Open AccessSuperparamagnetic relaxation times for mixed anisotropy and high energy barriers with intermediate to high damping: 1. Uniaxial axis in a 〈001〉 direction
Author(s) -
Newell Andrew J.
Publication year - 2006
Publication title -
geochemistry, geophysics, geosystems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.928
H-Index - 136
ISSN - 1525-2027
DOI - 10.1029/2005gc001146
Subject(s) - condensed matter physics , anisotropy , superparamagnetism , relaxation (psychology) , saddle point , moment (physics) , magnetic anisotropy , magnetic moment , anisotropy energy , maxima and minima , perpendicular , materials science , physics , magnetization , geometry , classical mechanics , magnetic field , mathematics , quantum mechanics , mathematical analysis , psychology , social psychology
The Néel‐Brown theory for superparamagnetic relaxation rates is generalized to ferromagnetic particles with mixed cubic and uniaxial anisotropy. In this article the uniaxial axis is in a 〈001〉 crystallographic direction, while in part 2 it is in a 〈111〉 direction. The calculations are for high energy barriers, so transitions between states (stable equilibria) are rare. Transition rates from an energy minimum across a saddle point are determined by the height of the energy barrier and the shape of the energy surface around these two points. To account for multiple connections between minima, a master equation is solved for the probability distribution and the effect on the magnetic moment is calculated. Some relaxation modes have no effect on the moment. There are as many as five distinct relaxation rates for the probability distribution, but at most two for the moment. One rate is for the component parallel to the uniaxial axis, while the other is for the perpendicular component. These rates are functions of the cubic anisotropy parameter K ′ 1 and the uniaxial parameter K u . The double relaxation rate can give rise to phenomena such as partial superparamagnetism and multiple blocking temperatures.