The unidirectional Seebeck detection of the N\'{e}el vector in the two-dimensional tetragonal $\mathcal{PT}$-symmetric antiferromagnetic materials

The efficient detection of the reversal (180$^{\circ}$ rotation) of the N\'{e}el vector is one of the crucial tasks in antiferromagnetic spintronics. Here, we propose a thermal approach to detect the reversal of the N\'{e}el vector in the tetragonal $\mathcal{PT}$ antiferromagnetic materials through the unidirectional Seebeck effect (USE). Being different from the previous works in which USE stems from the global Rashba spin-orbit coupling (SOC) or asymmetric magnon scattering, we find that the USE originates from the coupling of the hidden Rashba SOC and the N\'{e}el vector in the tetragonal $\mathcal{PT}$ antiferromagnetic materials in the absence of the global Rashba SOC. Using a generic minimal model, we analyse the behaviors of the USE for the two-dimensional tetragonal lattice $\mathcal{PT}$ antiferromagnet. Importantly, It's found that when the N\'{e}el vector is reversed, the sign of the USE changes, which can be utilized to detect the reversal of the N\'{e}el vector.