Current-induced switching of proximity-induced ferromagnetic surface states in a topological insulator.

Electrical manipulation of magnetization could be an essential function for energy-efficient spintronics technology. A magnetic topological insulator, possessing a magnetically gapped surface state with spin-polarized electrons, not only exhibits exotic topological phases relevant to the quantum anomalous Hall state but also enables the electrical control of its magnetic state at the surface. Here, we demonstrate efficient current-induced switching of the surface ferromagnetism in hetero-bilayers consisting of the topological insulator (Bi1-xSbx)2Te3 and the ferromagnetic insulator Cr2Ge2Te6, where the proximity-induced ferromagnetic surface states play two roles: efficient charge-to-spin current conversion and emergence of large anomalous Hall effect. The sign reversal of the surface ferromagnetic states with current injection is clearly observed, accompanying the nearly full magnetization reversal in the adjacent insulating Cr2Ge2Te6 layer of an optimal thickness range. The present results may facilitate an electrical control of dissipationless topological-current circuits.

Large non-reciprocal charge transport mediated by quantum anomalous Hall edge states.

The topological nature of the quantum anomalous Hall effect (QAHE) causes a dissipationless chiral edge current at the sample boundary1,2. Of fundamental interest is whether the chirality of the band structure manifests itself in charge transport properties. Here we report the observation of large non-reciprocal charge transport3 in a magnetic topological insulator, Cr-doped (Bi,Sb)2Te3. When the surface massive Dirac band is slightly carrier doped by a gate voltage, the edge state starts to dissipate and exhibits a current-direction-dependent resistance with a directional difference as large as 26%. The polarity of this diode effect depends on the magnetization direction as well as on the carrier type, electrons or holes. The correlation between the non-reciprocal resistance and the Hall resistance indicates that the non-reciprocity originates from the interplay between the chiral edge state and the Dirac surface state.

Anisotropic Quantum Transport through a Single Spin Channel in the Magnetic Semiconductor EuTiO3.

Magnetic semiconductors are a vital component in the understanding of quantum transport phenomena. To explore such delicate, yet fundamentally important, effects, it is crucial to maintain a high carrier mobility in the presence of magnetic moments. In practice, however, magnetization often diminishes the carrier mobility. Here, it is shown that EuTiO3 is a rare example of a magnetic semiconductor that can be desirably grown using the molecular beam epitaxy to possess a high carrier mobility exceeding 3000 cm2 V-1 s-1 at 2 K, while intrinsically hosting a large magnetization value, 7 µB per formula unit. This is demonstrated by measuring the Shubnikov-de Haas (SdH) oscillations in the ferromagnetic state of EuTiO3 films with various carrier densities. Using first-principles calculations, it is shown that the observed SdH oscillations originate genuinely from Ti 3d-t2g states which are fully spin-polarized due to their energetical proximity to the in-gap Eu 4f bands. Such an exchange coupling is further shown to have a profound effect on the effective mass and fermiology of the Ti 3d-t2g electrons, manifested by a directional anisotropy in the SdH oscillations. These findings suggest that EuTiO3 film is an ideal magnetic semiconductor, offering a fertile field to explore quantum phenomena suitable for spintronic applications.

Large Anomalous Hall Effect in Topological Insulators with Proximitized Ferromagnetic Insulators.

We report a proximity-driven large anomalous Hall effect in all-telluride heterostructures consisting of the ferromagnetic insulator Cr_{2}Ge_{2}Te_{6} and topological insulator (Bi,Sb)_{2}Te_{3}. Despite small magnetization in the (Bi,Sb)_{2}Te_{3} layer, the anomalous Hall conductivity reaches a large value of 0.2e^{2}/h in accord with a ferromagnetic response of the Cr_{2}Ge_{2}Te_{6}. The results show that the exchange coupling between the surface state of the topological insulator and the proximitized Cr_{2}Ge_{2}Te_{6} layer is effective and strong enough to open the sizable exchange gap in the surface state.

Nonreciprocal charge transport at topological insulator/superconductor interface.

Topological superconductor is attracting growing interest for its potential application to topological quantum computation. The superconducting proximity effect on the topological insulator surface state is one promising way to yield topological superconductivity. The superconductivity realized at the interface between Bi2Te3 and non-superconductor FeTe is one such candidate. Here, to detect the mutual interaction between superconductivity and topological surface state, we investigate nonreciprocal transport; i.e., current-direction dependent resistance, which is sensitive to the broken inversion symmetry of the electronic state. The largely enhanced nonreciprocal phenomenon is detected in the Bi2Te3/FeTe heterostructure associated with the superconducting transition. The emergent nonreciprocal signal at low magnetic fields is attributed to the current-induced modulation of supercurrent density under the in-plane magnetic fields due to the spin-momentum locking. The angular dependence of the signal reveals the symmetry of superconductivity and indicates the existence of another mechanism of nonreciprocal transport at high fields.

Anomalous Hall effect derived from multiple Weyl nodes in high-mobility EuTiO3 films.

EuTiO3, a magnetic semiconductor with a simple band structure, is one of the ideal systems to control the anomalous Hall effect (AHE) by tuning the Fermi level. The electrons in the conduction bands of La-doped EuTiO3 are subject to the spin-orbit interaction and Zeeman field from the spontaneous magnetization, which generates rich structures in the electron band such as Weyl nodes. This unique property makes EuTiO3 a relatively simple multiband system with its Berry curvature being controlled by electron doping and magnetic field. We report a nonmonotonic magnetic field dependence of the anomalous Hall resistivity, which is ascribed to the change of electronic bands induced by the Zeeman splitting during the magnetization process. The anomalous Hall resistivity measurement in high-mobility films grown by gas source molecular beam epitaxy shows additional terms in the AHE during the magnetization process, which is not proportional to the magnetization. Our theoretical calculation indicates that the change of Zeeman field in the process of canting the magnetic moments causes the type II Weyl nodes in the conduction band to move, resulting in a peculiar magnetic field dependence of the AHE; this is revealed by the high-quality films with a long scattering lifetime of conduction electrons.

Tailoring tricolor structure of magnetic topological insulator for robust axion insulator.

Exploration of novel electromagnetic phenomena is a subject of great interest in topological quantum materials. One of the unprecedented effects to be experimentally verified is the topological magnetoelectric (TME) effect originating from an unusual coupling of electric and magnetic fields in materials. A magnetic heterostructure of topological insulator (TI) hosts such exotic magnetoelectric coupling and can be expected to realize the TME effect as an axion insulator. We designed a magnetic TI with a tricolor structure where a nonmagnetic layer of (Bi, Sb)2Te3 is sandwiched by a soft ferromagnetic Cr-doped (Bi, Sb)2Te3 and a hard ferromagnetic V-doped (Bi, Sb)2Te3. Accompanied by the quantum anomalous Hall (QAH) effect, we observe zero Hall conductivity plateaus, which are a hallmark of the axion insulator state, in a wide range of magnetic fields between the coercive fields of Cr- and V-doped layers. The resistance of the axion insulator state reaches as high as 109 ohms, leading to a gigantic magnetoresistance ratio exceeding 10,000,000% upon the transition from the QAH state. The tricolor structure of the TI may not only be an ideal arena for the topologically distinct phenomena but can also provide magnetoresistive applications for advancing dissipation-less topological electronics.

Current-Driven Instability of the Quantum Anomalous Hall Effect in Ferromagnetic Topological Insulators.

The instability of the quantum anomalous Hall (QAH) effect has been studied as a function of the electric current and temperature in ferromagnetic topological insulator thin films. We find that a characteristic current for the breakdown of the QAH effect is roughly proportional to the Hall-bar width, indicating that the Hall electric field is relevant to the breakdown. We also find that electron transport is dominated by variable range hopping (VRH) at low temperatures. Combining the current and temperature dependences of the conductivity in the VRH regime, the localization length of the QAH state is evaluated to be about 5 µm. The long localization length suggests a marginally insulating nature of the QAH state due to a large number of in-gap states.

Terahertz spectroscopy on Faraday and Kerr rotations in a quantum anomalous Hall state.

Electrodynamic responses from three-dimensional topological insulators are characterized by the universal magnetoelectric term constituent of the Lagrangian formalism. The quantized magnetoelectric coupling, which is generally referred to as topological magnetoelectric effect, has been predicted to induce exotic phenomena including the universal low-energy magneto-optical effects. Here we report the experimental indication of the topological magnetoelectric effect, which is exemplified by magneto-optical Faraday and Kerr rotations in the quantum anomalous Hall states of magnetic topological insulator surfaces by terahertz magneto-optics. The universal relation composed of the observed Faraday and Kerr rotation angles but not of any material parameters (for example, dielectric constant and magnetic susceptibility) well exhibits the trajectory towards the fine structure constant in the quantized limit.

Weyl fermions and spin dynamics of metallic ferromagnet SrRuO3.

Weyl fermions that emerge at band crossings in momentum space caused by the spin-orbit interaction act as magnetic monopoles of the Berry curvature and contribute to a variety of novel transport phenomena such as anomalous Hall effect and magnetoresistance. However, their roles in other physical properties remain mostly unexplored. Here, we provide evidence by neutron Brillouin scattering that the spin dynamics of the metallic ferromagnet SrRuO3 in the very low energy range of milli-electron volts is closely relevant to Weyl fermions near Fermi energy. Although the observed spin wave dispersion is well described by the quadratic momentum dependence, the temperature dependence of the spin wave gap shows a nonmonotonous behaviour, which can be related to that of the anomalous Hall conductivity. This shows that the spin dynamics directly reflects the crucial role of Weyl fermions in the metallic ferromagnet.

Electrically tunable anomalous Hall effect in Pt thin films.

Pt is often considered to be an exchange-enhanced paramagnetic material, in which the Stoner criterion for ferromagnetism is nearly satisfied and, thus, external stimuli may induce unconventional magnetic characteristics. We report that a nonmagnetic perturbation in the form of a gate voltage applied via an ionic liquid induces an anomalous Hall effect (AHE) in Pt thin films, which resembles the AHE induced by the contact to Bi-doped yttrium iron garnet. Analysis of detailed temperature and magnetic field experiments indicates that the evolution of the AHE with temperature can be explained in terms of large local moments; the applied electric field induces magnetic moments as large as ~10 µ(B) that follow the Langevin function.

The anomalous Hall effect and magnetic monopoles in momentum space.

Efforts to find the magnetic monopole in real space have been made in cosmic rays and in particle accelerators, but there has not yet been any firm evidence for its existence because of its very heavy mass, approximately 10(16) giga-electron volts. We show that the magnetic monopole can appear in the crystal momentum space of solids in the accessible low-energy region (approximately 0.1 to 1 electron volts) in the context of the anomalous Hall effect. We report experimental results together with first-principles calculations on the ferromagnetic crystal SrRuO3 that provide evidence for the magnetic monopole in the crystal momentum space.