Realization of interlayer ferromagnetic interaction in $\mathrm{MnS}{\mathrm{b}}_2\mathrm{T}{\mathrm{e}}_4$ toward the magnetic Weyl semimetal state

Magnetic properties of $\mathrm{MnS}{\mathrm{b}}_2\mathrm{T}{\mathrm{e}}_4$ were examined through magnetic susceptibility, specific-heat, and neutron-diffraction measurements. As opposed to isostructural $\mathrm{MnB}{\mathrm{i}}_2\mathrm{T}{\mathrm{e}}_4$ with the antiferromagnetic ground state, $\mathrm{MnS}{\mathrm{b}}_2\mathrm{T}{\mathrm{e}}_4$ develops a spontaneous magnetization below 25 K. From our first-principles calculations on the material in a ferromagnetic state, the state could be interpreted as a type-II Weyl semimetal state with broken time-reversal symmetry. Detailed structural refinements using x-ray-diffraction and neutron-diffraction data reveal the presence of site mixing between Mn and Sb sites, leading to the ferrimagnetic ground state. With theoretical calculations, we found that the presence of site mixing plays an important role for the interlayer Mn-Mn ferromagnetic interactions.

Figure 1

(a) Crystal structure of $\mathrm{MnS}{\mathrm{b}}_2\mathrm{T}{\mathrm{e}}_4$. Pink, orange, and dark blue spheres represent Mn, Sb, and Te, respectively. Note that there are several antisite disorders between Sb and Mn sites. (b) Observed and calculated XRD patterns of $\mathrm{MnS}{\mathrm{b}}_2\mathrm{T}{\mathrm{e}}_4$. Red crosses and green and blue lines represent observed, calculated, and difference profiles. Green ticks are used to show the positions of the Bragg peaks.

Figure 2

(a) Left: Temperature dependence of magnetic susceptibility under an applied field of 0.1 T with zero-field cooling (red) and field cooling (blue) process. Right: Temperature dependence of inverse susceptibility. (b) Isothermal magnetization curves at 5 K (red) and 100 K (blue). The inset shows a hysteresis loop. (c) $M^2$ vs $H/M$ (Arrott plot) at various temperatures around $T_{\mathrm{C}}$.

Figure 3

(a) Temperature dependence of the specific heat divided by temperature. (b) Left: The magnetic part of the specific heat divided by temperature. Right: The magnetic entropy. The horizontal line indicates $Rln6$. (c) The magnetic part of the specific heat in full logarithmic scale.

Figure 4

Calculated band structures for $\mathrm{MnS}{\mathrm{b}}_2\mathrm{T}{\mathrm{e}}_4$ (a) without and (b) with SOC. In (a), the red (blue) color represents up-spin (down-spin) bands.

Figure 5

PND patterns of $\mathrm{MnS}{\mathrm{b}}_2\mathrm{T}{\mathrm{e}}_4$ at (a) 5 K and (b) 50 K. Red crosses and green and blue lines represent observed, calculated, and difference profiles. Green ticks are used to show the positions of the Bragg peaks. (c) Proposed magnetic structure obtained from 5-K data.