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Modern research areas, ranging from topological condensed matter and dissipationless quantum transport to spintronics, are built on a magnetic symmetry group theory which entangles magnetism and relativistic spin-orbit coupling. Here we return to the non-relativistic foundations of collinear magnetism and delimit Type-I spin groups containing no spin-rotation symmetry element, Type-II with a spin-rotation symmetry, and Type-III with symmetry elements combining spin and crystal rotations. We show that they describe, respectively, ferromagnets with spin-polarized electron bands, antiferromagnets with spin-degenerate bands, and a third class with alternating spin-polarizations in locked momentum and crystal space. We refer to the third class as altermagnets and identify their topological invariants which have a form of an even-integer spin winding number in the momentum space. Our band structure analysis reveals a spin splitting by an electrostatic crystal field as a unique spectroscopy signature of altermagnetism. We find altermagnetic material candidates ranging from high Neel temperature insulators and metals to a parent cuprate of high-temperature superconductivity.
The spin rotations and lattice rotations are locked in the Shubnikov magnetic space groups in describing magnetically ordered materials. However, real materials may contain symmetry elements whose spin and lattice operations are partially unlocked. T
We study spin-wave transport in a microstructured Ni81Fe19 waveguide exhibiting broken translational symmetry. We observe the conversion of a beam profile composed of symmetric spin-wave width modes with odd numbers of antinodes n=1,3,... into a mixe
We report room temperature long-distance spin transport of magnons in antiferromagnetic thin film hematite doped with Zn. The additional dopants significantly alter the magnetic anisotropies, resulting in a complex equilibrium spin structure that is
Time-reversal (T) symmetry breaking is a fundamental physics concept underpinning a broad science and technology area, including topological magnets, axion physics, dissipationless Hall currents, or spintronic memories. A best known conventional mode
In this paper, a 3-terminal spin-transfer torque nano-oscillator (STNO) is studied using the concurrent spin injection of a spin-polarized tunneling current and a spin Hall current exciting the free layer into dynamic regimes beyond what is achieved