Quasi-two-dimensional massless Dirac fermions in ${\mathrm{CaMnSb}}_2$

We report a study of the magnetic and magnetotransport properties of layered transition-metal pnictide ${\mathrm{CaMnSb}}_2$. ${\mathrm{CaMnSb}}_2$ is a quasi-two-dimensional system with an orthorhombic crystal structure, containing two distinct layers of a distorted Sb square sheet and an edge-sharing ${\mathrm{MnSb}}_4$ tetrahedron. It was found that ${\mathrm{CaMnSb}}_2$ orders antiferromagnetically below $T_{\mathrm{N}}$ = 302 K and exhibits the expected highly anisotropic magnetic and electrical transport properties. At low temperatures and high fields, we observed quantum oscillations in both magnetization and resistivity, which reveal the multiband Fermi surfaces with very small cross-sectional areas. Nonzero Berry phase, very small cyclotron mass, and high carrier mobility indicate the existence of nearly massless Dirac fermions in ${\mathrm{CaMnSb}}_2$.

Figure 1

(a) The crystal structure of ${\mathrm{CaMnSb}}_2$ with a space group of $Pnma$. (b) Schematic of the distorted Sb square net layer in ${\mathrm{CaMnSb}}_2$, where Sb atoms form zig-zag chains along the $b$ axis. (c) Schematic of the Bi square net layer in ${\mathrm{CaMnBi}}_2$. (d) Single-crystal XRD pattern of ${\mathrm{CaMnSb}}_2$.

Figure 2

Temperature dependence of magnetic susceptibility for the ${\mathrm{CaMnSb}}_2$ single crystal with magnetic field B = 1 T for B$\parallel a$ and B$\parallel bc$ in both zero-field-cooled (ZFC) and field-cooled (FC) mode. The inset shows magnetization M vs magnetic field B for B$\parallel a$ and B$\parallel bc$ at 2 K.

Figure 3

(a) The reciprocal of magnetic field dependence of dHvA oscillations $\mathrm{\Delta }\mathrm{M}$ at various temperatures for B$\parallel a$. The inset shows FFT spectra of dHvA oscillations. (b) Temperature dependence of dHvA oscillation amplitude (Amp.) plotted as Amp./T vs T for two frequencies. The solid line is the fitting results giving cyclotron mass. The values of Amp. and B are determined from the FFT results in the fitting process. (c) The experimental data $\mathrm{\Delta }\mathrm{M}$ and the fitting results (i.e., $\mathrm{\Delta }{\mathrm{M}}_{\alpha }$+$\mathrm{\Delta }{\mathrm{M}}_{\beta }$, $\mathrm{\Delta }{\mathrm{M}}_{\alpha }$, and $\mathrm{\Delta }{\mathrm{M}}_{\beta }$) by two oscillatory frequency components using the Lifshitz-Kosevich formula. The vertical dark cyan dash and blue dotted lines are the peak positions of $\mathrm{\Delta }{\mathrm{M}}_{\alpha }$ and $\mathrm{\Delta }{\mathrm{M}}_{\beta }$, respectively. (d) Landau-level index plots 1/B vs N for two frequencies.

Figure 4

(a) Temperature dependence of in-plane resistivity ${\rho }_{bc}$(T) and out-of-plane resistivity ${\rho }_a$(T). The inset shows temperature dependence of the ${\rho }_a$(T)/${\rho }_{bc}$(T) ratio. (b) Temperature dependence of in-plane resistivity ${\rho }_{bc}$(T) in the field of 0 and 9 T for both B$\parallel a$ and B$\parallel bc$. (c) Magnetic field dependence of magnetoresistance (MR) at 1.8 K for both B$\parallel a$ and B$\parallel bc$. (d) The in-plane resistivity ${\rho }_{bc}$ as a function of the tilt angle $\theta$ at 1.8 K in a magnetic field of 9 T. The red solid line is the fitting curve using $\mid \cos \theta \mid$. The inset shows the configuration of measurement.

Figure 5

(a) The magnetic field dependence of Hall resistivity ${\rho }_{xy}$ at various temperatures from 2 to 305 K. (b) Temperature dependence of carrier density and mobility.