We present a theoretical mapping to show that a ferromagnet with gain (loss) is equivalent to an antiferromagnet with an equal amount of loss (gain). Our finding indicates a novel first-order ferromagnet-antiferromagnet phase transition by tuning the gain-loss parameter. As an appealing application, we demonstrate the realization as well as the manipulation of the antiferromagnetic skyrmion, a stable topological quasiparticle not yet observed experimentally, in a chiral ferromagnetic thin film with gain. We also consider ferromagnetic bilayers with balanced gain and loss, and show that the antiferromagnetic skyrmion can be found only in the cases with broken parity-time symmetry phase. Our results pave a way for investigating the emerging antiferromagnetic spintronics and parity-time symmetric magnonics in ferromagnets.

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Higher-order topological insulator (HOTI) represents a new phase of matter, the characterization of which goes beyond the conventional bulk-boundary correspondence and is attracting significant attention by the broad community. Using a square-root operation, it has been suggested that a square-root HOTI may emerge in a hybrid honeycomb-kagome lattice.Here, we report the first experimental realization of the square-root HOTI in topological LC circuits. We show theoretically and experimentally that the square-root HOTI inherits the feature of wave function from its parent with corner states pinned to nonzero energies. The topological feature is fully characterized by the bulk polarization. To directly measure the finite-energy corner modes, we introduce extra grounded inductors to each node, which shifts corner states to zero-energy without affecting their spatial distributions. Our results experimentally substantiate the emerging square-root HOTI and pave the way to realizing exotic topological phases that are challenging to observe in condensed matter physics.