Abstract
The structural, magnetic properties of the rare-earth perovskites, DyFe${}_{1\ensuremath{-}x}$Mn${}_{x}$O${}_{3}$ (space group, orthorhombic Pbnm), were studied, and the magnetic phase diagram of the solid solution was investigated, which unveiled an unexplored hidden field-induced weak ferromagnetism in the material system with $x$ $=$ 0.5--0.9 (antiferromagnetically ordered along the $b$ axis and canted along the $c$ axis). In the solid solution, the Jahn-Teller distortion contributed by Mn${}^{3+}$ gives rise to the predominance of the bc plane sublattice with increasing Mn and also the effective onset of orbital ordering in the ab plane for $x$ $=$ 0.5 and above. These distinct features in the respective lattice and orbital degrees of freedom induce the Dy-(Fe,Mn) electronic interaction anisotropy primarily in the $\mathit{bc}$ plane and the growing in-($\mathit{ab}$)plane electronic anisotropy, effectively competing with each other above $x$ $=$ 0.5. The close entanglement of these anisotropies introduced by the various lattice, orbital, and correlated electronic characters results in the favoring of the Dzyaloshinskii-Moriya interaction dictating along the $a$ axis, in contrast to the conventionally observed $b$ axis and accounting for the hidden field-induced canted magnetic ordering in the $\mathit{bc}$ plane. The complex interplays of these multiple factors are discussed in this work and satisfactorily explain the rich magnetic phase diagram of the solid solution.
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