Ferromagnetic phase transition in topological crystalline insulator thin films: Interplay of anomalous Hall angle and magnetic anisotropy

In magnetic topological phases of matter, the quantum anomalous Hall (QAH) effect is an emergent phenomenon driven by ferromagnetic doping, magnetic proximity effects, and strain engineering. The realization of QAH states with multiple dissipationless edge and surface conduction channels defined by a Chern number $\mathcal{C}\ge 1$ was foreseen for the ferromagnetically ordered SnTe class of topological crystalline insulators (TCIs). From magnetotransport measurements on ${\mathrm{Sn}}_{1-x}{\mathrm{Mn}}_x\mathrm{Te}(0.00\le x\le 0.08)$ (111) epitaxial thin films grown by molecular beam epitaxy on ${\mathrm{BaF}}_2$ substrates, hole-mediated ferromagnetism is observed in samples with $x\ge 0.06$ and the highest $T_{\mathrm{c}}\sim 7.5\mathrm{K}$ is inferred from an anomalous Hall behavior in ${\mathrm{Sn}}_{0.92}{\mathrm{Mn}}_{0.08}\mathrm{Te}$. The sizable anomalous Hall angle $\sim 0.3$ obtained for ${\mathrm{Sn}}_{0.92}{\mathrm{Mn}}_{0.08}\mathrm{Te}$ is one of the greatest reported for magnetic topological materials. The ferromagnetic ordering with perpendicular magnetic anisotropy, complemented by the inception of the anomalous Hall effect in the ${\mathrm{Sn}}_{1-x}{\mathrm{Mn}}_x\mathrm{Te}$ layers for a thickness commensurate with the decay length of the top and bottom surface states, points at ${\mathrm{Sn}}_{1-x}{\mathrm{Mn}}_x\mathrm{Te}$ as a preferential platform for the realization of QAH states in ferromagnetic TCIs.

Figure 1

(a) Brillouin zone of undoped SnTe (111) grown on a ${\mathrm{BaF}}_2$ substrate with gapless Dirac cones at the TRIM of the BZ. (b) Brillouin zone of the ${\mathrm{Sn}}_{1-x}{\mathrm{Mn}}_x\mathrm{Te}$ with gapped Dirac cones at the TRIM due to a breaking of the $\mathcal{T}$ symmetry. $\mathrm{\Delta }$: Energy gap of the Dirac cone.

Figure 2

Hall bar devices used for the magnetotransport measurements: (a) Sketch; (b) photograph. $V_{\mathrm{xx}}$: Voltage due to longitudinal resistance; $V_{\mathrm{xy}}$: Hall voltage; $I_{\text{ac}}$: applied in-plane current; $H_{\parallel }$: parallel magnetic field and $H_{\perp }$: perpendicular magnetic field. $x-y-z$ defines the geometry of the sample with respect to the applied current and magnetic fields.

Figure 3

(a) ${\rho }_{\text{xx}}$ as a function of $T$ for ${\mathrm{Sn}}_{1-x}{\mathrm{Mn}}_x\mathrm{Te}$ layers. (b) Inverse of residual resistivity ratio as a function of $x$.

Figure 4

(a) Magnetoconductance of SnTe film measured for $H_{\parallel }$ and $H_{\perp }$ geometries at $T=1.8\mathrm{K}$. (b) Magnetoconductance of the ${\mathrm{Sn}}_{1-x}{\mathrm{Mn}}_x\mathrm{Te}$ thin films at $T=1.8\mathrm{K}$. Magnetoconductance as a function of $T$ for ${\mathrm{Sn}}_{1-x}{\mathrm{Mn}}_x\mathrm{Te}$ thin films with (c) $x=0.06$, and (d) $x=0.07$ recorded for the in-plane $H_{\parallel }$ geometry. (e) Magnetic anisotropy of ${\mathrm{Sn}}_{1-x}{\mathrm{Mn}}_x\mathrm{Te}$ at $T=1.8\mathrm{K}$, with $\mathrm{\Delta }\sigma$ measured for ${\mu }_0{H}_{\parallel }$ and ${\mu }_0{H}_{\perp }$.

Figure 5

Kohler plots of (a) SnTe, (b) ${\mathrm{Sn}}_{0.97}{\mathrm{Mn}}_{0.03}\mathrm{Te}$, and (c) ${\mathrm{Sn}}_{0.96}{\mathrm{Mn}}_{0.04}\mathrm{Te}$ epitaxial layers as a function of $T$.

Figure 6

Normalized Hall resistivity of ${\mathrm{Sn}}_{1-x}{\mathrm{Mn}}_x\mathrm{Te}$ at $T=1.8\mathrm{K}$ for (a) $x=0.00$, 0.03, and 0.04. (b) $x=0.06$, 0.07, and 0.08. (c) Normalized Hall resistivity of ${\mathrm{Sn}}_{1-x}{\mathrm{Mn}}_x\mathrm{Te}$ for $x=0.08$ as a function of $T$. (d) Field-cooled and zero-field-cooled ${\rho }_{\mathrm{xy}}$ vs $T$ for $x=0.08$ with ${\mu }_{0}H=0.02\mathrm{T}$. (e) Curie temperature $T_{\mathrm{c}}$, as a function of Mn content in ${\mathrm{Sn}}_{1-x}{\mathrm{Mn}}_x\mathrm{Te}$ samples. (f) Hole concentrations $p_{3\mathrm{D}}$ calculated for the ${\mathrm{Sn}}_{1-x}{\mathrm{Mn}}_x\mathrm{Te}$ samples.

Figure 7

(a) Anomalous Hall angle as a function of T for ${\mathrm{Sn}}_{1-x}{\mathrm{Mn}}_x\mathrm{Te}$ layers with $x=0.06$, 0.07, and 0.08. (b) Magnetic anisotropy of ${\mathrm{Sn}}_{1-x}{\mathrm{Mn}}_x\mathrm{Te}$ thin films with $x=0.06, x=0.07$, and $x=0.08$ recorded at $T=1.8\mathrm{K}$. (c) Magnetic anisotropy parameter ${\nu }_{\mathrm{anis}}$ measured at $T=1.8\mathrm{K}$ and ${\mu }_{0}H=+7\mathrm{T}$.