Transition from ferromagnetism to superparamagnetism in uniaxial nanoparticles. The role on non-uniformities in the magnetization

Summary form only given. Langevin dynamics is used to study the transition from ferromagnetic to superparamagnetic behavior upon reducing the particle size in uniaxial nanoparticles for observation times of a few nanoseconds and constant temperature T=300 K. Square particles of size d, thickness t=1 nm and damping constant /spl lambda/=0.1 are considered. The stochastic dynamic equation, interpreted in the Stratonovich sense, is solved on a two-dimensional grid of 1 nm square cells using a first-order Euler scheme augmented by the noise-induced drift term. The transition is studied in detail by monitoring the probability distribution of in-plane magnetization orientations during the time interval considered. The authors show the computed distributions for different particle sizes d. Large particles are clearly ferromagnetic because they present a sharp distribution around the initial equilibrium state (/spl phi/=0/spl deg/). As d is reduced, the distribution gradually widens up and the second peak (/spl phi/=180/spl deg/) becomes populated too. Smaller particles are superparamagnetic because they present a wide probability distribution with the two minima equally populated. This transition has been compared with the one computed assuming that the magnetization inside the particle is completely uniform (macrospin model). The result is shown with the average value of the normalized magnetization component along the easy axis is plotted as a function of particle size. It is observed that non-uniformities in the magnetization favor thermal relaxation and that the transition is moved roughly 1 nm towards larger particle sizes. It can be shown that this contribution is not due to the occurrence of highly non-uniform reversal modes nor to the presence of configurational anisotropy, which is negligible for the particles sizes considered here.