Question

can occur if these directions are not aligned (c) For small B, roughly how large (in energy per unit volume is the activation barrier for the system to get from the local minimum to the global minimum. (d) Can you make an estimate (in terms of actual num- bers) of how big this activation barrier would be for a fer- romagnetic crystal of magnetite that is a sphere of radius 1 nm? You may use the parameters given in Exercise 31.1.e (you may need to estimate some other parameters as well (21.2) Critical Field for Crystallite (a) Given that the energy of a crystallite in a magnetic field is given by Eo - |M||B| cos 0 - K'|M|2 (cos 0) E/V show that for |B| < Berit there is a local energy minimum where the magnetization points opposite the applied field, and find Berit. (b)* In part (a) we have assumed B is aligned with the anisotropy direction of the magnetization. Describe what

Answer 1

E/v = E_0 - Vertical-bar M Vertical-bar B Vertical-bar cos theta - k^1 Vertical-bar M Vertical-bar ^2 cos theta^2 let = cos theta E/V = E_0 - Vertical-bar M Vertical-bar B Vertical-bar z - k^1 Vertical-bar M Vertical-bar ^2 Z^2 if z > - 1 than there are two minima if theta = 0 rightdoublearrow obsolete minima theta pi rightdoublearrow Another minima where Z = - B/z k^1 Vertical-bar M Vertical-bar < 0 let B again pointing in Z^direction and anisotry direction oriented of on angle emptyset from Z^& E/V = E_0 - Vertical-bar M Vertical-bar Vertical-bar B Vertical-bar (cos (theta emptyset))^2 if y = R Vertical-bar M Vertical-bar /2 Vertical-bar B Vertical-bar is small than the minima will always be close to 0 IF this parameter is greater than 1/2 than there may be a metastable minimum if y almostequalto 1/2 monly a metastable minima y large than metastable minima always exist near emptyset and emptyset + pi B almostequalto small rightdoublearrow z rightdoublearrow 0 E_min = E - k Vertical-bar M Vertical-bar ^2 E_max = E_0 Borrier rightdoublearrow k Vertical-bar M Vertical-bar ^2 activation \r\n the activation BOrrier is total anisotrophy energy activation rightdoublearrow 1.35 times 10^4 I/m
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