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Nonlinear magnetically charged black holes in 4D Einstein-Gauss-Bonnet gravity

In this letter we present an exact spherically symmetric and magnetically charged black hole solution with exponential model of nonlinear electrodynamics [S. Kruglov, Annals Phys. 378, 59-70 (2017)] in the context of 4D Einstein-Gauss-Bonnet (EGB) gravity. We show that our $-$ve branch, in the limit of GB coupling coefficient $α\rightarrow 0$ and the nonlinear parameter $β\to 0$, reduces to the magnetically charged black hole of Einstein-Maxwell gravity in GR. In addition we study the embedding diagram of the black hole geometry and the thermodynamic properties such as the Hawking temperature and the heat capacity of our black hole solution.