Experimental Verification of the Van Vleck Nature of Long-Range Ferromagnetic Order in the Vanadium-Doped Three-Dimensional Topological Insulator ${\mathrm{Sb}}_2{\mathrm{Te}}_3$

We demonstrate by high resolution low temperature electron energy loss spectroscopy (EELS) measurements that the long range ferromagnetic (FM) order in the vanadium- (V-)doped topological insulator ${\mathrm{Sb}}_2{\mathrm{Te}}_3$ has the nature of van Vleck–type ferromagnetism. The positions and the relative amplitudes of two core-level peaks ($L_3$ and $L_2$) of the V EELS spectrum show unambiguous change when the sample is cooled from room temperature to $T=10\mathrm{K}$. Magnetotransport and comparison of the measured and simulated EELS spectra confirm that these changes originate from the onset of FM order. Crystal field analysis indicates that in V-doped ${\mathrm{Sb}}_2{\mathrm{Te}}_3$, partially filled core states contribute to the FM order. Since van Vleck magnetism is a result of summing over all states, this magnetization of core level verifies the van Vleck–type ferromagnetism in a direct manner.

Figure 1

(a) High-resolution image of the V-doped ${\mathrm{Sb}}_2{\mathrm{Te}}_3$ sample S3 grown on an etched Si substrate (bottom-left, brown region) viewed along the $[\overline{1}\overline{1}0]$ direction of ${\mathrm{Sb}}_{2-x}{V}_x{\mathrm{Te}}_3$. Another capping layer (top-right, yellow region) is mainly composed of amorphous Te protection layers. The upper right inset is a reflection of the high-energy electron diffraction (RHEED) image showing the ultrahigh crystalline quality of the MBE-grown film. (b) Diffractogram from (a). One set of spots as indicated by green arrows can be indexed as a $(0\overline{1}1)$ pattern of Si, while the other set of spots indicated by red arrows can be indexed as a $(\overline{1}\overline{1}0)$ pattern of a rhombohedral lattice with $a=0.42$ and $c=3.03\mathrm{nm}$, which is basically the same as the ${\mathrm{Sb}}_2{\mathrm{Te}}_3$ lattice, indicating negligible influence of V dopants to the lattice. The [001] ${\mathrm{Sb}}_2{\mathrm{Te}}_3$ is slightly misaligned ($\sim 3°$) with [111] Si. (c) Select-area electron diffraction pattern from the area containing both the film and substrate.

Figure 2

EELS spectra of V $L$ and Te $M_{4,5}$ edges at RT (red curve; lower curve in inset) and $10\mathrm{K}$ (blue curve; upper curve in inset) for sample S2, normalized with Te $M_{4,5}$ edge intensity. The energy position of Te $M_{4,5}$ edge is invariant of temperature (green vertical line $\sim 615\mathrm{e}\mathrm{V}$), while there is a clear redshift of vanadium’s $L_3$ and $L_2$ positions (yellow vertical lines in inset) and a drop of $L_3/L_2$ ratio. The energy scale has been accurately calibrated by simultaneously acquiring and aligning of the zero-loss peak.

Figure 3

(a) FEFF simulation of the high-loss EELS spectrum of V-doped ${\mathrm{Sb}}_2{\mathrm{Te}}_3$, using a nanosphere (inset) with a scattering center in the middle. (b)–(d) Experimental EELS peak positions and shifts. (b) The $\mathrm{V}\text{−}{L}_2$ peak positions, showing a similar trend of redshift for all three samples. The two algorithms show consistent results. (c) The $\mathrm{V}\text{−}{L}_3$ peak positions, where sample S2 with the highest V concentration shows the highest redshift. A horizontal yellow line marks the energy position from nonmagnetic simulation, which is slightly higher than the RT magnitudes. (d) The V’s $L_3/L_2$ peak intensity ratio change. At $T=10\mathrm{K}$, the ratio drops, which is also consistent with the simulation, where for a nonmagnetic system the ratio is even higher.

Figure 4

(a) Crystal field splitting in the cubic crystal field. $T_{2g}$ levels allow the spin alignment from all three $3d$ electrons of V (red arrows), leading to a possible FM order. (b) Crystal field splitting under rhombohedral $D_{3\mathrm{d}}$ crystal field. Since the energy only splits into a twofold level and only 1 electron has unpaired spin, it is too weak to form a FM order.

Figure 5

(a) Longitudinal resistance $R_{xx}$ as a function of temperature at zero field. (b) Normalized magnetic-field dependent longitudinal resistance $R_{xx}$ at various temperature. Above 70 K, it shows weak antilocalization behavior, while below 70 K, the butterfly shape indicates the onset of FM order. (c) Magnetic-field dependent Hall resistance $R_{xy}$. The opening up of a hysteresis loop below 70 K is quite consistent with (a) and (b), indicating an onset of FM order.