Designed metal-insulator transition in low-symmetry magnetic intermetallics

Compounds exhibiting half-metallic character and metal-insulator transitions draw considerable attention in condensed-matter and materials physics due to their potential use in spintronics. Here we show that specific electron doping plays a crucial role in tailoring thermodynamic, structural, electronic, and magnetic properties of materials derived from low-symmetry magnetic intermetallics, exemplified on triclinic ${\mathrm{Mn}}_4{\mathrm{Al}}_{11}$. Upon chemical doping of Al by Ge, we predict improved phase stability and adherence to a generalized “18-n rule” governing closed-shell configurations in intermetallic with narrow bandgaps. Validating experiments include measurements of phase stability and electronic transport properties of electron-doped ${\mathrm{Mn}}_4{\mathrm{Al}}_{10}\mathrm{Ge}$ that crystallizes in the ${\mathrm{Mn}}_4{\mathrm{Al}}_{11}$-type structure, confirming the bandgap opening as predicted by chemical analysis and density-functional theory. We also demonstrate theoretically that hydrostatic pressure enhances the predicted half-metallic gap in the up-spin channel, which leads to a ferrimagnetic-to-ferromagnetic transition driven by Mn-Mn charge ordering in the ${\mathrm{Mn}}_4{\mathrm{Al}}_{11}$ parent. We have also discussed the generality of our approach in predicting the design of other classes of intermetallics including half and full Heusler compounds.

Figure 1

For $P\overline{1}$ ${\mathrm{Mn}}_4{\mathrm{Al}}_{11}$: (a) band dispersion, (b) partial DOS $({\mathrm{Mn}}_1=\mathrm{black},{\mathrm{Mn}}_2=\mathrm{red},\mathrm{Al}=\mathrm{cyan})$, (c) phonon dispersion (with negative values indicating imaginary frequencies), and (d) charge-density ($e$/${\AA }^3$) distribution in the (-313) crystallographic plane (sites: red, Mn; gray, Al).

Figure 2

Charge density of (a) ${\mathrm{Mn}}_4{\mathrm{Al}}_{11}$ and (b) ${\mathrm{Mn}}_4{\mathrm{Al}}_{10}\mathrm{Ge}$, while (c) is the charge-density difference between ${\mathrm{Mn}}_4{\mathrm{Al}}_{11}$ and ${\mathrm{Mn}}_4{\mathrm{Al}}_{10}\mathrm{Ge}$. (d) Charge density of ${\mathrm{Mn}}_4{\mathrm{Al}}_{11}$ under pressure (20.6 GPa), while (e) is the charge-density difference between (a) ${\mathrm{Mn}}_4{\mathrm{Al}}_{11}$ (0 GPa) and (d) ${\mathrm{Mn}}_4{\mathrm{Al}}_{11}$ (20.6 GPa). The isosurface value of 0.05 $e$/${\AA }^3$ was used. Yellow and blue isosurfaces in (c) and (d) represent charge loss and gain with respect to pure phase, respectively.

Figure 3

The magnetization density for (a) ${\mathrm{Mn}}_4{\mathrm{Al}}_{11}$ (0 GPa), (b) ${\mathrm{Mn}}_4{\mathrm{Al}}_{10}\mathrm{Ge}$ (0 GPa), and (c) ${\mathrm{Mn}}_4{\mathrm{Al}}_{11}$ (20.6 GPa); the isosurface value of 0.05 $e$/${\AA }^3$ was used. Yellow (Mn2) and blue (Mn1) isosurfaces represent up and down moments, respectively.

Figure 4

(a) Formation energy, $E_{\mathrm{form}}$, of ${\mathrm{Mn}}_4{\mathrm{Al}}_{11-x}{\mathrm{T}}_x$ with $T=\mathrm{Ge}$ or Si and $x=1$ [i.e., Ge at (0,0,0)], or 2 (Ge at inequivalent Al sites; numbering is consistent with Supplemental Material Table S2), which fully replaces Al in one of the six symmetry inequivalent sites [see Fig. 5]. For $x=1$, we have ${\mathrm{Mn}}_4{\mathrm{Al}}_{10}\mathrm{T}$ while for $x=1$, it will be ${\mathrm{Mn}}_4{\mathrm{Al}}_9{\mathrm{T}}_2$, where $T=\mathrm{Ge}$ or Si. On the $x$ axis, 1–6 represent six inequivalent Al sites; at site #1, it means the energy belongs to either ${\mathrm{Mn}}_4{\mathrm{Al}}_{10}\mathrm{Si}$ or ${\mathrm{Mn}}_4{\mathrm{Al}}_{10}\mathrm{Ge}$. Similarly, for $x=2$, energy belongs to either ${\mathrm{Mn}}_4{\mathrm{Al}}_{10}\mathrm{Si}$ or ${\mathrm{Mn}}_4{\mathrm{Al}}_9{\mathrm{Ge}}_2$. (b) $E_{\mathrm{form}}$ of binary intermetallic compounds known to form in Mn-Al, Mn-Si, and Mn-Ge systems along with the new prediction for ${\mathrm{Mn}}_4{\mathrm{Al}}_{10}\mathrm{Ge}$.

Figure 5

(a) A unit cell of $P\overline{1}$ ${\mathrm{Mn}}_4{\mathrm{Al}}_{11}$ showing Mn sites in magenta and Al in cyan (see Supplemental Material, Tables S1 and S2). (b) Phonon spectra as a function of hydrostatic pressure for ${\mathrm{Mn}}_4{\mathrm{Al}}_{11}$. (c) A Ge- (purple) substituted unit cell of ${\mathrm{Mn}}_4{\mathrm{Al}}_{11}$ at site #1. (d) Phonon dispersion for Ge substitution at sites 1–6 in (a). Inset in (d) illustrates the hydrostatic pressure (1.1 GPa) for Ge at site #5. Dashed lines in (b) and (d) at zero are guides to the eyes.

Figure 6

Spin-polarized electronic structure (see zoomed band structure in Fig. S4), phonon dispersion (see in Fig. S5), and 2D-projected charge density on the given $hkl=-313$ crystallographic plane of (a)–(d) ${\mathrm{Mn}}_4{\mathrm{Al}}_{11}$ $(P=20.6\mathrm{GPa})$ and (e)–(h) ${\mathrm{Mn}}_4{\mathrm{Al}}_{10}\mathrm{Ge}$ $(P=0\mathrm{GPa})$. The black and red in (a) and (b) are up- and down-spins.

Figure 7

Rietveld refinement of powder x-ray diffraction (PXRD) for (a) ${\mathrm{Mn}}_4{\mathrm{Al}}_{11}$, (b) ${\mathrm{Mn}}_4{\mathrm{Al}}_{10}\mathrm{Ge}$, and (c) ${\mathrm{Mn}}_4{\mathrm{Al}}_9{\mathrm{Ge}}_2$. The tick marks represent the Bragg peak locations of ${\mathrm{Mn}}_{9.52}{\mathrm{Al}}_{16.48}$ (purple) and ${\mathrm{Mn}}_4{\mathrm{Al}}_{11}$ (black) crystal structures.

Figure 8

For ${\mathrm{Mn}}_4{\mathrm{Al}}_{10}\mathrm{Ge}$: (a) heat capacity ($C_P$) measured in zero magnetic field shown as $C_P$/T with the inset illustrating $C_P$(T), as well as (b) electrical resistivity (ρ) measured in 0 and 20 kOe applied magnetic fields, and the corresponding magnetoresistance (MR), with the inset illustrating a weak, saddlelike anomalies.

Figure 9

(a) dc magnetization of ${\mathrm{Mn}}_4{\mathrm{Al}}_{10}\mathrm{Ge}$ as a function of temperature for $\mathrm{H}=10$, 20, and 50 kOe. (b) ac magnetic susceptibility of ${\mathrm{Mn}}_4{\mathrm{Al}}_{10}\mathrm{Ge}$ measured in a 5 Oe driving field at 10, 50, and 100 Hz frequencies. Closed and open points represent, respectively, real and imaginary components of the ac susceptibility.