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Coexistence of Ferromagnetism and Topology by Charge Carrier Engineering in intrinsic magnetic topological insulator MnBi4Te7

Intrinsic magnetic topological insulators (MTIs) MnBi2Te4 and MnBi2Te4/(Bi2Te3)n are expected to realize the high-temperature quantum anomalous Hall effect (QAHE) and dissipationless electrical transport. Extensive efforts have been made on this field but there is still lack of ideal MTI candidate with magnetic ordering of ferromagnetic (FM) ground state. Here, we demonstrate a MTI sample of Mn(Bi0.7Sb0.3)4Te7 which holds the coexistence of FM ground state and topological non-triviality. The dramatic modulation of the magnetism is induced by a charge carrier engineering process by the way of Sb substitution in MnBi4Te7 matrix with AFM ordering. The evolution of magnetism in Mn(Bi1-xSbx)4Te7 is systematically investigated by magnetic measurements and theoretical calculations. The clear topological surface states of the FM sample of x = 0.3 are also verified by angle-resolved photoemission spectra. We also aware that the FM sample of x = 0.3 is close to the charge neutral point. Therefore, the demonstration of intrinsic FM-MTI of Mn(Bi0.7Sb0.3)4Te7 in this work sheds light to the further studies of QAHE realization and optimizations.


Introduction
Topological insulators, combined with the magnetism, can host various intriguing phenomena, such as quantum anomalous Hall effect (QAHE), topological electromagnetic effect, axion state and so on 1-6 . However, due to the confinement of the rare materials candidates, the research of the magnetic topological insulators (MTIs) is limited in the magnetic doped topological insulators or the magnetic proximity in heterostructures [7][8][9][10] . In recent years, intrinsic magnetic topological insulators MnBi2Te4 and a series of MnBi2Te4/(Bi2Te3)n materials have sprung up, in which the spontaneous magnetization derives from the internal manganese atoms instead of the external impurities [11][12][13][14][15][16][17] . Unfortunately, because of the compensated antiferromagnetic (AFM) ground state, the intensity of magnetism in MnBi2Te4 is rather weak under the zero field.
MnBi2Te4/(Bi2Te3)n series can significantly reduce the interlayer AFM exchange interaction by intercalated Bi2Te3 quintuple layers into MnBi2Te4 martrix 18,19 , but the AFM ground state still possesses the lower energy than ferromagnetic (FM) state and a small magnetic field is still essential to align the opposite magnetic moments.
Furthermore, in all of these recent known intrinsic MTI candidates, the ineluctable antisite defects between the manganese and bismuth atoms will induce the heavy n-type trivial bulk carriers 13,20 , covering the transport of the novel chiral edge state. Up to now, QAHE can only be realized at MnBi2Te4 thin films with the high magnetic field up to 6 T from three to eight septuple layers (SLs) or near zero field with the high bias voltage (~200V) at 5 SLs [21][22][23] . Ultra-high magnetic field due to AFM ground state and the huge bias voltage resulting from the antisite defects obstruct the further application of MnBi2Te4 in the AFM spintronics and dissipationless quantum devices. In MnBi2Te4, the Sb substitution at the Bi sites can neutralize the excess bulk carrier efficiently, while the AFM state is still robust 24,25 . However, in the case of MnBi4Te7, the comparable AFM-FM energy difference paves the way to modify the AFM state and carrier density at the meantime, with no-magnetic elements doping.
In this work, we grow a serials single crystals of Mn(Bi1-xSbx)4Te7 from x = 0.15 to x = 0.46. Angle-resolved photoemission spectra (ARPES), magnetic and electrical transport measurement are conducted to explore the influence of the Sb substitution in Mn(Bi1-xSbx)4Te7. Via no-magnetic element Sb doping, the AFM ground state evolves into ferromagnetic (FM) state at x = 0.3 and return to AFM when continuously increasing Sb ratio to x = 0.46, hosting an unexpected FM region in the middle.
According to the theoretical calculation, the energy difference between AFM and FM in Mn(Bi1-xSbx)4Te7 family is only ~ 0.2 meV, indicating that the magnetic ordering could be easily affected by external conditions. The calculation also reveals a distinct dip of the energy difference value between the AFM and FM at x ~ 0.3, qualitatively matching with the trend displayed in our experimental results. Furthermore, according to the electrical transport, we find that similar to the case of MnBi2Te4 24,25 , Sb doping is also an effective way to modulate the carrier densities. Specifically, the heavy n-type bulk carriers in pure MnBi4Te7 are significantly suppressed by Sb doping, and an n-p transition occurs between x = 0.36 and 0.4. One may notice that the electrical neutral point of Sb doping MnBi4Te7 is close to the FM state region. In ARPES measurement, the clear surface Dirac cone of the Bi2Te3 termination prove the robust topological property at x = 0.3 in Mn(Bi1-xSbx)4Te7. Our work demonstrates the obvious engineering of the both magnetism and the charge carriers in MnBi4Te7 by Sb doping. Mn(Bi1-xSbx)4Te7 with x around 0.3 is a promised candidate of MTI with FM ground state and low bulk carrier concentrations, which provides a prospective avenue to accomplish the QAHE at the zero field as well as other exotic topological effects..

Results
Mn(Bi1-xSbx)4Te7 is a layered rhombohedral material with the space group P3 m1 (164) [26][27][28][29] . The Mn(Bi1-xSbx)2Te4/(Bi1-xSbx)2Te3 superlattice stacks along the c axis through the weak van der Waals forces as is drawn in Figure 1  To explore the magnetic variation in the Mn(Bi1-xSbx)4Te7 samples, we conduct the magnetic measurement of the field cool (FC) and zero-field cool (ZFC) processes from 300 K to 2 K by vibrating sample magnetometer. The magnetic field is applied perpendicular to the sample cleave surfaces with the magnitude at 500 Oe. In the pure MnBi4Te7, the FC-ZFC curves show the expected antiferromagnetic peaks at 13 K and the overlapped ones diverge at lower temperature (~ 5K), corresponding with previous articles 31, 33 . The magnetic field dependence of the magnetization curves exhibit the zigzag shape at 2 K and the hysteresis loop divides into two jump points deviating from the zero field at 10 K. Compared with the MnBi2Te4 (~ 7T) 13,20 , the saturation field to approach the FM region in the MnBi4Te7, less than 0.3 tesla, is much smaller. But as is shown in the Figure 2(b), in the as-grown MnBi4Te7, the magnetic ground state is still AFM and external magnetic field is still essential to form FM state.
Due to the Bi2Te3 intercalation which enlarges the distance between the neighboring MnBi2Te4 SL, the energy difference between the AFM and FM is relatively small in   10 19 cm -3 (p type) respectively, ten times smaller than the value in pure MnBi4Te7.
Since the electrical neutral point has been verified, we then take more attention to the magneto transport behavior of the samples which are near the electrical neutral point.
As is shown Figure 4 Figure 5(b). Therefore, another factor may play a no-negligible role and involve in the magnetic competition, which deserves further consideration. In the pure MnBi2Te4 and MnBi4Te7, antisite defects between Mn and Bi atoms are believed to exist 13,20,39 .
Although we substitute the Bi with Sb exactly, a few Sb atoms will inevitably participate in the antisite replacement with Mn atoms. According to the theoretical prediction, Mn/Sb antisite will decrease the energy difference between FM and AFM markedly 40,41 . In the Mn(Bi1-xSbx)4Te7 samples, antisite defects between Sb and Mn atoms will shift down the energy difference curve in the whole, which will create a narrow zone of negative value, account for the FM region at x = 0.3. Along with the further increase of the doping ratio, the influence of the Mn/Sb defects will enhance, which is the origin of the emergence of the ferrimagnetism at x = 0.46 42 . It is obvious that the internal mechanisms are complex in Mn(Bi1-xSbx)4Te7. Due to the close energy difference between the AFM and FM, the magnetic ground state can be affected and disturbed by the tiny perturbations. Although the theoretical calculations cannot exactly match with the experiment results, the overall tendency extracted from the first principle calculation can be useful to investigate and understand the anomalous magnetic transition at x ~ 0.3.

Conclusion
In summary, the magnetism and the carrier density have been modulated Note Added: During preparing this manuscript, we notice another independent work (arXiv: 2008.09097) also focusing on Mn(Bi1-xSbx)4Te7 but with wider Sb doping ratio range 42 . These two works complement each other, and combing them can get more comprehensive understanding on this material system.