Surface structure and surface-spin induced magnetic properties and spin-glass transition in nanometer Co-granules of FCC crystal structure

Abstract

Separated Co-granules, of an average diameter as small as D = 2.0 nm, of FCC crystal structure have been synthesized by co-reducing Co²⁺ cations dispersed in a liquid. They exhibit an enhancedsaturation magnetization σ_s by as much as ∼34% with a more than an order of enhanced magnitude for the effective anisotropy constant K _eff over the bulk values at 4.2 K. An irreversibility in the ZFC-FC (zero field cooled-field cooled) thermomagnetograms occurs at temperatures T ≤ T _B, where T _B is their blocking temperature. The ZFC thermomagnetogram peaks at T _B according to their K _eff and volume V. T _B = 152 K has been found for D = 10 nm granules in an applied magnetic field of H = 1 kA/m. The sample, which is superparamagnetic(coercivity H _c = 0) in nature at T ≥ T _B, develops H _c at T < T _B with a unique dependence on temperature, H _c(T) = H _c(0)[1 − T/T _B]^1/2, with H _c(0) = 40.0 kA/m. The results are discussed with a two-phase modelstructure of granules. In this model, the grain-surface atoms have amodified magnetic structure of the core atoms. An inter-couplingbetween the magnetic spins in the two regions occurs in aferromagnetic or antiferromagnetic manner according to theirinterface that mediates their exchange interactions through it. Thestudies of σ, K _eff, or H _c as a function of temperature (4.2 to 380 K) and/or size D (2 to 20 nm) demonstrate their strong correlation with the dynamics of the surface spins (DSS). An enhanced surfaceanisotropy with large total interface-energy in small granulesgoverns the DSS. An average value of the surface anisotropy constantK _s = 2.28 mJ/m² is determined by a linear plot of K _eff with D ⁻¹ at D ≤ 2.9 nm. Larger granules follow a modified K _eff − D ⁻¹ plot with an order of smaller K _s-value. The surface spins form a surface-spin-glass, which undergoes a magnetic transition to a spin-frozen state at a critical temperature T _F = 71 K. The T _F evolves following the well-known de Almeida-Thouless line, δ T _F ∝ H ^2/3, at H≤ 42 kA/m.