Néel vector controlled exceptional contours in $p$-wave magnet-ferromagnet junctions

Abstract

Non-Hermitian systems can host exceptional degeneracies where not only the eigenvalues, but also the corresponding eigenvectors coalesce. Recently, $p$-wave magnets have been introduced, which are characterized by their unusual odd parity. In this work, we propose the emergence of non-Hermitian degeneracies at the interface of $p$-wave magnets and ferromagnets. We demonstrate that this setup offers a remarkable tunability allowing realization of exceptional lines and rings, which can be controlled via the orientation of the $p$-wave Néel vector. We present the origin of these exceptional contours based on symmetry, and characterize them using phase rigidity. Our works puts forward a versatile platform to realize controllable non-Hermitian degeneracies at odd parity magnetic interfaces.

Figures (4)

• Figure 1: Proposed setup with $p$-wave magnet-FM junction. Illustration of the $p$-wave magnet-FM junction at $z=0$, with FM region extending for $z<0$. The Fermi surface with red and blue color shaded regions shows the odd parity behavior of $p$-wave magnets. We propose the appearance of symmetry protected exceptional rings and exceptional lines at such junctions, as shown schematically in the dotted box. To occur such degeneracy the N'eel vector $\mathbf{n}$ (red arrow) must lie within the $x$–$y$ plane.
• Figure 2: Exceptional rings in $p-$wave magnet-FM junctions. (a), (b) Real and (c), (d) imaginary parts of the eigenvalues for $\phi=\pi$ and $\phi=\pi/4$ respectively. Note that eigenvalues merge along the ellipses. The phase rigidity, $r$, is plotted in (e) and (f). Note that $r$ goes to zero along the ellipses, signaling their exceptional nature. We find that the orientation and size of the exceptional ring depends on $\phi$, i.e, on the orientation of the Néel vector. Here we choose $t=1$, $\lambda=1$$\theta=\pi/2$, $J=1$ and $\gamma=\textcolor{black}{-}1$.
• Figure 3: Exceptional lines in $p-$wave magnet-FM junctions. (a), (b) Real and (c), (d) imaginary parts of the eigenvalues for $(\phi,\lambda)=(3\pi/2, 1)$ and $(\phi,\lambda)=(3\pi/2, 0)$, respectively. Note that eigenvalues merge along a pair of parallel lines. The phase rigidity, $r$, is plotted for the above conditions in (e) and (f). The deep blue color along two parallel lines indicates $r=0$, which confirms the coalescing of eigenvectors. We observe that the orientation and distance between lines depend on junction parameters and the orientation of the Néel vector. Here we choose $t=1$, $J=1$, $\theta=\pi/2$ and $\gamma=\textcolor{black}{-}1$.
• Figure A1: Exceptional contours and EPs in $f$-wave magnet-FM junctions. (a)-(b) Real and (c)-(d) imaginary parts of the eigenvalues for $\theta = \pi/2$ and $\theta = \pi/4$, respectively. Note that eigenvalues merge along an intricate structure of contours for $\theta = \pi/2$. On the other hand, they merge at specific points for $\theta \neq \pi/2$ case. The red dots represent the locations of the EPs. Here we choose $t=1$, $\lambda=1$, $J=1$, $\phi=\pi/4$, $\gamma=-1$ and $\Gamma=0$.