Session Y4: Microscopic Physics of Magnetization Damping

Intrinsic spin-orbit contribution to precessional damping in transition metals

Landau-Lifshitz or equivalently Gilbert damping describe the decay of an precessing magnetization towards equilibrium. Both of these forms describe this decay accurately; that is, very few if any experiments have been analyzed to show that these forms are inadequate. These forms of damping can be derived theoretically from a variety of approaches and for a variety of mechanisms. In many of these mechanisms, spin-orbit coupling plays a crucial role. The spin-orbit coupling can be associated with defects or can be an intrinsic part of the electronic structure of the pure material. In this talk, I describe calculations of the Gilbert damping for the transition metals, Fe, Co, and Ni. These calculations show that damping due to the intrinsic spin-orbit coupling agrees with the measured temperature dependence of the damping. In the presence of a current in the ferromagnet, the damping is modified. I discuss how this modification gives rise to a contribution to the so-called non-adiabatic spin transfer torque and show calculations of this contribution for Fe and Ni.   

Ab-initio study of the resistivity, Gilbert damping and spin-flip diffusion in transition metal alloys

Using a formulation of first-principles scattering theory that includes disorder and spin-orbit coupling on an equal footing, we calculate the resistivity $\rho $, spin-flip diffusion length $\lambda _{sf}$ and the Gilbert damping parameter $\alpha $ for Fe$_{x}$Ni$_{1-x}$ substitutional alloys as a function of x over the entire concentration range. For the technologically very important Fe$_{20}$Ni$_{80}$ alloy, permalloy, we calculate values of $\rho $ = 3.7$\pm $0.5 Ohm-cm, $\lambda _{sf}$ = 5.2$\pm $0.2 nm and $\alpha $ = 0.0046$\pm $0.002 compared to experimental low-temperature values in the range 4.4-5.1 Ohm-cm for $\rho $, 5.0-6.0 nm for $\lambda _{sf}$ and 0.005-0.009 for $\alpha $ indicating that our scattering theoretical formulation captures the most important contributions to these parameters. Work carried out with A.A. Starikov in collaboration with A. Brataas, Y. Tserkovnyak and G.E.W. Bauer.   

Scattering Theory of Mesoscopic Gilbert Damping

Magnetic damping determines the performance of magnetic devices including high-frequency oscillators, hard drives, magnetic random access memories, magnetic logic devices, and magnetic field sensors. The drive to improve these devices, to reduce the response time of sensors and the physical dimensions has led to a greater focus on studying the friction force a changing magnetization experiences. We study the magnetization dynamics of single domain ferromagnets and domain walls in contact with a thermal bath by scattering theory. We recover the Landau-Lifshitz-Gilbert equation and express the Gilbert damping tensor in terms of the scattering matrix [1,2]. Dissipation of magnetic energy equals energy current pumped out of the system by the time-dependent magnetization, with separable spin-relaxation induced bulk and spin-pumping generated interface contributions [3]. The scattering theory of Gilbert damping is suitable for first-principles calculations that include disorder and spin-orbit coupling on an equal footing [4]. In linear response, our scattering theory for the Gilbert damping tensor is equivalent with the Kubo formalism. \\[4pt] [1] A. Brataas, Y. Tserkovnyak, and G. E. W. Bauer, Phys. Rev. Lett. 101, 037207 (2008). \\[0pt] [2] K. M. D. Hals, A. K. Nguyen, and A. Brataas, Phys. Rev. Lett. 102, 256601 (2009). \\[0pt] [3] Y. Tserkovnyak, A. Brataas, G. E. W. Bauer, and B. I. Halperin, Rev. Mod. Phys. 77, 1375 (2005). \\[0pt] [4] A. A. Starikov, P. J. Kelly, A. Brataas, Y. Tserkovnyak, and G. E. W. Bauer, unpublished.   

Gilbert Damping Mechanisms in Half-metallic Heusler Alloys

Manipulation of fast magnetization dynamics is crucial for spintronics devices, such as magnetic random access memory with spin-transfer torque switching or spin-transfer torque oscillator. Especially, Gilbert damping is one of the important factors for reducing current density required in the devices. Half-metallic Heusler alloy is one of the promising materials for device electrodes because it exhibits not only large magnetoresistance but also small Gilbert damping [1,2]. According to our previous studies, Gilbert damping for Heusler alloys depends on atomic ordering [1,3,4] and composition [5], and there seems to be a correlation between Gilbert damping and total valence electron number in B2 or L2$_{1}$ ordered Heusler alloys [4,5]. Although Gilbert damping mechanisms are still open questions, our results imply that Gilbert damping is related to not only spin-orbit interaction but also density of states at Fermi level because it is well known that the density of states at Fermi level in Heusler alloy varies systematically with total valence electron number. In this talk, we present the overview of our previous results on Gilbert damping for Heusler alloys (Co$_{2}$MnSi, Co$_{2}$MnAl, Co$_{2}$FeAl, Co$_{2}$FeSi), the recent results on the composition dependence and temperature dependence of Gilbert damping for quaternary Co-based full Heusler alloys (Co$_{2}$Mn$_{1-x}$Fe$_{x}$Si and Co$_{2}$MnAl$_{1-x }$Si$_{x})$, and a discussion of possible mechanisms.\\[4pt] [1] R. Yilgin et al., Jpn. J. Appl. Phys. \textbf{46}, L205 (2007).\\[0pt] [2] S. Mizukami et al., J. Phys. Conference series (in-press).\\[0pt] [3] M. Oogane et al., J. Appl. Phys. \textbf{101}, 09J501 (2007).\\[0pt] [4] S. Mizukami et al., J. Appl. Phys. \textbf{105}, 07D306 (2009).\\[0pt] [5] T. Kubota et al., Appl. Phys. Lett., \textbf{94}, 122504 (2009).   

Magnetic relaxation due to earth impurities in Ni$_{80}$Fe$_{20}$

The functionality of magnetic devices depends to a large extent on the spin relaxation characteristics of the magnetic materials. Understanding the underlying physics is required in order to tailor the relaxation properties. Here the relaxation due to rare earth impurities in Ni$_{80}$Fe$_{20}$ is discussed. When rare earth atoms are incorporated into a 3d ferromagnet the magnetization is reduced due to the antiferromagnetic 3d-5d coupling. In addition the Gilbert damping constant can be increased by two orders of magnitude. We investigate the frequency and temperature dependence of the ferromagnetic resonance linewidth of Ni$_{80}$Fe$_{20}$ films doped with various concentrations of Gd, Tb, Dy, and Ho. From these experiments we conclude that the slow relaxing impurity mechanism driven by the anisotropic 4f-5d exchange interaction is responsible for the strong damping observed in Ni$_{80}$Fe$_{20}$- rare earth intermetallic alloy films [1]. Using femtosecond laser pulses in an all-optical pump-probe experiment, one can directly study the processes which are responsible for the relaxation of the spin system down to the femtosecond time scale. The magnetization dynamics is probed by the magneto-optic Kerr effect. By studying the above lanthanide doped Ni$_{80}$Fe$_{20}$ films with this technique we find that films doped by Tb, Dy and Ho show a gradual increase of the demagnetization time from approximately 60 fs for pure NiFe to about 150 fs. In contrast, Gd concentrations of up to 15\% do not influence the time scale of the photoinduced quenching of the magnetization. This behavior is a natural consequence of the slow relaxing impurity mechanism [1]. Thus, we propose a demagnetization mechanism that relies on the ``magnetic inertia'' of the rare-earth impurities which stabilize the ferromagnetic ordering on a picosecond time scale [2]. \\[4pt] [1] G. Woltersdorf, M. Kiessling, G. Meyer, J.-U. Thiele, and C.H. Back, Phys. Rev. Lett. 102, 257602 (2009) \\[0pt] [2] I. Radu, G. Woltersdorf, M. Kiessling, J.-U. Thiele, A. Melnikov, U. Bovensiepen, and C.H. Back, Phys. Rev. Lett. 102, 117201 (2009)