# P4: Topological solitons in chiral magnets

## Project Description

With the detection of relevant Dzyaloshinskii-Moriya (DM) interactions in ultra-thin films deposited on metal surfaces^{(1)}, a new research chapter was started in the field of low-dimensional magnetism. The DM interaction can lead to very complex homo-chiral magnetic structures such as multidimensional solitons (skyrmions) as observed in the nano-skyrmion lattice of iron on iridium^{(2)}. Such multidimensional localised states of the size of a few nanometers are not only of interest in modern physics but also for spintronics as was outlined recently^{(3)}. Such complex magnetic structures are understood as a result of a competition between different spin interactions: the Heisenberg-, the DM, and the four-spin biquadratic interaction to name the most relevant ones. Currently, there are three research trusts approaching the investigation of topological solitons in chiral magnets in reduced dimensions and thin films: (i) atomic scale nanostructures of adatoms on surfaces exhibiting a DM interaction through a large Rashba effect, (ii) ultrathin magnetic films on substrates with large spin-orbit interactions, and (iii) films of cubic helimagnets. In reduced dimensions thermal fluctuations are of particular relevance. Our goal is therefore to investigate such chiral magnetic systems at finite temperature. Of interest are the exploration of the magnetic phase diagram \((B, T)\) of these systems, the investigation of more exotic thermodynamic phases where the vector and scalar spin chirality are order parameters, or the stability of the topological nature against thermal fluctuations. For this purpose, at first the strengths of the different spin interactions are determined by mapping the energy landscape of magnetic states calculated using the material specific density functional theory methods^{(4)-(7)} onto the spin-models. So far this mapping was made mainly for Heisenberg interactions. In this project the process should now be extended to isotropic and anisotropic interactions of higher order. We will employ the electronic structure programs^{(8)}, particularly the* FLEUR* program and the KKR method developed by us. The thermodynamic properties of the chiral nanomagnets are then to be examined on the basis of the effective spin-models with realistic spin-coupling constants by means of the stochastic atomistic spin dynamic *juSpinX* and Monte Carlo methods^{(9)}. Depending on the expected complexity of the magnetic energy landscape and phase space structures also extended ensemble methods, such as the Wang-Landau method^{(10), (11)} and parallel tempering^{(12),(13)} and hybrid methods will be applied. Also effective methods for the treatment of extensive spin interactions^{(14)} will be studied here.

This project can benefit from progress in P1 , P2, and P18 in particular in order to account for quantum effects in the effective spin interaction. The spin-quadrupol transport of P14 is also related to the four-spin biquadratic interaction studied here.

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Nature Phys. **7**, 713 (2011)

(3) A. Fert, V. Cross and J. Sampaio, Nature Nanotech. **8**, 152 (2013)

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(8) DFT from Forschungszentrum Jülich

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