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.

Magnetometers with exceptional sensitivity are highly demanded in solving a variety of physical and engineering problems, such as measuring Earth's weak magnetic fields and prospecting mineral deposits and geological structures. It has been shown that the non-Hermitian degeneracy at exceptional points (EPs) can provide a new route for that purpose, because of the nonlinear response to external perturbations. One recent work [H. Yang et al., Phys. Rev. Lett. 121, 197201 (2018)] has made the first step to realize the second-order magnonic EP in ferromangetic bilayers respecting the parity-time symmetry. In this paper, we generalize the idea to higher-order cases by considering ferromagnetic trilayers consisting of a gain, a neutral, and a (balanced-)loss layer. We observe both second-and third-order magnonic EPs by tuning the interlayer coupling strength, the external magnetic field, and the gain-loss parameter. We show that the magnetic sensitivity can be enhanced by 3 orders of magnitude comparing to the conventional magnetic tunneling junction based sensors. Our results pave the way for studying high-order EPs in purely magnetic system and for designing magnetic sensors with ultrahigh sensitivity. arXiv:2002.03085v1 [cond-mat.mtrl-sci]

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