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We demonstrate by high resolution low temperature electron energy lossspectroscopy (EELS) measurements that the long range ferromagnetic (FM) orderin vanadium (V)-doped topological insulator Sb$_2$Te$_3$ has the nature of vanVleck-type ferromagnetism. The positions and the relative amplitudes of twocore-level peaks (L$_3$ and L$_2$) of the V EELS spectrum show unambiguouschange when the sample is cooled from room temperature to T=10K.Magnetotransport and comparison of the measured and simulated EELS spectraconfirm that these changes originate from onset of FM order. Crystal fieldanalysis indicates that in V-doped Sb$_2$Te$_3$, partially filled core statescontribute to the FM order. Since van Vleck magnetism is a result of summingover all states, this magnetization of core level verifies the van Vleck-typeferromagnetism in a direct manner.

physical review letters

Experimental Verification of Van Vleck Nature of Long-Range  Ferromagnetic Order in Vanadium-Doped Three-Dimensional Topological Insulator  Sb$_{2}$Te$_{3}$