Effect of size reduction on cation distribution and magnetic transitions in CoCr$_{2}$ O$_{4}$ multiferroic: EXAFS, magnetic and diffused neutron scattering measurements

A rich sequence of magnetic transitions such as para to long-range ferrimagnetic transition at Curie temperature, TC, to a short range non-collinear spiral ordering at spiral ordering temperature, TS, and finally to a lock in transition, TL, are examined in ∼10 and ∼50 nm samples of CoCr2O4 multiferroic through dc, ac magnetic measurements and diffused neutron scattering using polarized neutrons. Analysis of extended X-ray absorption fine structure (EXAFS) spectra and Fourier transforms of Co and Cr edges in real (r) and momentum (k) space show no change in cation distribution among A and B sites even after reducing the size to the nanometer range due to the high crystal field stabilisation energy of Cr3+ towards the B site. While TS remains independent, TC increases from 97.2 to 100.1 K and TL increases from 5 to 8.5 K with varying size from 10 to 50 nm. Temperature dependent ac susceptibility (χ) measurements demonstrate that χ′ and χ′′ do not show any dispersion behaviour in the 10 nm sample. However, we observe splitting of χ′′ into two peaks and one of them shows dispersion behaviour in the 50 nm sample, indicating a core–shell structure. Magnetization vs. magnetic field measurement show hysteresis behaviour with unsaturated magnetization at high magnetic field indicating a ferrimagnetic core surrounded by disordered surface spins. Fitting of χ′′ with an empirical relation Φ = ΔTB/TBΔlog10 ω, and memory effect measurement, further confirm the spin-glass behaviour of the shell in the 50 nm sample. Magnetic ordering temperatures are examined through neutron scattering using a polarized neutron beam, and reveal that while the para- to ferrimagnetic transition, TC, is continuous and long-range in both nanocrystalline particles, TS is found to be sharp, short-range, and commensurate in 50 nm sampl