Field-induced spin reorientation transition in Ca$_2$Ru$_{1-x}$Fe$_x$O$_4$*

Ca$_2$RuO$_4$ serves as a promising arena for exploring Mott physics. The persistent controversies regarding the nature of its magnetic ground state stem from the uncertain effect of the spin-orbit coupling. Two similar magnetic orders, A-centered and B-centered, were found to compete in Ca$_2$RuO$_4$ and its derivative compounds. This neuron scattering investigation on Ca$_2$Ru$_{1-x}$Fe$_x$O$_4$ (x=0.02, 0.05 and 0.08) reveals that the magnetic field, when applied in the right direction, has strong effect on tipping the balance between the two magnetic orders, evidencing the subtle canting of the Ru$^{3+}$ spins, the existence of antisymmetric exchange and the role of spin-orbit coupling.