First-principles calculations of magnetization relaxation in pure Fe, Co, and Ni with frozen thermal lattice disorder

The effect of the electron-phonon interaction on magnetization relaxation is studied within the framework of first-principles scattering theory for Fe, Co, and Ni by displacing atoms in the scattering region randomly with a thermal distribution. This “frozen thermal lattice disorder” approach reproduces the nonmonotonic damping behavior observed in ferromagnetic resonance measurements and yields reasonable quantitative agreement between calculated and experimental values. It can be readily applied to alloys and easily extended by determining the atomic displacements from ab initio phonon spectra.

Figure 1

Schematic picture of the proposed frozen thermal lattice disorder. Atoms (red dots) on the ideal lattice (left panel) are displaced with a random Gaussian distribution and form a static configuration (right panel) in the electronic transport calculation. The displacement of atom $i$ is denoted as ${\mathbf{u}}_i$ (blowup).

Figure 2

Total resistance (a) and damping (b) as functions of the thickness of the ferromagnetic slab for Au$|$Fe$|$Au(001) with $\Delta =0.0259\hspace{0.5em}{a}_{\mathrm{Fe}}$. Dots indicate the calculated values averaged over five configurations while the solid line is a linear fit.

Figure 3

Calculated Gilbert damping and resistivity for bcc Fe, hcp Co, and fcc Ni as functions of the rms displacements measured in units of the corresponding lattice constants, $a$. The error bars reflect the configuration spread. Experimental resistivities (Ref. 27) are used to label a number of resistivity values with a temperature.

Figure 4

Gilbert damping frequency as a function of resistivity for bcc Fe, hcp Co, and fcc Ni. Calculated results are shown as lines: for frozen thermal lattice disorder as (black) solid lines and for frozen spin disorder as a (red) dashed line (Fe only). $g=2$ is used in the calculations. Symbols are experimental damping values from Ref. 5 ($◯$), Ref. 4 ($\square$), and Ref. 7 ($▵$). The corresponding resistivity values are take from Refs. 27 and 29. Experimental damping frequencies have been multiplied by $4\pi$; see the Appendix for details.