Energetics of magnetic ring and disk elements: Uniform versus vortex state

Abstract

Magnetic energy expressions for the uniform and vortex states of ring elements are derived and compared with the results of micromagnetic simulations. In particular, the effect of roughness on the energy of the vortex state is considered and an expression for the magnetometric demagnetizing factor of rings is found. These energy expressions allow us to calculate the phase diagram separating the uniform from the vortex state. Our results suggest that the roughness contribution to the magnetic energy is sizable in the vortex state and is magnetostatic in origin and its effect is to increase the energy of the vortex state. For the case of rings, the vortex state is favoured with respect to the uniform state on account of the extra magnetostatic energy arising from the inner surface of the ring.

Orientation Mediated Enhancement on Magnetic Hyperthermia of Fe3O4 Nanodisc

“…The cell size is 4 nm. It is smaller than the exchange length (≈8.6 nm) as defined by L ex = (2 A / μ 0 M s 2 ) 0.5 to assure the accuracy of our simulation . The Gilbert damping coefficient α was used as 0.5.…”

Ferromagnetic nanorings

“…Numerical calculations suggest that the roughness contribution to the magnetic energy is sizeable for the vortex state (and also by implication for the onion state), is magnetostatic in origin and its effect is to increase the energy of the vortex state [55]. However, as far as energetics is concerned, roughness affects the relative stability of the vortex state vis-à-vis other magnetic states, such as the uniform state.…”

“…However, as far as energetics is concerned, roughness affects the relative stability of the vortex state vis-à-vis other magnetic states, such as the uniform state. The problem of determining the relative stability of the vortex and onion state in rings is an important one; micromagnetic simulations and experimental observations suggest that the range of stability of these states extends over a large range of parameter values, with outer diameters from 200 nm to 5 μm, depending on the ring width and to a lesser extent on the thickness [8,55,56]. Roughness plays a more visible role in small elements in determining the nucleation f eld for magnetization reversal [12,49,54,[57][58][59][60][61][62], the dynamics of the magnetic reversal [63] and the stabilization of metastable equilibrium states [6,9,64].…”

Magnetization ground states and phase diagrams for a nanosized Co hollow sphere: An onion-type magnetization state

“…22 The method of finite difference calculation adopted by this program has been demonstrated to be effective for investigating the magnetic properties of nanomagnets. 12,13,[17][18][19] For the modeling, we select the parameters of bulk hcp Co, i.e., the saturation magnetization, M S = 1.4×10 6 A/m (~157.3 emu/g) and the exchange stiffness constant, A = 30 pJ/m. 11 In addition, for the single crystal hollow sphere, the magnetocrystalline anisotropy of bulk hcp Co is used, K mag = 4.0×10 5 J/m 3 , 11 whereas for the polycrystalline, K mag = 0.…”