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Altermagnets have attracted intense interest because they have the advantages of both ferromagnets and antiferromagnets. However, their experimental identification remains challenging, in particular for the A-type altermagnets that account…
Ruthenium oxide with the rutile structure is one of example of altermagnets. These systems are characterized by compensated magnetic moments (typical for antiferromagnets) and strong time reversal symmetry breaking (typical for…
Altermagnetism, a recently discovered magnetic phase characterized by spin-split bands without net magnetization, has emerged as promising platform for novel physics and potential applications. However, its stability against…
Orbital susceptibility for Bloch electrons is calculated for the first time up to the first order with respect to overlap integrals between the neighboring atomic orbitals, assuming single-band models. A general and rigorous theory of…
Recent developments have introduced a groundbreaking form of collinear magnetism known as "altermagnetism". This emerging magnetic phase is characterized by robust time-reversal symmetry breaking, antiparallel magnetic order, and…
For all collinear altermagnets, we sort out piezomagnetic free-energy invariants allowed in the nonrelativistic limit and relativistic piezomagnetic invariants bilinear in the N\'eel vector $\mathbf{L}$ and magnetization $\mathbf{M}$, which…
The orbital magnetization of the electron gas on a two-dimensional kagome lattice under a perpendicular magnetic field is theoretically investigated. The interplay between the lattice geometry and magnetic field induce nontrivial $k$-space…
Altermagnets is a class of antiferromagnetic materials which has electron bands with lifted spin degeneracy in momentum space but vanishing net magnetization and no stray magnetic fields. Because of these properties, altermagnets have…
Altermagnets break a combination of time-reversal and rotational symmetries without generating a net magnetization. As such, the order parameter of $d$-wave altermagnets has the same symmetry as magnetic multipoles, and couples to the…
In 3d-electron magnetic systems, the magnetic structures that transform each other by spin rotation have very close degenerate energies due to small spin-orbit coupling and can be easily controlled by chemical substitution and external…
We propose a nonlinear orbital magnetoelectric effect, which generates orbital magnetization quadratically in centrosymmetric materials where the linear orbital magnetoelectric effect is strictly forbidden. Using extended semiclassical…
Altermagnets constitute a class of collinear compensated N\'eel ordered magnets that break time-reversal symmetry and feature spin-split band structures. Based on versatile microscopic models able to capture the altermagnetic sublattice…
By means of ab initio calculations and spin-polarized scanning tunneling microscopy experiments we show how to manipulate the local spin-polarization of a ferromagnetic surface by creating a complex energy dependent magnetic structure. We…
Two-dimensional compounds with non-zero Berry curvature are ideal systems to study exotic and technologically favourable thermoelectric and magnetoelectric properties. Within this class of materials, the topological trivial and non-trivial…
Altermagnets combine vanishing net magnetization with nonrelativistic, momentum-dependent spin splitting, offering a new paradigm for spintronics. Spin-crystal symmetry coupling, namely spin-lattice locking, is the defining mechanism of…
Altermagnetism represents a type of collinear magnetism, that is in some aspects distinct from ferromagnetism and from conventional antiferromagnetism. In contrast to the latter, sublattices of opposite spin are related by spatial rotations…
The research landscape of magnetism has been recently enriched by the discovery of altermagnetism. It is an unconventional phase of matter characterized by a d-wave (or higher even-parity-wave) collinear compensated spin ordering, which…
The recent discovery of altermagnets has opened new perspectives in the field of ordered phases in condensed matter. In strongly-correlated superfluids, the nodal p-wave and d-wave ordered phases of $^{3}$He and cuprates play a prominent…
Within the wave-packet semiclassical approach, the Bloch electron energy is derived to second order in the magnetic field and classified into gauge-invariant terms with clear physical meaning, yielding a fresh understanding of the complex…
In a collinear magnet, the predominant magnetic moments are collectively aligned along a specific spatial orientation, and this alignment may yield intriguing phenomena such as spin orientation driven polarization. It is well known that…