The magnetic field effect on the two competing magnetic phases in Ca$_2$Ru$_{0.92}$Fe$_{0.08}$O$_4$

Substitution of Fe for Ru in Ca$_2$RuO$_4$ weakens the structural distortion and induces negative thermal expansion. Additionally, it introduces a $B$-centered stacking in the collinear magnetic structure and competes with the original $A$-centered magnetic phase. As the Fe-doping increases, the $B$-center phase becomes more predominant and eventually takes over as the substitution reaches 12 percent. The competition of these two magnetic phases is also susceptible to magnetic field. Our neutron diffraction measurement on Ca$_2$Ru$_{0.92}$Fe$_{0.08}$O$_4$ illustrates the field-effect on the two magnetic sublattices and underlines the importance of orbital physics.