Role of hidden spin polarization in non-reciprocal transport of antiferromagnets

The discovery of hidden spin polarization (HSP) in centrosymmetric nonmagnetic crystals, i.e., spatially distributed spin polarization originated from local symmetry breaking, has promised an expanded material pool for future spintronics. However, the measurements of such exotic effects have been limited to subtle space- and momentum-resolved techniques, unfortunately hindering their applications. Here, we theoretically predict macroscopic non-reciprocal transports induced by HSP when coupling another spatially distributed quantity, such as staggered local moments in a PT-symmetric anti-ferromagnet. By using a four-band model Hamiltonian, we demonstrate that HSP plays a crucial role in determining the asymmetric bands with respect to opposite momenta. Such band asymmetry leads to non-reciprocal nonlinear conductivity, exemplified by tetragonal CuMnAs via first-principles calculations. We further provide the material design principles for large nonlinear conductivity, including two-dimensional nature, multiple band crossings near the Fermi level, and symmetry protected HSP. Our work not only reveals direct spintronic applications of HSP (such as N\'eel order detection), but also sheds light on finding observables of other ''hidden effects'', such as hidden optical polarization and hidden Berry curvature.