Levitation and lateral forces between a point magnetic dipole and a superconducting sphere

Abstract

The dipole-dipole interaction model is employed to investigate the angular dependence of the levitation and lateral forces acting on a small magnet in an anti-symmetric magnet/superconducting sphere system. Breaking the symmetry of the system enables us to study the lateral force which is important in the stability of the magnet above a superconducting sphere in the Meissner state. Under the assumption that the lateral displacement of the magnet is small compared to the physical dimensions of our proposed system, analytical expressions are obtained for the levitation and lateral forces as a function of the geometrical parameters of the superconductor as well as the height, the lateral displacement, and the orientation of the magnetic moment of the magnet. The dependence of the levitation force on the height of the levitating magnet is similar to that in the symmetric magnet/superconducting sphere system within the range of proposed lateral displacements. It is found that the levitation force is linearly dependent on the lateral displacement whereas the lateral force is independent of this displacement. A sinusoidal variation of both forces as a function of the polar and azimuthal angles specifying the orientation of the magnetic moment is observed. The relationship between the stability and the orientation of the magnetic moment is discussed for different orientations.

Study of magnetic and optical properties of Zn 1− x TM x Te ( TM = Mn, Fe, Co, Ni) diluted magnetic semiconductors: First principle approach

“…The studied compounds have shown strong p-d exchange interaction within the valence band of ZnTe to induce a p-type carrier induced ferromagnetism. The large exchange splitting occurs from Mn to Ni, which is due to the increasing number of d-electrons (Mn-3d 5 , Fe-3d 6 , Co-3d 7 , Ni-3d 8 ). Furthermore, the tetrahedral environment formed by the Te anions produce a crystal field that is responsible for splitting 3d-states of the T Ms into two states of e g (d z 2 , d x 2 −y 2 ) and three states of t 2g (d xy , d yz , d zx ).…”

“…3-II). The five 3d 5 + states further divided into two e + and three t + energy states. Similarly, 3d 0 − states also split into two e − and three t − energy states (see Fig.…”

“…A wide range of theoretical and experimental reports, available in the literature, depict huge motivations to explore interesting materials for versatile device functionalities. [1][2][3][4][5][6][7][8][9][10] The semiconductors belonging to II-VI, III-VI, IV-VI, are extensively being explored for various applications. Particularly, the II-VI based DMSs, for example ZnS, ZnSe, and ZnTe, are considered to be attractive owing to their wide direct band gaps, which can offer versatile opto-electronic characteristics, therefore, could be expected to replace the existing siliconbased devices.…”

Long range magnetic dipole-dipole interaction mediated by a superconductor

“…Analytical solutions are generally only available for simple symmetric geometries, such as planes, spheres and cylinders. Those cases have been widely studied, mostly for calculating the interaction and levitation forces [14][15][16][17][18][19][20][21][22][23][24][25]. Moreover, numerical solutions are usually either for bulk samples [26] or simple geometries [27][28][29], and are generally very time and/or resource intensive.…”

Interaction Force between a Small Magnet and a Superconducting Sphere

“…Maglev is used for magnetic applications, transportation and product display purposes. The problem of an elevated magnet above a superconducting material has been investigated by many researchers [1,2,3] . The case of a small magnet elevated above a semi-infinite superconducting material has no discrepancy in literature regardless of the method used to estimate the interaction or the elevated force between the magnet and the semi-infinite superconducting material.…”