Skyrmion dynamics in multiferroic insulators
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Recent discovery of Skyrmion crystal phase in insulating multiferroic compound Cu$_2$OSeO$_3$ calls for new ways and ideas to manipulate the Skyrmions in the absence of spin transfer torque from the conduction electrons. It is shown here that the position-dependent electric field, pointed along the direction of the average induced dipole moment of the Skyrmion, can induce the Hall motion of Skyrmion with its velocity orthogonal to the field gradient. Finite Gilbert damping produces longitudinal motion. We find a rich variety of resonance modes excited by a.c. electric field.Keywords:
Skyrmion
Abstract : New formulas for the electric and magnetic fields produced by the four elementary dipole antennas have been developed for the subsurface-to- subsurface, subsurface-to-surface, surface-to-subsurface, and surface-to-surface propagation cases. These formulas are of rather simple, but useful, form and are completely general (i.e., the air can easily be replaced by the sea bottom). They are valid at any frequency and at any range beyond a certain minimum distance for the flat-earth case. The main restrictions on these formulas are that the square of the index of refraction is >or= 10 and that the horizontal separation is >or= 3 times the sum of the depths of burial of the transmitting and receiving point sources. With these new formulas, computer evaluation can be reduced to fractions of a minute, compared with hours for the complete numerical evaluation of the exact Sommerfeld integrals. There also will be an interference pattern set up under certain close-range conditions because the three waves (direct, modified mirror image, and lateral may interfere, either constructively or destructively, with each other.
Horizontal and vertical
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Abstract The fields scattered by a target buried beneath the ground and observed above the ground are perturbed from their values with no target present. These perturbed fields are evaluated using a Sommerfeld approach for all possible cases of transmitting antenna; i.e., VMD, HMD, VED and HED. For frequencies in the 1 to 30 KHz range, the scattered fields have a quasi-static behavior. The exact expressions for the Sommerfeld integrals are evaluated numerically, and compared with their quasi-static approximations. The scatter from the buried target is generated by the induced electric and magnetic dipole moments from the incident dipole field at the dipole source and propagate to the target. The induced dipole moments then reradiate to an observer. All components of E and H are considered. Several examples are given for various combinations for the transmitting antenna, buried object and layer properties.
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Star (game theory)
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Abstract Skyrmions are important in topological quantum field theory for being soliton solutions of nonlinear sigma model and magnetics for their attractive applications in information technology. Either isolated skyrmions or skyrmion crystals may exist in a given chiral magnet, but not both at the same time. When skyrmion crystals, in which skyrmions often arrange themselves into triangular lattices, can be observed in a chiral magnet, stripy spin textures in various forms appear also and even mix with skyrmion crystals. People believe that skyrmions are circular objects and stripy spin textures have zero skyrmion number. Those stripy spin textures are called anything such as spiral, helical, and cycloid spin orders, but not skyrmions. Here we present convincing evidences showing that those stripy spin textures are skyrmions, ``siblings" of circular skyrmions in skyrmion crystals and ``cousins" of isolated circular skyrmions. Specifically, isolated skyrmions are excitations of chiral magnetic films whose ground states are ferromagnetic and skyrmion formation energy is positive. When the skyrmion formation energy is negative (relative to the single domain state), condensed skyrmions are the ground states and stripe skyrmions appear spontaneously. The density of skyrmion number determines the morphology of condensed skyrmion states. At the extreme of one skyrmion in the whole sample, the skyrmion has a ramified stripe structure that maximizes the skyrmion wall length in order to lower system energy. As the skyrmion number density increases, individual skyrmion shapes gradually change from ramified stripes to rectangular stripes, and eventually to disk-like objects due to the competition between negative formation energy and stripe-stripe or skyrmion-skyrmion repulsion. At a low skyrmion number density, the natural width of stripes is proportional to the ratio between the exchange stiffness constant and Dzyaloshinskii-Moriya interaction coefficient. At a high skyrmion number density, skyrmion crystals are the preferred states. Our findings reveal the nature and properties of stripy spin texture, and open a new avenue for manipulating skyrmions, especially condensed skyrmions such as skyrmion crystals.
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Abstract Several magnetic materials consisting of dipoles owe their properties to the specific nature of the dipole–dipole interaction. In the present work, systems of particles possessing a dipole moment arranged on various types of 2D and 3D structures, completely arbitrary and, in some 2D instances, periodic (albeit finite), are studied. Noteworthy, the work is in the regime of strong dipole moments where a classical treatment is possible. The ultimate goal is to quantitatively address the unknown relation existing between the minimum possible energy of a system of dipoles and the concomitant total dipole moment. To such an end, classical numerical methods are used to the previous minimum energy–total dipole moment tandem for various magnetic configurations at zero temperature. An analytic bound for the minimal energy valid for any dimension is also obtained. With this exploration, new light is shed on the connection between the two former physical quantities, establishing an analytic inequality for particles, and describing other instances of physical interest.
Bond dipole moment
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We describe a simple undergraduate lab in which students determine how the force between two magnetic dipoles depends on their separation. We consider the case where both dipoles are permanent and the case where one of the dipoles is induced by the field of the other (permanent) dipole. Agreement with theoretically expected results is quite good.
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Skyrmions are important in topological quantum field theory for being soliton solutions of a nonlinear sigma model and in information technology for their attractive applications. Skyrmions are believed to be circular and stripy spin textures appeared in the vicinity of skyrmion crystals are termed spiral, helical, and cycloid spin orders, but not skyrmions. Here we present convincing evidences showing that those stripy spin textures are skyrmions, "siblings" of circular skyrmions in skyrmion crystals and "cousins" of isolated circular skyrmions. Specifically, isolated skyrmions are excitations when skyrmion formation energy is positive. The skyrmion morphologies are various stripy structures when the ground states of chiral magnetic films are skyrmions. The density of skyrmion number determines the morphology of condensed skyrmion states. At the extreme of one skyrmion in the whole sample, the skyrmion is a ramified stripe. As the skyrmion number density increases, individual skyrmion shapes gradually change from ramified stripes to rectangular stripes, and eventually to disk-like objects. At a low skyrmion number density, the natural width of stripes is proportional to the ratio between the exchange stiffness constant and Dzyaloshinskii-Moriya interaction coefficient. At a high skyrmion number density, skyrmion crystals are the preferred states. Our findings reveal the nature and properties of stripy spin texture, and open a new avenue for manipulating skyrmions, especially condensed skyrmions such as skyrmion crystals.
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Abstract The effect of dislocation dipoles on the broadening of a NMR line is studied. The shape of the satellite line is determined. The line width is obtained as a function of the dipole concentration, the dipole length and the relative orientation of the dipole and the external constant magnetic field. The shape of the central line is also determined. The shape function of the central line is presented for certain relative orientations of the dipole and the magnetic field.
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Geomagnetic pole
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