First-principles investigation of chemical and structural disorder in magnetic Ni${}_2$Mn${}_{1+x}$Sn${}_{1-x}$ Heusler alloys

We present ab initio calculations of magnetic exchange parameters of stoichiometric Heusler compound Ni${}_2$MnSn and a few nonstoichiometric Ni${}_2$Mn${}_{1+x}$Sn${}_{1-x}$ cases. Use of the exchange parameters in subsequent Monte Carlo simulations allows us to evaluate the magnetization curves as a function of temperature and composition as well as the critical temperatures of the magnetic phase transitions. The latter are compared to those obtained from a mean-field approximation using the Heisenberg model. We find that the variation of the experimental Curie temperatures of nonstoichiometric alloys can be explained theoretically if we assume that the main impact of disorder is the intermixing of manganese and tin on their corresponding sublattices and the simultaneous appearance of strong antiferromagnetic trends which originate from the nearest-neighbor Mn-Mn interactions on different sublattices. The Curie temperatures of the Ni-Mn-Sn alloys which have been obtained from the Monte Carlo simulations are in qualitative agreement with the experimental transition temperatures.

Figure 1

(a)–(d) The ab initio magnetic exchange parameters $J_{ij}$ of Ni${}_2$Mn${}_{1+x}$Sn${}_{1-x}$ for $x=0,0.4,0.52,0.8$ as a function of the distance $d/a$ between the atoms in units of the lattice constant $a$. For instance, Mn${}_1$-Mn${}_2$ in the panel denotes the exchange interaction between the first atom (Mn${}_1$) at the origin and the second atom (Mn${}_2$) a distance $d/a$ apart. (e) Composition dependence of magnetic exchange parameters in the first coordination shell of Ni${}_2$Mn${}_{1+x}$Sn${}_{1-x}$.

Figure 2

The experimental and theoretical (for the ordered structure) concentration dependence of the magnetic moment of Ni${}_2$Mn${}_{1+x}$Sn${}_{1-x}$ alloys. The open (filled) symbols refer to the experimental (ab initio) data with experimental data from Ref. 8.

Figure 3

The dependence of the ab initio magnetic exchange parameters of the first coordination shell of Ni${}_2$Mn${}_{1+x}$Sn${}_{1-x}$ on composition and disorder between Mn and Sn atoms. (a) The variation of the Mn${}_1$-Mn${}_1$ exchange parameters as a function of $x$ for different degrees of disorder ($y$) ranging from zero to 50$\%$. (b) The Mn${}_1$-Mn${}_2$ and (c) and (d) the Mn${}_1$-Ni (filled symbols) and Mn${}_2$-Ni (open symbols) exchange parameters. (e) and (f) The dependence of the exchange parameters from the degree of disorder for two compositions ($x$ = 0.21 and $x$ = 0.31).

Figure 4

The total electronic DOS curves for the cubic structure of (a) Ni${}_2$Mn${}_{1.21}$Sn${}_{0.79}$ and (b) Ni${}_2$Mn${}_{1.31}$Sn${}_{0.69}$ with different degrees of disorder ($y$).

Figure 5

The compositional dependence of the spin-down DOS at the Fermi level of Ni${}_2$Mn${}_{1+x}$Sn${}_{1-x}$ as a function of $x$ and different degrees of disorder.

Figure 6

Theoretical magnetic moments per formula unit of Ni${}_2$Mn${}_{1+x}$Sn${}_{1-x}$ as a function of the composition $x$ and structural disorder ($y$) showing the (a) dependence of the total magnetic moment (${\mu }^{\mathrm{tot}}$) and (b) dependence of the magnetic moments ${\mu }_{{\mathrm{Mn}}_1}$ and ${\mu }_{{\mathrm{Mn}}_2}$. Lines with filled (open) symbols mark ${\mu }_{{\mathrm{Mn}}_1}$ and ${\mu }_{{\mathrm{Mn}}_2}$, respectively.

Figure 7

Calculated composition-disorder phase diagram of Ni${}_2$Mn${}_{1+x}$Sn${}_{1-x}$ (Ni${}_2$Mn${}_{1-y}$Sn${}_y$Mn${}_{x+y}$Sn${}_{1-x-y}$). Here FM marks the region of the ferromagnetic phase while AFM and FRM denotes the antiferromagnetic or ferrimagnetic one.

Figure 8

(a) Magnetization curves of Ni${}_2$Mn${}_{1+x}$Sn${}_{1-x}$ ($0\le x\le 0.4$) as a function of temperature in zero magnetic field and vanishing disorder ($y=0$). (b) Magnetization curves of Ni${}_2$Mn${}_{1+x}$Sn${}_{1-x}$ ($0\le x\le 0.31$) in zero magnetic field for 25$\%$ disorder. (c) Experimental $(T,x)$ phase diagram of Ni${}_2$Mn${}_{1+x}$Sn${}_{1-x}$ to which the theoretical Curie temperatures have been added. The curves with open (filled) symbols mark the experimental (theoretical) data where the experimental data have been taken from Ref. 8.