Competing correlated states around the zero-field Wigner crystallization transition of electrons in two dimensions.

The competition between kinetic energy and Coulomb interactions in electronic systems leads to complex many-body ground states with competing orders. Here we present zinc oxide-based two-dimensional electron systems as a high-mobility system to study the low-temperature phases of strongly interacting electrons. An analysis of the electronic transport provides evidence for competing correlated metallic and insulating states with varying degrees of spin polarization. Some features bear quantitative resemblance to quantum Monte Carlo simulation results, including the transition point from the paramagnetic Fermi liquid to Wigner crystal and the absence of a Stoner transition. At very low temperatures, we resolve a non-monotonic spin polarizability of electrons across the phase transition, pointing towards a low spin phase of electrons, and a two-order-of-magnitude positive magnetoresistance that is challenging to understand within traditional metallic transport paradigms. This work establishes zinc oxide as a platform for studying strongly correlated electrons in two dimensions.

Magneto-optical spectroscopy on Weyl nodes for anomalous and topological Hall effects in chiral MnGe.

Physics of Weyl electrons has been attracting considerable interests and further accelerated by recent discoveries of giant anomalous Hall effect (AHE) and topological Hall effect (THE) in several magnetic systems including non-coplanar magnets with spin chirality or small-size skyrmions. These AHEs/THEs are often attributed to the intense Berry curvature generated around the Weyl nodes accompanied by band anti-crossings, yet the direct experimental evidence still remains elusive. Here, we demonstrate an essential role of the band anti-crossing for the giant AHE and THE in MnGe thin film by using the terahertz magneto-optical spectroscopy. The low-energy resonance structures around ~ 1.2 meV in the optical Hall conductivity show the enhanced AHE and THE, indicating the emergence of at least two distinct anti-crossings near the Fermi level. The theoretical analysis demonstrates that the competition of these resonances with opposite signs is a cause of the strong temperature and magnetic-field dependences of observed DC Hall conductivity. These results lead to the comprehensive understanding of the interplay among the transport phenomena, optical responses and electronic/spin structures.

Direct Observation of the Statics and Dynamics of Emergent Magnetic Monopoles in a Chiral Magnet.

In the three-dimensional (3D) Heisenberg model, topological point defects known as spin hedgehogs behave as emergent magnetic monopoles, i.e., quantized sources and sinks of gauge fields that couple strongly to conduction electrons, and cause unconventional transport responses such as the gigantic Hall effect. We observe a dramatic change in the Hall effect upon the transformation of a spin hedgehog crystal in a chiral magnet MnGe through combined measurements of magnetotransport and small-angle neutron scattering (SANS). At low temperatures, well-defined SANS peaks and a negative Hall signal are each consistent with expectations for a static hedgehog lattice. In contrast, a positive Hall signal takes over when the hedgehog lattice fluctuates at higher temperatures, with a diffuse SANS signal observed upon decomposition of the hedgehog lattice. Our approach provides a simple way to both distinguish and disentangle the roles of static and dynamic emergent monopoles on the augmented Hall motion of conduction electrons.

Giant magneto-optical responses in magnetic Weyl semimetal Co3Sn2S2.

The Weyl semimetal (WSM), which hosts pairs of Weyl points and accompanying Berry curvature in momentum space near Fermi level, is expected to exhibit novel electromagnetic phenomena. Although the large optical/electronic responses such as nonlinear optical effects and intrinsic anomalous Hall effect (AHE) have recently been demonstrated indeed, the conclusive evidence for their topological origins has remained elusive. Here, we report the gigantic magneto-optical (MO) response arising from the topological electronic structure with intense Berry curvature in magnetic WSM Co3Sn2S2. The low-energy MO spectroscopy and the first-principles calculation reveal that the interband transitions on the nodal rings connected to the Weyl points show the resonance of the optical Hall conductivity and give rise to the giant intrinsic AHE in dc limit. The terahertz Faraday and infrared Kerr rotations are found to be remarkably enhanced by these resonances with topological electronic structures, demonstrating the novel low-energy optical response inherent to the magnetic WSM.

Electric dipole effect in PdCoO2/ß-Ga2O3 Schottky diodes for high-temperature operation.

High-temperature operation of semiconductor devices is widely demanded for switching/sensing purposes in automobiles, plants, and aerospace applications. As alternatives to conventional Si-based Schottky diodes usable only at 200°C or less, Schottky interfaces based on wide-bandgap semiconductors have been extensively studied to realize a large Schottky barrier height that makes high-temperature operation possible. Here, we report a unique crystalline Schottky interface composed of a wide-gap semiconductor ß-Ga2O3 and a layered metal PdCoO2. At the thermally stable all-oxide interface, the polar layered structure of PdCoO2 generates electric dipoles, realizing a large Schottky barrier height of ~1.8 eV, well beyond the 0.7 eV expected from the basal Schottky-Mott relation. Because of the naturally formed homogeneous electric dipoles, this junction achieved current rectification with a large on/off ratio approaching 108 even at a high temperature of 350°C. The exceptional performance of the PdCoO2/ß-Ga2O3 Schottky diodes makes power/sensing devices possible for extreme environments.

Erratum: Large Unidirectional Magnetoresistance in a Magnetic Topological Insulator [Phys. Rev. Lett. 117, 127202 (2016)].

This corrects the article DOI: 10.1103/PhysRevLett.117.127202.

Fe-Sn nanocrystalline films for flexible magnetic sensors with high thermal stability.

The interplay of magnetism and spin-orbit coupling on an Fe kagome lattice in Fe3Sn2 crystal produces a unique band structure leading to an order of magnitude larger anomalous Hall effect than in conventional ferromagnetic metals. In this work, we demonstrate that Fe-Sn nanocrystalline films also exhibit a large anomalous Hall effect, being applicable to magnetic sensors that satisfy both high sensitivity and thermal stability. In the films prepared by a co-sputtering technique at room temperature, the partial development of crystalline lattice order appears as nanocrystals of the Fe-Sn kagome layer. The tangent of Hall angle, the ratio of Hall resistivity to longitudinal resistivity, is maximized in the optimal alloy composition of close to Fe3Sn2, implying the possible contribution of the kagome origin even though the films are composed of nanocrystal and amorphous-like domains. These ferromagnetic Fe-Sn films possess great advantages as a Hall sensor over semiconductors in thermal stability owing to the weak temperature dependence of the anomalous Hall responses. Moreover, the room-temperature fabrication enables us to develop a mechanically flexible Hall sensor on an organic substrate. These demonstrations manifest the potential of ferromagnetic kagome metals as untapped reservoir for designing new functional devices.

Current-driven magnetization switching in ferromagnetic bulk Rashba semiconductor (Ge,Mn)Te.

Multiferroic materials with both ferroelectric and ferromagnetic orders provide a promising arena for the electrical manipulation of magnetization through the mutual correlation between those ferroic orders. Such a concept of multiferroics may expand to semiconductor with both broken symmetries of spatial inversion and time reversal, that is, polar ferromagnetic semiconductors. Here, we report the observation of current-driven magnetization switching in one such example, (Ge,Mn)Te thin films. The ferromagnetism caused by Mn doping opens an exchange gap in original massless Dirac band of the polar semiconductor GeTe with Rashba-type spin-split bands. The anomalous Hall conductivity is enhanced with increasing hole carrier density, indicating that the contribution of the Berry phase is maximized as the Fermi level approaches the exchange gap. By means of pulse-current injection, the electrical switching of the magnetization is observed in the (Ge,Mn)Te thin films as thick as 200 nm, pointing to the Rashba-Edelstein effect of bulk origin. The efficiency of this effect strongly depends on the Fermi-level position owing to the efficient spin accumulation at around the gap. The magnetic bulk Rashba system will be a promising platform for exploring the functional correlations among electric polarization, magnetization, and current.

Large magneto-thermopower in MnGe with topological spin texture.

Quantum states characterized by nontrivial topology produce interesting electrodynamics and versatile electronic functionalities. One source for such remarkable phenomena is emergent electromagnetic field, which is the outcome of interplay between topological spin structures with scalar spin chirality and conduction electrons. However, it has scarcely been exploited for emergent function related to heat-electricity conversion. Here we report an unusually enhanced thermopower by application of magnetic field in MnGe hosting topological spin textures. By considering all conceivable origins through quantitative investigations of electronic structures and properties, a possible origin of large magneto-thermopower is assigned to the strong energy dependence of charge-transport lifetime caused by unconventional carrier scattering via the dynamics of emergent magnetic field. Furthermore, high-magnetic-field measurements corroborate the presence of residual magnetic fluctuations even in the nominally ferromagnetic region, leading to a subsisting behavior of field-enhanced thermopower. The present finding may pave a way for thermoelectric function of topological magnets.

Quantized chiral edge conduction on domain walls of a magnetic topological insulator.

Electronic ordering in magnetic and dielectric materials forms domains with different signs of order parameters. The control of configuration and motion of the domain walls (DWs) enables nonvolatile responses against minute external fields. Here, we realize chiral edge states (CESs) on the magnetic DWs of a magnetic topological insulator. We design and fabricate the magnetic domains in the quantum anomalous Hall state with the tip of a magnetic force microscope and prove the existence of the chiral one-dimensional edge conduction along the prescribed DWs through transport measurements. The proof-of-concept devices based on reconfigurable CESs and Landauer-Büttiker formalism are realized for multiple-domain configurations with well-defined DW channels. Our results may lead to the realization of low-power-consumption spintronic devices.

Observation of anomalous Hall effect in a non-magnetic two-dimensional electron system.

Anomalous Hall effect, a manifestation of Hall effect occurring in systems without time-reversal symmetry, has been mostly observed in ferromagnetically ordered materials. However, its realization in high-mobility two-dimensional electron system remains elusive, as the incorporation of magnetic moments deteriorates the device performance compared to non-doped structure. Here we observe systematic emergence of anomalous Hall effect in various MgZnO/ZnO heterostructures that exhibit quantum Hall effect. At low temperatures, our nominally non-magnetic heterostructures display an anomalous Hall effect response similar to that of a clean ferromagnetic metal, while keeping a large anomalous Hall effect angle θAHE≈20°. Such a behaviour is consistent with Giovannini-Kondo model in which the anomalous Hall effect arises from the skew scattering of electrons by localized paramagnetic centres. Our study unveils a new aspect of many-body interactions in two-dimensional electron systems and shows how the anomalous Hall effect can emerge in a non-magnetic system.

A magnetic heterostructure of topological insulators as a candidate for an axion insulator.

The axion insulator which may exhibit an exotic quantized magnetoelectric effect is one of the most interesting quantum phases predicted for the three-dimensional topological insulator (TI). The axion insulator state is expected to show up in magnetically doped TIs with magnetizations pointing inwards and outwards from the respective surfaces. Towards the realization of the axion insulator, we here engineered a TI heterostructure in which magnetic ions (Cr) are modulation-doped only in the vicinity of the top and bottom surfaces of the TI ((Bi,Sb)2Te3) film. A separation layer between the two magnetic layers weakens interlayer coupling between them, enabling the magnetization reversal of individual layers. We demonstrate the realization of the axion insulator by observing a zero Hall plateau (ZHP) (where both the Hall and longitudinal conductivity become zero) in the electric transport properties, excluding the other possible origins for the ZHP. The manifestation of the axion insulator can lead to a new stage of research on novel magnetoelectric responses in topological matter.

Current-Nonlinear Hall Effect and Spin-Orbit Torque Magnetization Switching in a Magnetic Topological Insulator.

The current-nonlinear Hall effect or second harmonic Hall voltage is widely used as one of the methods for estimating charge-spin conversion efficiency, which is attributed to the magnetization oscillation by spin-orbit torque (SOT). Here, we argue the second harmonic Hall voltage under a large in-plane magnetic field with an in-plane magnetization configuration in magnetic-nonmagnetic topological insulator (TI) heterostructures, Cr_{x}(Bi_{1-y}Sb_{y})_{2-x}Te_{3}/(Bi_{1-y}Sb_{y})_{2}Te_{3}, where it is clearly shown that the large second harmonic voltage is governed not by SOT but mainly by asymmetric magnon scattering without macroscopic magnetization oscillation. Thus, this method does not allow an accurate estimation of charge-spin conversion efficiency in TI. Instead, the SOT contribution is exemplified by current pulse induced nonvolatile magnetization switching, which is realized with a current density of 2.5×10^{10} A m^{-2}, showing its potential as a spintronic material.

Large Unidirectional Magnetoresistance in a Magnetic Topological Insulator.

We report current-direction dependent or unidirectional magnetoresistance (UMR) in magnetic or nonmagnetic topological insulator (TI) heterostructures, Cr_{x}(Bi_{1-y}Sb_{y})_{2-x}Te_{3}/(Bi_{1-y}Sb_{y})_{2}Te_{3}, that is several orders of magnitude larger than in other reported systems. From the magnetic field and temperature dependence, the UMR is identified to originate from the asymmetric scattering of electrons by magnons. In particular, the large magnitude of UMR is an outcome of spin-momentum locking and a small Fermi wave number at the surface of TI. In fact, the UMR is maximized around the Dirac point with the minimal Fermi wave number.

Zero-bias photocurrent in ferromagnetic topological insulator.

Magnetic interactions in topological insulators cause essential modifications in the originally mass-less surface states. They offer a mass gap at the Dirac point and/or largely deform the energy dispersion, providing a new path towards exotic physics and applications to realize dissipation-less electronics. The nonequilibrium electron dynamics at these modified Dirac states unveil additional functions, such as highly efficient photon to spin-current conversion. Here we demonstrate the generation of large zero-bias photocurrent in magnetic topological insulator thin films on mid-infrared photoexcitation, pointing to the controllable band asymmetry in the momentum space. The photocurrent spectra with a maximal response to the intra-Dirac-band excitations can be a sensitive measure for the correlation between Dirac electrons and magnetic moments.

Observation of the quantum Hall effect in δ-doped SrTiO3.

The quantum Hall effect is a macroscopic quantum phenomenon in a two-dimensional electron system. The two-dimensional electron system in SrTiO3 has sparked a great deal of interest, mainly because of the strong electron correlation effects expected from the 3d orbitals. Here we report the observation of the quantum Hall effect in a dilute La-doped SrTiO3-two-dimensional electron system, fabricated by metal organic molecular-beam epitaxy. The quantized Hall plateaus are found to be solely stemming from the low Landau levels with even integer-filling factors, ν=4 and 6 without any contribution from odd ν's. For ν=4, the corresponding plateau disappears on decreasing the carrier density. Such peculiar behaviours are proposed to be due to the crossing between the Landau levels originating from the two subbands composed of d orbitals with different effective masses. Our findings pave a way to explore unprecedented quantum phenomena in d-electron systems.

Spin-Selective Electron Quantum Transport in Nonmagnetic MgZnO/ZnO Heterostructures.

We report magnetotransport measurements on a high-mobility two-dimensional electron system at the nonmagnetic MgZnO/ZnO heterointerface showing distinct behavior for electrons with spin-up and spin-down orientations. The low-field Shubnikov-de Haas oscillations manifest alternating resistance peak heights which can be attributed to distinct scattering rates for different spin orientations. The tilt-field measurements at a half-integer filling factor reveal that the majority spins show usual diffusive behavior, i.e., peaks with the magnitude proportional to the index of the Landau level at the Fermi energy. By contrast, the minority spins develop "plateaus" with the magnitude of dissipative resistivity that is fairly independent of the Landau level index and is of the order of the zero-field resistivity.

Quantum Hall states stabilized in semi-magnetic bilayers of topological insulators.

By breaking the time-reversal symmetry in three-dimensional topological insulators with the introduction of spontaneous magnetization or application of magnetic field, the surface states become gapped, leading to quantum anomalous Hall effect or quantum Hall effect, when the chemical potential locates inside the gap. Further breaking of inversion symmetry is possible by employing magnetic topological insulator heterostructures that host non-degenerate top and bottom surface states. Here we demonstrate the tailored-material approach for the realization of robust quantum Hall states in the bilayer system, in which the cooperative or cancelling combination of the anomalous and ordinary Hall responses from the respective magnetic and non-magnetic layers is exemplified. The appearance of quantum Hall states at filling factor 0 and +1 can be understood by the relationship of energy band diagrams for the two independent surface states. The designable heterostructures of magnetic topological insulator may explore a new arena for intriguing topological transport and functionality.

Magnetic Field-Induced Insulator-Semimetal Transition in a Pyrochlore Nd2Ir2O7.

We investigate magnetotransport properties in a single crystal of pyrochore-type Nd2Ir2O7. The metallic conduction is observed on the antiferromagnetic domain walls of the all-in-all-out-type Ir 5d moment ordered insulating bulk state that can be finely controlled by an external magnetic field along [111]. On the other hand, an applied field along [001] induces the bulk phase transition from insulator to semimetal as a consequence of the field-induced modification of the Nd 4f and Ir 5d moment configurations. A theoretical calculation consistently describing the experimentally observed features suggests a variety of exotic topological states as functions of electron correlation and Ir 5d moment orders, which can be finely tuned by the choice of rare-earth ion and magnetic field, respectively.

Odd-parity magnetoresistance in pyrochlore iridate thin films with broken time-reversal symmetry.

A new class of materials termed topological insulators have been intensively investigated due to their unique Dirac surface state carrying dissipationless edge spin currents. Recently, it has been theoretically proposed that the three dimensional analogue of this type of band structure, the Weyl Semimetal phase, is materialized in pyrochlore oxides with strong spin-orbit coupling, accompanied by all-in-all-out spin ordering. Here, we report on the fabrication and magnetotransport of Eu2Ir2O7 single crystalline thin films. We reveal that one of the two degenerate all-in-all-out domain structures, which are connected by time-reversal operation, can be selectively formed by the polarity of the cooling magnetic field. Once formed, the domain is robust against an oppositely polarised magnetic field, as evidenced by an unusual odd field dependent term in the magnetoresistance and an anomalous term in the Hall resistance. Our findings pave the way for exploring the predicted novel quantum transport phenomenon at the surfaces/interfaces or magnetic domain walls of pyrochlore iridates.