Intrinsic magnetic topological materials

doi:10.1007/s11467-022-1250-6

Front. Phys.

2023, Vol. 18

Issue (2) : 21304 https://doi.org/10.1007/s11467-022-1250-6

TOPICAL REVIEW

Intrinsic magnetic topological materials

Yuan Wang, Fayuan Zhang, Meng Zeng, Hongyi Sun, Zhanyang Hao, Yongqing Cai, Hongtao Rong, Chengcheng Zhang, Cai Liu, Xiaoming Ma, Le Wang, Shu Guo, Junhao Lin, Qihang Liu, Chang Liu(

), Chaoyu Chen(

)

Shenzhen Institute for Quantum Science and Engineering (SIQSE) and Department of Physics, Southern University of Science and Technology (SUSTech), Shenzhen 518055, China

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Abstract

Topological states of matter possess bulk electronic structures categorized by topological invariants and edge/surface states due to the bulk-boundary correspondence. Topological materials hold great potential in the development of dissipationless spintronics, information storage and quantum computation, particularly if combined with magnetic order intrinsically or extrinsically. Here, we review the recent progress in the exploration of intrinsic magnetic topological materials, including but not limited to magnetic topological insulators, magnetic topological metals, and magnetic Weyl semimetals. We pay special attention to their characteristic band features such as the gap of topological surface state, gapped Dirac cone induced by magnetization (either bulk or surface), Weyl nodal point/line and Fermi arc, as well as the exotic transport responses resulting from such band features. We conclude with a brief envision for experimental explorations of new physics or effects by incorporating other orders in intrinsic magnetic topological materials.

Keywords intrinsic magnetic topological insulator magnetic topological metals magnetic Weyl semimetal topological surface states magnetic gap

Corresponding Author(s): Chang Liu,Chaoyu Chen

Just Accepted Date: 16 January 2023 Issue Date: 28 February 2023

Cite this article:

Yuan Wang,Fayuan Zhang,Meng Zeng, et al. Intrinsic magnetic topological materials[J]. Front. Phys. , 2023, 18(2): 21304.

URL:

https://academic.hep.com.cn/fop/EN/10.1007/s11467-022-1250-6
https://academic.hep.com.cn/fop/EN/Y2023/V18/I2/21304

Fig.1 Family tree of intrinsic magnetic topological materials. The combination of intrinsic magnetism and band topology gives birth to exotic states of matter such as axion insulator (a, reproduced from Ref. [45]), Chern insulator (b, reproduced from Ref. [45]), and topological Möbius insulator (c, reproduced from Ref. [44]), manifesting novel properties such as QAH effect (d, reproduced from Ref. [46]), quantized magneto−optical effect (Kerr rotation, e, reproduced from Ref. [47]), giant anomalous Hall conductance (f, reproduced from Ref. [48]), chiral anomaly (g, reproduced from Ref. [49]), and giant anomalous Nernst effect (h, reproduced from Refs. [50, 51]). Magnetic topological materials can be roughly categorized into magnetic TIs, magnetic Weyl/Dirac semimetals and other magnetic topological metals, with each of these states being realized based on various materials systems as listed. As schematically shown by the band cartoon, magnetic TIs are characterized by gapped bulk state and TSSs which can be either gapped or gapless, depending on the specific magnetic structure and surface termination; magnetic Weyl/Dirac semimetals are characterized by gapless band crossings which can be described by Weyl/Dirac equation; other magnetic topological metals share gapped bulk state and TSSs similar to the magnetic TIs, but compromised by the coexisting trivial bands.

Fig.2 (a) Crystal structure of MnBi₂Te₄·(Bi₂Te₃)_n. (b−e) Magnetic properties of MnBi₂Te₄·(Bi₂Te₃)_n (n = 0, 1, 2, 3) [69-72]. (f) Summary of lattice constants for MnBi₂Te₄·(Bi₂Te₃)_n.

Fig.3 (a) Observation of nearly gapless TSS in MnBi₂Te₄ single crystal (0001) surface (left, reproduced from Ref. [69]) and the variation of TSS gap in different samples (right, reproduced from Ref. [83]). (b, c, d) APRES spectra measured from the SL- and QL- (double QL-, triple QL-) terminations of MnBi₄Te₇ [97], MnBi₆Te₁₀ [79] and MnBi₈Te₁₃ [72], respectively. (e) Observation of QAH effect (I, reproduced from Ref. [93]), axion insulator phase (II, reproduced from Ref. [45]) and high-Chern number Chern insulator (III, reproduced from Ref. [94]) based on MnBi₂Te₄ films with different number of layers.

Fig.4 Crystal structure (a, e), magnetic transport properties (b, f) and band structure (c, g) of MnSb₄Te₇ and MnSb₆Te₁₀, respectively [107,111]. (d) The pressure dependence of superconducting transition temperature

T C

, AFM transition temperature

T N

(upper panel), Hall coefficient

R H

and carrier concentration(lower panel) at 10 K (different symbols represent different samples in the upper panel) [110].

Fig.5 (a, e, i) Crystal structures of EuSn₂As₂ [114], EuMg₂Bi₂ [115] and EuIn₂As₂ [116], respectively. In (a), Eu atoms are shown in orange, Sn in gray and As in bule. (b, f, j) Magnetic transport properties of EuSn₂As₂ [74], EuMg₂Bi₂ [117] and EuIn₂As₂ [118], respectively. (c) Band structure of EuSn₂As₂ measured by pump-probe ARPES [74]. (d) The pressure dependence of resistance for EuSn₂As₂ [119]. (g, h) Band structure of EuMg₂Bi₂ along M−K−M and K−Γ−K, respectively [115]. (k, l) Calculated band structure of EuIn₂As₂ [120].

Fig.6 (a) FeSn lattice structure and magnetic configuration, reproduced from Ref. [149]. (b) Magnetization as a function of temperature under field cooling (FC) with an applied magnetic field of 500 Oe, reproduced from Ref. [150]. (c, d, e) ARPES Fermi surface mapping and spectra reveal two Dirac cones features around

K

point (d) and flat band close to the Fermi level (e), reproduced from Ref. [151]. (f) Planar tunneling spectroscopy reveals an anomalous enhancement in tunneling conductance within a finite energy range of FeSn (black diamond), attributed to a spin-polarized flat band, reproduced from Ref. [152].

Fig.7 (a) Co₃Sn₂S₂ lattice structure and magnetic configuration, reproduced from Ref. [48]. (b) Calculated Fermi surface (i) and experimental Fermi surfaces under different photon energies (ii−vi) around K′ points in Co₃Sn₂S₂, SFA: surface Fermi arc, BS: bulk state, reproduced from Ref. [137]. (c) Intrinsic band structure (left), and band structure after potassium dosing and from calculation (red lines) of Co₃Sn₂S₂, reproduced from Ref. [137]. (d) Field dependence of the Hall conductivity

σ H

, reproduced from Ref. [48]. (e) Temperature dependences of the anomalous Hall conductivity (

σ H A

), the charge conductivity (

σ

) and the anomalous Hall angle (

σ H A

σ

) at zero magnetic field, reproduced from Ref. [48]. (f) Measured magnetoconductance for

B ⊥ I

and B//I, reproduced from Ref. [48].

Fig.8 (a) Mn₃Ge lattice structure and (b) magnetic configuration, reproduced from Ref. [139]. (c) Band structure calculation reveals the existence of one pair of Weyl points close to the Fermi level around K points in Mn₃Sn, reproduced from Ref. [138]. (d) Fermi surface mapped by ARPES and from calculation (purple curves) of Mn₃Sn, reproduced from Ref. [138]. (e, f) Field dependent Hall resistance at different temperatures show AHE behavior and temperature dependent zero-field component of the AHE in Mn₃Sn, reproduced from Ref. [140]. (g) Anomalous Nernst voltage

V A N E

image mapped by scanning thermal gradient microscopy reveal the existence of magnetic domain and domain writing, reproduced from Ref. [163].

Fig.9 (a) Crystal structure of Co₂MnAl [178]. (b) Comparison of anomalous Hall angle

tan Θ H = σ AHE / σ x x

and anomalous Hall conductivity

σ AHE

between Co₂MnAl and other magnetic conductors [178]. (c) Hopf link which consists of two rings on the mirror planes and intertwined each other [179]. (d−f) Linked Weyl loops in Co₂MnGa [180]. M1- and M2-loop Fermi surfaces plotted in adjacent bulk Brillouin zones (d). Same as (d) but for the M2- and M3-Fermi surfaces (e) and the M1- and M3-Fermi surfaces (f).

Fig.10 (a) Crystal structure of EuB₆ and its longitudinal resistivity as a function of temperature [193]. (b) Temperature dependent band structure of B-terminated surface along M−X, which is taken with

h ν = 135 e V

[194]. (c) The intrinsic anomalous Hall conductivity as a function of different magnetization at 2 K [193].

Fig.11 (a) Fe₃GeTe₂ lattice structure, magnetic configuration and (b) magnetic properties, reproduced from Refs. [206, 207]. (c) ARPES measured Fermi surface of Fe₃GeTe₂, reproduced from Ref. [207]. (d) Hall resistance of a four-layers Fe₃GeTe₂ flake [208]. (e) The dependence of AHC and magnetic moment per layer on the number of layers, reproduced from Ref. [209]. (f) Calculated electronic structures of Fe₃GeTe₂ without (I) and with (II) SOC. Majority spins: solid. Minority spins: dashed. (III) Calculated Berry curvature along the symmetry lines, reproduced from Ref. [210]. (g) Hall resistance with varying numbers of layers [208].

Fig.12 (a) Crystal structure of EuCd₂As₂, from [224]. (b) Proposed A-type AFM structure on Eu sites with the moments lying out-of-plane, from [224]. (c) Proposed A-type AFM structure with the moments lying in-plane, from [225]. (d) Best-fit magnetic structure from neutron diffraction measurement with moments along the (210) direction with

30 °

canting, from [226]. (e) ARPES spectral along

Z − Γ − Z

presents an “M”-shaped feature around

Γ

, from [227]. (f, g), Negative magnetoresistance and anomalous Hall resistance with three different orientations between

H

and

E

, from [226]. (h) Magnetic-field dependence of the Hall resistivity at different temperatures shows giant nonlinear behavior, from [228].

Fig.13 (a) Crystal structure schematic of Fe₃Sn₂, reproduced from Ref. [237]. (b) Fermi surface (I), high symmetry line band structure (II) and gapped Dirac cones at

K

point (III), reproduced from Ref. [238]. (c) Field dependent Hall resistivity and the extracted ordinary and anomalous Hall coefficients, reproduced from Ref. [238]. (d) Under-focused Lorentz transmission electron microscopy images of skyrmionic bubbles in the 600 nm nanostripe taken at temperature

630 K

with magnetic field

70 m T

Fig.14 (a)RMn₆Sn₆ lattice structure comprised of different layers of Mn₃Sn, RSn, and Sn atoms, from [252]. (b) Magnetic structure of RMn₆Sn₆ with the direction of magnetic moments depending on the R site element, from [253] (c) Fitting the Landau fan data from field dependent scanning tunneling spectroscopy measurements on TbMn₆Se₆ (open circles) with the spin polarized and Chern gapped Dirac dispersion (solid lines) (I) resulting field dependent size of the Dirac gap (II). Such gap is located above the Fermi level as indicated by the ARPES spectra in (III), from [253]. (d) Temperature dependent AHC of LiMn₆Sn₆ for magnetic field parallel to the z axis, from [254]. (e) Comparison of the intrinsic AHC of LiMn₆Sn₆ with those of RMn₆Sn₆, where FIM denotes the ferrimagnet and FM is the ferromagnet, from [254].

Fig.15 (a) Crystal structure of EuAs₃ [268]. (b) Magnetoresistance measurements [268]. (c) Carrier concentration and mobility [268]. (d) The Brillouin zone of EuAs₃, with high-symmetry points and (010) surface labeled [268]. (e) The band dispersions along

k y

direction probed by different photon energies. The red ellipse illustrates the topological nontrivial nodal loop schematically [268].

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