Effect of correlation and disorder on the spin-wave spectra of ${\mathrm{Pd}}_2\mathrm{MnSn}, {\mathrm{Ni}}_2\mathrm{MnSn}$, and ${\mathrm{Cu}}_2\mathrm{MnAl}$ Heusler alloys: A first-principles study

Spin waves, also known as magnons, are low-lying collective excitations in magnetic materials, for which it is hard to achieve agreement between first-principles electronic structure calculations and experiments. It has been shown in literature [I. Galanakis and E. Şaşıoğlu, J. Mater. Sci. 47, 7668 (2012)] using as a prototype three full Heusler alloys—${\mathrm{Pd}}_2\mathrm{MnSn}, {\mathrm{Ni}}_2\mathrm{MnSn}$, and ${\mathrm{Cu}}_2\mathrm{MnAl}$—that usual density-functional calculations for perfectly ordered compounds fail by a large margin to reproduce neutron scattering measurements of spin waves. We show for these three compounds that the inclusion of correlation effects in the form of the $\mathrm{GGA}+U$ approach and/or substitutional disorder accounted via the coherent potential approximation affects considerably the calculated magnetic properties and their agreement to the experimental data. We expect our results to pave the way for further studies on magnetic materials for which experimental magnonic data exist.

Figure 1

The $L{2}_1$-type crystal structure of the Heusler alloys. Blue spheres represent the X component, light blue ones Y, and red ones Z.

Figure 2

Atom-, orbital- and spin-projected density of states (DOS) for the three investigated Heusler compounds in perfect $L{2}_1$-type structure using the standard GGA fomalism. Positive (negative) DOS values correspond to the majority (minority) spin electrons.

Figure 3

Experimental (from Ref. [15]) and GGA-calculated Heisenberg exchange parameters between the Mn atoms as a function of distance for ${\mathrm{Pd}}_2\mathrm{MnSn}$. Shells 1 to 8 around each Mn atom contain, respectively, 12, 6, 24, 12, 24, 8, 48, and 6 elements. Distances are given in multiples of the nearest neighbor distance between two Mn atoms $R_1$.

Figure 4

Experimental (triangles, from Ref. [15]) and calculated spin-wave dispersion for ${\mathrm{Pd}}_2\mathrm{MnSn}$ for different types of disorder and for $\mathrm{GGA}+U$ corrections. See text for details.

Figure 5

Experimental (taken from Ref. [15]) and GGA-calculated Heisenberg exchange parameters between Mn-Mn (filled spheres) and Mn-Ni (empty spheres) atoms for ${\mathrm{Ni}}_2\mathrm{MnSn}$. Distances are given in multiples of the nearest neighbor distance between two Mn atoms $R_1$.

Figure 6

Experimental (taken from Ref. [15]) and calculated spin-wave dispersion for ${\mathrm{Ni}}_2\mathrm{MnSn}$. The $B2$-type disordered structure has an optical branch in the spin-wave dispersion, which is also shown in order to explain the kink around X.

Figure 7

Experimental (taken from Ref. [15]) and calculated spin-wave dispersion for ${\mathrm{Ni}}_2\mathrm{MnSn}$, assuming 5% Sn vacancies on the 4b sites.

Figure 8

Experimental (taken from Ref. [9]) and GGA-calculated Mn-Mn Heisenberg exchange parameters for ${\mathrm{Cu}}_2\mathrm{MnAl}$. Distances are given in multiples of the nearest neighbor distance between two Mn atoms $R_1$.

Figure 9

Experimental (taken from Ref. [9]) and calculated spin-wave dispersion for ${\mathrm{Cu}}_2\mathrm{MnAl}$.

Figure 10

Experimental spin-wave dispersion (taken from Ref. [9]) compared with the calculated spin-wave dispersion for the ${\mathrm{Cu}}_{1.5}{\mathrm{MnAl}}_{0.5}$ alloy.