Pressure-tunable large anomalous Hall effect of the ferromagnetic kagome-lattice Weyl semimetal ${\mathrm{Co}}_3{\mathrm{Sn}}_2{\mathrm{S}}_2$

We report a systematic high-pressure study of magnetic topological semimetal ${\mathrm{Co}}_3{\mathrm{Sn}}_2{\mathrm{S}}_2$ through measurements of synchrotron x-ray diffraction (XRD), magnetization, electrical, and Hall transports combined with first-principle theoretical calculations. No evident trace of structural phase transition is detected through synchrotron x-ray diffraction over the measured pressure range of 0.2–50.9 GPa. We find that the ferromagnetism and the anomalous Hall resistivity are monotonically suppressed as increasing pressure and almost vanish around 22 GPa. The anomalous Hall conductivity varies nonmonotonically against pressure at low temperatures, involving competition between original and emergent Weyl nodes. Combined with first-principle calculations, we reveal that the intrinsic mechanism due to the Berry curvature dominates the anomalous Hall effect under high pressure.

Figure 1

(a) Synchrotron XRD patterns of ${\mathrm{Co}}_3{\mathrm{Sn}}_2{\mathrm{S}}_2$ at various pressures up to 50.9 GPa ($\lambda =0.6199\AA$). (b) and (c) Fits of the XRD patterns at 0.2 and 50.9 GPa. (d) and (e) Evolutions of lattice parameters versus pressure. (f) Ratio of lattice parameters $c/a$ as a function of pressure. The red line is a linear fit to the data. (g) The unit-cell volume versus pressure. The data (black circle) is fitted by the third-order Birch-Murnaghan formula (red line).

Figure 2

(a) Temperature dependence of magnetization $M$ under different pressures to 7.2 GPa with an applied magnetic field of 100 Oe. (b) Temperature dependence of electric resistivity ${\rho }_{xx}$ at selected pressures up to 44.9 GPa.

Figure 3

(a)–(g) Magnetic field dependence of the Hall resistivity ${\rho }_H$ at various temperatures and selected pressures. (h) Temperature dependence of the coercive field $H_C$ at different pressures.

Figure 4

(a) Temperature dependence of the anomalous Hall resistivity ${\rho }_{xy}^A$ under different pressures. Inset shows an enlarged view of ${\rho }_{xy}^A-T$ from 7.1 to 17.6 GPa. (b) Temperature dependence of the AHC ${\sigma }_{xy}^A$ under different pressures. (c) Plot of AHC ${\sigma }_{xy}^A$ as a function of ${\sigma }_{xx}$. (d) Anomalous Hall resistivity ${\rho }_{xy}^A$ as a function of ${\rho }_{xx}^2$. Only data below $T_{\text{max}}$ is taken. (e) Temperature versus pressure phase diagram for ${\mathrm{Co}}_3{\mathrm{Sn}}_2{\mathrm{S}}_2$. PM and FM stand for paramagnetic and ferromagnetic phases, respectively. $\mathrm{FM}+\mathrm{AFM}$ refers to a mixture of ferromagnetic and antiferromagnetic phases as speculated by Guguchia et al. $P_C$, obtained by linear extrapolations of the low-pressure data, denotes a critical pressure where the ferromagnetism and AHE vanish completely.

Figure 5

(a) and (b) Electronic band structures at zero pressure and a high pressure of 18.13 GPa. (c) Doping electron number per unit cell ($N_e$) dependent intrinsic AHC at selected pressures, where $N_e=0$ refers to the case without doping ($E_F=0)$. Insert in (c) plots the pressure dependent AHC at $N_e=1.03$ (vertical dashed line in the main figure). (d)–(f) Evolution of Weyl nodes labeled by red and blue dots near the Fermi level at selected pressures, where ${\mathrm{\Delta }}_d^{\text{red}}$ (${\mathrm{\Delta }}_d^{\text{blue}}$) represents the length of the vector connecting the red (blue) Weyl nodes and ${\mathrm{\Delta }}_d^{\text{eff}}={\mathrm{\Delta }}_d^{\text{red}}-{\mathrm{\Delta }}_d^{\text{blue}}$ means the effective Weyl nodes distance. $\pm$ refers to the chirality of each Weyl point.

Figure 6

(a) Powdered and (b) single crystal XRD at room temperature. Le Bail method was used to fit the powdered XRD pattern with the RIETICA program. The refinement results are $a=5.370703\AA$, $c=13.183318\AA$, $V=329.32{\AA }^3$, $R_{wp}=0.0620$, $R_p=0.0548$, and ${\chi }^2=16.47$. (c) Temperature dependence of magnetization for single crystal ${\mathrm{Co}}_3{\mathrm{Sn}}_2{\mathrm{S}}_2$ under field-cooled (FC) and zero-field-cooled (ZFC) sequences at $c$-axis magnetic field of 100 Oe. (d) Magnetic field dependence of magnetization $M$ at 50 K with the field parallel to the $c$ axis. (e) Longitudinal resistivity ${\rho }_{xx}$ versus $T$. The arrow indicates a kink at the Curie temperature $T_C$ corresponding to a paramagnetic-to-ferromagnetic transition. (f) Hall resistivity ${\rho }_H$ versus ${\mu }_{0}H$ measured at 35 K with the field parallel to the $c$ axis.

Figure 7

Magnetic field dependence of the ordinary Hall resistivity near or above $T_C$.

Figure 8

Band structures of ${\mathrm{Co}}_3{\mathrm{Sn}}_2{\mathrm{S}}_2$ along the W-U-L-G-T path at various pressures obtained from first-principle calculations.

Figure 9

Distributions of the Berry curvature ${\mathrm{\Omega }}_{xy}\left(k\right)$ at the $k_x\text{−}{k}_y$ plane ($k_z=0)$ in the Brillouin zone for ${\mathrm{Co}}_3{\mathrm{Sn}}_2{\mathrm{S}}_2$ at various pressures.