Magnetization Dynamics and Damping

The dynamics and the damping of magnetization are of paramount importance to understand and predict the properties of magnetic materials used in a variety of applications. For example, spin-transfer torque magnetic random-access memory cells (STT-MRAM) are expected to switch fast, reliably, and with low power consumption, which requires low damping materials. New spintronic devices based on magnetic skyrmions, which also demand precise control of the magnetization dynamics, are another example. The Landau-Lifshitz-Gilbert equation of motion [1, 2] and extensions thereof [3] have been extremely successful in enabling predictions of the magnetization dynamics of materials both analytically and using micromagnetic simulations. Experimentally the magnetization dynamics can be elegantly probed in the frequency domain using ferromagnetic resonance (FMR). Recent progress in broadband ferromagnetic resonance techniques have provided valuable new insights in the magnetization dynamics and the damping mechanisms of magnetic materials.

In this lecture, I will introduce the fundamentals of magnetization dynamics and damping. I will discuss their importance for many applications, including hard drive read heads, spin-transfer torque magnetic random-access memories and new skyrmions based devices. I will talk about various mechanisms that can contribute to the damping of the magnetization in thin films including spin-orbit relaxation, spin pumping, and two-magnon scattering. The presentation will show how recent developments in broadband ferromagnetic resonance enable precise measurements of the dynamics and damping in thin magnetic films and multilayers especially when combined with angle and temperature dependent measurements [4]. This will include a discussion of the recently discovered anisotropic damping in exchange biased films [5, 6].

[1] T. L. Gilbert, "A Lagrangian formulation of the gyromagnetic equation of the magnetization fields (abstract only)," Phys. Rev., vol. 100, p. 1243, (1955).
[2] T. L. Gilbert, "A phenomenological theory of damping in ferromagnetic materials," Magnetics, IEEE Transactions on, vol. 40, no. 6, pp. 3443-3449, (2004).
[3] V. G. Bar’yakhtar and A. G. Danilevich, "Dissipation function of magnetic media," Low Temperature Physics, vol. 36, no. 4, pp. 303-309, (2010).
[4] B. Khodadadi, A. Rai, A. Sapkota et al., "Conductivity-Like Gilbert Damping due to Intraband Scattering in Epitaxial Iron," arXiv preprint arXiv:1906.10326, (2019).
[5] T. Mewes, R. L. Stamps, H. Lee et al., "Unidirectional Magnetization Relaxation in Exchange-Biased Films," Magnetics Letters, IEEE, vol. 1, pp. 3500204-3500204, (2010).
[6] J. Beik Mohammadi, J. M. Jones, S. Paul et al., "Broadband ferromagnetic resonance characterization of anisotropies and relaxation in exchange-biased IrMn/CoFe bilayers," Physical Review B, vol. 95, no. 6, p. 064414, 02/15/ (2017).