Spin–orbit torque (SOT) is an emerging technology that enables the efficient manipulation of
spintronic devices. The initial processes of interest in SOTs involved electric fields, spin …

The Hall effect, in which a current flows perpendicular to an electrical bias, has been
prominent in the history of condensed matter physics. Appearing variously in classical …

The anomalous Hall effect is a time-reversal symmetry-breaking magneto-electronic
phenomenon originally discovered in ferromagnets. Recently, ruthenium dioxide (RuO2) …

Spatial, momentum and energy separation of electronic spins in condensed-matter systems
guides the development of new devices in which spin-polarized current is generated and …

Fundamental physical properties, such as phase transitions, electronic structures, and spin
excitations, in all magnetic ordered materials, were ultimately believed to rely on the …

Symmetries of three-dimensional periodic scalar fields are described by 230 space groups
(SGs). Symmetries of three-dimensional periodic (pseudo) vector fields, however, are …

In solids, electronic Bloch states are formed by atomic orbitals. While it is natural to expect
that orbital composition and information about Bloch states can be manipulated and …

In ferromagnets, an electric current generally induces a transverse Hall voltage in proportion
to the internal magnetization. This effect is frequently used for the electrical readout of the …

Electrons, commonly moving along the applied electric field, acquire in certain magnets a
dissipationless transverse velocity. This spontaneous Hall effect, found more than a century …

A temperature gradient in a ferromagnetic conductor can generate a transverse voltage drop
perpendicular to both the magnetization and heat current. This anomalous Nernst effect has …