Spin-disorder resistivity of random fcc-NiFe alloys

The spin-disorder resistivity (SDR) of a disordered fcc-(${\mathrm{Ni}}_{1-x},{\mathrm{Fe}}_x$) alloy is determined from first principles. We identify the SDR at and above the critical temperature with the residual resistivity of the corresponding paramagnetic state evaluated in the framework of the disordered local moment (DLM) model. The underlying electronic structure is determined by means of the tight-binding linear muffin-tin orbital method, which employs the coherent potential approximation (CPA) to describe both the DLM state and the chemical disorder in alloys. An extension of the DLM fixed-spin moment method for two independent magnetic moments is used and combined with the paramagnetic lattice gas entropy to determine local moments by minimizing the corresponding free energy. The effect of phonon scattering is included through the mapping of static atomic displacements into a multicomponent random alloy which is then treated in the CPA. Finally, the Kubo-Greenwood-CPA approach is employed to estimate the SDR. We also address the problem of the validity of the Matthiessen rule at the Curie point. Good agreement of calculated and measured SDR is obtained over the whole studied concentration range; the results point to the importance of nonzero Ni magnetic moments in the limit of pure nickel.

Figure 1

The schematic illustration of the temperature-dependent resistivity and its main contributions due to impurities, phonons, and spin fluctuations which assumes the validity of the Matthiessen rule. How the SDR is determined experimentally from the ${\rho }_{\mathrm{ext}}$ found by extrapolation from the high-temperature region and the residual (impurity) resistivity ${\rho }_{\mathrm{imp}}$ as ${\rho }_{\mathrm{SDR}}={\rho }_{\mathrm{ext}}-{\rho }_{\mathrm{imp}}$ is also shown.

Figure 2

The local Ni (solid circles) and Fe (open circles) magnetic moments for the disordered fcc-(${\mathrm{Ni}}_{1-x},{\mathrm{Fe}}_x$) alloy as a function of the Fe concentration: (a) calculated in the FM state and (b) calculated in the DLM state without and with the FSM method. Local Ni moments collapse to zero for all concentrations in the DLM state and are not shown. The DLM-FSM values for $x_{\mathrm{Fe}}=0.05$ and 0.35 were obtained with the help of interpolated experimental values [9] of $T_{\mathrm{C}}$ for $x_{\mathrm{Fe}}=0.0$ and 0.1 and $x_{\mathrm{Fe}}=0.3$ and 0.4, respectively.

Figure 3

Calculated SDR (solid circles) for disordered fcc-(${\mathrm{Ni}}_{1-x},{\mathrm{Fe}}_x$) as a function of the Fe concentration: (a) the DLM method and (b) the DLM-FSM method. Theoretical (th) results are compared with the experiment [9] (exp) in both cases. No experimental data are available for $x_{\mathrm{Fe}}=0.05$ and 0.35 concentrations.

Figure 4

The validity of the Matthiessen rule: (a) The resistivity of the fcc-(${\mathrm{Ni}}_{75},{\mathrm{Fe}}_{25}$) alloy as a function of the rms displacement $\sqrt{\langle u^2\rangle }$. The label “imp+ph” (open circles) denotes the model in which impurities (imp) and static displacements (ph, phonons) are present, while the label “imp+sf+ph” (solid circles) denotes the model in which spin fluctuations (sf) are also present. All types of disorder are treated on the same footing by using the multicomponent CPA. (b) The same as in (a), but for the fcc-(${\mathrm{Ni}}_{50},{\mathrm{Fe}}_{50}$) alloy. The long vertical lines indicate the rms displacement at $T_{\mathrm{C}}$ estimated from the Debye theory [1, 33].

Figure 5

Magnetic part of the free energy of the fcc-(${\mathrm{Ni}}_{75},{\mathrm{Fe}}_{25}$) alloy as a function of averaged local magnetic moments $m$(Ni) and $m$(Fe) on Ni and Fe atoms at the Curie temperature (850 K). The numbers attached to isolines are values of the free energy in Ry units. The cross indicates the position of the free-energy minimum. The corresponding local moments are then $0.22{\mu }_{\mathrm{B}}$ and $2.45{\mu }_{\mathrm{B}}$ for Ni and Fe, respectively.