First-principles modeling of longitudinal spin fluctuations in itinerant electron antiferromagnets: High Néel temperature in the ${\mathrm{V}}_3\mathrm{Al}$ alloy

The ${\mathrm{V}}_3\mathrm{Al}$ alloy with $\mathrm{D}{\mathrm{O}}_3$ crystal structure belongs to the family of the very few metallic materials that exhibit a magnetically ordered state with a high ordering temperature (∼600 K) and consist only of nonmagnetic elements. We show that, similarly to the ferromagnetism in the fcc Ni (with ordering temperature at about 630 K), the antiferromagnetism in ${\mathrm{V}}_3\mathrm{Al}$ has itinerant character, and the high value of the Néel temperature is the result of the strong longitudinal spin fluctuations in the paramagnetic state. In order to develop an ab initio–based theory of the magnetic ordering at finite temperatures, we employ an effective magnetic Heisenberg-like Hamiltonian with varying values of the on-site magnetic moments. Using a set of approximations we map this model onto the results of the first-principle-based disordered local moment formalism and the magnetoforce theorem applied in the framework of the Korringa-Kohn-Rostoker method. Our high-temperature approach is shown to describe the experimental Néel temperature of ${\mathrm{V}}_3\mathrm{Al}$ very well and thus underlines the importance of the longitudinal spin-fluctuation mechanism of formation of the vanadium magnetic moment at high temperatures.

Figure 1

The $\mathrm{D}{\mathrm{O}}_3$ structure of ${\mathrm{V}}_3\mathrm{Al}$ alloy. The green circles are magnetic V($8c$) atomic sites. The arrows show the ground-state antiferromagnetic ordering.

Figure 2

Magnetic exchange interactions in ${\mathrm{V}}_3\mathrm{Al}$ calculated in the AFM ground state plotted as a function of the interatomic distance. Squares are results of GGA-PBE and circles are results of LSDA calculations. The double values at third-nearest-neighbor interatomic distance mark nonequivalent interactions through V($4b$) and Al sites.

Figure 3

Calculated total energies of disordered local moment states as function of the local spin moment. Open squares, fcc Ni; closed squares, bcc Fe; circles, ${\mathrm{V}}_3\mathrm{Al}$ (open-LSDA, closed – GGA results). The energies are given in kelvins per magnetic site. The lines are polynomial fits to the data.

Figure 4

Temperature dependence of the average local spin moment in the paramagnetic state of ${\mathrm{V}}_3\mathrm{Al}$. The values are derived by a numerical integration of the DLM energies obtained with the LSDA and GGA, respectively, at each temperature point.

Figure 5

Magnetic exchange interactions in ${\mathrm{V}}_3\mathrm{Al}$ calculated in the DLM state (with the GGA) with fixed moments $m=1.2{\mu }_B/\mathrm{V}\left(8c\right)$ (circles) and $1{\mu }_B/\mathrm{V}\left(8c\right)$ (filled squares). The values obtained for the AFM ground state are shown as open squares for comparison.

Figure 6

Estimation of the Néel temperature of ${\mathrm{V}}_3\mathrm{Al}$. Calculated Néel temperatures (Monte Carlo simulations) with exchange constants obtained for given values of the local spin moments in disordered local moment states (filled circles). Open (LSDA results) and closed (GGA results) squares are the temperatures at which given average local moments are stabilized (inverted Fig. 4). The crossing points of the MC Néel temperature curve (circles) with the last two curves (squares) mark the estimated physical Néel temperature of ${\mathrm{V}}_3\mathrm{Al}$. Note that exchange constants calculated with the LSDA and GGA for the same values of the local moment fixed in the DLM state are almost indistinguishable and thus only one common Néel temperature curve is plotted.