Magnetotransport in ${\mathrm{Sr}}_3\mathrm{PbO}$ antiperovskite

Novel topological phenomena are anticipated for three-dimensional (3D) Dirac electrons. The magnetotransport properties of cubic ${\mathrm{Sr}}_3\mathrm{PbO}$ antiperovskite, theoretically proposed to be a 3D massive Dirac electron system, are studied. The measurements of Shubnikov–de Haas oscillations and Hall resistivity indicate the presence of a low density ($\sim 1\times {10}^{18}{\mathrm{cm}}^{-3}$) of holes with an extremely small cyclotron mass of $0.01–0.06m_e$. The magnetoresistance $\mathrm{\Delta }{\rho }_{xx}\left(B\right)$ is linear in magnetic field $B$ with the magnitude independent of temperature. These results are fully consistent with the presence of 3D massive Dirac electrons in ${\mathrm{Sr}}_3\mathrm{PbO}$. The chemical flexibility of the antiperovskites and our findings in the family member ${\mathrm{Sr}}_3\mathrm{PbO}$ point to their potential as a model system in which to explore exotic topological phases.

Figure 1

Crystal structure, Fermi surface, and transport properties of ${\mathrm{Sr}}_3\mathrm{PbO}$ antiperovskite. (a) Cubic antiperovskite structure of ${\mathrm{Sr}}_3\mathrm{PbO}$. The positions of metal elements and O are swapped as compared to those of normal cubic perovskite oxides. O is at the center of the ${\mathrm{Sr}}_6$ octahedron. Pb fills the space between the ${\mathrm{OSr}}_6$ octahedra. (b) The first Brillouin zone of antiperovskite and the anisotropic Fermi surface on the (100) axis. Dirac points are located at $(\pm k_c,0,0)$, $(0,\pm k_c,0)$, and $(0,0,\pm k_c)$ on the $\mathrm{\Gamma }\mathrm{-}\mathrm{X}$ lines which are ${\mathrm{C}}_4$ rotational axes in $k$ space. (c) Temperature dependence of resistivity ${\rho }_{xx}\left(T\right)$ of ${\mathrm{Sr}}_3\mathrm{PbO}$ single crystal from 2 to 300 K. A metallic behavior is observed. The inset shows the Hall coefficient $R_H$ in the limit of zero magnetic field, which is temperature independent.

Figure 2

Hall resistivity ${\rho }_{xy}\left(B\right)$ of antiperovskite ${\mathrm{Sr}}_3\mathrm{PbO}$ single crystal. (a) Magnetic field ($B$) dependence of Hall resistivity ${\rho }_{xy}\left(B\right)$ is nonlinear in $B$ and not strongly $T$ dependent at least up to 200 K. Positive and $T$-independent $R_H=+3.8{\mathrm{cm}}^3/\mathrm{C}$ is observed in the zero field limit, yielding a hole density of $1.6\times {10}^{18}{\mathrm{cm}}^{-3}$. (b) The nonlinear behavior of ${\rho }_{xy}\left(B\right)$ is better recognized in the derivative of Hall resistivity $d{\rho }_{xy}/dB$. A crossover from low-field $T$-independent to high-field $T$-independent behavior can be seen in the inset.

Figure 3

Magnetoresistance and its crossover of ${\mathrm{Sr}}_3\mathrm{PbO}$. (a) Magnetic field ($B$) dependence of $\mathrm{\Delta }{\rho }_{xx}\left(B\right)={\rho }_{xx}\left(B\right)-{\rho }_{xx}\left(0\right)$ and magnetoresistance ratio $\mathrm{\Delta }{\rho }_{xx}\left(B\right)/{\rho }_{xx}\left(0\right)$. At $T=2$ K, a large magnetoresistance ratio over 10 at $B=14$ T is observed as seen in the inset. A $B$-linear behavior is observed at high fields. The $B$-linear contribution of $\mathrm{\Delta }{\rho }_{xx}\left(B\right)$ is $T$ independent up to 200 K at high fields. (b) $T$-independent and $B$-linear behavior of $\mathrm{\Delta }{\rho }_{xx}\left(B\right)$ is better recognized in $T$-independent and constant derivative of resistivity $d{\rho }_{xx}/dB$ at high fields. SdH oscillations are clearly observed above 1 T. A crossover from $B^2$ behavior to $B$-linear behavior in $\mathrm{\Delta }{\rho }_{xx}\left(B\right)$ is emphasized in the inset. (c) The crossover fields $B_c$ defined by the peak in $d{\rho }_{xx}/dB$ denoted by the black arrow in Fig. 3 (circle) and by the dip in $d{\rho }_{xy}/dB$ denoted by the black arrow in Fig. 2 (square) seem to be scaled with ${\rho }_{xx}\left(T\right)$ (line).

Figure 4

SdH oscillations of ${\mathrm{Sr}}_3\mathrm{PbO}$. (a) SdH oscillations are derived from ${\rho }_{xx}^{\mathrm{Osc}}\left(B\right)$ obtained by numerically subtracting a polynomial background from ${\rho }_{xx}\left(B\right)$. Two sets of oscillations are observed with frequencies of 5 and 32 T. The oscillations with a frequency of 32 T above 6 T are emphasized in the inset. (b) Landau fan diagram of oscillations with frequencies of 5 and 32 T at 2 K to extract the phase offsets. Both peaks (closed symbols) and dips (open symbols) of SdH oscillations are plotted. Extrema of SdH oscillations and their errors were determined by Gaussian fitting of SdH oscillation peaks. The linear fits to the 5-T oscillations for $n\ge 1.5$ and to the 32-T oscillations for $n\ge 2.5$ yield $\beta =0.76\pm 0.16$ and $\beta =0.44\pm 0.26$, respectively. The inset shows the Lifshitz-Kosevitch fitting to derive the cyclotron effective mass $m_c^{*}$. The oscillation amplitudes at 0.64 ${\mathrm{T}}^{-1}$ [black arrow in panel (a)] and 0.11 ${\mathrm{T}}^{-1}$ [black arrow in the inset to panel (a)] are plotted as a function of temperature, representing 5- and 32-T oscillations. The extracted $m_c^{*}$ for 0.64 ${\mathrm{T}}^{-1}$ and 0.11 ${\mathrm{T}}^{-1}$ are extremely light values of $0.011m_e$ and $0.057m_e$, respectively.