Completely compensated ferrimagnetism and sublattice spin crossing in the half-metallic Heusler compound ${\mathrm{Mn}}_{1.5}{\mathrm{FeV}}_{0.5}\mathrm{Al}$

The Slater-Pauling rule states that $L{2}_1$ Heusler compounds with 24 valence electrons never exhibit a total spin magnetic moment. In the case of strongly localized magnetic moments at one of the atoms (here Mn) they will exhibit a fully compensated half-metallic ferrimagnetic state instead, in particular, when symmetry does not allow for antiferromagnetic order. With the aid of magnetic and anomalous Hall effect measurements, it is experimentally demonstrated that ${\mathrm{Mn}}_{1.5}{\mathrm{V}}_{0.5}\mathrm{FeAl}$ follows such a scenario. The ferrimagnetic state is tuned by the composition. A small residual magnetization, which arises due to a slight mismatch of the magnetic moments in the different sublattices, results in a pronounced change of the temperature dependence of the ferrimagnet. A compensation point is confirmed by observation of magnetic reversal and sign change of the anomalous Hall effect. Theoretical models are presented that correlate the electronic structure and the compensation mechanisms of the different half-metallic ferrimagnetic states in the Mn-V-Fe-Al Heusler system.

Figure 1

Crystalline and electronic structure of ${\mathrm{Mn}}_{1.5}{\mathrm{V}}_{0.5}\mathrm{FeAl}$. (a) The $L{2}_1$-type cubic Heusler structure with space group $Fm\overline{3}m$ (225). (b) The $X$-type inverse cubic Heusler structure with space group $F\overline{4}3m$ (216). Different atoms are represented by balls with different colors, shown in between the two structures. The spin resolved density of states is shown for $Fm\overline{3}m$ in (c) and for $F\overline{4}3m$ in (d).

Figure 2

Magnetization of ${\mathrm{Mn}}_{1.5}{\mathrm{FeV}}_{0.5}\mathrm{Al}$. (a) shows the temperature dependence of the magnetization $M\left(T\right)$, measured for a completely compensated sample. (b) shows the temperature dependence of the magnetization measured for an overcompensated sample in different fields. The theoretical behavior of a two-sublattice ferrimagnet in the molecular field approximation is shown in (c) and (d): (c) shows the magnetization for a completely compensated ferrimagnet with $|m_{\text{II}}|=|2m_{\text{I}}|$; (d) shows the case with $|m_{\text{II}}|<|2m_{\text{I}}|$. $m_i$ are the average magnetic moments of the atoms on the $i\mathrm{th}$ sublattice at $T=0$.

Figure 3

Field dependent magnetization of ${\mathrm{Mn}}_{1.5}{\mathrm{FeV}}_{0.5}\mathrm{Al}$. Shown is the magnetization $M\left(H\right)$ at 2 and 263 K. Inset (a) shows the low temperature behavior on an enlarged scale. Inset (b) shows the temperature variation of the coercive field.

Figure 4

Magnetic and transport properties of overcompensated ${\mathrm{Mn}}_{1.5}{\mathrm{FeV}}_{0.5}\mathrm{Al}$. (a) Isothermal magnetization loops, $M\left(H\right)$, at different temperatures. (b) ZFC and FC $M\left(T\right)$ curves measured in a small field of 2 mT. (c) Field dependence of the Hall effect measured at different temperatures. (d) Temperature dependence of Hall resistivity measured at $\pm 0.1$ T.