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Electronic and Magnetic Properties of the New Iron -- Based Superconductor [Li$_{1-x}$Fe$_x$OH]FeSe

We present the results of paramagnetic LDA band structure calculations: band dispersions, densities of states and Fermi surfaces, for the new iron based high-temperature superconductor LiOHFeSe. Main structural motif providing bands in the vicinity of the Fermi level is FeSe layer which is isostructural to the bulk FeSe prototype superconductor. The bands crossing the Fermi level and Fermi surfaces of the new compound are typical for other iron based superconductors. Experimentally it was shown that introduction of Fe ions into LiOH layer gives rise to ferromagnetic ordering of the Fe ions at T$_C$=10K. To study magnetic properties of [Li$_{0.8}$Fe$_{0.2}$OH]FeSe system we have performed LSDA calculations for $\sqrt 5 \times \sqrt 5$ superlattice and found ferromagnetism within the Li$_4$Fe(OH) layer. To estimate the Curie temperature we obtained Fe-Fe exchange interaction parameters for Heisenberg model from our LSDA calculations, leading to theoretical value of Curie temperature 10.4K in close agreement with experiment.