Session W43: Axion Insulators

Quantized Magnetoelectric Effect in antiferromagnetic MnBi2Te4 Tunnel Junctions

Intrinsic magnetic topological insulators such as layered MnBi₂Te₄ are believed to be axion insulators exhibiting exotic physical properties at low temperatures. However, direct identification of axion insulators remains experimentally elusive because the observed vanishing Hall resistance, while indicating the onset of the axion field, is insufficient to distinguish between an axion insulator and a trivial insulator. We conceive a tunnel junction with the barrier being an antiferromagnetic topological insulator and study its magnetoelectric responses arising from the axion field. Using time-dependent non-equilibrium Green's functions, we theoretically demonstrate that if the tunnel barrier is indeed an axion insulator, it should be directly reflected in the quantized tunnel current density. We benchmark our results against multiple material factors such as system size and concentration of impurities, confirming unambiguously the validity of our proposed setup in identifying axion insulators.   

Transport and tunneling studies of ferromagnetic Mn(Bi,Sb)6Te10

Two-dimensional van der Waals magnets with topological phases can host novel quantum states. For example, combining a topological insulator, Bi₂Te₃, with magnetism into a single crystal provides a tunable platform to study the quantum anomalous Hall effect and the axion insulator state. In this work, we synthesize Mn(Bi,Sb)₆Te₁₀ crystals with a ferromagnetic ground state and study exfoliated sheets of several tens of nm in thickness using Hall bar and tunnel junction structures prepared inside a glovebox. In transport, we observed a clear Curie temperature of ~ 11 K and a coercive field of ~ 0.02 T at 2 K, in agreement with bulk measurements. We build vertical tunnel junctions of Mn(Bi_0.88,Sb_0.18)₆Te₁₀ using a graphite electrode, a thin h-BN barrier and the dry transfer method to probe the density of states of the sample surface. We observe suppressed differential tunneling conductance in a small range of biases (~ 15 mV) near V_dc = 0, which disappears at elevated temperatures. This is reminiscent of a magnetic exchange gap observed in ARPES measurements (Yan et al, axiv:2107.08137v1). The tunneling spectra evolve with a perpendicular magnetic field, showing a number of intriguing features. We discuss possible interpretations and the implications on the band structure and magnetism in Mn(Bi,Sb)₆Te₁₀.   

    

The Axion Insulator State in Hundred-Nanometer-Thick Magnetic Topological Insulator Sandwich Heterostructures

One unique feature of the magnetic topological materials is that their electromagnetic response includes a topological coupling θ term, in addition to the ordinary Maxwell’s Lagrangian, leading to the so-called “axion electrodynamics”. An axion insulator is viewed as a 3D topological insulator (TI) with a quantized non-zero θ parameter in the bulk and the surface states gapped by surface magnetization. To date, the axion insulator states have been claimed in both molecular beam epitaxy (MBE)-grown magnetic TI sandwiches and exfoliated MnBi₂Te₄ flakes with “even” number layers. All these samples have a thickness of less than ~12 nm, which is still near the 2D-to-3D boundary. In this work, we use MBE to synthesize magnetic TI sandwich heterostructures with thicknesses up to 106 nm. We find a robust axion insulator state appears in all these magnetic TI heterostructures. Moreover, we find when the thickness of the middle undoped TI layer is less than 3nm, the zero Hall conductance plateau disappears, and thus the samples transition to the standard quantum anomalous Hall (QAH) insulating state. The realization of the hundred-nanometer-thick axion insulators provides an outstanding platform for the exploration of the emergent topological states in 3D magnetic TI multilayers, including the high-order TI phase.

    

Axion optical induction of antiferromagnetic order

Using circularly-polarized light to control quantum matter is a highly intriguing topic in physics, chemistry and biology. Previous studies have demonstrated helicity-dependent optical control of spatial chirality and magnetization M. In our work, we report the surprising observation of helicity-dependent optical control of fully-compensated antiferromagnetic (AFM) order in 2D even-layered MnBi2Te4, a topological Axion insulator with neither chirality nor M. By shining circularly-polarized light while cooling across the Néel temperature, surprisingly, we found that light helicity and wavelength can directly control the AFM order parameter. We further demonstrate the optical creation of AFM domain walls by double induction beams and the direct switching of AFM domains by ultrafast pulses. To understand this optical control, we study a novel type of circular dichroism (CD) proportional to the AFM order, which only shows up in reflection but is absent in transmission. We show that the optical control and CD both arise from the optical Axion electrodynamics, which can be visualized as a Berry curvature real space dipole.

    

Polar Kerr effect in antiferromagnets by optical axion electrodynamics

While the polar Kerr effect is considered a measure of the net magnetic moment in materials, it may also occur in fully compensated antiferromagnets because of magneto-electric coupling. Since electromagnetic response properties unique to antiferromagnets are rarely known, the magneto-electric Kerr effect is potentially an important tool to detect and manipulate the antiferromagnetic order. However, theoretical analysis of this effect is challenging because of the difficulty in calculating the isotropic part (i.e., the axion part) of the optical magneto-electric coupling in periodic systems. The peculiar property of the axion magneto-electric coupling leads to the quantization in the static limit, allowing calculations based on topological analysis, which is hard to generalize to optical frequencies beyond the band gap. In this talk, I will introduce a theory of optical axion electrodynamics that allows for a simple quantitative analysis. Then I will apply our theory to the Kerr effect in a topological antiferromagnet MnBi2Te4.   

Topological magnetoelectric effects in magnetic topological insulator thin films via first-principles calculations

Broken time-reversal symmetry in topological insulators (TI) gives rise to novel quantum phases without the need of external magnetic fields. Most well-known is the Quantum Anomalous Hall (QAH) phase characterized by a non-zero Chern number and chiral edge-states localized at the boundary of the samples. Another important phase is the axion insulator (AI) phase, which has a zero Chern number and expected to display a quantized topological magnetoelectric effect (QTME). Recent experimental work on intrinsic antiferromagnetic TIs (such as MnBi₂Se₄/Te₄) suggests the possibility of realizing both the QAH and the AI phase in quasi–two-dimensional thin films of the same material by simply controlling the number of constituent septuple layers. Nevertheless, a direct verification of the elusive QTME in these systems has not yet been achieved due to the complexity and lack of precise control of the layered structure. To elucidate salient features of the AI phase, we present here a first-principles study of the crystal and electronic structure of multilayered magnetized TI thins films. The resulting microscopic tight-binding model is compared with a simplified effective model (1) based on coupled Dirac cone degrees of freedom on both surfaces of each septuple layer. We use these models to analyze theoretically the topological characteristics of these materials and investigate their response to external electric and magnetic fields.

(1) C. Lei, S. Chen, and A. H. MacDonald PNAS, 117(44), 27224–27230 (2020).   

High throughput search of magnetic topological materials II

It has been shown that in systems with broken time reversal symmetry, the topological crystalline classification of solids is extended. In particular, new phases of matter such as axion insulators can occur. It is still hard to identify which realistic material can host these phases since it had to be done case by case. In this work, we apply the formalism of magnetic topological quantum chemistry, which provides a connection between the symmetry properties of Bloch functions topology. We analyzed 379 experimentally reported magnetic structures and found that 176 of them present non-trivial topology for some value of the Hubbard U parameter, either topological insulators, enforced semimetals or both. We also report 43 obstructed atomic insulators, diagnosed via real space indicators. We choose 4 examplary high-quality systems to perform a more detailed analysis of its topological properties, such as axion angle, topological invariants and surface spectrum. Our results enlarge the family of experimentally reachable magnetic topological materials.   

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

Intrinsic magnetic topological materials provide a more fertile playground to give rise to nontrivial topological phases, such as a quantum anomalous Hall effect and axion insulator states. EuIn₂As₂ has been theoretically recognized as a long-awaited intrinsic antiferromagnetic bulk axion insulator. In this talk, we will discuss the magnetotransport properties of this material through our magnetoresistance (MR) and Hall measurements. The concomitant field dependence of MR and that of magnetization observed below the Néel temperature provide evidence that the transport phenomena are strongly influenced by the spin configuration of the Eu moment in this system. Most importantly, an anomalous Hall effect (AHE) and a large topological Hall effect (THE) are observed. We suggest that the AHE originated from a nonvanishing net Berry curvature due to the helical spin structure. The THE is caused by the formation of a noncoplanar spin texture induced by the external magnetic field in EuIn₂As₂. Our studies provide a platform to understand the influence of the interplay between the topology of electronic bands and field-induced magnetic structure on magnetoelectric transport properties.

    

Modeling the complex magnetic phase diagram of the axion insulator candidate EuIn2As2 in a magnetic field

The axion insulator candidate EuIn2As2 exhibits a broken-helix magnetic ground state [S. X. M. Riberolles et al., Nature communications, 12(1), 1-7. (2021)] that breaks inversion but respects the product of twofold rotation and time-reversal (2’) symmetry. This 2’ symmetry is predicted to lead to exotic protected gapless surface states on select crystal faces. Motivated by the recent neutron scattering experiments that report a complex magnetic behavior in an external magnetic field, we design and study a minimal symmetry-constrained spin model that exhibits a broken-helix ground state. In addition to first, second, and third neighbor bilinear exchange interactions, we identify a first-neighbor biquadratic exchange coupling as the crucial ingredient to capture the unique physics of the material. We map out the phase diagram in a magnetic field, focusing on the evolution of the different helical magnetic domains observed in the ground state. We find that different domains are characterized by different symmetries in a magnetic field, pointing to the intriguing possibility of protected gapless modes located at internal domain wall boundaries in the material.   

Coexisting magnetic domains with distinct field-induced symmetries in the topological magnet EuIn2As2.

Hexagonal EuIn₂As₂ exhibits low-symmetry helical antiferromagnetic order that makes the compound a candidate stoichiometric magnetic topological-crystalline axion insulator with exotic surface states [1]. It is predicted that the surface states can be tuned by the direction and strength of an applied magnetic field [1]. We here report results from in-field single-crystal neutron diffraction experiments on EuIn₂As₂ with H||b, revealing successive field-induced changes to the magnetic order and discuss the implications to the system’s topology. With increasing field, magnetic domains displaying different symmetries are stabilized. Out of the three zero-field orthorhombic magnetic domains, one transitions to a canted A-type structure, while the other two both stabilize a fan-type structure. We find these domain related orders to coexist in our single crystal sample until full magnetic saturation is achieved at approximately 1 T. We predict that the presence of domains with differing magnetic symmetries has the potential to induce bulk topological edge modes at the magnetic domain boundaries.

[1] S. X. M. Riberolles et al., Nat Commun, 12, 999 (2021)   

Unraveling Magnetoelectric effect in Axion insulator candidate EuIn2As2

Topological materials have taken center stage of condensed matter physics. The Axion insulator is theoretically predicted as a novel class of topological materals, while experimental realization is lacking. EuIn2As2 has been proposed to be a promising candidate for the Axion insulator. In this work, we perform optical Second Harmonic Generation(SHG) and symmetry analysis to understand its magnetic order. We also surprisingly find the SHG anisotropy is sensitive to tiny external magnetic field. While breaking both P and T by the intrinsic magnetic order, it allows for magnetoelectric effect. Our work suggests exciting potential to use Axion insulators as functional magnetoelectric devices.   

Gapped surface states in axion insulator candidate EuIn2As2 imaged by Scanning Tunneling Microscopy

Axion insulators are a proposed class of magnetic topological insulators in which time-reversal-symmetry (TRS) is broken either intrinsically or externally. EuIn2As2 is predicted to be an axion insulator that intrinsically breaks TRS. Here we use scanning tunneling microscopy (STM) and quasiparticle interference (QPI) imaging to measure the band structure of EuIn2As2. We discover three types of cleaved surfaces through imaging on pristine, La-doped, and Sb-doped samples: a 2x1 reconstructed Eu surface, a maze-like reconstruction of the In layer, and an intermediate As layer. Our QPI imaging on the Eu 2x1 surface shows scattering vectors corresponding to both bulk bands and surface states. We identify a bulk band gap ~ 150 meV and a surface state gap ~ 50 meV, which support the theoretical prediction that EuIn2As2 is an axion insulator. Our findings support EuIn2As2 as a platform to study axion insulator related phenomena.   

Realizing Dirac and Weyl fermions in magnetically tunable Zintl materials

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  SrIn₂As₂ materials family into various topological phases. Our first-principles calculations and symmetry analysis reveal that SrIn₂As₂ is a dual topological insulator with Z₂=(1;000) and mirror Chern number C_M=-1. Its isostructural and isovalent antiferromagnetic cousin EuIn₂As₂ is found to be an axion insulator  (Z₄ = 2). The broken time-reversal symmetry via Eu doping results in a higher-order or topological crystalline insulator state in Sr_1-xEu_xIn₂As_2, depending on the orientation of the magnetic easy axis. We also find that antiferromagnetic EuIn₂P₂ is a trivial insulator (Z₄ = 0). It undergoes a magnetic-field-driven transition to an ideal Weyl fermion or nodal fermion state (Z₄ = 1) with an applied magnetic field. Our study identifies Sr_1-xEu_xIn₂(As, 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.