Pressure effect on the anomalous Hall effect of ferromagnetic Weyl semimetal $\mathrm{C}{\mathrm{o}}_3\mathrm{S}{\mathrm{n}}_2{\mathrm{S}}_2$

The magnetic Weyl semimetal $\mathrm{C}{\mathrm{o}}_3\mathrm{S}{\mathrm{n}}_2{\mathrm{S}}_2$ exhibits large anomalous Hall effect (AHE) due to its nontrivial band topology with enhanced Berry curvature. Here we investigate the pressure effect on the AHE of $\mathrm{C}{\mathrm{o}}_3\mathrm{S}{\mathrm{n}}_2{\mathrm{S}}_2$ up to 12 GPa with a palm cubic anvil cell apparatus and first-principles calculations simulation. We find that both the ferromagnetic transition temperature and the AHE are suppressed monotonically upon the application of high pressure. Data analyses revealed that in the investigated pressure range the intrinsic mechanism due to Berry curvature dominates the AHE as reflected by the validation of ${\rho }_{xy}^A\propto {\rho }_{xx}^2$. However, both the anomalous Hall conductivity and anomalous Hall angle are reduced gradually into the regime for conventional ferromagnetic metals with trivial band topology. Combined with theoretical calculations, our results indicate that the distance between Weyl points with opposite chirality in $\mathrm{C}{\mathrm{o}}_3\mathrm{S}{\mathrm{n}}_2{\mathrm{S}}_2$ is substantially reduced accompanying the suppression of ferromagnetism by pressure, thus providing an experimental route to tune the AHE of magnetic Weyl semimetals via modifying the nontrivial band topology.

Figure 1

(a) Temperature dependence of zero-field resistivity ρ($T$) of $\mathrm{C}{\mathrm{o}}_3\mathrm{S}{\mathrm{n}}_2{\mathrm{S}}_2$ under various pressures up to 12 GPa. (b) Pressure dependence of the ferromagnetic transition temperature $T_{\mathrm{C}}$ of $\mathrm{C}{\mathrm{o}}_3\mathrm{S}{\mathrm{n}}_2{\mathrm{S}}_2$. The PM and FM represent for paramagnetism and ferromagnetism.

Figure 2

Field dependence of Hall resistivity ${\rho }_{xy}\left(H\right)$ of $\mathrm{C}{\mathrm{o}}_3\mathrm{S}{\mathrm{n}}_2{\mathrm{S}}_2$ at various temperatures and pressures up to 12 GPa for $H$ // $c$ axis, respectively.

Figure 3

Anomalous Hall effect of $\mathrm{C}{\mathrm{o}}_3\mathrm{S}{\mathrm{n}}_2{\mathrm{S}}_2$ under various pressures up to 12 GPa. (a) Temperature dependence of the anomalous Hall resistivity ${{\rho }_{xy}}^{\mathrm{A}}$. (b) $ln{{\rho }_{xy}}^{\mathrm{A}}$ as a function of $ln{\rho }_{\mathrm{xx}}$. The solid lines are the linear fitting curves to get the coefficient α from ${{\rho }_{xy}}^{\mathrm{A}}\propto {{\rho }^{\alpha }}_{xx}$. (c) Temperature dependence of the anomalous Hall conductivity ${{\sigma }_{xy}}^{\mathrm{A}}$ at zero magnetic field. (d) ${{\sigma }_{xy}}^{\mathrm{A}}$ as a function of the conductivity ${\sigma }_{xx}$.

Figure 4

(a) Temperature dependences of the anomalous Hall angle ${{\sigma }_{xy}}^{\mathrm{A}}/{\sigma }_{xx}$, the charge conductivity ${\sigma }_{xx}$ and the anomalous Hall conductivity ${{\sigma }_{xy}}^{\mathrm{A}}$ of $\mathrm{C}{\mathrm{o}}_3\mathrm{S}{\mathrm{n}}_2{\mathrm{S}}_2$ at 2 GPa. (b) Pressure dependences of anomalous Hall angle ${{\sigma }_{xy}}^{\mathrm{A}}/{\sigma }_{xx}$ and the peak temperature where the anomalous Hall angle reaches the maximum. (c) Comparison of our results and previously reported data on anomalous Hall angle ${{\sigma }_{xy}}^{\mathrm{A}}/{\sigma }_{xx}$ as a function of anomalous Hall conductivity ${{\sigma }_{xy}}^{\mathrm{A}}$. Lable (f) represents thin-film materials. The black and red dashed lines are guided to eyes.

Figure 5

The calculated band structures of $\mathrm{C}{\mathrm{o}}_3\mathrm{S}{\mathrm{n}}_2{\mathrm{S}}_2$ with SOC at (a) ambient pressure, (b) 12 GPa with fixed magnetic moments (fixed $M$) and (c) fixed lattice constants (fixed lattice). (d) The pressure dependent magnetic moments from experiments (Ref. [36]), fixed-$M$ calculations, and fixed-lattice calculations. (e) The pressure dependent intrinsic AHC from experiments, fixed-$M$ and fixed-lattice calculations. (f) The pressure dependent intrinsic AHC from experiments and from estimations based on the calculated WPs distances in the fixed-$M$ and fixed-lattice calculations.