Positive linear magnetoresistance effect in disordered $L{2}_{1}B$-type ${\mathrm{Mn}}_2\mathrm{CoAl}$ epitaxial films

The inverse Heusler alloy ${\mathrm{Mn}}_2\mathrm{CoAl}$ is known as a spin gapless semiconductor (SGS). It is believed that the positive linear magnetoresistance (PLMR) effect observed at low temperatures indicates the quantum linear MR effect in the gapless electronic band structures near the Fermi level, i.e., evidence of the realization of a SGS [Ouardi et al., Phys. Rev. Lett. 110, 100401 (2013)]. For this reason, one presumes that the observation of the PLMR effect is indirect proof of the demonstration of $XA$-type ${\mathrm{Mn}}_2\mathrm{CoAl}$ consisting of the inverse Heusler structure. In this paper, we observe the PLMR effect at 10 K in homogeneous and single-phase ${\mathrm{Mn}}_2\mathrm{CoAl}$ epitaxial films grown by low-temperature molecular beam epitaxy at $100{}^{\circ }\mathrm{C}$. From anomalous x-ray diffraction measurements and analyses, we clarify that the $100{}^{\circ }\mathrm{C}$-grown ${\mathrm{Mn}}_2\mathrm{CoAl}$ epitaxial film is not composed of the $XA$-type structure but a disordered $L{2}_{1}B$-type structure including some amount of Mn(A site) $\iff \mathrm{Co}$(C site) swapping and Mn(B site) $\iff \mathrm{Al}$(D site) swapping. On the basis of first-principles density-functional theory calculations, we discuss the correlation between the PLMR effect observed at 10 K and the possible electronic band structure in the disordered $L{2}_{1}B$-type ${\mathrm{Mn}}_2\mathrm{CoAl}$.

Figure 1

(a) Crystal structures of inverse Heusler $XA$-type (left) and $L{2}_{1}B$-type (right) ${\mathrm{Mn}}_2\mathrm{CoAl}$. The A, B, C, and D sites correspond to $4a,4c,4b$, and $4d$ Wyckoff positions, respectively. (b) $\theta -2\theta$ XRD pattern of the $100{}^{\circ }\mathrm{C}$-grown ${\mathrm{Mn}}_2\mathrm{CoAl}$ film grown on ${\mathrm{MgAl}}_2{\mathrm{O}}_4$(001) (red), together with that for a ${\mathrm{MgAl}}_2{\mathrm{O}}_4$(001) substrate (black). The inset shows a RHEED image of the ${\mathrm{Mn}}_2\mathrm{CoAl}$ surface after the growth. (c) and (d) XRD $\varphi$-scan profiles in {202} and {111}, respectively, for the $100{}^{\circ }\mathrm{C}$-grown ${\mathrm{Mn}}_2\mathrm{CoAl}$ film.

Figure 2

(a) HAADF-STEM image of the 100 ${}^{\circ }\mathrm{C}$-grown ${\mathrm{Mn}}_2\mathrm{CoAl}$ film on ${\mathrm{MgAl}}_2{\mathrm{O}}_4$(001), together with EDX line profiles of Mn, Co, Al. (b) EDX elemental maps of Mn, Co, and Al for the same ${\mathrm{Mn}}_2\mathrm{CoAl}$/${\mathrm{MgAl}}_2{\mathrm{O}}_4$(001) heterostructure.

Figure 3

(a) Temperature dependence of the electrical resistivity $\rho$ and (b) Hall conductivity ${\sigma }_{\mathrm{yx}}$ as a function of out-of-plane external magnetic fields at various temperatures for the $100{}^{\circ }\mathrm{C}$-grown ${\mathrm{Mn}}_2\mathrm{CoAl}$ film. The inset pictures show micrographs of the fabricated Hall-bar devices including the measurement scheme and $M\text{−}{B}_{\mathrm{y}}$ curve at 10 and 300 K for the $100{}^{\circ }\mathrm{C}$-grown ${\mathrm{Mn}}_2\mathrm{CoAl}$ film.

Figure 4

Magnetoresistance (MR) ratio as a function of in-plane external magnetic fields at various temperatures. The inset shows an MR curve for another device at 10 K.

Figure 5

X-ray energy dependence of the calculated and experimental (a) $I_{002}$/$I_{004}$ with the Mn(B $\mathrm{site})\iff \mathrm{Co}$(C site) disorder and (b) $I_{111}$/$I_{004}$ with the Mn(A $\mathrm{site})\iff$ Co(C site) disorder near the Mn $K$ absorption edge. (c) Comparison of $I_{111}$/$I_{004}$ between the experiment and the calculation with the presence of the 40% Mn(B $\mathrm{site})\iff \mathrm{Al}$(D site) swapping, together with the 50% Mn(A $\mathrm{site})\iff \mathrm{Co}$(C site) swapping.

Figure 6

Spin-resolved total density of states (DOS) of $L{2}_{1}B$-type ${\mathrm{Mn}}_2\mathrm{CoAl}$ in the presence of (a) 10%, (b) 30%, and (c) 50% Mn(A $\mathrm{site})\iff \mathrm{Co}$(C site) swapping. (d) Spin-resolved total DOS of disordered $L{2}_{1}B$-type ${\mathrm{Mn}}_2\mathrm{CoAl}$ in the presence of both the 50% Mn(A $\mathrm{site})\iff \mathrm{Co}$(C site) swapping and the 40% Mn(B $\mathrm{site})\iff \mathrm{Al}$(D site) swapping.