Naoto Nagaosa

Emergent phenomena at oxide interfaces

Recent technical advances in the atomic-scale synthesis of oxide heterostructures have provided a fertile new ground for creating novel states at their interfaces. Different symmetry constraints can be used to design structures exhibiting phenomena not found in the bulk constituents. A characteristic feature is the reconstruction of the charge, spin and orbital states at interfaces on the nanometre scale. Examples such as interface superconductivity, magneto-electric coupling, and the quantum Hall effect in oxide heterostructures are representative of the scientific and technological opportunities in this rapidly emerging field.

Real-space observation of a two-dimensional skyrmion crystal

Crystal order is not restricted to the periodic atomic array, but can also be found in electronic systems such as the Wigner crystal or in the form of orbital order, stripe order and magnetic order. In the case of magnetic order, spins align parallel to each other in ferromagnets and antiparallel in antiferromagnets. In other, less conventional, cases, spins can sometimes form highly nontrivial structures called spin textures. Among them is the unusual, topologically stable skyrmion spin texture, in which the spins point in all the directions wrapping a sphere. The skyrmion configuration in a magnetic solid is anticipated to produce unconventional spin–electronic phenomena such as the topological Hall effect. The crystallization of skyrmions as driven by thermal fluctuations has recently been confirmed in a narrow region of the temperature/magnetic field (T–B) phase diagram in neutron scattering studies of the three-dimensional helical magnets MnSi (ref. 17) and Fe1−xCoxSi (ref. 22). Here we report real-space imaging of a two-dimensional skyrmion lattice in a thin film of Fe0.5Co0.5Si using Lorentz transmission electron microscopy. With a magnetic field of 50–70 mT applied normal to the film, we observe skyrmions in the form of a hexagonal arrangement of swirling spin textures, with a lattice spacing of 90 nm. The related T–B phase diagram is found to be in good agreement with Monte Carlo simulations. In this two-dimensional case, the skyrmion crystal seems very stable and appears over a wide range of the phase diagram, including near zero temperature. Such a controlled nanometre-scale spin topology in a thin film may be useful in observing unconventional magneto-transport effects.

Spin Current and Magnetoelectric Effect in Noncollinear Magnets

A new mechanism of the magnetoelectric effect based on the spin supercurrent is theoretically presented in terms of a microscopic electronic model for noncollinear magnets. The electric polarization P(ij) produced between the two magnetic moments S(i) and S(j) is given by P proportional e(ij) X (S(i) X S(j)) with e(ij) being the unit vector connecting the sites i and j. Applications to the spiral spin structure and the gauge theoretical interpretation are discussed.

Anomalous Hall effect

We present a review of experimental and theoretical studies of the anomalous Hall effect (AHE), focusing on recent developments that have provided a more complete framework for understanding this subtle phenomenon and have, in many instances, replaced controversy by clarity. Synergy between experimental and theoretical work, both playing a crucial role, has been at the heart of these advances. On the theoretical front, the adoption of Berry-phase concepts has established a link between the AHE and the topological nature of the Hall currents which originate from spin-orbit coupling. On the experimental front, new experimental studies of the AHE in transition metals, transition-metal oxides, spinels, pyrochlores, and metallic dilute magnetic semiconductors, have more clearly established systematic trends. These two developments in concert with first-principles electronic structure calculations, strongly favor the dominance of an intrinsic Berry-phase-related AHE mechanism in metallic ferromagnets with moderate conductivity. The intrinsic AHE can be expressed in terms of Berry-phase curvatures and it is therefore an intrinsic quantum mechanical property of a perfect cyrstal. An extrinsic mechanism, skew scattering from disorder, tends to dominate the AHE in highly conductive ferromagnets. We review the full modern semiclassical treatment of the AHE together with the more rigorous quantum-mechanical treatments based on the Kubo and Keldysh formalisms, taking into account multiband effects, and demonstrate the equivalence of all three linear response theories in the metallic regime. Finally we discuss outstanding issues and avenues for future investigation.

Dissipationless Quantum Spin Current at Room Temperature

Although microscopic laws of physics are invariant under the reversal of the arrow of time, the transport of energy and information in most devices is an irreversible process. It is this irreversibility that leads to intrinsic dissipations in electronic devices and limits the possibility of quantum computation. We theoretically predict that the electric field can induce a substantial amount of dissipationless quantum spin current at room temperature, in hole-doped semiconductors such as Si, Ge, and GaAs. On the basis of a generalization of the quantum Hall effect, the predicted effect leads to efficient spin injection without the need for metallic ferromagnets. Principles found here could enable quantum spintronic devices with integrated information processing and storage units, operating with low power consumption and performing reversible quantum computation.

Topological properties and dynamics of magnetic skyrmions

Magnetic skyrmions are particle-like nanometre-sized spin textures of topological origin found in several magnetic materials, and are characterized by a long lifetime. Skyrmions have been observed both by means of neutron scattering in momentum space and microscopy techniques in real space, and their properties include novel Hall effects, current-driven motion with ultralow current density and multiferroic behaviour. These properties can be understood from a unified viewpoint, namely the emergent electromagnetism associated with the non-coplanar spin structure of skyrmions. From this description, potential applications of skyrmions as information carriers in magnetic information storage and processing devices are envisaged.

Hall Effect of Light

We derive the semiclassical equation of motion for the wave packet of light taking into account the Berry curvature in momentum-space. This equation naturally describes the interplay between orbital and spin angular momenta, i.e., the conservation of the total angular momentum of light. This leads to the shift of wave-packet motion perpendicular to the gradient of the dielectric constant, i.e., the polarization-dependent Hall effect of light. An enhancement of this effect in photonic crystals is also proposed.

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, ∼1016 giga–electron volts. We show that the magnetic monopole can appear in the crystal momentum space of solids in the accessible low-energy region (∼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.

Giant Rashba-type spin splitting in bulk BiTeI

There has been increasing interest in phenomena emerging from relativistic electrons in a solid, which have a potential impact on spintronics and magnetoelectrics. One example is the Rashba effect, which lifts the electron-spin degeneracy as a consequence of spin-orbit interaction under broken inversion symmetry. A high-energy-scale Rashba spin splitting is highly desirable for enhancing the coupling between electron spins and electricity relevant for spintronic functions. Here we describe the finding of a huge spin-orbit interaction effect in a polar semiconductor composed of heavy elements, BiTeI, where the bulk carriers are ruled by large Rashba-like spin splitting. The band splitting and its spin polarization obtained by spin- and angle-resolved photoemission spectroscopy are well in accord with relativistic first-principles calculations, confirming that the spin splitting is indeed derived from bulk atomic configurations. Together with the feasibility of carrier-doping control, the giant-Rashba semiconductor BiTeI possesses excellent potential for application to various spin-dependent electronic functions.

Current-induced skyrmion dynamics in constricted geometries

Magnetic skyrmions--vortex-like swirling spin structures with a quantized topological number that are observed in chiral magnets--are appealing for potential applications in spintronics because it is possible to control their motion with ultralow current density. To realize skyrmion-based spintronic devices, it is essential to understand skyrmion motions in confined geometries. Here we show by micromagnetic simulations that the current-induced motion of skyrmions in the presence of geometrical boundaries is very different from that in an infinite plane. In a channel of finite width, transverse confinement results in steady-state characteristics of the skyrmion velocity as a function of current that are similar to those of domain walls in ferromagnets, whereas the transient behaviour depends on the initial distance of the skyrmion from the boundary. Furthermore, we show that a single skyrmion can be created by an electric current in a simple constricted geometry comprising a plate-shaped specimen of suitable size and geometry. These findings could guide the design of skyrmion-based devices in which skyrmions are used as information carriers.