Minimal Models and Transport Properties of Unconventional $p$-Wave Magnets

New unconventional compensated magnets with a $p$-wave spin polarization protected by a composite time-reversal translation symmetry have been proposed in the wake of altermagnets. To facilitate the experimental discovery and applications of these unconventional magnets, we construct an effective analytical model. The effective model is based on a minimal tight-binding model for unconventional $p$-wave magnets that clarifies the relation to other magnets with $p$-wave spin-polarized bands. One of the most prominent advantages of our analytical model is the possibility to employ various analytical approaches while capturing essential features of $p$-wave magnets. We illustrate the effective model by evaluating the tunneling conductance in junctions with $p$-wave magnets, revealing a large magnetoresistance, spin filtering, and anisotropic bulk spin conductivity beyond linear response despite the absence of a net magnetization. These results show that unconventional $p$-wave magnets offer several useful functionalities, broadening the material selection for spintronics devices.