Unveiling the structure-property relationship in metastable Heusler compounds by systematic disorder tuning

Heusler compounds represent a unique class of materials that exhibit a wide range of fascinating and tuneable properties such as exotic magnetic phases, superconductivity, band topology, or thermoelectricity. An exceptional, but for Heusler compounds common, feature is that they are prone to antisite defects and disorder. In this regard, the $\mathrm{Fe}{}_2\mathrm{VAl}$ Heusler compound has been a particularly interesting and disputed candidate. Even though various theoretical scenarios for the interplay of physical properties and disorder have been proposed, the metastable disordered A2 phase hitherto precluded experimental investigation in bulk samples. Here, we report experimental results on disorder-tuned $\mathrm{Fe}{}_2{\mathrm{VAl}}_{0.9}{\mathrm{Si}}_{0.1}$ alloys all the way toward the A2 phase, which we realized via rapidly quenching our samples from high temperatures. We measured the thermoelectric properties of these materials in a wide temperature range (4 to 700 K); they suggest a gradual semimetal/narrow-gap semiconductor $\to$ metal transition upon increasing the disorder. We also find a large anomalous Hall effect in the disordered A2 phase, arising from the side-jump scattering of charge carriers at the antisite magnetic moments. This is corroborated by measurements of the temperature- and field-dependent magnetization, which increases dramatically up to $\approx 2.5{\mu }_{\text{B}}/\mathrm{f}.\mathrm{u}.$ as compared to the ordered compound ($<0.1{\mu }_{\text{B}}/\mathrm{f}.\mathrm{u}.$). This study provides an experimental realization of the metastable A2 structure in bulk $\mathrm{Fe}{}_2\mathrm{VAl}$-based alloys and grants insight into the structure-property relationship of these materials. Our work confirms that temperature-induced antisite disorder, occurring during thermal heat treatment, can be a precisely tuneable parameter in the family of Heusler compounds.

Figure 1

(a) Order-disorder transitions in $\mathrm{Fe}{}_2\mathrm{VAl}$ from the fully ordered $\mathrm{L}{2}_1$ phase into the partly disordered B2 and fully disordered A2 phase, occurring at high temperatures. (b) Differential thermal analysis (DTA) of $\mathrm{Fe}{}_2{\mathrm{VAl}}_{0.9}{\mathrm{Si}}_{0.1}$ upon heating and cooling. (c) Effective pair interactions in a random bcc ${\mathrm{Fe}}_{0.5}{\mathrm{V}}_{0.25}{\mathrm{Al}}_{0.225}{\mathrm{Si}}_{0.025}$ alloy at $T=1500\mathrm{K}$ from ab initio thermodynamics simulations. (d) X-ray powder diffraction (XRD) patterns of disorder-tuned $\mathrm{Fe}{}_2{\mathrm{VAl}}_{0.9}{\mathrm{Si}}_{0.1}$ Heusler compounds. (e) XRD patterns near the (111) and (200) Bragg positions, showcasing the order-disorder transitions into the B2 and A2 phases in our samples. Inset shows the lattice parameter for the different samples.

Figure 2

(a) Temperature-dependent electrical resistivity and (b) residual resistivity ratio of disorder-tuned $\mathrm{Fe}{}_2{\mathrm{VAl}}_{0.9}{\mathrm{Si}}_{0.1}$ Heusler compounds. Solid lines are guides to the eye.

Figure 3

Temperature-dependent Seebeck coefficient of disorder-tuned $\mathrm{Fe}{}_2{\mathrm{VAl}}_{0.9}{\mathrm{Si}}_{0.1}$ Heusler compounds. Solid lines are least-squares fits employing a triple parabolic band model as explained in the text (for further modeling details see Ref. [31]).

Figure 4

(a) Isothermal magnetization as a function of the magnetic field at $T=4\mathrm{K}$. We compare ordered ($\mathrm{L}{2}_1$) and fully disordered (A2) $\mathrm{Fe}{}_2{\mathrm{VAl}}_{0.9}{\mathrm{Si}}_{0.1}$ Heusler compounds as well as stoichiometric undoped $\mathrm{Fe}{}_2\mathrm{VAl}$ under the same heat treatment conditions. Inset shows a magnification of the field-dependent behavior for the ordered compounds. (b) Temperature-dependent magnetization of ordered ($\mathrm{L}{2}_1$) and fully disordered (A2) $\mathrm{Fe}{}_2{\mathrm{VAl}}_{0.9}{\mathrm{Si}}_{0.1}$. Inset shows the inverse temperature-dependent magnetic susceptibility for the ordered compound.

Figure 5

Isothermal Hall resistivity as a function of the magnetic field at different temperatures. We compare ordered ($\mathrm{L}{2}_1$) and fully disordered (A2) $\mathrm{Fe}{}_2{\mathrm{VAl}}_{0.9}{\mathrm{Si}}_{0.1}$ Heusler compounds. For the latter, an anomalous Hall effect, which increases with temperature, can be observed.

Figure 6

(a) Sketch of the qualitative evolution of the energy gap between valence band maximum (VBM) and conduction band minimum (CBM) as a function of quenching temperature in disordered $\mathrm{Fe}{}_2{\mathrm{VAl}}_{0.9}{\mathrm{Si}}_{0.1}$ Heusler compounds. For simplification only the two bands around $E_{\text{F}}$ are drawn. It should be noted that absolute values of the gap merely represent an average effective gap extracted from a phenomenological two-band model as described in the text, which may not correspond to the true (pseudo)gap. (b) Evolution of the effective energy gaps from least-squares fitting the temperature-dependent Seebeck coefficient shown as solid lines in Fig. 3. Insets sketch the order-disorder transition in $\mathrm{Fe}{}_2\mathrm{VAl}$-based compounds.

Figure 7

Low-temperature anomalies in the temperature-dependent Seebeck coefficient of disordered B2- and A2-$\mathrm{Fe}{}_2{\mathrm{VAl}}_{0.9}{\mathrm{Si}}_{0.1}$ Heusler compounds. Dashed and solid lines are least-squares fits employing an extended parabolic band model which takes into account a delocalized impurity band with a variable bandwidth $W$ as explained in the text (for further details see Ref. [69]). Inset shows schematic of the density of states featuring a valence and a conduction band as well as the impurity band that has been used to model B2-$\mathrm{Fe}{}_2{\mathrm{VAl}}_{0.9}{\mathrm{Si}}_{0.1}$. Due to the metallic nature, only a single parabolic conduction band needs to be included in addition to the impurity band for describing $S\left(T\right)$ of A2-$\mathrm{Fe}{}_2{\mathrm{VAl}}_{0.9}{\mathrm{Si}}_{0.1}$ in a broad temperature range. Sharp kinks marked by black stars are most likely an artifact from the measurement setup observed in most of our samples.