Lecture 6: Spin Dynamics

Transcription

1 Lecture 6: Spin Dynamics All kinds of resonance spectroscopies deliver (at least) 3 informations: 1. The resonance position. The width of the resonance (and its shape) 3. The area under the resonance From Para- and Ferromagnetic Resonance (EPR, FMR) we get: 1. T h e a n i s o t r o p y f i e l d ( K / M, 4pM ), g-tensor => lecture. Relaxation rate => this lecture 3. Magnetization 1

2 Local moment ESR in superconductors

3 Solid State Communications 1, 977 (1973) 3

4 In situ UHV-FMR set up FMR in ferromagnetic nanostructure pressure: 1-11 mbar temperature: K - 5K lhe cryostat 7. ML Ni/Cu(1) T=97 K thermocouple cavity sample UHV electromagnet quartzfinger M. Zomak et al., Surf. Sci , 618 (1986) J. Lindner, K.B. J. Phys.: Cond. Matt 1 5, R193 (3) W. Platow, Ph.D. thesis (1999) 4

5 For thin films the Curie temperature can be manipulated 6 Ni(1)/Cu(1) Paramagn. finite size Fe V O / SrTiO 3 4 T=3K d=7.6 M M 5 1 thickness (ML) Ferromagn. Th.v. Waldkirch, K.A. Müller, W. Berlinger, PRB (1973) P. Poulopoulos and K. B. J. Phys.: Condens. Matter 1 1, 9495 (1999) Yi Li, K. B., PRL 68, 18 (199) 5

6 Thermodynamics of thin ferromagnetic films in R.P. Erickson & D.L. Mills PRB 44, 1185 (91) 1 π Spin wave branches = ω + D{ k [ ] } II + Nd A criterion for a crossover from quasi D to 3D is N C hd π = kt d D: stiffness const. Ni: hd evå ; d=.3å T = 3 ~ 5 K N C 6 5 layers STAN4 6

7 6a Magnon- magnon scattering and Gilbert damping 7

8 1 γ Landau-Lifshitz-Gilbert equation M t G M = M H eff ( Jint er, K) + M γ M S t viscous damping, energy dissipation G i l b e r t damping contribution: linear in frequency ( ω) = H Gilbert α = 3 γ G γ M S G M S ω H T w o-magnon scattering: degenerate states created by dipole-dipole interaction due to surface defects non-linear frequency dependence magnon ( ω) = Γarcsin ω ω + ( ω + ( ω / ) / ) ω + ω / / R. Arias et al., PRB 6, 7395 (1999) ω =γm eff 8

9 FMR Li n e w i d t h - D a m p i ng Landau-Lifshitz-Gilbert-Equation -magnon-scattering 1 γ M t = _ (M H) G γm M eff + ( M ) S t R. Arias, and D.L. Mills, Phys. Rev. B 6, 7395 (1999); D.L. Mills and S.M. Rezende in Spin Dynamics in Confined Magnetic Structures, edt. by B. Hillebrands and K. Ounadjela, Springer Verlag ω(k ) ϕ k > ϕ c ϕk < ϕ ω FMR c Gilbert-damping ~ω k Gil H ( ω) = G γ M S ω H Mag ( ω) = Γarcsin 1/ [ω+( ω/) ] - ω / 1/ [ω+( ω/)] + ω / ω = γ(k - 4πM), S γ =( µ B/h)g K - uniaxial anisotropy constant M- saturation magnetization S 9

10 1 H (Oe) 1 Non-Gilbert-Type spin-wave damping H H Gilb only H only mag H * M a gn on- M a g n o n s c a t te ring a t i n t e rf aces of nanostructure s R. Arias et al., J. Appl. Phys. () H inhomogeneous broadening ω/ π (GHz) H(Oe) d χ /dh (arb. units) GHz 9.4 GHz H [11], T=96K 17.6 GHz Fe 4 /V 4 Fe 4 /V 69 GHz H (koe),i Fe 4 /V ; H [1] Fe 4 /V 4 ; H [1] Fe 4 /V ; H [11] Fe 4 /V 4 ; H [11] ω/ π (GHz) J. Lindner et al. Phys. Rev. B 68, 61(R) (3) CA 3 / 9

11 11 Linewidth in magnetic resonance ESR FMR T 1 = long. relaxation, spin-phonon T = transv. relaxation 1 γ Landau-Lifshitz-Gilbert equation M t = M H ( J int er, K) + γ G M eff S M M t

12 1 H PP (Oe) Oe! 4 8 t w o- magnon scattering observed in Fe/V superlattices interface defects J. Lindner et al., PRB 68, 61(R) (3) HF FMR A. Janossy et al. Budapest Univ. of Technology and Econ f (GHz) Γ γ Γ G α H (koe) (1 8 s -1 ) (1 8 s -1 ) (1-3 ) (Oe) Fe 4 V ; H [1] Fe 4 V 4 ; H [1] Fe 4 V ; H [11] Fe 4 V 4 ; H [11] Fe 4 V 4 ; H [1] recent publications with similar results: Pd/Fe on GaAs(1) network of misfit dislocations G. Woltersdorf et al. PRB 69, (4) NiMnSb films on InGaAs/InP B. Heinrich et al. JAP 95, 746 (4)

13 13 6b Spin pump e f f e c t s, s - d- exchange between spin wave and s-electron R.H. Silsbee, A. Janossy, P. Monod, PRB 1 9, 438 (1979) Y. Tserkovnyak, A. Brataas, G.E.W. Bauer, PRB 66, 443 () Landau-Lifshitz equation + extension precession Gilbert-damping spin-pump current d M G d M = γ M H eff + M d t γm S dt + γ M S V S I p u m p (5) Precession drives spin current into NM NM-substrate acts as spin-sink I S back = h d M d M I S pump = Ar M Ai 4π dt dt torque is carried away Gilbert damping enhanced by spin-pump effect!

14 14 in-situ FMR in coupled films Ni 8 Cu n Ni 9 substrate theory FMR in-situ UHV-experiment J. Lindner, K. B. Topical Rev., J. Phys. Condens. Matter 15, R193-R3 (3)

15 acoustical mode optical mode M M M M at point of contact compensation of pumped currents decrease the linewidth B. Heinrich et al., PRL 9, (3) s d NM λ SF no spin-accumulation I back = Gilbert-damping enhanced by spin-pump effect compensation, if both films precess simultaneously (H res1=h res) only Gilbert contribution remains! K. Lenz et al., Phys. Rev. B 69, 1444 (4) 15

16 Trilayers with non-collinear easy axes Cu 5 Ni 9 Cu 5 Ni 6 substrate strong decrease in H when H ac =H op H op = H ac < H uni K. Lenz et al. SCM 4, Physica Status Solidi (c) 1, 36 (4) 16

17 H as function of J inter and d Cu respectively 17

18 H (Oe) Ni 9 Cu 1 Ni 9 Cu 5 Ni 9 Cu 5 Ni 8 Cu 5 Ni 9 Cu 5 Ni 8 Cu 5 Ni 9 Tolinski et al. Mol. Phys. Rep. 4, 164 (4) 18

19 19 H opt - H ac as function of d Cu (see Heinrich plot)

20 Conclusion High sensitivity of ESR/FMR to investigate submonolayers in-situ UHV-ESR/FMR Large frequency range of 1 to >GHz is needed to study relaxation, dynamics spin dynamics cannot be described by viscous damping, only. Scattering within the magnetic system is also important, before energy dissipates to the thermal bath. Spin pumping is an old phenomenon ( mid 197 th s). Today s experiments measure a phenomenological number, superimposing many different mechanisms (i.e. cuplayer effects, J inter, different modes of spin waves, etc.)