Finite-temperature magnetism of ${\text{Fe}}_x{\text{Pd}}_{1-x}$ and ${\text{Co}}_x{\text{Pt}}_{1-x}$ alloys

The finite-temperature magnetic properties of ${\text{Fe}}_x{\text{Pd}}_{1-x}$ and ${\text{Co}}_x{\text{Pt}}_{1-x}$ alloys have been investigated. It is shown that the temperature-dependent magnetic behavior of these alloys cannot be described properly unless the coupling between the magnetic moments at the Fe and Co mediated through the interactions with the induced magnetic moments of the nonmagnetic Pd and Pt atoms is included. A scheme for the calculation of the Curie temperature $\left(T_C\right)$ for this type of systems is presented that is based on the extended Heisenberg Hamiltonian with the appropriate exchange parameters $J_{ij}$ obtained from ab initio electronic-structure calculations. Within the present study the Korringa-Kohn-Rostoker Green’s-function method has been used to calculate the $J_{ij}$ parameters. The Curie temperatures obtained for ${\text{Fe}}_x{\text{Pd}}_{1-x}$ and ${\text{Co}}_x{\text{Pt}}_{1-x}$ alloys are compared with the corresponding experimental data. The experimental results for ${\text{Fe}}_x{\text{Pd}}_{1-x}$ alloys have been obtained within anomalous Hall-effect measurements. The agreement between theoretical results and all available experimental data is rather good.

Figure 1

(Color online) Exchange coupling parameters $J^{\text{Fe-Fe}}$ (a) and $J^{\text{Fe-Pd}}$ (b) for ${\text{Fe}}_x{\text{Pd}}_{1-x}$ alloys at different concentrations. The dashed lines represent results for ordered ${\text{FePd}}_3$ (note that in this case for the Fe atoms the nearest-neighbor interaction $J^{\text{Fe-Fe}}$ is absent because there are only Pd nearest neighbors).

Figure 2

Results of spin-spiral calculations for ordered ${\text{FePd}}_3$ and disordered ${\text{Fe}}_{0.25}{\text{Pd}}_{0.75}$: (a) the energy of spin spirals as a function of the wave vector $q=\frac{\pi }{a}\left(0,0,q_z\right)$, obtained for the disordered alloy (full circles), for the ordered compound with nonzero Pd magnetic moments (full squares), and for the ordered compound with Pd magnetic moments forced to be zero (open squares); (b) magnetic moment of inequivalent Pd atoms in ordered ${\text{FePd}}_3$ as a function of the wave vector $q_z$. Fe and Pd2 atoms occupy the sites (0,0,0) and $\left(\frac{1}{2},\frac{1}{2},0\right)$, respectively, Pd1 atoms occupy the sites $\left(0,\frac{1}{2},\frac{1}{2}\right)$ and $\left(\frac{1}{2},0,\frac{1}{2}\right)$.

Figure 3

(Color online) (a) Pd DOS in ${\text{Fe}}_x{\text{Pd}}_{1-x}$ for $x=0.003$ and $x=0.15$ for spin-down (upper panel) and spin-up (lower panel) states. Ground-state characteristics of ${\text{Fe}}_x{\text{Pd}}_{1-x}$ alloys vs Fe concentration; (b) density of states of Pd at the Fermi level; (c) Pd spin magnetic moments; and (d) Fe spin magnetic moments.

Figure 4

(Color online) Magnetic moment distribution in Pd around a single Fe impurity, as a function of the distance from the magnetic atom. Full squares represent the Pd magnetic moments self-consistently obtained within a cluster with three atomic shells of Pd around an Fe impurity embedded into a Pd host and full circles give the results obtained for the same system but with the exchange potential switched off. The open circles represent the induced magnetic moments in Pd calculated within linear-response formalism using Eq. (A1) in the Appendix.

Figure 5

(Color online) Results of ab initio calculations by using the uncompensated DLM approximation: induced Pd moment in three Fe-Pd alloys as a function of the Fe average magnetic moment.

Figure 6

(Color online) ${\text{Fe}}_x{\text{Pd}}_{1-x}$ alloy with $2\text{at}\text{.}\mathrm{\%}$ Fe: the magnetic moment snapshot configuration in a unit cell used within the MC simulations $\left(T=0.1\text{K}\right)$ (a) without and (b) with the induced Pd moments taken into account. Large arrows correspond to the Fe magnetic moments and small arrows to Pd magnetic moments.

Figure 7

(Color online) The Curie temperature for different Fe concentrations in ${\text{Fe}}_x{\text{Pd}}_{1-x}$ alloys: present results vs theoretical results of Mohn and Schwarz (Ref. 15) and experimental data.

Figure 8

(Color online) Exchange coupling constants $J_{ij}$ between moments of Co atom on site $i$ and on other surrounding Co atoms $\left(j\right)$ (left panels) and between moments on Co atom $\left(i\right)$ and on surrounding Pt atoms $\left(j\right)$ (right panel), for ordered and disordered ${\text{Co}}_x{\text{Pt}}_{1-x}$ alloys. The horizontal axis shows the distance $R_{ij}$ between $i$ and $j$ atoms in units of lattice constants.