In solids, electron orbital angular momentum has been believed to be strongly suppressed by the crystal field. However, this common wisdom is being challenged by recent theoretical reports, which predict that electron orbital angular momentum can be generated and transported rather easily in various materials. There are ongoing experimental efforts to test the theoretical predictions, which are slowly gaining experimental support. It is also getting realized that some spin properties originate from orbital angular momentum properties. This paper explains in a pedagogical way how electrons may gain orbital angular momentum despite the strong suppression by the crystal field. It also briefly reviews recent developments in the orbital angular momentum dynamics study.

Over the past 25 years, mostly based on the first principles calculations, the compensated half-metals (CHMs) (or half-metallic antiferromagnet) have been investigated as a promising candidate for spintronics applications. Since a few CHMs were successfully observed several years ago, interest in CHMs has very stimulated. In this paper, we will address representative candidates for CHMs focused on our previous research for beginners in this area. Besides, we will briefly discuss the unconventional characters, anticipated so far, and points to be noted in its research. This is expected to provide a useful strategy for beginners on how to design and synthesize CHMs.

We introduce so-called ‘magnetic force response theory’ which has been suggested and formulated 1980s and is still under active development. Combined with first-principles electronic structure calculations, this theory becomes such an useful theoretical tool that many of complex magnetic materials and their intriguing phenomena have been unveiled through the unique information it provides. Here we introduce the basic idea and formalism of magnetic force theorem and discuss some of recent developments including the extension to anisotropic interactions and to correlated electron materials. The current status of the related research activities and the available codes are outlined.

Efficient methods to numerically solve frustrated low-dimensional spin models in the zero-temperature limit are crucial in the study of magnetism. Conventional methods such as Metropolis algorithm or simulated annealing yield good solutions in most cases, but close to critical points such methods suffer critical slowing down. In this work we employ quantum annealing method, running on D-Wave quantum processing unit, to study frustrated J₁-J₂ Ising model on a two-dimensional square lattice. We compare quantum and classical simulated annealing methods, show pros and cons of the quantum annealing method employed in comparison to classical counterparts, and discuss potential parameter tuning for better solutions.

Anomalous Hall effect is investigated in perpendicular magnetic CoSiB/Pt multilayers with different layer structures. The anomalous Hall resistivity shows a non-monotonic temperature dependence for certain series of structures whereas the longitudinal resistivity always decreases monotonically with decreasing temperature. For those samples with non-monotonic temperature dependence, the conventional power-law scaling with a single dominant mechanism does not hold between the anomalous Hall resistivity and the longitudinal resistivity. An empirical scaling, which includes several contributions together such as skew scattering, side jump, and the intrinsic contributions, appears to be invalid as well when only the impurity effect is considered for the skew scattering. The anomalous Hall resistivity of the multilayers is well fitted with a new scaling where the temperature-dependent phonon skew scattering is included. This is in direct contradiction to the theoretical studies, which predict a negligibly small phonon contribution to the skew scattering, but supports more recent experimental results that evinced the phonon skew scattering. The relative magnitudes of the phonon skew-scattering with respect to the sum of the impurity skew scattering and the side jump fall into a narrow range for all the samples studied.