

Complex analysis and mathematical physics
November 27, 2018 16:00–18:00, Moscow, Steklov Mathematical Institute, Room 430 (8 Gubkina)






Vortex textures for doubly periodic planar nanomagnet with inclusions
A. B. Bogatyrev^{} ^{} Institute of Numerical Mathematics of the Russian Academy of Sciences, Moscow

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Abstract:
We consider periodic states inside a thin film ferromagnetic element with
periodic nanoscale array of nonmagnetic holes. The starting point is the
model [1], which is based on the existence of a welldefined energy
hierarchy within a nanostructured magnet with Heisenberg exchange
interaction being dominant. From a mathematical point of view the
metastable states are the harmonic maps of the domain to the sphere. For
the case of a continuous thin film A.A. Belavin and A.M. Polyakov in 1975
and D. Gross in 1978 proposed a series of local solutions with
singularities modeling the magnetic vortexes. In the multiplyconnected
case the solutions are similar, but there are additional constraints on
the vortex positions [2,3]. Here we present the full set of constraints
for the infinitelyconnected case (thin film with periodic array of
inclusions). We parametrize all the metastable states in terms of genus
two Riemann surfaces. For 6parametric shapes of inclusions the exact
solutions are given. (Joint study with K.L. Metlov.)
[1] K. L. Metlov, 'Magnetization patterns in ferromagnetic nanoelements
as functions of complex variable'// Phys. Rev. Lett. 105, 107201 (2010)
[2] Bogatyrev A.B., Metlov K.L. 'Topological constraints on positions of
magnetic solitons in multiplyconnected planar magnetic nanoelements'
Phys. Rev. B 95:2, 024403 (2017) arXiv:1609.02509
[3] A. B. Bogatyrev, “Real meromorphic differentials: A language for
describing meron configurations in planar magnetic nanoelements”, Theoret.
and Math. Phys., 193:1 (2017), 1547–1559; arXiv: 1610.04984.

