Large anomalous Hall effect in the kagome ferromagnet ${\mathrm{LiMn}}_6{\mathrm{Sn}}_6$

Kagome magnets are believed to have numerous exotic physical properties due to the possible interplay between lattice geometry, electron correlation and band topology. Here, we report the large anomalous Hall effect in the kagome ferromagnet ${\mathrm{LiMn}}_6{\mathrm{Sn}}_6$, which has a Curie temperature of 382 K and easy plane along with the kagome lattice. At low temperatures, unsaturated positive magnetoresistance and opposite signs of ordinary Hall coefficient for ${\rho }_{xz}$ and ${\rho }_{yx}$ indicate the coexistence of electrons and holes in the system. A large intrinsic anomalous Hall conductivity of $380{\mathrm{\Omega }}^{-1}{\mathrm{cm}}^{-1}$, or $0.44e^2/h$ per Mn layer, is observed in ${\sigma }_{xy}^A$. This value is significantly larger than those in other $R{\mathrm{Mn}}_6{\mathrm{Sn}}_6$ ($R$ = rare earth elements) kagome compounds. Band structure calculations show several band crossings, including a spin-polarized Dirac point at the K point, close to the Fermi energy. The calculated intrinsic Hall conductivity agrees well with the experimental value, and shows a maximum peak near the Fermi energy. We attribute the large anomalous Hall effect in ${\mathrm{LiMn}}_6{\mathrm{Sn}}_6$ to the band crossings closely located near the Fermi energy.

Figure 1

(a) Crystal structure of ${\mathrm{LiMn}}_6{\mathrm{Sn}}_6$. (b) XRD pattern of a ${\mathrm{LiMn}}_6{\mathrm{Sn}}_6$ single crystal with $\left(00l\right)$ reflections. (c) Temperature dependence of resistivity with current along $a$ axis. The inset illustrates the definition of a Cartesian coordinate system based on the hexagonal lattice. (d) Temperature dependence of the magnetization under magnetic field of $H=100$ Oe lying in and perpendicular to the $ab$ plane. The inset shows the derivative of the magnetization $dM/dT$ vs $T$ for $H\parallel y$. (e) The isothermal magnetization at $T=2\mathrm{K}$ for $H\parallel y$ and $H\parallel z$.

Figure 2

(a), (b) Magnetic field dependence of magnetoresistance at various temperatures measured with $H\parallel y$ and $H\parallel z$, respectively. The insets show the corresponding measurement geometries. (c), (d) Magnetic field dependence of Hall resistivity at various temperatures with the same measurement geometries with (a) and (b), respectively.

Figure 3

(a), (b) Anomalous part of the Hall conductivity ${\sigma }_{zx}^A$ and ${\sigma }_{xy}^A$ as the function of magnetic field at various temperatures measured with $H\parallel y$ and $H\parallel z$, respectively. (c), (d) The anomalous Hall conductivity ${\sigma }_{zx}^A$ and ${\sigma }_{xy}^A$ versus ${\sigma }_{xx}^2$ with fitting lines, respectively.

Figure 4

(a) The band structure of ${\mathrm{LiMn}}_6{\mathrm{Sn}}_6$ without SOC. The spin-up bands appear in blue lines, and the spin-down bands appear in green lines. (b) Energy dependence of the intrinsic AHC ${\sigma }_{xy}^{\mathrm{int}}$, with the $E_{\mathrm{F}}$ of ${\mathrm{LiMn}}_6{\mathrm{Sn}}_6$ is 0. The upper dashed line denotes the lifted $E_{\mathrm{F}}$ with extra two electrons per formula unit. (c) Spin-resolved total and orbital-projected densities of states in the vicinity of $E_{\mathrm{F}}$.