Axion Insulator Research Articles

Magnetic ordering and topology in Mn2Bi2Te5 and Mn2Sb2Te5 van der Waals materials

Using density functional theory calculations we study atomic, electronic, and magnetic structures and their influence on the topological phase of ${\mathrm{Mn}}_{2}{\mathrm{Bi}}_{2}{\mathrm{Te}}_{5}$ and ${\mathrm{Mn}}_{2}{\mathrm{Sb}}_{2}{\mathrm{Te}}_{5}$ van der Waals compounds. Our results show that the antiferromagnetic topological insulator (AFM TI) phase in ${\mathrm{Mn}}_{2}{\mathrm{Bi}}_{2}{\mathrm{Te}}_{5}$ is robust both to details of the magnetic ordering within its structural units, nonuple layer (NL) blocks, and the type of atomic layer stacking, NaCl-type ABC or NiAs-type ABAC, within the (${\mathrm{MnTe})}_{2}$ sublattice. The structure with the NiAs-type stacking is energetically more favorable for both compounds. However, for ${\mathrm{Mn}}_{2}{\mathrm{Sb}}_{2}{\mathrm{Te}}_{5}$ the AFM TI phase is realized in the unstable structure with ABC stacking while it is a Dirac semimetal in favorable structure with NiAs stacking within a (${\mathrm{MnTe})}_{2}$ sublattice. We also show that imposing the overall ferromagnetic state by applying an external magnetic field can drive the ${\mathrm{Mn}}_{2}\mathrm{Bi}{(\mathrm{Sb})}_{2}{\mathrm{Te}}_{5}$ compounds into different topologically nontrivial phases like axion insulator or Weyl semimetal.

Magnetically tunable Dirac and Weyl fermions in the Zintl materials family

Recent classification efforts encompassing crystalline symmetries have revealed rich possibilities for solid-state systems to support a tapestry of exotic topological states. However, finding materials that realize such states remains a daunting challenge. Here, we show how the interplay of topology, symmetry, and magnetism combined with doping and external electric and magnetic field controls can be used to drive the ${\mathrm{SrIn}}_{2}{\mathrm{As}}_{2}$ materials family into a variety of topological phases. Our first-principles calculations and symmetry analysis reveal that ${\mathrm{SrIn}}_{2}{\mathrm{As}}_{2}$ is a dual topological insulator with ${Z}_{2}=(1;000)$ and mirror Chern number ${C}_{M}=\ensuremath{-}1$. Its isostructural and isovalent antiferromagnetic cousin ${\mathrm{EuIn}}_{2}{\mathrm{As}}_{2}$ is found to be an axion insulator with ${Z}_{4}=2$. The broken time-reversal symmetry via Eu doping in ${\mathrm{Sr}}_{1\ensuremath{-}x}{\mathrm{Eu}}_{x}{\mathrm{In}}_{2}{\mathrm{As}}_{2}$ results in a higher-order or topological crystalline insulator state depending on the orientation of the magnetic easy axis. We also find that antiferromagnetic ${\mathrm{EuIn}}_{2}{\mathrm{P}}_{2}$ is a trivial insulator with ${Z}_{4}=0$, and that it undergoes a magnetic-field-driven transition to an ideal Weyl fermion or nodal fermion state with ${Z}_{4}=1$ with applied magnetic field. Our study identifies ${\mathrm{Sr}}_{1\ensuremath{-}x}{\mathrm{Eu}}_{x}{\mathrm{In}}_{2}{(\text{As},\mathrm{P})}_{2}$ as a tunable materials platform for investigating the physics and applications of Weyl and nodal fermions in the scaffolding of crystalline and axion insulator states.

Facet dependent surface energy gap on magnetic topological insulators

Magnetic topological insulators $({\mathrm{MnBi}}_{2}{\mathrm{Te}}_{4}){({\mathrm{Bi}}_{2}{\mathrm{Te}}_{3})}_{n}$ ($n=0,1,2,3$) are promising to realize exotic topological states such as the quantum anomalous Hall effect (QAHE) and axion insulator (AI), where the ${\mathrm{Bi}}_{2}{\mathrm{Te}}_{3}$ layer introduces versatility to engineer electronic and magnetic properties. However, whether surface states on the ${\mathrm{Bi}}_{2}{\mathrm{Te}}_{3}$ terminated facet are gapless or gapped is debated, and its consequences in thin-film properties are rarely discussed. In this work, we find that the ${\mathrm{Bi}}_{2}{\mathrm{Te}}_{3}$ terminated facets are gapless for $n\ensuremath{\ge}1$ compounds by calculations. Although the surface ${\mathrm{Bi}}_{2}{\mathrm{Te}}_{3}$ (one layer or more) and underlying ${\mathrm{MnBi}}_{2}{\mathrm{Te}}_{4}$ layers hybridize and give rise to a gap, such a hybridization gap may overlap with bulk valence bands, leading to a gapless surface after all. Such a metallic surface poses a fundamental challenge to realize QAHE or AI, which requires an insulating gap in thin films with at least one ${\mathrm{Bi}}_{2}{\mathrm{Te}}_{3}$ surface. In theory, the insulating phase can still be realized in a film if both surfaces are ${\mathrm{MnBi}}_{2}{\mathrm{Te}}_{4}$ layers. Otherwise, it requires that the film thickness be less than $10--20\phantom{\rule{4pt}{0ex}}\mathrm{nm}$ to push down bulk valence bands via the size effect. Our work paves the way to understand surface states and design bulk-insulating quantum devices in magnetic topological materials.

Intrinsic ferromagnetic and antiferromagnetic axion insulators in van der Waals materials MnX2B2T6 family

The ${\mathrm{MnBi}}_{2}{\mathrm{Te}}_{4}$ family has attracted significant attention due to its rich topological states such as the quantum anomalous Hall (QAH) insulator state, the axion insulator state, and the magnetic Weyl semimetal state. Nevertheless, the intrinsic antiferromagnetic (AFM) interlayer coupling in ${\mathrm{MnBi}}_{2}{\mathrm{Te}}_{4}$ partly hinders the realization of the ``high-temperature'' QAH effect. Here, by using first-principles electronic structure calculations, we design a new class of materials $\mathrm{Mn}{X}_{2}{B}_{2}{T}_{6}$ ($X=\text{Ge}$, Sn, or Pb; $B=\text{Sb}$ or Bi; $T=\text{Se}$ or Te) based on the ${X}_{2}{B}_{2}{T}_{5}$ structures rather than the ${\mathrm{Bi}}_{2}{\mathrm{Te}}_{3}$ family. We find that each septuple-layer $\mathrm{Mn}{B}_{2}{T}_{4}$ is sandwiched by two $[XT]$ layers, which may turn the AFM interlayer coupling into a ferromagnetic (FM) coupling. The calculations specifically demonstrate that ${\text{MnGe}}_{2}{\text{Sb}}_{2}{\text{Te}}_{6}$, ${\text{MnGe}}_{2}{\text{Bi}}_{2}{\text{Te}}_{6}$, and ${\text{MnPb}}_{2}{\text{Bi}}_{2}{\text{Te}}_{6}$ are FM axion insulators, while ${\mathrm{MnGe}}_{2}{\mathrm{Sb}}_{2}{\mathrm{Se}}_{6}$, ${\mathrm{MnGe}}_{2}{\mathrm{Bi}}_{2}{\mathrm{Se}}_{6}$, ${\mathrm{MnSn}}_{2}{\mathrm{Sb}}_{2}{\mathrm{Te}}_{6}$, and ${\mathrm{MnSn}}_{2}{\mathrm{Bi}}_{2}{\mathrm{Te}}_{6}$ are A-type AFM axion insulators. These seven materials all have an out-of-plane easy axis of magnetization. The $\mathrm{Mn}{X}_{2}{B}_{2}{T}_{6}$ family thus offers a promising platform beyond the ${\mathrm{MnBi}}_{2}{\mathrm{Te}}_{4}$ family for the realization of the quantized magnetoelectric effect and ``high-temperature'' QAH effect in future experiments.

Effects of phosphorus doping on the physical properties of axion insulator candidate EuIn2As2

We report an investigation on the single crystal growth, magnetic and transport properties of EuIn2(As1−x P x )2 (0 ≤ x ≤ 1). The physical properties of axion insulator candidate EuIn2As2 can be effectively tuned by P-doping. With increasing x, the c-axis lattice parameter decreases linearly, the magnetic transition temperature gradually increases and ferromagnetic interactions are enhanced. This is similar to the previously reported high pressure effect on EuIn2As2. For x = 0.40, a spin glass state at T g = 10 K emerges together with the observations of a butter-fly shaped magnetic hysteresis and slow magnetic behavior. Besides, magnetic transition has great influence on the charge carriers in this system and negative colossal magnetoresistance is observed for all P-doped samples. Our findings suggest that EuIn2(As1−x P x )2 is a promising material playground for exploring novel topological states.

Topological Antiferromagnetic Van der Waals Phase in Topological Insulator/Ferromagnet Heterostructures Synthesized by a CMOS-Compatible Sputtering Technique.

Breaking time-reversal symmetry by introducing magnetic order, thereby opening a gap in the topological surface state bands, is essential for realizing useful topological properties such as the quantum anomalous Hall and axion insulator states. In this work, a novel topological antiferromagnetic (AFM) phase is created at the interface of a sputtered, c-axis-oriented, topological insulator/ferromagnet heterostructure-Bi2 Te3 /Ni80 Fe20 because of diffusion of Ni in Bi2 Te3 (Ni-Bi2 Te3 ). The AFM property of the Ni-Bi2 Te3 interfacial layer is established by observation of spontaneous exchange bias in the magnetic hysteresis loop and compensated moments in the depth profile of the magnetization using polarized neutron reflectometry. Analysis of the structural and chemical properties of the Ni-Bi2 Te3 layer is carried out using selected-area electron diffraction, electron energy loss spectroscopy, and X-ray photoelectron spectroscopy. These studies, in parallel with first-principles calculations, indicate a solid-state chemical reaction that leads to the formation of Ni-Te bonds and the presence of topological antiferromagnetic (AFM) compound NiBi2 Te4 in the Ni-Bi2 Te3 interface layer. The Neél temperature of the Ni-Bi2 Te3 layer is ≈63 K, which is higher than that of typical magnetic topological insulators (MTIs). The presented results provide a pathway toward industrial complementary metal-oxide-semiconductor (CMOS)-process-compatible sputtered-MTI heterostructures, leading to novel materials for topological quantum devices.

Field-induced topological Hall effect in antiferromagnetic axion insulator candidate EuIn2As2

Magnetic topological materials have attracted significant attention due to their potential realization of a variety of novel quantum phenomena. ${\mathrm{EuIn}}_{2}{\mathrm{As}}_{2}$ has recently been theoretically recognized as a long-awaited intrinsic antiferromagnetic bulk axion insulator. However, experimental studies of the transport properties arising from the topological states in this material are scarce. In this paper, we perform detailed magnetoresistance (MR) and Hall measurements to study the magnetotransport properties of this material. We find that the transport is strongly influenced by the spin configuration of the Eu moments from the concomitant change in the field dependence of the MR and that of the magnetization below the N\'eel temperature. Most importantly, an anomalous Hall effect (AHE) and a large topological Hall effect (THE) are observed. We suggest that the AHE is originated from a nonvanishing net Berry curvature due to the helical spin structure and that the THE is attributed to the formation of a noncoplanar spin texture with a finite scalar spin chirality induced by the external magnetic field in ${\mathrm{EuIn}}_{2}{\mathrm{As}}_{2}$. Our studies provide a platform to understand the influence of the interplay between the topology of electronic bands and the field-induced magnetic structure on magnetoelectric transport properties. In addition, our observations give a hint to realize axion insulator states and higher-order topological insulator states through manipulating the magnetic state of ${\mathrm{EuIn}}_{2}{\mathrm{As}}_{2}$.

Local manifestations of thickness-dependent topology and edge states in the topological magnet MnBi2Te4

The interplay of non-trivial band topology and magnetism gives rise to a series of exotic quantum phenomena, such as the emergent quantum anomalous Hall (QAH) effect and topological magnetoelectric effect. Many of these quantum phenomena have local manifestations when the global symmetry is broken. Here, we report local signatures of the thickness dependent topology in intrinsic magnetic topological insulator MnBi$_2$Te$_4$(MBT), using scanning tunneling microscopy and spectroscopy on molecular beam epitaxy grown MBT thin films. A thickness-dependent band gap with an oscillatory feature is revealed, which we reproduce with theoretical calculations. Our theoretical results indicate a topological quantum phase transition beyond a film thickness of one monolayer, with alternating QAH and axion insulating states for even and odd layers, respectively. At an even-odd layer step, a localized gapped electronic state is observed, in agreement with an axion insulator edge state that results from a phase transition across the step. The demonstration of thickness-dependent topological properties highlights the role of nanoscale control over novel quantum states, reinforcing the necessity of thin film technology in quantum information science applications.

Evidence of magnetism-induced topological protection in the axion insulator candidate EuSn2P2

We unravel the interplay of topological properties and the layered (anti)ferromagnetic ordering in EuSn2P2, using spin and chemical selective electron and X-ray spectroscopies supported by first-principle calculations. We reveal the presence of in-plane long-range ferromagnetic order triggering topological invariants and resulting in the multiple protection of topological Dirac states. We provide clear evidence that layer-dependent spin-momentum locking coexists with ferromagnetism in this material, a cohabitation that promotes EuSn2P2 as a prime candidate axion insulator for topological antiferromagnetic spintronics applications.

Enhancement of anomalous Hall effect in epitaxial thin films of intrinsic magnetic topological insulator MnBi2Te4 with Fermi-level tuning

The recently discovered intrinsic magnetic topological insulator MnBi2Te4 has attracted keen interest for exotic quantum states such as a quantum anomalous Hall insulator and an axion insulator. Such quantum states of MnBi2Te4 have been intensively studied mainly in atomically thin exfoliated samples, yet thin film samples with critically tuned Fermi level would be indispensable for further pursuit of topological functionality in MnBi2Te4 and related heterointerfaces. Here, we report on fabrication of an Sb-doped MnBi2Te4 thin film by molecular beam epitaxy and their transport properties. The Sb-substitution induces the change in the carrier type and the subsequent increase in resistivity, demonstrating the tuning of the Fermi level (EF) across the bulk bandgap and the phase change to the topologically nontrivial phase. The EF is further finely controlled in a field-effect transistor device. We observe the enhancement of the anomalous Hall conductivity at the charge neutral point, confirming the opening of the magnetic exchange gap in surface Dirac states. The precise control of the band structure and the Fermi level in the thin-film form will lead to exploring exotic phenomena based on intrinsic magnetic topological insulators.

Topological spintronics and magnetoelectronics.

Topological electronic materials, such as topological insulators, are distinct from trivial materials in the topology of their electronic band structures that lead to robust, unconventional topological states, which could bring revolutionary developments in electronics. This Perspective summarizes developments of topological insulators in various electronic applications including spintronics and magnetoelectronics. We group and analyse several important phenomena in spintronics using topological insulators, including spin-orbit torque, the magnetic proximity effect, interplay between antiferromagnetism and topology, and the formation of topological spin textures. We also outline recent developments in magnetoelectronics such as the axion insulator and the topological magnetoelectric effect observed using different topological insulators.

Band gap opening in the BiSbTeSe2 topological surface state induced by ferromagnetic surface reordering

Introducing magnetic exchange interaction into topological insulators is known to break the time-reversal symmetry and to open a gap at the Dirac point in the otherwise gapless topological surface states. This allows various novel topological quantum phenomena to be attained, including the quantum anomalous Hall effect and can lead to the emergence of the axion insulator phase. Among the different approaches, magnetic doping is an effective, but still experimentally challenging pathway to provide the magnetic exchange interaction. Here we demonstrate that epitaxial deposition of Co and Mn magnetic atoms onto the (0001) surface of the ${\mathrm{BiSbTeSe}}_{2}$ topological insulator with a coverage between 0.6 and 3 atoms per surface cell performed in a finely tuned temperature range of ${300}^{\ensuremath{\circ}}$--${330}^{\ensuremath{\circ}}\mathrm{C}$ leads to the substitution of pnictogen atoms in the surface layer with magnetic atoms and to the formation of a two-dimensional magnetic phase with out-of-plane magnetization as proved by SQUID magnetometry. This magnetic layer is responsible for the appearance of a gap in the Dirac surface state as revealed by laser-based microfocused angle-resolved photoelectron spectroscopy. Our measurements have shown that the gap exists within the temperature range of 15--100 K, where the out-of-plane magnetization persists. The presented experimental results are supported by relativistic ab initio calculations.

Gate-tunable magnetoresistance in six-septuple-layer MnBi2Te4

The recently discovered antiferromagnetic topological insulator MnBi2Te4 hosts many exotic topological quantum phases such as the axion insulator and the Chern insulator. Here we report on systematic gate-voltage-dependent magneto-transport studies in six-septuple-layer MnBi2Te4. In the p-type carrier regime, we observe positive linear magnetoresistance (MR) when MnBi2Te4 is polarized in the ferromagnetic state by an out-of-plane magnetic field. Whereas in the n-type regime, distinct negative MR behaviors are observed. The behaviors of magnetoresistance in both regimes are highly robust against temperature up to the Néel temperature. Within the antiferromagnetic regime, the behavior of MR exhibits a transition from negative to positive under the control of gate voltage. The boundaries of the MR phase diagram can be explicitly marked by the gate-voltage-independent magnetic fields that characterize the processes of the spin-flop transition. The rich transport phenomena demonstrate the intricate interplay between topology, magnetism and dimensionality in MnBi2Te4.

PT-Symmetry-Enabled Spin Circular Photogalvanic Effect in Antiferromagnetic Insulators.

The short timescale spin dynamics in antiferromagnets is an attractive feature from the standpoint of ultrafast spintronics. Yet generating highly polarized spin current at room temperature remains a fundamental challenge for antiferromagnets. We propose a spin circular photogalvanic effect (spin CPGE), in which circularly polarized light can produce a highly spin-polarized current at room temperature, through an "injection-current-like" mechanism in parity-time (PT)-symmetric antiferromagnetic (AFM) insulators. We demonstrate this effect by first-principles simulations of bilayer CrI_{3} and room-temperature-AFM hematite. The spin CPGE is significant, and the magnitude of spin photocurrent is comparable with the widely observed charge photocurrent in ferroelectric materials. Interestingly, this spin photocurrent is not sensitive to spin-orbit interactions, which were regarded as fundamental mechanisms for generating spin current. Given the fast response of light-matter interactions, large energy scale, and insensitivity to spin-orbit interactions, our work gives hope to realizing fast-dynamic and temperature-robust pure spin current in a wide range of PT-symmetric AFM materials, including topological axion insulators and weak-relativistic magnetic insulators.

A Majorana perspective on understanding and identifying axion insulators

An axion insulator is theoretically introduced to harbor unique surface states with half-integer Chern number {{{{{{{mathcal{C}}}}}}}}. Recently, experimental progress has been made in different candidate systems, while a unique Hall response to directly reflect the half-integer Chern number is still lacking to distinguish an axion state from other possible insulators. Here we show that the {{{{{{{mathcal{C}}}}}}}}=frac{1}{2} axion state corresponds to a topological state with Chern number {{{{{{{mathcal{N}}}}}}}}=1 in the Majorana basis. In proximity to an s − wave superconductor, a topological phase transition to an {{{{{{{mathcal{N}}}}}}}}=0 phase takes place at critical superconducting pairing strength. Our theoretical analysis shows that a chiral Majorana hinge mode emerges at the boundary of {{{{{{{mathcal{N}}}}}}}}=1 and {{{{{{{mathcal{N}}}}}}}}=0 regions on the surface of an axion insulator. Furthermore, we propose a half-integer quantized thermal Hall conductance via a thermal transport measurement, which is a signature of the gapless chiral Majorana mode and thus confirms the {{{{{{{mathcal{C}}}}}}}}=frac{1}{2} ({{{{{{{mathcal{N}}}}}}}}=1) topological nature of an axion state. Our proposals help to theoretically comprehend and experimentally identify the axion insulator and may benefit the research of topological quantum computation.

Nonlocal sidewall response and deviation from exact quantization of the topological magnetoelectric effect in axion-insulator thin films

Topological insulator (TI) thin films with surface magnetism are expected to exhibit a quantized anomalous Hall effect (QAHE) when the magnetizations on the top and bottom surfaces are parallel, and a quantized topological magnetoelectric (QTME) response when the magnetizations have opposing orientations (axion insulator phase) and the films are sufficiently thick. We present a unified picture of both effects that associates deviations from exact quantization of the QTME caused by finite thickness with non-locality in the side-wall current response function. Using realistic tight-binding model calculations, we show that in $Bi_2Se_3$ TI thin films deviations from quantization in the axion insulator-phase are reduced in size when the exchange coupling of tight-binding model basis states to the local magnetization near the surface is strengthened. Stronger exchange coupling also reduces the effect of potential disorder, which is unimportant for the QAHE but detrimental for the QTME, which requires that the Fermi energy lie inside the gap at all positions.

Topological descendants of a multicritical Dirac semimetal with magnetism and strain

The past decades have seen an ever increasing rise in classification and characterization of topological materials. One of the most important questions is how to control and manipulate topological phases. Here, the authors predict a multicritical topological paradigm in EuTl${}_{2}$. Starting from a paramagnetic Dirac semimetallic phase, a plethora of descendant topological phases are accessible with magnetism and strain, including Dirac and Weyl magnetic semimetals, axion insulators, and a variety of other topological crystalline insulators protected by different symmetries.

Detection of Magnetic Gap in Topological Surface States of MnBi2Te4 Supported by the National Key Research and Development Program of China (Grant Nos. 2017YFA0303302, 2018YFA0305604, and 2018YFA0307100), the National Natural Science Foundation of China (Grant Nos. 11888101, 11774008, 11704279, 11874035, and 51788104), the Strategic Priority Research Program of Chinese Academy of Sciences (Grant No. XDB28000000), the Beijing Natural Science Foundation

Recently, intrinsic antiferromagnetic topological insulator MnBi2Te4 has drawn intense research interest and leads to plenty of significant progress in physics and materials science by hosting quantum anomalous Hall effect, axion insulator state, and other quantum phases. An essential ingredient to realize these quantum states is the magnetic gap in the topological surface states induced by the out-of-plane ferromagnetism on the surface of MnBi2Te4. However, the experimental observations of the surface gap remain controversial. Here, we report the observation of the surface gap via the point contact tunneling spectroscopy. In agreement with theoretical calculations, the gap size is around 50 meV, which vanishes as the sample becomes paramagnetic with increasing temperature. The magnetoresistance hysteresis is detected through the point contact junction on the sample surface with an out-of-plane magnetic field, substantiating the surface ferromagnetism. Furthermore, the non-zero transport spin polarization coming from the ferromagnetism is determined by the point contact Andreev reflection spectroscopy. Combining these results, the magnetism-induced gap in topological surface states of MnBi2Te4 is revealed.

Tuning magnetism and band topology through antisite defects in Sb-doped MnBi4Te7

The fine control of magnetism and electronic structure is crucial since the interplay between magnetism and band topology can lead to various novel magnetic topological states including axion insulators, magnetic Weyl semimetals and Chern insulators etc. Through crystal growth, transport, thermodynamic, neutron diffraction measurements, we show that with Sb-doping, the newly-discovered intrinsic antiferromagnetic topological insulator MnBi4Te7 evolves from antiferro-magnetic to ferromagnetic and then ferrimagnetic. We attribute this to the formation of Mn(Bi,Sb) antisites upon doping, which result in additional Mn sublattices that modify the delicate interlayer magnetic interactions and cause the dominant Mn sublattice to go from antiferromagnetic to ferro-magnetic. We further investigate the effect of antisites on the band topology using the first-principles calculations. Without considering antisites, the series evolves from antiferromagnetic topological insulator (x = 0) to ferromagnetic axion insulators. In the exaggerated case of 16.7% of periodic antisites, the band topology is modified and type-I magnetic Weyl semimetal phase can be realized at intermediate dopings. Therefore, this doping series provides a fruitful platform with continuously tunable magnetism and topology for investigating emergent phenomena, including quantum anomalous Hall effect, Fermi arc states, etc.

Growth and characterization of the dynamical axion insulator candidateMn2Bi2Te5with intrinsic antiferromagnetism

Intrinsic antiferromagnetic ${\mathrm{Mn}}_{2}{\mathrm{Bi}}_{2}{\mathrm{Te}}_{5}$ crystals, a candidate of dynamical axion insulator proposed theoretically recently, were successfully grown by the self-flux method. The crystal structure and chemical composition of ${\mathrm{Mn}}_{2}{\mathrm{Bi}}_{2}{\mathrm{Te}}_{5}$ crystals were experimentally substantiated. Temperature-dependent resistivity of ${\mathrm{Mn}}_{2}{\mathrm{Bi}}_{2}{\mathrm{Te}}_{5}$ shows a metallic behavior $(d\ensuremath{\rho}/dT>0)$ when temperature $T>25\phantom{\rule{0.28em}{0ex}}\mathrm{K}$ and a subsequently semiconductorlike feature $(d\ensuremath{\rho}/dT<0)$. Magnetic measurement verifies that ${\mathrm{Mn}}_{2}{\mathrm{Bi}}_{2}{\mathrm{Te}}_{5}$ is ferromagnetic at $ab$ plane but antiferromagnetic along the $c$ axis, whose N\'eel temperature is around 20 K. Analysis of magnetic hysteresis loops measured at different temperatures substantiates that critical indices of magnetic-paramagnetic phase transition in ${\mathrm{Mn}}_{2}{\mathrm{Bi}}_{2}{\mathrm{Te}}_{5}$ are satisfied to the prediction of Landau mean-field theory. When $T<20\phantom{\rule{0.16em}{0ex}}\mathrm{K}$, there are unconventional Hall effects, including both anomalous Hall effect and topological Hall effect, when magnetic field $B<3.4\phantom{\rule{0.16em}{0ex}}\mathrm{T}$. Based on theoretical electronic-band structure of ${\mathrm{Mn}}_{2}{\mathrm{Bi}}_{2}{\mathrm{Te}}_{5}$, the anomalous Hall effect of ${\mathrm{Mn}}_{2}{\mathrm{Bi}}_{2}{\mathrm{Te}}_{5}$ can be described by the Karplus-Luttinger (Berry curvature) mechanism, while the topological Hall effect of ${\mathrm{Mn}}_{2}{\mathrm{Bi}}_{2}{\mathrm{Te}}_{5}$, under $B<3.4\phantom{\rule{0.16em}{0ex}}\mathrm{T}$, is attributed to noncollinear spin structure. Our results strongly suggest that ${\mathrm{Mn}}_{2}{\mathrm{Bi}}_{2}{\mathrm{Te}}_{5}$ is an axion insulator.