High electron mobility and large magnetoresistance in the half-Heusler semimetal LuPtBi

Materials with high carrier mobility showing large magnetoresistance (MR) have recently received much attention because of potential applications in future high-performance magnetoelectric devices. Here, we report on an electron-hole-compensated half-Heusler semimetal LuPtBi that exhibits an extremely high electron mobility of up to $79000\mathrm{c}{\mathrm{m}}^2/\mathrm{V}\mathrm{s}$ with a nonsaturating positive MR as large as $3200\%$ at 2 K. Remarkably, the mobility at 300 K is found to exceed $10500\mathrm{c}{\mathrm{m}}^2/\mathrm{V}\mathrm{s}$, which is among the highest values reported in three-dimensional bulk materials thus far. The clean Shubnikov–de Haas quantum oscillation observed at low temperatures and the first-principles calculations together indicate that the high electron mobility is due to a rather small effective carrier mass caused by the distinctive band structure of the crystal. Our findings provide a different approach for finding large, high-mobility MR materials by designing an appropriate Fermi surface topology starting from simple electron-hole-compensated semimetals.

Figure 1

(a) The crystal structure of LuPtBi. The blue arrow shows the normal of the natural cleavage plane along the (111) surface. (b) The projected view of the lattice along the [111] direction, displaying Lu, Pt, and Bi stacked layers. (c) Photographs of synthesized single-crystal LuPtBi placed on a millimeter grid. One division represents 1 mm in the diagram; crystals were grown to $1.5\times 1.0\times 0.8\mathrm{m}{\mathrm{m}}^3$, with mirrorlike surfaces and were robust in air. (d) XRD patterns with the x rays along the perpendicular direction of the hexagonal surfaces are presented.

Figure 2

(a) A SEM image of a typical single crystal of LuPtBi after removing excess Bi flux; bottom plane. The color maps are elemental distributions of Lu (blue), Pt (yellow), and Bi (green) acquired by scanning EDX. (b) Observed (red line) powder XRD patterns of crushed LuPtBi single crystals at room temperature show the results of structural refinement (green circles). The pink segments indicate the expected diffraction peaks. LuPtBi reflections are indexed within the MgAgAs-type structure (space group $F\overline{4}3m$, 216) and the refined lattice parameter is $a=6.5861\AA$. The inset shows a structural view of the conventional LuPtBi unit cell, with four formula units.

Figure 3

(a) The schematic for the focused ion beam (FIB) process along the [110] zone axis. (b) Top plane: STEM images at different scales along the [100] stacking axis, where no evidence of Bi thin layers or nanoclusters was observed; Bottom plane: Elemental maps of Lu, Pt, and Bi acquired by scanning EDX, demonstrating the uniform distribution of Lu, Pt, and Bi across the surface. (c) The atomic-resolution STEM image along the [100] stacking axis and selected diffraction patterns from the same plate, confirming the absence of Bi impurities.

Figure 4

(a) Temperature dependence of zero-field resistivity ${\rho }_{xx}$ curves for six representative crystals with various RRRs. (b) MR curves for samples S1, S5, S6, and S12 measured at 2 K.

Figure 5

(a) Temperature dependence of the resistivity $\left({\rho }_{xx}\right)$ of sample S1 at magnetic fields ranging from 0 to 10 T. At 0 T, ${\rho }_{xx}$ exhibits a metallic behavior. The external magnetic field increases the resistivity and changes the temperature-dependent behavior. (b) The magnetic field dependence of ${\rho }_{xx}$ at different temperatures. The MR ratio $\left\{\left[{\rho }_{xx}\left(H\right)-{\rho }_{xx}\left(0\right)\right]/{\rho }_{xx}\left(0\right)\right\}$ increases monotonically with the increase of the external magnetic field, without a saturation up to 10 T. High MR ratios of $3200\%$ and $260\%$ are obtained at 2 and 300 K, respectively. (c) The Kohler plot: the MR ratio as a function of $H/{\rho }_{xx}\left(0\right)$. The solid and dashed lines are the fitted lines with the equations $aH\left[1.5\right]$ and $bH$, respectively. The MR data can be scaled by the equation $aH\left[1.5\right]$ at high temperatures and in the very low-field regime at low temperatures below 50 K but completely deviate from Kohler's rule. At low temperatures and high-field regime, all the MR data collapse onto a single universal curve scaled linearly with $H$.

Figure 6

(a) The magnetic field dependence of Hall resistivity $\left({\rho }_{xy}\right)$ for sample S1 at temperatures ranging from 300 to 2 K. The inset presents the amplification of the region where ${\rho }_{xy}$ is close to zero and clearly exhibits the sign change in ${\rho }_{xy}$. At 300 K, the negative slope of ${\rho }_{xy}$ indicates the predominance of electron carriers under a magnetic field below 2 T. However, the sign changes to a positive value at higher magnetic field, indicating the further importance of hole carriers. (b) The temperature dependence of the Seebeck coefficient $\left(S\right)$ at 0 and 9 T. The inset exhibits the magnetic field dependence of $S$ at 10 and 300 K. At 0 T, the Seebeck coefficient changes sign near 80 K, confirming the two-carrier model. On the other hand, the Seebeck coefficient shows a positive value only under a magnetic field of 9 T. This indicates that the hole carrier dominates at high fields, agreeing well with Hall resistivity results.

Figure 7

(a),(b) Magnetic field dependence of the Hall conductivity ${\sigma }_{xy}$ and the longitudinal conductivity ${\sigma }_{xx}$ for sample S1. The solid curves are the results of calculations using the two-carrier model (see the Supplemental Material [30]). (c) Temperature dependence of the electron concentration $n_e$ and the hole concentration $n_h$ estimated from the conductivity ${\sigma }_{xy}$. (d) Temperature dependence of the electron mobility ${\mu }_e$ and hole mobility ${\mu }_h$ estimated from the conductivity ${\sigma }_{xy}$.

Figure 8

The normalized ${\mu }_H\left(T\right)/{\mu }_H\left(2\mathrm{K}\right)$ of LuPtBi is compared with those of several of the most researched high-mobility systems. Clearly, the mobility of the $\mathrm{SrTi}{\mathrm{O}}_3/\mathrm{LaAl}{\mathrm{O}}_3$ interface (blue) and La-doped $\mathrm{SrTi}{\mathrm{O}}_3$ films (dark cyan) dropped rapidly with increasing temperature, while for semimetal systems, such as the Bi film (orange), Ni-doped CuAgSe (green), and LuPtBi (red), the temperature dependence is weak, preserving relatively high carrier mobility at room temperature. The solid lines are the fitting curves (see text for more details).

Figure 9

(a) Temperature dependence of the SdH oscillations $d^2{\rho }_{xx}/d{H}^2$ as a function of the inverse magnetic field $1/H$. The inset shows the fast Fourier transform (FFT) spectra of SdH oscillations at different temperatures, in which $F_1$ and $F_2$ denote the electron and hole Fermi pockets, respectively. (b) Temperature dependence of the normalized FFT amplitude for the electron and hole Fermi pockets. The red and blue solid lines are the fits with the standard Lifshitz-Kosevich formula, yielding the small effective masses $0.11m_e$ and $0.23m_e$ for the electron and hole Fermi pockets, respectively.

Figure 10

(a) The total density of states (DOS) and local DOS from Lu, Pt, and Bi in the LuPtBi complex. The main peaks of the total DOS are located far from the Fermi level and Lu, Pt, and Bi contribute equally to the total DOS. (b) The calculated band structure of LuPtBi. The black line at $E=0$ shows the Fermi level position. The coexistence of electron and hole pockets agrees well with the two-carrier analysis. (c) The bulk Brillouin zone (left plane) and the Fermi surface of bulk LuPtBi showing electron (middle plane) and hole (right plane) pockets.