First-principles study of spin-disorder resistivity of heavy rare-earth metals: Gd–Tm series

Abstract

Electrical resistivity of heavy rare-earth metals has a dominant contribution from thermal spin disorder scattering. Here this spin-disorder resistivity is calculated for the Gd-Tm series of metals in the paramagnetic state. Calculations are performed within the tight-binding linear muffin-tin orbital method using two complementary methods: (1) averaging of the Landauer-Büttiker conductance of a supercell over random noncollinear spin-disorder configurations, and (2) linear response calculations with the spin-disordered state described in the coherent potential approximation. The agreement between these two methods is found to be excellent. The spin-disorder resistivity in the series follows an almost universal dependence on the exchange splitting. While the crystallographic anisotropy of the spin-disorder resistivity agrees well with experiment, its magnitude is significantly underestimated compared to experiment. These results suggest that the classical picture of slowly rotating self-consistent local moments is inadequate for rare-earth metals. A simple quantum correction improves agreement with experiment but does not fully account for the discrepancy, suggesting that more complicated scattering mechanisms may be important.

High‐Efficiency Spin–Orbit Torque Switching Using a Single Heavy‐Metal Alloy with Opposite Spin Hall Angles

“…Theoretical studies have shown that the resistivity (ρ) in normal metals and alloys contains two dominant mechanisms, namely, the scattering of conduction electrons on impurities and other structural defects. [ 43–45 ] In our work, the gradual increase in the Pt 1‐x Gd x alloy compositions can be viewed as strong interface modification. With a much larger atomic radius of Gd (0.97 Å) than that of the Pt (0.63 Å), the replacement of Gd to Pt will result in an increase in lattice constant, which will modify the interface morphology.…”

Spin caloric transport from density-functional theory

“…probability between the two leads is calculated for pairs of atoms in atomic layers which are chosen at a distance enough far away from the interface with the scattering region as to ensure their bulk-like potentials [222]. The disorder effect in diverse material properties was previously modeled employing the supercell approach, e.g., the spin-disorder resistivity [215,217,218,219], or the frozen thermal lattice disorder effect on the Gilbert damping and the spin-flip diffusion length [223,224]. The disordered local moment method in the coherent potential approximation, begin computationally cheap, can be also used to evaluate the spin disorder effect but a complete disorder saturation above the critical temperature due to the missing short range order can lead to significant differences in the results [216].…”

“…We estimate the spin disorder contribution to the resistivity from the slope of the resistance as a function of the TL thickness (leadto-lead distance) at T = 500 K with almost fully saturated spin disorder. Assuming that the Ohmic limit is fulfilled for the thickness of 9 Cr layers [217,218], the spin disorder contribution to the resistivity…”

“…The electron-transport phenomena in magnetic materials at high temperatures are, however, strongly affected by the formation of a spin-disordered state as a result of local-moment fluctuations which induce spin-conserving and spin-flip scattering. The well-known spin disorder resistivity in ferromagnetic materials has been experimentally studied in the past [212,213] and ab initio techniques were successfully used to model this effect [214][215][216][217][218]. The moment fluctuations in bulk are small for temperatures significantly lower than the critical temperature, but the surface-to-volume ratio in nanostructures is large and the fluctuations are correspondingly stronger.…”

Calculating linear-response functions for finite temperatures on the basis of the alloy analogy model

“…Again, the alloy analogy has been exploited extensively in the past when dealing with the impact of spin fluctuations on various response quantities. The representation of a frozen spin configuration by means of supercell calculations has been applied for calculations of the Gilbert parameter for α [18] as well as for the resistivity or conductivity [18,22,23]. Also, the CPA has been used for calculations of α [24] as well as the resistivity [21,25].…”