Ferromagnetism and spin-dependent transport in $n$-type Mn-doped bismuth telluride thin films

We describe a detailed study of the structural, magnetic, and magnetotransport properties of single-crystal, $n$-type, Mn-doped bismuth telluride thin films grown by molecular beam epitaxy. With increasing Mn concentration, the crystal structure changes from the tetradymite structure of the ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ parent crystal at low Mn concentrations towards a BiTe phase in the (${\mathrm{Bi}}_2{\mathrm{Te}}_3{)}_m({\mathrm{Bi}}_2{)}_n$ homologous series. Magnetization measurements reveal the onset of ferromagnetism with a Curie temperature in the range 13.8–17 K in films with $\sim$2%$-$$\sim$10% Mn concentration. Magnetization hysteresis loops reveal that the magnetic easy axis is along the $c$ axis of the crystal (perpendicular to the plane). Polarized neutron reflectivity measurements of a 68-nm-thick sample show that the magnetization is uniform through the film. The presence of ferromagnetism is also manifest in a strong anomalous Hall effect and a hysteretic magnetoresistance arising from domain-wall scattering. Ordinary Hall effect measurements show that the carrier density is $n$ type, increases with Mn doping, and is high enough ($\ge 2.8\times {10}^{13}$ cm${}^{-2}$) to place the chemical potential in the conduction band. Thus the observed ferromagnetism is likely associated with both bulk and surface states. Surprisingly, the Curie temperature does not show any clear dependence on the carrier density but does increase with Mn concentration. Our results suggest that the ferromagnetism probed in these Mn-doped bismuth telluride films is not mediated by carriers in the conduction band or in an impurity band.

Figure 1

(a) XRD of undoped (S1) and Mn-doped bismuth telluride thin films (S3, S4, and S5). (003) and (006) peaks of Bi${}_2$Te${}_3$ shift in opposite directions (black arrows) with increasing Mn concentration, while the (111) peak of InP does not change with Mn doping. Curves are offset for clarity. (b) A HAADF-STEM image of a Mn-doped bismuth telluride thin film on an InP(111)A substrate with 5% Mn concentration (S4). Dotted yellow lines indicate QLs and unit layers composed of a Bi bilayer sandwiched between two QLs. The atomic crystal structures of (c) a QL-Bi${}_2$-QL unit layer and (d) two Bi${}_2$Te${}_3$QLs, with Bi partially substituted by Mn.

Figure 2

SQUID magnetometry. (a) Temperature dependence of magnetization with perpendicular-to-the-plane magnetic field for Mn-doped bismuth telluride thin films with 2% (S3), 5% (S4), and 10% (S5) Mn concentration. Inset plots $T_{\mathrm{C}}$ as a function of Mn concentration. (b) Magnetic field sweep of magnetization with perpendicular-to-the-plane magnetic field for a Mn-doped bismuth telluride thin film with 2% Mn concentration (S3). Inset shows magnetization with in-plane magnetic field sweep for S3 at 5 K (red), 10 K (green), and 25 K (blue). Note that the background magnetization of the InP substrate has been subtracted in (b), but not in the inset due to the negligible contribution of in-plane background. Error bars in (a) and (b) represent standard deviations for magnetization over multiple measurements.

Figure 3

PNR magnetometry measured with an in-plane 8-kOe magnetic field. Reflectivity curves and fits (solid lines) for up ($++$) and down ($--$) spin neutrons are plotted on a normalized Fresnel scale at (a) 5 K, (b) 20 K, and (c) 45 K. (d) Spin asymmetry and fit at 5 K. The error bars represent an uncertainly of +/− standard deviation. (e) Structural and magnetic scattering length densities from the 5-K fits for each layer of the sample. The magnetization, proportional to ${\rho }_M$ (green curve), is uniform across the Mn-doped bismuth telluride layer. (f) Fits to spin asymmetry show a small but measurable magnetization persisting to 45 K, well above the $T_{\mathrm{C}}$ measured by SQUID magnetometry.

Figure 4

Hall and longitudinal conductivity obtained from magnetotransport measurements. A schematic of the measurement setup and a photo image of a Hall bar are shown in (d) and (e), respectively. Panels (a)–(c) show the temperature dependence of the Hall conductivity ${\sigma }_{xy}$ for Mn-doped bismuth telluride films with 2% Mn (S3), 5% Mn (S4), and 10% (S5) Mn concentration. (f) Anomalous Hall conductivity ${\sigma }_{xy}^H$ at 0.5 K for various Mn concentrations (S3, S4, and S5). (g) Temperature dependence of ${\sigma }_{xy}$ at zero magnetic field with different Mn concentrations (S3: red circles, S4: green squares, and S5: blue triangles). The inset plots $T_{\mathrm{C}}$ as a function of the Mn concentration. Black solid line is a linear fit. (h) Temperature dependence of longitudinal MC $\Delta {\sigma }_{xx}$ from sample S3. Ferromagnetic hysteresis is shown below 4 K. (i) Longitudinal conductivity $\Delta {\sigma }_{xx}$ (red) and Hall conductivity ${\sigma }_{xy}$ (black) at 0.5 K.

Figure 5

Angular dependence of Hall conductivity and longitudinal conductivity of a Mn-doped bismuth telluride thin film with 2% Mn concentration (S3) at 0.3 K. A schematic of a channel with Cartesian coordinate and the corresponding crystal directions is shown in (a) inset. (a) Transverse conductivity ${\sigma }_{xy}$ and (b) longitudinal MC $\Delta {\sigma }_{xx}$ with polar angles of the magnetic field from $\theta =0^{\circ }$ (perpendicular to the plane) to $\theta ={90}^{\circ }$ (in-plane along channel direction). Solid (dashed) curves are up sweeps (down sweeps). (c) Longitudinal MC $\Delta {\sigma }_{xx}$ with an in-plane magnetic field from $\varphi =0^{\circ }$ (along current direction) to $\varphi ={90}^{\circ }$ (perpendicular to the current direction). Offset for clarity.

Figure 6

Ferromagnetic signatures of AMR in the Mn-doped bismuth telluride film with 2% Mn concentration (S3). Normalized resistivity ${\rho }_{xx}/{\rho }_{\mathrm{avg}}$ at a fixed magnetic field (0.5 kOe) (a) with azimuthal angle $\varphi$ in the $xy$ plane and (b) with polar angle $\theta$ in the $zx$ plane at different temperatures. In (a), solid lines are fits by Eq. (1).