Magnetization reversal of a nanoscale ferromagnetic disk placed above a superconductor

Using numerical simulation we have studied a magnetization distribution and a process of magnetization reversal in nanoscale magnets placed above a superconductor plane. In order to consider an influence of the superconductor on the magnetization distribution in the nanomagnet we have used the London approximation. We have found that for usual values of London penetration depth the ground state magnetization is mostly unchanged. But at the same time the fields of vortex nucleation and annihilation change significantly: the interval where the vortex is stable enlarges on 100–200 Oe for the particle above the superconductor. Such fields are experimentally observable so there is a possibility of some practical applications of this effect.

Figure 1

Ferromagnetic nanoparticle above the surface of superconductor.

Figure 2

The energy of interaction of a single-domain (filled circles) and vortexlike (open circles) magnetized particle with a superconductor as a function of ${\lambda }_L$.

Figure 3

Phase diagram of the vortex-single domain state transition. Filled circles—${\lambda }_L=\infty$, open circles—${\lambda }_L=0$, triangles—${\lambda }_L=10\mathrm{nm}$, and rhombus—${\lambda }_L=50\mathrm{nm}$.

Figure 4

Example of the metastability area (between the curves) of the vortexlike state. The upper curve (filled circles) is the boundary of the vortexlike state stability region, the lower curve (open circles) is the phase boundary between the vortexlike and single-domain ground states.

Figure 5

The critical field $H_{\mathit{ann}}$ of vortex annihilation as a function of diameter $D$. The height of the particle $h=20\mathrm{nm}$. The curve marked with filled circles is for ${\lambda }_L=\infty$, with open circles for $\lambda =50\mathrm{nm}$.

Figure 6

The critical field $H_{\mathit{nucl}}$ of vortex nucleation as a function of diameter $D$. The height of the particle $h=20\mathrm{nm}$. The curve marked with filled circles is for ${\lambda }_L=\infty$, with empty circles for $\lambda =50\mathrm{nm}$.

Figure 7

(1) The process of magnetization reversal for ${\lambda }_L=\infty$ (open circles) and ${\lambda }_L=50\mathrm{nm}$ (filled circles). The particle dimensions are $h=20\mathrm{nm},D=100\mathrm{nm}$, (a),(d) single-domain states, (b),(c) vortexlike state. (2) The evolution of magnetization distribution during the process of magnetization reversal.

Figure 8

(a)-(c) The level curves for the components $⟨H_{sx}⟩,⟨H_{sy}⟩,⟨H_{sz}⟩$ of the magnetic field produced by the superconducting current. (d) Magnetization of the particle. $D=150\mathrm{nm},h=20\mathrm{nm},{\lambda }_L=50\mathrm{nm}$.

Figure 9

(1) Part of the magnetization curve near the annihilation of the vortex. (2) Selective magnetization reversal in an array of ferromagnetic particles.