Existence of a critical canting angle of magnetic moments to induce multiferroicity in the Haldane spin-chain system Tb2BaNiO5

We report an unusual canted magnetism due to $3d$ and $4f$ electrons, occupying two different crystallographic sites, with its consequence to electric dipole order. This is based on neutron powder diffraction measurements on ${\mathrm{Tb}}₂{\mathrm{BaNiO}}₅$ (orthorhombic, $Immm$ centrosymmetric space group), exhibiting N\'eel order below $({T}_N=)\phantom{\rule{0.28em}{0ex}}63\phantom{\rule{0.16em}{0ex}}\mathrm{K}$, to understand multiferroic behavior below 25 K. The magnetic structure is made up of Ni and Tb magnetic moments, which are found to be mutually canted in the entire temperature range below ${T}_N$, though collinearity is seen within each sublattice, as known in the past. First-principles density functional theory calculations ($\mathrm{GGA}\phantom{\rule{0.16em}{0ex}}+\phantom{\rule{0.16em}{0ex}}\mathrm{SO}$ and $\mathrm{GGA}+\mathrm{U}+\mathrm{SO}$ approximations) support such a canted ground state. The intriguing finding, being reported here, is that there is a sudden increase in this Tb-Ni relative canting angle at the temperature (that is, at 25 K) at which spontaneous electric polarization sets in, with bond distance and bond angle anomalies. This finding emphasizes the need for a new spin-driven polarization mechanism---that is, a critical canting angle coupled with exchange striction---to induce multiferroicity in magnetic insulators with canted spins.