Lattice expansion and noncollinear to collinear ferrimagnetic order in a MnCr 2 O 4 nanoparticle

We report the magnetic behavior of spinel chromite $\mathrm{Mn}{\mathrm{Cr}}_{2}{\mathrm{O}}_{4}$. Bulk $\mathrm{Mn}{\mathrm{Cr}}_{2}{\mathrm{O}}_{4}$ shows a sequence of magnetic states, i.e., paramagnetic (PM) to collinear ferrimagnetic (FM) state below ${T}_{C}\ensuremath{\sim}45\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ and collinear FM state to noncollinear FM state below ${T}_{S}\ensuremath{\sim}18\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. Decrease of particle size reduces the noncollinear spin structure and consequently, magnetic transition at ${T}_{S}$ decreases in nanoparticle samples. However, ferrimagnetic order is still dominating in nanoparticles, except the observation of superparamagnetic-like blocking and decrease of spontaneous magnetization. This, according to the core-shell model of ferrimagnetic nanoparticles, may be due to surface disorder effects of nanoparticles. The system also shows the increase of ${T}_{C}$ in nanoparticle samples, which is not consistent with the core-shell model. The analysis of the $M(T)$ data, applying spin wave theory, has shown an unusual Bloch exponent value 3.35 for bulk $\mathrm{Mn}{\mathrm{Cr}}_{2}{\mathrm{O}}_{4}$, which decreases and approaches 1.5, a typical value for any standard ferromagnet, with decreasing particle size. We have also observed the lattice expansion in $\mathrm{Mn}{\mathrm{Cr}}_{2}{\mathrm{O}}_{4}$ nanoparticles. The present work shows the correlation between a systematic increase of lattice parameter and the gradual decrease of $B$ site noncollinear spin structure in $\mathrm{Mn}{\mathrm{Cr}}_{2}{\mathrm{O}}_{4}$.