Piezomagnetic properties in altermagnetic MnTe

We examined the piezomagnetic effect in an antiferromagnet MnTe, which is a candidate material for altermagnetism with a high critical temperature. We observed that the magnetization develops with the application of stress and revealed that the piezomagnetic coefficient $Q$ is $1.38\times {10}^{-8}$ ${\mu }_{\mathrm{B}}$/Mn/MPa at 300 K. The poling-field dependence of magnetization indicates that the antiferromagnetic domain can be controlled using the piezomagnetic effect. We demonstrate that piezomagnetic effect is one of the suitable methods for the detection of broken time-reversal symmetry and the domain control in antiferromagnets with broken time-reversal symmetry, including altermagnets.

Figure 1

(a) Crystal and magnetic structure of MnTe viewed from the $c$ axis. Mn ions (purple) are in the octahedral sites between two close-packed layers of Te (gold). Red arrows represent the magnetic moments of the ${\mathrm{Mn}}^{2+}$ ions. The symmetry operations allowed in the magnetic ordered phase are shown in projection onto the $c$ plane. The indexes of 2 and $m$ indicate twofold rotation and mirror operations. The superscipt of prime (${}^{\prime }$) is time-reversal symmetry operation. The left (right) panel is corresponding to the magnetic point group of $m^{\prime }{m}^{\prime }m$ ($mmm$). (b) Two inequivalent antiferromagnetic domains ($\alpha$ and $\beta$), which are formed below $T_{\mathrm{N}}$. Antiferromagnetic domains $\alpha$ and $\beta$ are mutually transformed by the time-reversal symmetry operation (see text for details). Therefore, the sign of the piezomagnetic tensor ($Q_{ijk}$) is opposite in between, so the application of stress ($\sigma$) produces a net magnetization ($M$) in the opposite direction. $A$ and $B$ represent the closed-packed layers of Te.

Figure 2

Temperature dependence of (a) the $c$-plane electrical resistivity ($\rho$), (b) the magnetization divided by the magnetic field $M/H$, and (c) the strain ($\frac{\mathrm{\Delta }L}{L}$) in the $c$ plane. Inset of (b) represents the magnetization taken at $H$ = 10 Oe in a heating process, after cooling from the paramagnetic phase at $H$ = $10000$ Oe. Inset of (c) is thermal expansion coefficient $[\alpha$ = $\partial \left(\frac{\mathrm{\Delta }L}{L}\right)/\partial T]$.

Figure 3

(a) Temperature dependence of magnetization (M) for polycrystalline MnTe measured under various stresses. Measurements were performed at $H$ = 10 Oe during a heating process, after cooling from 320 K to 250 K at $H$ = 10 Oe. (b) Stress dependence of $\mathrm{\Delta }M$ at 250 and 300 K, where $\mathrm{\Delta }M$ represents the relative change in magnetization from 320 K. The $\mathrm{\Delta }M$ value includes no contributions from the paramagnetic susceptibility.

Figure 4

(a) Poling field ($H_{\mathrm{pol}}$) dependence of magnetization at $\sigma$ = 167 MPa and $H_{\mathrm{meas}}$ = 10 Oe. After cooling from 330 to 250 K at $\sigma$ = 167 MPa and $H_{\mathrm{meas}}$ = 10 Oe, measurements were performed during a heating process at $H_{\mathrm{meas}}$ = 10 Oe. (b) Poling-field dependence of magnetization at various temperatures.