Electronic structure calculations in ordered and disordered solids with spiral magnetic order

A scheme to calculate the electronic structure of systems having a spiral magnetic structure is presented. The approach is based on the Korringa-Kohn-Rostoker Green’s function formalism which allows, in combination with the coherent potential approximation alloy theory, dealing with chemically disordered materials. It is applied to the magnetic random alloys Fe${}_x$Ni${}_{1-x}$, Fe${}_x$Co${}_{1-x}$, and Fe${}_x$Mn${}_{1-x}$. For these systems the stability of their magnetic structure was analyzed. For Fe${}_x$Ni${}_{1-x}$ the spin stiffness for was determined as a function of concentration that was found in satisfying agreement with experiment. Performing spin spiral calculations the longitudinal momentum-dependent magnetic susceptibility was calculated for pure elemental systems (Cr, Ni) in the nonmagnetic state as well as for random alloys (Ag${}_x$Pt${}_{1-x}$). The obtained susceptibility was used to analyze the stability of the paramagnetic state of these systems.

Figure 1

Geometry of a spin spiral with the wave vector $\mathrm{q⃗}$ along the $z$ direction.

Figure 2

(a) The energy of spin spiral magnetic structure in Fe${}_x$Ni${}_{1-x}$ alloys. (b) Local magnetic moments on Ni atoms as a function of the wave vector $\mathrm{q⃗}=\frac{\pi }{a}(0,0,q_z)$.

Figure 3

Spin stiffness constant of Fe${}_x$Ni${}_{1-x}$ alloys as a function of the concentration in comparison with experiment: Nakai[22] (filled circles), Hatherly et al.[23] (open circles), and Rusov[24] (filled squares).

Figure 4

(a) The energy of spin spiral magnetic structure in Fe${}_{0.5}$Co${}_{0.5}$ calculated for the wave vector $\mathrm{q⃗}=\frac{\pi }{a}(0,0,q_z)$ along the [001] direction. (b) Local magnetic moments on Fe and Co atoms separately, as a function of wave vector of spin spirals.

Figure 5

(a) The energy of spin spiral magnetic structure in Fe${}_x$Mn${}_{1-x}$ alloys calculated for the wave vector $\mathrm{q⃗}=\frac{\pi }{a}(0,0,q_z)$ along the [001] direction. (b) Local magnetic moments on Fe and Mn atoms separately, as a function of wave vector of spin spirals.

Figure 6

(a) Wave-vector [$\mathrm{q⃗}=\frac{\pi }{a}(0,0,q_z)$] dependent magnetic susceptibility of the paramagnetic disordered Ag${}_x$Pt${}_{1-x}$ for various concentrations. (b) Comparison of the present results for the susceptibility for $q=0$ with the results of Deng et al.[21] obtained via linear response theory.

Figure 7

Wave-vector dependent [$\mathrm{q⃗}=\frac{\pi }{a}(0,0,q_z)$] spin susceptibility of paramagnetic Ni having lattice parameter $a=6.65$ a.u. together with local Ni magnetic moment as a function of wave-vector characterizing noncollinear spiral magnetic structure (a). The wave-vector dependent unenhanced (b) and enhanced (c) magnetic susceptibilities for paramagnetic Ni calculated for different lattice parameters.

Figure 8

Wave-vector dependent [$\mathrm{q⃗}=\frac{\pi }{a}(0,0,q_z)$] enhanced (a) and unenhanced (b) spin susceptibilities of paramagnetic Cr. For comparison, the unenhanced susceptibility is plotted also in panel (a).