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In physics, a topological quantum number (also called topological charge) is any quantity, in a physical theory, that takes on only one of a discrete set of values, due to topological considerations. Most commonly, topological quantum numbers are topological invariants associated with topological defects or soliton-type solutions of some set of differential equations modeling a physical system, as the solitons themselves owe their stability to topological considerations. The specific "topological considerations" are usually due to the appearance of the fundamental group or a higher-dimensional homotopy group in the description of the problem, quite often because the boundary, on which the boundary conditions are specified, has a non-trivial homotopy group that is preserved by the differential equations. The topological quantum number of a solution is sometimes called the winding number of the solution, or, more precisely, it is the degree of a continuous mapping. Recent ideas about the nature of phase transitions indicates that topological quantum numbers, and their associated solutions, can be created or destroyed during a phase transition. In particle physics, an example is given by the Skyrmion, for which the baryon number is a topological quantum number. The origin comes from the fact that the isospin is modelled by SU(2), which is isomorphic to the 3-sphere and inherits the group structure of SU(2) through its bijective association, so the isomorphism is in the category of topological groups. By taking real three-dimensional space, and closing it with a point at infinity, one also gets a 3-sphere. Solutions to Skyrme's equations in real three-dimensional space map a point in "real" (physical; Euclidean) space to a point on the 3-manifold SU(2). Topologically distinct solutions "wrap" the one sphere around the other, such that one solution, no matter how it is deformed, cannot be "unwrapped" without creating a discontinuity in the solution. In physics, such discontinuities are associated with infinite energy, and are thus not allowed.

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Topological quantum number

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Electric Field Eect on Skyrmion phase in Chiral lattice Ferrimagnet Cu2OSeO3

Naman Agarwal

Insulator materials are the recent research interest in Spintronics because of the absence of joule heating. There has been continued interest in insulator material Cu2OSeO3 because it possesses the novel Skyrmion phase [1], specific type of spin vortices in the lattice, characterized by quantized topological number, near the paramagnetic phase boundary [2]. This Skyrmion phase can be harnessed for the switching applications in the data storage devices [3–6]. We study the effect of positive or negative DC electric field on the Skyrmion phase boundary of this material by magnetoelectric susceptibility(dM/dE)measurements, which is a sensitive technique for scanning phase boundary [7,8]. We scan out the phase diagram for positive, negative and zero DC electric fields and find that electric field effect is maximum at the phase boundaries and decreases inside the phase There is no cut-off for the electric field effect. Also, the electric field effect is maximum at upper skyrmion boundary compared to other phase boundaries. We also show the small expansion(contraction) of Skyrmion phase along temperature axis with the application of positive(negative) DC electric field.

2016

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