Multiferroicity with coexisting isotropic and anisotropic spins in Ca$_{3}$Co$_{2-x}$Mn$_{x}$O$_{6}$

We study magnetic and multiferroic behavior in Ca$_3$Co$_{2-x}$Mn$_{x}$O$_6$ ($x \sim$0.97) by high-field measurements of magnetization ($M$), magnetostriction ($L$($H$)/$L$), electric polarization ($P$), and magnetocaloric effect. This study also gives insight into the zero and low magnetic field magnetic structure and magnetoelectric coupling mechanisms. We measured $M$ and $\Delta$$L$/$L$ up to pulsed magnetic fields of 92 T, and determined the saturation moment and field. On the controversial topic of the spin states of Co$^{2+}$ and Mn$^{4+}$ ions, we find evidence for $S$ = 3/2 spins for both ions with no magnetic field-induced spin-state crossovers. Our data also indicate that Mn$^{4+}$ spins are quasi-isotropic and develop components in the $ab$-plane in applied magnetic fields of 10 T. These spins cant until saturation at 85 T whereas the Ising Co$^{2+}$ spins saturate by 25 T. Furthermore, our results imply that mechanism for suppression of electric polarization with magnetic fields near 10 T is flopping of the Mn$^{4+}$ spins into the $ab$-plane, indicating that appropriate models must include the coexistence of Ising and quasi-isotropic spins.