Theoretical description of the high-field susceptibility of magnetically ordered transition metal systems with applications to Fe, Co, Ni, and ${\mathrm{Fe}}_{1-x}{\mathrm{Co}}_x$

A theoretical description of the high-field susceptibility of magnetically ordered transition metal systems is presented that is based on linear response theory formulated using the Green’s function technique. The approach allows to treat all spin and orbital contributions in a consistent way on the same footing. In contrast to previous work, the Landau susceptibility is included and spin-orbit induced contributions to the susceptibility are accessible by using a fully relativistic formulation. As an application of our approach, results obtained for the ferromagnetic transition metals Fe, Co, and Ni, as well as for the alloy system ${\mathrm{Fe}}_{1-x}{\mathrm{Co}}_x$, are presented. These are discussed and compared to corresponding experimental data.

Figure 1

Spatially resolved particle density susceptibility ${\chi }^c\left(r\right)$ (multiplied by $r^2$) of bcc-Fe together with the integral function $I^c\left(r\right)={\int }_0^r{r}^{\prime 2}d{r}^{\prime }{\chi }^c\left(r^{\prime }\right)$. The vertical dashed line indicates the Wigner-Seitz radius $r_{WS}$.

Figure 2

Spatially resolved exchange-correlation interaction kernels $J\left(r\right)$, $K\left(r\right)$, and $L\left(r\right)$ [defined in Eq. (5)] of bcc Fe.

Figure 3

Partial spatially resolved particle density susceptibility ${\chi }_{\alpha }^c\left(r\right)$ (multiplied by $r^2$) for $\alpha =\mathrm{Fe}$ and Co in the compound FeCo. The dotted line gives the integral function $I^c\left(r\right)={\int }_0^r{r}^{\prime 2}d{r}^{\prime }[{\chi }_{\mathrm{Fe}}^c\left(r^{\prime }\right)+{\chi }_{\mathrm{Co}}^c\left(r^{\prime }\right)]$.

Figure 4

Element-resolved integral function $I_{\alpha }^c\left(r_{WS}\right)={\chi }_{\alpha }^c$ for the particle number of Fe and Co in disordered ${\mathrm{Fe}}_{1-x}{\mathrm{Co}}_x$ reflecting the charge transfer from Co to Fe.

Figure 5

Element-resolved contributions to the spin-magnetic susceptibility ${\chi }_{\alpha }^s$ of Fe and Co in disordered bcc ${\mathrm{Fe}}_{1-x}{\mathrm{Co}}_x$.

Figure 6

Element-resolved contributions to the orbital-magnetic susceptibility ${\chi }_{\alpha }^o$ of Fe and Co in disordered bcc ${\mathrm{Fe}}_{1-x}{\mathrm{Co}}_x$.

Figure 7

Total high-field magnetic susceptibility of bcc ${\mathrm{Fe}}_{1-x}{\mathrm{Co}}_x$ alloys. Empty circles correspond to randomly disordered alloys, while empty squares correspond to partially ordered alloys (see text). Experimental data are given by filled circles (Ref. 37).