2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/100529We study the effects of spin-orbit coupling in the $d$-density wave (DDW) phase. In the low-temperature orthorhombic phase of La$_{2-x}$Ba$_x$CuO$_4$, we find that spin-orbit coupling induces a ferromagnetic moment in the DDW phase, which is polarized along the [110] direction with a considerable magnitude. This effect does not exist in the superconducting phase. On the other hand, if the $d$-density wave order does not exist at zero field, a magnetic field along the [110] direction always induces such a staggered orbital current. We discuss experimental constraints on the DDW states in light of our theoretical predictions.4 pages, 5 figures, accepted by Phys. Rev. LettSuperconductivityStrongly Correlated Electronstext