Crystal design of altermagnetism

Symmetry plays a fundamental role in condensed matter. The unique entanglement between magnetic sublattices and alternating crystal environment in altermagnets provides a unique opportunity for designing magnetic space symmetry. There have been extensive experimental efforts concentrated on tuning the Neel vector to reconstruct altermagnetic symmetry. However, it remains challenging to modulate the altermagnetic symmetry through the crystal aspect. Here, the crystal design of altermagnetism is successfully realized, by breaking glide mirrors and magnetic mirrors of the (0001) crystallographic plane in CrSb films via crystal distortion. We establish a locking relationship between altermagnetic symmetry and the emergent Dzyaloshinskii-Moriya (DM) vectors in different CrSb films, realizing unprecedentedly room-temperature spontaneous anomalous Hall effect in an altermagnetic metal. The concept of exchange-coupling torques is broadened to include both antiferromagnetic exchange-coupling torque and DM torque. Their relationship is designable, determining electrical manipulation modes, e.g., field-assisted switching for CrSb(1-100)/Pt and field-free switching for W/CrSb(11-20). Particularly, the unprecedentedly field-free 100-percent switching of Neel vectors is realized by making these two torques parallel or antiparallel, dependent on Neel vector orientation. Besides unravelling the rich mechanisms for electrical manipulation of altermagnetism rooted in broadened concept of exchange-coupling torques, we list other material candidates and propose that crystal design of altermagnetism would bring rich designability to magnonics, topology, etc.