The magnetic structure and spin-flop transition in the A-site columnar-ordered quadruple perovskite $\mathrm{T}\mathrm{m}\mathrm{M}{\mathrm{n}}_3{\mathrm{O}}_6$

We present the magnetic structure of $\mathrm{T}\mathrm{m}\mathrm{M}{\mathrm{n}}_3{\mathrm{O}}_6$, solved via neutron powder diffraction - the first such study of any $R\mathrm{M}{\mathrm{n}}_3{\mathrm{O}}_6$ A-site columnar-ordered quadruple perovskite to be reported. We demonstrate that long range magnetic order develops below 74 K, and at 28 K a spin-flop transition occurs driven by $f$-$d$ exchange and rare earth single ion anisotropy. In both magnetic phases the magnetic structure may be described as a collinear ferrimagnet, contrary to conventional theories of magnetic order in the manganite perovskites. Instead, we show that these magnetic structures can be understood to arise due to ferro-orbital order, the A, A${}^{\mathrm{\prime }}$ and A${}^{\mathrm{\prime }\mathrm{\prime }}$ site point symmetry, $mm2$, and the dominance of A-B exchange over both A-A and B-B exchange, which together are unique to the $R\mathrm{M}{\mathrm{n}}_3{\mathrm{O}}_6$ perovskites.