Higher-order exceptional points in ferromagnetic trilayers

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 ferromagnetic 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 three 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.