10 ns) B s a m p l i n g o s c i l l o s c o p e magneto resistive ( 5 0 G H z ) device: TMR, GMR M I detection line sampling current oscilloscope source (50 Ω) V(M,t) MR response