Abstract
Using the rigid magnetic vortex model, we develop a substantially modified Landau theory approach for analytically studying phase transitions between different spin arrangements in circular submicron magnetic dots subject to an in-plane externally-applied magnetic field. We introduce a novel order parameter: the inverse distance between the center of the circular dot and the vortex core. This order parameter is suitable for describing closed spin configurations such as curved or bent-spin structures and magnetic vortices. Depending on the radius and thickness of the dot as well as the exchange coupling, there are five different regimes for the magnetization reversal process when decreasing the in-plane magnetic field. The magnetization-reversal regimes obtained here cover practically all possible magnetization reversal processes. Moreover, we have derived the change of the dynamical response of the spins near the phase transitions and obtained a ``critical slowing down'' at the second order phase transition from the high-field parallel-spin state to the curved (C-shaped) spin phase. We predict a transition between the vortex and the parallel-spin state by quickly changing the magnetic field---providing the possibility to control the magnetic state of dots by changing either the value of the external magnetic field and/or its sweep rate. We study an illuminating mechanical analog (buckling instability) of the transition between the parallel-spin state and the curved spin state (i.e., a magnetic buckling transition). In analogy to the magnetic-disk case, we also develop a modified Landau theory for studying mechanical buckling instabilities of a compressed elastic rod embedded in an elastic medium. We show that the transition to a buckled state can be either first or second order depending on the ratio of the elasticity of the rod and the elasticity of the external medium. We derive the critical slowing down for the second-order mechanical buckling transition.
Highlights
We found that the buckling transition can be either first or second order depending on the ratio of the rod and external-medium elasticity
In the region of parameters between the continuous and dashed curves in Fig. 3(a), the magnetic vortex can be either stable or metastable at low magnetic fields but the vortex state does not contribute to the magnetization reversal process
(5) How to best study driven nonequilibrium phase transitions like the Portevin-Le Châtelier effect, and complete the five cells at bottom of Table II [e.g., what is the analog of the free energy for the Portevin-Le Châtelier (PLC) effect? Can we consider the PLC effect as a generalized cascade of buckling transitions?]
Summary
Recent achievements in nanotechnology allow the fabrication of different arrays of small magnetic dots of various shapes and different interdot spacings.[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18] The size of these small magnetic dots range from several tens to several hundred nanometers in length and from a few to several tens of nanometers in thickness. Recent simulations[22,23,24] pose the question of why, in some region of parameters, the vortex state does not contribute to the reversal magnetization process even though it provides the minimum energy at zero magnetic field. Another related unclear issue is how one magnetic spin configuration loses its stability and transforms into another one and what happens with the dynamical response of magnetic dots when the spin configuration changes near the phase boundaries. It is very desirable to explore alternative ways to study this problem without the use of micromagnetic computer codes
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