Enhancing the Quantum Anomalous Hall Effect by Magnetic Codoping in a Topological Insulator

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1 Communication Topological Insulators Enhancing the Quantum Anomalous Hall Effect by Magnetic Codoping in a Topological Insulator Yunbo Ou, Chang Liu, Gaoyuan Jiang, Yang Feng, Dongyang Zhao, Weixiong Wu, Xiao-Xiao Wang, Wei Li, Canli Song, Li-Li Wang, Wenbo Wang, Weida Wu, Yayu Wang,* Ke He,* Xu-Cun Ma, and Qi-Kun Xue The quantum anomalous Hall (QAH) effect, which has been realized in magnetic topological insulators (TIs), is the key to applications of dissipationless quantum Hall edge states in electronic devices. However, investigations and utilizations of the QAH effect are limited by the ultralow temperatures needed to reach full quantization usually below 100 mk in either Cr- or V-doped (Bi,Sb) 2 Te 3 of the two experimentally confirmed QAH materials. Here it is shown that by codoping Cr and V magnetic elements in (Bi,Sb) 2 Te 3 TI, the temperature of the QAH effect can be significantly increased such that full quantization is achieved at 300 mk, and zero-field Hall resistance of 0.97 h/e 2 is observed at 1.5 K. A systematic transport study of the codoped (Bi,Sb) 2 Te 3 films with varied Cr/V ratios reveals that magnetic codoping improves the homogeneity of ferromagnetism and modulates the surface band structure. This work demonstrates magnetic codoping to be an effective strategy for achieving high-temperature QAH effect in TIs. The quantum anomalous Hall (QAH) effect results from 2D electronic band structure with topologically nontrivial property characterized by a nonzero Chern number. [1 9] After remaining as a theoretical hypothesis for over two decades, [1 6] the effect was experimentally realized in molecular beam epitaxy (MBE)-grown thin films of magnetically doped 3D topological insulators (TIs). [10 16] A 3D TI has gapped bulk bands Dr. Y. Ou, C. Liu, G. Jiang, Y. Feng, D. Zhao, W. Wu, X.-X. Wang, Prof. W. Li, Prof. C. Song, Prof. L.-L. Wang, Prof. Y. Wang, Prof. K. He, Prof. X.-C. Ma, Prof. Q.-K. Xue State Key Laboratory of Low Dimensional Quantum Physics Department of Physics Tsinghua University Beijing , China yayuwang@tsinghua.edu.cn; kehe@tsinghua.edu.cn Dr. Y. Ou, C. Liu, G. Jiang, Y. Feng, D. Zhao, W. Wu, X.-X. Wang, Prof. W. Li, Prof. C. Song, Prof. L.-L. Wang, Prof. Y. Wang, Prof. K. He, Prof. X.-C. Ma, Prof. Q.-K. Xue Collaborative Innovation Center of Quantum Matter Beijing , P. R. China W. Wang, Prof. W. Wu Department of Physics and Astronomy School of Arts and Sciences Rutgers University Piscataway, NJ 08854, USA The ORCID identification number(s) for the author(s) of this article can be found under DOI: /adma and topologically protected gapless surface states with Dirac-like linear band dispersion. [17,18] Introducing ferromagnetism into a 3D TI can open a gap at the Dirac surface states, which, in a film of appropriate thickness, will lead to the QAH effect. [4] Up to now the QAH effect has only been observed in Cr- [10 13] or V-doped [14 16] (Bi,Sb) 2 Te 3 TI films. The two magnetically doped TI materials exhibit distinct magnetic and QAH behaviors, but a temperature <100 mk is always required to achieve perfect quantization in either case. [10 16] The ultralow temperature needed is still the biggest challenge and puzzle for the studies on the QAH effect. Recently Mogi et al. reported the observation of QAH effect at higher temperature in modulation-cr-doped (Bi,Sb) 2 Te 3 films which however involve a highly complex heterostructure difficult to fabricate and investigate. [19] Several recent experiments with different techniques on magnetically doped (Bi,Sb) 2 Te 3 TI films revealed evidences for very inhomogeneous ferromagnetism which is suspected of contributing to the unexpected low temperature of the QAH effect. [16,20 22] Alloying is a common and effective way to refine the performance of ferromagnetic metals, and, similarly, codoping of dilute magnetic semiconductors (DMSs) can promote ferromagnetic coupling in those systems. [23] It has recently been proposed that codoping V and I in Sb 2 Te 3 TIs may increase the quantization temperature of the QAH effect. [24] In our study, we prepared Cr and V codoped (Bi,Sb) 2 Te 3 films with MBE and found a significant increase in the temperature of the QAH effect. We report both our new approach to achieving higher temperature QAH materials and our investigations of the factors determining the temperature for the QAH effect in magnetically doped TIs. We grew a series of (Cr y V 1-y ) 0.19 (Bi x Sb 1-x ) 1.81 Te 3 films with the nominal Cr concentration y = 0, 0.05, 0.16, 0.32, 0.54, 0.75, and 1 on SrTiO 3 (111) substrates by MBE. The nominal Bi concentration x is 0.4 and is modified for each sample in order to keep them nearly charge neutral. All the films have a thickness d = 5 quintuple-layer (QL), which is confirmed with atom force microcopy. [10] The SrTiO 3 substrate serves as a dielectric layer for an applied bottom gate voltage (V g ), which permits the chemical potential of the films to be finely tuned during transport measurements (see the Supporting Information). [25] (1 of 6)

2 Figure 1. Magnetotransport properties of Cr V codoped (Bi,Sb) 2 Te 3 films with different Cr/V ratios measured at 1.5 K. a g) Hall traces (ρ yx vs μ 0 H) of 5 QL (Cr y V 1-y ) 0.19 (Bi x Sb 1-x ) 1.81 Te 3 films with V g = V 0. h n) MR curves (ρ xx vs μ 0 H) of the films with V g = V 0. Figure 1a g and Figure 1h n display the Hall traces (ρ yx vs μ 0 H) and magnetoresistance (MR) curves (ρ xx vs μ 0 H) of the (Cr y V 1-y ) 0.19 (Bi x Sb 1-x ) 1.81 Te 3 films with seven different y values, respectively. The data were taken at 1.5 K with the gate voltage V g tuned for ρ yx to reach the maximum at zero magnetic field (hereafter referred to as V 0 ). The ρ yx and ρ xx values at specific magnetic field at 1.5 K mentioned below are extracted from these Hall traces and MR curves. The V g dependences of ρ yx and ρ xx at 0 and 1.5 T are shown in the top and bottom panels of Figure 2, respectively. The position of V 0 is indicated with a dashed-dotted line in each panel. All the Hall and MR curves exhibit the typical behaviors of ferromagnetic films with perpendicular magnetic anisotropy. The coercivity (H c ) of the singly V-doped film (0.67 T) is much larger than that of the singly Cr-doped one (0.08 T), consistent with early reports, [10,14] and decreases monotonically with increasing Cr concentration. For the singly Cr-doped film (Figure 1g,n), ρ yx and ρ xx reach 0.82 h/e 2 and 0.60 h/e 2 at 1.5 T, respectively, which are close to those of the Cr-doped (Bi,Sb) 2 Te 3 QAH samples in previous studies at the same temperature. Such a film is expected to exhibit full quantization at 30 mk. [10] The singly V-doped film (Figure 1a) shows similar ρ yx but rather large ρ xx (8.6 h/e 2 at 1.5 T). The large ρ xx is probably because the V-doped (Bi,Sb) 2 Te 3 film is near the boundary between the QAH and ordinary insulator phases, [26] since the V-doped films exhibiting unambiguous QAH effect either have lower V concentration [14,15] or higher thickness (see the Supporting Information). [16] Codoping a small amount of Cr (y = 0.05) in V-doped film significantly promotes the QAH state: ρ yx is elevated to 0.88 h/e 2 (Figure 1b) and ρ xx is reduced to 0.54 h/e 2 (Figure 1i). Similarly, codoping 1.5 K y y y y y y y V Figure 2. Gate dependent magnetotransport properties of Cr V codoped (Bi,Sb) 2 Te 3 films with different Cr/V ratios measured at 1.5 K. a g) V g dependence of ρ yx at 0 T (cyan line) and 1.5 T (blue line). h n) V g dependence of ρ xx at 0 T (magenta line) and 1.5 T (red line). The dashed lines indicate the position of V 0. All the data are extracted from the Hall traces and MR curves at different gate voltages (2 of 6)

3 Figure 3. The QAH effect of the optimized Cr V codoped (Bi,Sb) 2 Te 3 film. a) Hall trace of the 5 QL (Cr 0.16 V 0.84 ) 0.19 (Bi x Sb 1-x ) 1.81 Te 3 film with V g = V 0 measured at 300 mk. b) MR curve of the film with V g = V 0 measured at 300 mk. c) V g dependence of ρ 0 yx and ρ 0 xx (ρ yx and ρ xx at zero magnetic field). d) Temperature dependence of ρ 0 yx and ρ 0 xx. The data for T > 6 K are extracted from the Hall traces and MR curves taken at each temperature in a He 4 refrigerator. The data for T < 6 K are acquired in He 3 refrigerator after magnetic training at V g = V 0. e) The dependence of σ 0 xx in logarithmic scale on 1/T. The dashed line is the Arrhenius fit with the activation energy of 1.4 K. The data shown here are acquired in dilution refrigerator after magnetic training at V g = V 0. V also drives the Cr-doped sample closer to quantization (see Figure 1d f and Figure 1k m). In the optimized y = 0.16 sample, ρ yx reaches 0.97 h/e 2 with ρ xx = 0.19 h/e 2 at 0 T (Figure 1c,j). Such a quantization level has only been observed at 100 mk in either singly Cr-doped or V-doped samples. [10 16] We measured the transport properties of the optimized sample (y = 0.16) at 300 mk in a He 3 refrigerator. Figure 3a,b shows the Hall trace and MR curve of the sample with V g =V 0, respectively. Full quantization is achieved with ρ yx = h/e 2 within experimental uncertainty, and the residual ρ xx is as small as h/e 2, varying slightly with magnetic field. The small fluctuations in ρ xx around zero field (Figure 3b) may come from magnetization reversals of some areas with weaker ferromagnetism. Figure 3c displays the V g dependences of ρ 0 xx and ρ 0 yx (ρ xx and ρ yx at zero field, respectively), which exhibit a welldefined quantized plateau. The temperature dependences of ρ 0 xx and ρ 0 yx are shown in Figure 3d. ρ 0 xx starts dropping as the temperature is reduced from 22 K (below the Curie temperature, T C = 25 K) and then decreases to zero, accompanied by a continuous increase of ρ 0 yx to h/e 2. The observation can be attributed to a significant contribution of the dissipationless QAH edge states to the sample conductance below T C. The temperature dependence of σ 0 xx (σ xx at zero field) shown in Figure 3e (black filled squares) exhibits the typical behavior of quantum Hall systems. The curve above 0.5 K can be fitted with the Arrhenius relationship: σ 0 xx exp( Δ/k B T), from which we can extract the activation energy Δ/k B as 1.4 K. It is much larger than that of the singly Cr-doped or V-doped QAH samples [10 16] (the σ 0 xx data of a Cr-doped (Bi,Sb) 2 Te 3 film are plotted with red filled circles in Figure 3e for comparison) and similar to that of the modulation-cr-doped sample. [19] Next we investigate why Cr-V codoped (Bi,Sb) 2 Te 3 films show the QAH effect at higher temperature. From the Hall traces of the series of samples in Figure 1a g, we notice that the samples closer to quantization exhibit more squared hysteresis loops. More precisely, the magnetization reversal at coercive field is steeper, and elsewhere both ρ yx and ρ xx show weak H dependence. This is measured by the widths of the MR peaks. In Figure 4b we plot the full width at half maximum (FWHM) of the MR peaks relative to H c of the samples with different Cr/V ratios. The H c values of the samples are also shown for reference. Comparing the Cr concentration dependence of the relative MR peak width (Figure 4b) to that of Hall and longitudinal resistances (Figure 4a), we can see that the samples closer to quantization show steeper magnetization reversal. In the optimized sample (y = 0.16), magnetization reversal basically happens at the coercive field, while in other ones, magnetization reversals occur in a wider range of magnetic field. Further, the samples closer to quantization exhibit weaker magnetic field dependence of their transport properties away from coercive fields, as seen in Figure 2 and the Supporting Information. These observations suggest that the film with elevated QAH temperature has more homogeneous ferromagnetism. Ferromagnetic disorder is a common phenomenon in magnetically doped semiconductors with low carrier density. It usually manifests itself as a linear or concave magnetization versus temperature (M T) curve below T C, which means that uniform magnetization cannot establish until at a very low temperature. [27 29] By contrast, the M T curves of ordinary ferromagnetic metals usually have a convex shape, indicating immediate formation of uniform magnetization below T C. The magnetically doped TI thin films studied here cannot generate sufficiently strong magnetic signals for M T measurements with a standard SQUID magnetometer. We instead plot the temperature dependences of the anomalous Hall resistance (ρ 0 yx) of the samples with different Cr/V ratios in Figure 4c which basically reflect the M T away from the quantum plateau. [30,31] For (3 of 6)

4 y y Figure 4. Dependence of the properties of Cr V codoped films on Cr/V ratios. a) Dependence of zero magnetic field ρ yx (blue) and ρ xx (red) on Cr concentration (y). b) Dependence of FWHM of the MR peaks relative to H c (black solid squares) and H c (green hollow circles) on y. c) Temperature dependence of the anomalous Hall resistance (ρ 0 yx) of the samples with different y. The anomalous Hall resistance data are normalized to those at l.5 K. ease of comparison, the data are normalized to those at l.5 K. As shown in Figure 4c, the optimized sample (y = 0.16) shows the most convex (the blue one), i.e., the most mean-field-like, ρ 0 yx T curve. The ρ 0 yx T curves of dominantly V-doped samples are more mean-field-like than those of dominantly Crdoped ones. This, like the FWHM/H c data, indicates that the sample with QAH at higher temperatures also have reduced ferromagnetic inhomogeneity. Finally, we have carried out magnetic force microscopy measurements on the films around H c and found that the Cr V codoped film shows larger size and stronger magnetic signal of the magnetic domains than singly doped ones, which directly demonstrates the enhanced ferromagnetic homogeneity by Cr V codoping (see the Supporting Information). [32] The above evidences for the improved ferromagnetic homogeneity in codoped films indicate that it contributes to the increased temperature of the QAH effect. Inhomogeneous ferromagnetism and spatial distribution of magnetic gap of magnetically doped (Bi,Sb) 2 Te 3 have been reported by several studies with different techniques. [16,20 22] The inhomogeneity suggests the existence of regions with small exchange energy and magnetic gap size in the magnetically doped TI films. The chiral QAH edge states passing through these regions would be strongly scattered into bulk or surface states, which brings dissipation to the chiral edge states and deteriorates the QAH effect. As a result, the quantization temperature of a magnetic TI sample with disordered ferromagnetism is limited by the regions with the smallest magnetic gap. The improvement of the ferromagnetic order in codoped samples can thus significantly elevate the temperature of QAH effect. We propose that the improvement in ferromagnetic homogeneity can be seen as deriving from the separately known properties of Cr- and V-doped (Bi,Sb) 2 Te 3 as follows: The magnetic impurities of Cr-doped (Bi,Sb) 2 Te 3 have larger atomic magnetic moment than those of V-doped one. [33] V-doped (Bi,Sb) 2 Te 3, on the other hand, has stronger perpendicular magnetic anisotropy as shown by the large coercivity. The size of magnetic gap, i.e., the width of the QAH plateau, in a magnetically doped topological insulator is determined by the perpendicular component of its average impurity magnetic moment (S z ). S z can be enhanced in Cr V codoped films by a combination of a large magnetic moment and a strong perpendicular magnetic anisotropy. The larger S z in Cr V codoped samples contributes to larger magnetic gap which can sustain the QAH effect at higher temperature [33] and stabilize the ferromagnetic order. [34] Other factors may also play roles in the enhancement of the QAH effect and ferromagnetism in codoped samples. We found that the minimum substrate temperature for film growth decreased significantly in codoping versus single-dopant processes, from 240 to 200 C, which suggests that Cr atoms may promote integration of V atoms into the (Bi,Sb) 2 Te 3 host. The reduced temperature, moreover, likely leads to more uniform distribution of V atoms, since MBE growth at lower substrate temperature reduces the diffusion processes that cause clustering of magnetic impurities. A recent theoretical work predicted that V and I codoped Sb 2 Te 3 can show the QAH effect at higher temperature because compensation of the charges induced by the two dopants preserves the bulk gap. This mechanism may also be at work in Cr V codoped samples studied here. A comprehensive understanding of the kinetics (4 of 6)

5 Figure 5. Ferromagnetic coupling mechanisms of Cr V codoped films with different Cr/V ratios. a) V g dependences of normalized H c (H c /H c (V g = V 0 )) of the samples with different Cr/V ratios. The curves are shifted horizontally such that their V 0 values are aligned and shifted vertically by an offset of 0.2. b) Schematics of the band structures of singly V-doped (left) and Cr-doped (Bi,Sb) 2 Te 3 (right). of the Cr V codoping process and resulting electronic structure requires further investigation. The dependence of the coercivity on the chemical potential also elucidates the elevated temperature of the QAH effect in the codoped samples. Figure 5a shows the V g dependences of H c of the films with different Cr/V ratios. For ease of comparison, we shift the curves to align their V 0 values, and the H c values of each curve are normalized to that at V 0. The curve for the singly Cr-doped sample shows a clear minimum at V g = V 0. However, for other samples, H c decreases with V g, showing no minimum at V g = V 0. In ordinary DMSs that are dominated by Ruderman Kittel Kasuya Yosida (RKKY)-like magnetic coupling mediated by bulk carriers, ferromagnetism weakens with decreasing density of bulk carriers. The decreasing H c with increasing V g toward V 0 can be attributed to weakening of the RKKY-like ferromagnetism by the gradual depletion of the carriers of the bulk valence bands. The absence of a minimum at V g = V 0 in the curves for the V-doped samples implies that the valence band is not emptied yet at the energy corresponding to the chiral edge states. Our observation is consistent with a recent angle-resolved photoemission spectroscopy observation of the valence band maximum (VBM) above the Dirac point in a V-doped (Bi,Sb) 2 Te 3 QAH film (see the schematic band structure in Figure 5b, left). [35] With such a band structure, a quite low temperature is required to localize the remaining bulk carriers for a sample to exhibit full quantization. This explains why V-doped (Bi,Sb) 2 Te 3, despite its much stronger magnetic anisotropy and more homogeneous ferromagnetism than Cr-doped (Bi,Sb) 2 Te 3, does not exhibit the QAH effect at significantly higher temperatures. By contrast, the H c minimum observed at V g = V 0 in the singly Cr-doped film indicates that the chiral edge states are isolated in a full bulk gap (see the schematic in Figure 5b, right). With increasing Cr concentration in Cr V codoped films, due to the downward shift of VBM, the residual bulk carriers at V g = V 0 have a lower density and are thus easier to localize at low temperature. But an excessive Cr concentration leads to less homogeneous ferromagnetism in the film. The optimization of the two processes may result in the enhanced QAH effect in codoped samples. This study demonstrates that magnetic codoping is an effective way to improve the ferromagnetism and QAH effect in magnetically doped TIs. Further progress can be achieved with other combinations of magnetic and nonmagnetic codoping methods. Since the codoping method and the modulation doping method reported earlier [19] are independent approaches of enhancing the QAH effect, a combination of the two ways may further increase the QAH temperature. The independent and joint characteristics of Cr- and V-doped (Bi,Sb) 2 Te 3 revealed in this work provide insight into the strategy of designing and fabricating more satisfactory QAH systems. Experimental Section The (Cr y V 1-y ) 0.19 (Bi x Sb 1-x ) 1.81 Te 3 films were grown on insulating SrTiO 3 (111) substrates along the [001] by an MBE coevaporation method similar to ref. [10]. Before film growth, the substrate was degassed at 500 C for 10 min and then to 600 C for 25 min in the MBE chamber. High purity Bi ( %), Sb ( %), Cr (99.999%), V (99.7%), and Te ( %) were coevaporated with commercial Knudsen cells. The growth of 5 QL (Cr y V 1-y ) 0.19 (Bi x Sb 1-x ) 1.81 Te 3 was conducted under Te-rich conditions at a substrate temperature of 200 C (except for the y = 0 film) with a typical Te/(Bi,Sb) flux ratio of 10. The y = 0 sample was grown with substrate temperature of 240 C. A protective 2 nm Al layer was then deposited in situ at room temperature and was oxidized in air into highly insulating AlO x. The Cr/V ratio in the films is controlled by the evaporation temperatures of Cr and V sources. The transport measurements were performed in He 4 refrigerators (Oxford Instruments, 1.5 K, 9 T and Quantum Design, 1.9 K, 9 T), a He 3 refrigerator (Oxford Instruments, 0.3 K, 15 T), and a dilution refrigerator (Oxford Instruments, 0.01 K, 14 T). The film was manually etched into a Hall bar geometry, as described previously, [10] and electrodes were made by pressing small pieces of indium onto the contact areas of the film. The typical Hall bar has dimensions 500 µm 200 µm. The longitudinal sheet and Hall resistances were measured by using standard fourprobe ac lock-in method with an excitation current I = 0.2 µa (He 4 refrigerators), I = 0.1 µa (He 3 refrigerator), and I = 10 na (dilution refrigerator). Supporting Information Supporting Information is available from the Wiley Online Library or from the author (5 of 6)

6 Acknowledgements Y.O. and C.L. contributed equally to this work. This work was supported by National Natural Science Foundation of China and the Ministry of Science and Technology of China. This work at Rutgers was supported by the Office of Basic Energy Sciences, Division of Materials Sciences and Engineering, U.S. Department of Energy under Award No.DE-SC Conflict of Interest The authors declare no conflict of interest. Keywords ferromagnetic homogeneity, magnetic codoping, quantum anomalous Hall effect, topological insulators Received: June 1, 2017 Revised: August 18, 2017 Published online: November 10, 2017 [1] F. D. M. Haldane, Phys. Rev. Lett. 1988, 61, [2] M. Onoda, N. Nagaosa, Phys. Rev. Lett. 2003, 90, [3] X. L. Qi, Y. S. Wu, S. C. Zhang, Phys. Rev. B 2006, 74, [4] X. L. Qi, T. L. Hughes, S. C. Zhang, Phys. Rev. B 2008, 78, [5] C. X. Liu, X. L. Qi, X. Dai, Z. Fang, S. C. Zhang, Phys. Rev. Lett. 2008, 101, [6] R. Yu, W. Zhang, H. J. Zhang, S. C. Zhang, X. Dai, Z. Fang, Science 2010, 329, 61. [7] K. He, Y. Wang, Q. K. Xue, Natl. Sci. Rev. 2013, 1, 38. [8] J. Wang, B. Lian, S. C. Zhang, Phys. Scr. 2015, 2015, [9] X. F. Kou, Y. B. Fan, M. R. Lang, P. Upadhyaya, K. L. Wang, Solid State Commun. 2015, 215, 34. [10] C. Z. Chang, J. Zhang, X. Feng, J. Shen, Z. Zhang, M. Guo, K. Li, Y. Ou, P. Wei, L. L. Wang, Z. Q. Ji, Y. Feng, S. Ji, X. Chen, J. Jia, X. Dai, Z. Fang, S. C. Zhang, K. He, Y. Wang, L. Lu, X. C. Ma, Q. K. Xue, Science 2013, 340, 167. [11] J. G. Checkelsky, R. Yoshimi, A. Tsukazaki, K. S. Takahashi, Y. Kozuka, J. Falson, M. Kawasaki, Y. Tokura, Nat. Phys. 2014, 10, 731. [12] X. F. Kou, S. T. Guo, Y. B. Fan, L. Pan, M. R. Lang, Y. Jiang, Q. M. Shao, T. X. Nie, K. Murata, J. S. Tang, Y. Wang, L. He, T. K. Lee, W. L. Lee, K. L. Wang, Phys. Rev. Lett. 2014, 113, [13] A. Kandala, A. Richardella, S. Kempinger, C. X. Liu, N. Samarth, Nat. Commun. 2015, 6, [14] C. Z. Chang, W. W. Zhao, D. Y. Kim, H. J. Zhang, B. A. Assaf, D. Heiman, S. C. Zhang, C. X. Liu, M. H. W. Chan, J. S. Moodera, Nat. Mater. 2015, 14, 473. [15] C. Z. Chang, W. W. Zhao, D. Y. Kim, P. Wei, J. K. Jain, C. X. Liu, M. H. W. Chan, J. S. Moodera, Phys. Rev. Lett. 2015, 115, [16] S. Grauer, S. Schreyeck, M. Winnerlein, K. Brunner, C. Gould, L. W. Molenkamp, Phys. Rev. B 2015, 92, [17] M. Z. Hasan, C. L. Kane, Rev. Mod. Phys. 2010, 82, [18] X. L. Qi, S. C. Zhang, Rev. Mod. Phys. 2011, 83, [19] M. Mogi, R. Yoshimi, A. Tsukazaki, K. Yasuda, Y. Kozuka, K. S. Takahashi, M. Kawasaki, Y. Tokura, Appl. Phys. Lett. 2015, 107, [20] I. Lee, C. K. Kim, J. Lee, S. J. L. Billinge, R. D. Zhong, J. A. Schneeloch, T. S. Liu, T. Valla, J. M. Tranquada, G. D. Gu, J. C. S. Davis, Proc. Natl. Acad. Sci. USA 2015, 112, [21] E. O. Lachman, A. F. Young, A. Richardella, J. Cuppens, H. R. Naren, Y. Anahory, A. Y. Meltzer, A. Kandala, S. Kempinger, Y. Myasoedov, M. E. Huber, N. Samarth, E. Zeldov, Sci. Adv. 2015, 1, e [22] X. Feng, Y. Feng, J. Wang, Y. Ou, Z. Hao, C. Liu, Z. Zhang, L. Zhang, C. Lin, J. Liao, Y. Li, L.-L. Wang, S.-H. Ji, X. Chen, X. Ma, S.-C. Zhang, Y. Wang, K. He, Q.-K. Xue, Adv. Mater. 2016, 28, [23] A. N. Andriotis, M. Menon, Phys. Rev. B 2013, 87, [24] S. F. Qi, Z. H. Qiao, X. Z. Deng, E. D. Cubuk, H. Chen, W. G. Zhu, E. Kaxiras, S. B. Zhang, X. H. Xu, Z. Y. Zhang, Phys. Rev. Lett. 2016, 117, [25] J. Chen, H. J. Qin, F. Yang, J. Liu, T. Guan, F. M. Qu, G. H. Zhang, J. R. Shi, X. C. Xie, C. L. Yang, K. H. Wu, Y. Q. Li, L. Lu, Phys. Rev. Lett. 2010, 105, [26] Y. Ou, C. Liu, L. Zhang, Y. Feng, G. Jiang, D. Zhao, Y. Zang, Q. Zhang, L. Gu, Y. Wang, K. He, X. Ma, Q.-K. Xue, APL Mater. 2016, 4, [27] M. Berciu, R. N. Bhatt, Phys. Rev. Lett. 2001, 87, [28] C. Timm, J. Phys.: Condens. Matter 2003, 15, R1865. [29] S. Das Sarma, E. H. Hwang, A. Kaminski, Phys. Rev. B 2003, 67, [30] A. Arrott, Phys. Rev. 1957, 108, [31] H. Ohno, Science 1998, 281, 951. [32] W. B. Wang, Y. Ou, C. Liu, Y. Wang, K. He, Q. K. Xue, unpublished. [33] C. Drasar, J. Kasparova, P. Lostak, X. Shi, C. Uher, Phys. Status Solidi B 2007, 244, [34] Q. Liu, C. -X. Liu, C. Xu, X. -L. Qi, S. -C. Zhang, Phys. Rev. Lett. 2009, 102, [35] W. Li, M. Claassen, C.-Z. Chang, B. Moritz, T. Jia, C. Zhang, S. Rebec, J. J. Lee, M. Hashimoto, D. H. Lu, R. G. Moore, J. S. Moodera, T. P. Devereaux, Z. X. Shen, Sci. Rep. 2016, 6, (6 of 6)