Fingerprint of non-Hermiticity in a <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>d</mml:mi></mml:math>-wave altermagnet

We develop the non-Hermitian counterpart of a new class of collinear magnets, dubbed altermagnets, delineated by net-zero magnetization with momentum-dependent spin-splitting bands. The application of an imaginary gauge field in a two-dimensional $d$-wave altermagnet injects a nonreciprocal intercell hopping without hosting exceptional points (EPs). This non-Hermitian phase hosts a point gap which remains robust in the presence and absence of Rashba spin-orbit coupling. By attaching a ferromagnetic lead with the altermagnet, we uncover the emergence of two pairs of second-order EPs. We establish that each of the EPs is associated with a half-integer quantized topological charge, a hallmark signature of the non-Hermitian topology. The existence of this non-Hermitian exceptional phase has been further confirmed by linear variation with the respective momentum and coalescence of the spin expectation value at the EPs. Finally, we demonstrate that the application of a planar magnetic field to the junction not only tunes the location of the EPs but also can annihilate a single pair or even all pairs of EPs with opposite topological charges depending upon the field strength and direction.