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

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. 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.

Figure 1

Area-resistance product $RA$ vs the thickness $L$ of the disordered region for both transport directions for Gd, Tb, and Tm (LB method). Each point corresponds to an average of 15 or more random spin-disorder configurations. (a) In-plane direction, open shapes; (b) $c$-axis direction, closed shapes. Triangles: Gd; circles: Tb; squares: Tm.

Figure 2

Spin-projected local DOS of paramagnetic Gd averaged over 64-atom supercells with random noncollinear local-moment orientations. The valence basis includes $s$, $p$, and $d$ states, while the fully spin-polarized $4f$ shell is included in the open-core approximation. The total (input) local moment is 7.44 ${\mu }_B$. (Note the excellent agreement with the DLM result of Ref. 38.)

Figure 3

SDR as a function of the squared exchange splitting ${\Delta }^2$ in the open-core approximation (or as indicated). Filled shapes: in-plane SDR; open shapes: $c$-axis SDR. Circles: Gd; squares: Tb; triangles: Dy; inverted triangles: Ho; diamonds: Er; crosses: in-plane Tm; pluses: $c$-axis Tm. Points labeled 50/50 Ising LDA+$U$: calculations with LDA+$U$ for $4f$ orbitals in the basis set and Ising spin disorder.

Figure 4

Comparison of calculated SDR with experiment and the effect of quantum corrections. (a) In-plane direction, (b) $c$-axis direction. Insets: enlarged scale. Crosses: experimental data (Legvold et al.); filled circles: LB calculations with atomic potentials taken from the ferromagnetic state. Filled diamonds: LB results multiplied by $(S+1)/S$; open circles: LB results multiplied by $(J+1)/J$.

Figure 5

Band structures calculated using TB-LMTO and full-potential linear augmented plane wave (FLAPW) methods. Solid red line: majority-spin LMTO; dashed blue line: minority-spin LMTO. Open red circles: majority-spin FLAPW; blue plus signs: minority-spin FLAPW. (a) No empty spheres in the LMTO basis set. (b) With empty spheres in the LMTO basis set. Note the improved agreement along the H-K and K-$\Gamma$ symmetry lines.