Origin of pressure-induced anomalies in the nodal-line ferrimagnet Mn$_3$Si$_2$Te$_6$

Abstract

A pressure-induced insulator-to-metal transition (IMT) has recently been discovered in the nodal-line ferrimagnet Mn$_3$Si$_2$Te$_6$. The electronic phase transition is accompanied by anomalies in the magnetic ordering temperature and the anomalous Hall conductivity, which peak at or near the critical pressure of the IMT. We perform density functional theory (DFT) calculations as a function of pressure to establish the connection between the IMT and the magnetic anomalies in Mn$_3$Si$_2$Te$_6$. We extract Heisenberg Hamiltonians as a function of pressure based on our DFT calculations. Our classical Monte Carlo simulations for these Hamiltonians yield ordering temperatures and magnetic ordering patterns, in agreement with the experimental data. Although we can accurately explain the evolution of magnetism with pressure, it seems that the anomalous Hall conductivity in Mn$_3$Si$_2$Te$_6$ can only be accounted for by extrinsic contributions or moderate electron doping of the samples in the experiment.

Figures (5)

• Figure 1: Electronic structure and total Berry curvature of Mn3Si2Te6 in the ferrimagnetic ground state as a function of pressure and spin quantization axis. (a,c) show the total Berry curvature $\Omega_x$ and $\Omega_z$ (in units of squared Bohr radii $a_0^2$) and (b,d) show the electronic band structure with orbital weights on a high-symmetry path through the Brillouin zone for spin quantization axis parallel to the $a$ direction at a pressure of 16 and 23 GPa, respectively. (e) and (f) show cuts of the total Berry curvature $\Omega_z$ in the $k_x$-$k_y$ plane at $k_z=0$ for the same pressures and the same orientation of spin quantization axis. The colour scale is cut off at a value of $\pm 60$. The grey shaded area represents the Fermi surface. (g-l) show the electronic structure and total Berry curvature for spin quantization axis parallel to the $c$ direction and all other parameters equal to (a-f).
• Figure 2: Anomalous Hall conductivity of Mn3Si2Te6 in the ferrimagnetic ground state as a function of pressure and spin quantization axis. (a) and (b) show the intrinsic contribution to the anomalous Hall conductivity in the $xy$, $xz$ and $yz$ planes as a function of pressure calculated from relativistic DFT calculations (i.e. including spin-orbital coupling) in the ferrimagnetic state with spin quantization axis parallel to the $a$ direction (easy axis) and the $c$ direction (hard axis), respectively. (c) shows the calculated AHC in the $xy$ plane with shifted chemical potential $\mu$, which simulates charge doping of Mn3Si2Te6, in comparison to the experimental data from Ref. Susilo2024.
• Figure 3: DFT energy mapping and exchange pathways for Mn3Si2Te6. (a) DFT calculated exchange parameters for Mn3Si2Te6 at ambient pressure as a function of the on-site Coulomb repulsion $U$. The dashed line denotes the value of on-site Coulomb repulsion $U=4.2$ eV, which we choose for the remainder of our study. For this interaction strength, we obtain $\Theta_\mathrm{CW} = -247$ K as the mean-field Curie-Weiss temperature and $T_\mathrm{C} = 65$ K as the ordering temperature in classical Monte Carlo, which both agree well with experimental values. (b) Relevant exchange paths in Mn3Si2Te6, shown for the high symmetry, trigonal $P\bar{3}1c$ space group. (c) Charge gap of the ferrimagnetic ground state and average charge gap of all magnetic configurations included in the DFT energy mapping as a function of pressure. In the high-pressure phase, the charge gap is zero. (d) Relevant exchange paths in Mn3Si2Te6, shown for the low symmetry, monoclinic $C2/c$ space group. (e) Antiferromagnetic intra-trimer (nearest neighbour) exchange coupling $J_1$ as a function of pressure. (f) Next-nearest neighbour and longer range exchange couplings between Mn atoms as a function of pressure. The interaction parameters are $U=4.2$ eV and $J_{\rm H}=0.76$ eV.
• Figure 4: Single-ion and nearest-neighbour exchange anisotropies of Mn3Si2Te6 from the DFT energy mapping as a function of pressure. All data points were calculated with $U = 4.2$ eV. Labels $C2/c$ and $P\bar{3}1c$ denote the crystal symmetries on both sides of the phase transition. (a) shows the raw energy differences per Mn atom (also divided by the square of the spin $S=5/2$) for the ferromagnetic state with three possible spin quantization axes and as a function of pressure. (b) shows the raw energy differences per Mn atom (also divided by the square of the spin $S=5/2$) for the ferrimagnetic ground state and compares these energy differences to the experimentally determined $c$ axis spin-flop fields from Ref. Susilo2024. (c) shows the anisotropic single-ion ($K^y$ and $K^z$) and nearest-neighbour exchange ($J_1^{yy}$ and $J_1^{zz}$) parameters as a function of pressure determined from raw energy differences.
• Figure 5: Predicted ferrimagnetic ordering temperatures for Mn3Si2Te6 as a function of pressure. Theoretical values are shown in blue, while experimental data from Ref. Susilo2024 are shown in yellow, orange and green symbols for comparison. The theoretical prediction is based on the isotropic Hamiltonian determined from the DFT energy mapping, which we use to simulate magnetic configurations in classical Monte Carlo.