Review on band structure and spin polarization of altermagnetic materials

Recent theoretical and experimental efforts have revealed the existence of a new class of magnetic materials, altermagnets, characterized by distinct symmetries in spin and real space. Combining the properties of ferromagnets, such as band spin polarization and time-reversal symmetry breaking responses, and antiferromagnets, like vanishing stray field and terahertz magnon dynamics, altermagnets are attracting enormous attention in both magnetism and spintronics community. While numerous altermagnetic candidates and emerging physical properties have been studied in theory extensively and enthusiastically, the experimental investigation of altermagnetism is struggling against the lack of proper altermagnetic materials and the controversial results reported for specific candidates. In this review, we first give a general description on the concept and key properties of altermagnetism, outline its distinction from other compensated magnetic order from the aspects of time-reversal symmetry in the spin momentum locking texture and time-reversal symmetry breaking responses. The main body of this review concentrates on the progress in altermagnetic material study with special focus on their band structure and spin polarization features, as well as the controversies over several candidate materials. Going forward, we point out several directions which altermagnetic material investigation might follow and guidelines which could help to avoid the pitfalls in the experimental pursuit of ideal altermagnets.