Design of altermagnetic models from spin clusters

Altermagnetism, a new class of collinear compensated magnetic phase, has garnered tremendous interest because of its rich physics and promising applications. Physical models and verified material candidates for altermagnetism remain limited. Here, we propose a general scheme to construct altermagnetic models, which explicitly exhibits the blend of ferromagnetic and antiferromagnetic correlations in real space via the design of spin clusters, echoing the observation that properties of altermagnets resemble a mixture of ferromagnets and antiferromagnets. We show that in some of our models, the desired altermagnetic order can be spontaneously realized by electron-electron interaction in a broad range of the phase diagram. This development facilitates the study of fascinating physics of altermagnetism and sheds light on the discovery of new altermagnetic materials.