Large anisotropic magnetoresistance in $α$-MnTe induced by strain

Abstract

$α\textrm{-MnTe}$ is a p-type semiconducting altermagnet with a Néel temperature near $300\thinspace\textrm{K}$. Due to the altermagnetic nature, $\mathcal{PT}$ symmetry is broken, and Kramers degeneracy is lifted in the valence band maxima along the $Γ\textrm{-K}$ line and the A point. However, the energy difference is found to be small, and any small shift in the spectrum can dramatically change the linear-response transport properties. Here we show that a strain modulating the [0001] axis of the unit cell by $\sim\pm0.5\%$ can significantly change the transport signature by switching the thermal window between the two regions of the valence band. When the $Γ\textrm{-K}$ line is dominating, the planar Hall effect and the anisotropic magnetoresistance can be enhanced by an order of magnitude, with the maximum up to $\sim70\%$.

Figures (4)

• Figure 1: The crystal structure of $\alpha$-MnTe illustrated in (a) the main view and (b-d) the top views. Purple, Green and yellow balls represent Mn atoms and the two distinct Te sublattice sites, respectively. Arrows in (a) display the 3-dimensional colinear antiferromagnetic ordering. In (b), $\varphi$ and $\theta$ represents the angle definition of the Néel vector and the electric fields, respectively. (c) and (d) show two groups of the Néel vectors, each containing three equivalent directions.
• Figure 2: The SOC band structure when the Néel vector is aligned along (a) $\varphi=0\degree$ and (b) $\varphi=90\degree$ with $U=3.0{\,\textrm{eV}}, J=0.9{\,\textrm{eV}}$. VBM is set to zero. (c) the Brillouin zone of MnTe with all high symmetric $k$-points: $\Gamma$, $M$ and $K$ are in $k_z=0$ plane and $A$, $L$, $H$ are in $k_z=\pi/c$ plane. The $k$-point path for band plotting is also displayed in (b). (d-e) the Fermi surfaces corresponding to the case of (a) and (b), respectively. The Fermi energy is $0.02{\,\textrm{eV}}$ lower than VBM. Red and blue indicate the spin components in the directions labeled on the side.
• Figure 3: The anisotropic magnetoresistance (AMR) and the planar Hall effect (PHE) when rotating the transport direction with respect to the lattice. Here $\theta$ labels the direction of the electric field, whereas $\varphi$ denotes the direction of the Néel vector, both with respect to the $+x$ direction as illustrated in Fig. \ref{['fig:1']}(b). Curves in (a) and (b) correspond to the $j_\parallel$ and $j_\perp/j_\parallel$ in the $\Gamma$-top case, respectively. Those in (c) and (d) correspond to the $j_\parallel$ and $j_\perp/j_\parallel$ in the $A$-top case, respectively. The centers of all curves are shifted in the figure and each $j_\perp/j_\parallel$ curve has the actual central value of zero. In both cases, the Fermi energy is set to $0.02{\,\textrm{eV}}$ lower than the VBM. The AMR ratio and the maximum of $j_\perp/j_\parallel$ are marked beside each curve. (e) the convergence of numerical results of conductivities $\sigma_{xx}$ and $\sigma_{yy}$ after mesh refinement. The Insets compare the first and the fifth refinement of the fermi surfaces for $\Gamma$-top case with $\varphi=0\degree$.
• Figure 4: (a) Under different magnitudes of the strain along [0001] (the $c$-axis), the conductivity anisotropy $\beta=(\sigma_{xx}-\sigma_{yy})/\sigma_{xx}$ as a function of the Fermi energy measured from the VBM. Two cases of the Néel vector $\mathbf{n}=\hat{x}$ ($\varphi=0\degree$) and $\mathbf{n}=\hat{y}$ ($\varphi=90\degree$) are considered, and three different magnitudes of strain ($-0.5\%$, $0\%$ and $+0.5\%$) are demonstrated for each case. (b) Fermi surfaces in all the 6 cases with the numbering corresponding to the ones in panel (a). (c) The AMR longitudinal current density $j_\parallel$ as a function of the angle of the electric field. Cases 1 and 2 (elongation) and Cases 5 and 6 (compress) are illustrated. Dashed lines correspond to the case of $\mathbf{n}=\hat{x}$ and the solid lines are for $\mathbf{n}=\hat{y}$, respectively.