  We theoretically study spin pumping from a layered van der Waals
antiferromagnet in its canted ground state into an adjacent normal metal. We
find that the resulting dc spin pumping current bears contributions along all
spin directions. Our analysis allows for detecting intra- and cross-sublattice
spin-mixing conductances via measuring the two in-plane spin current
components. We further show that sublattice symmetry-breaking Gilbert damping
can be realized via interface engineering and induces a dissipative coupling
between the optical and acoustic magnon modes. This realizes magnon level
attraction and exceptional points in the system. Furthermore, the dissipative
coupling and cross-sublattice spin pumping contrive to produce an
unconventional spin current in the out-of-plane direction. Our findings provide
a route to extract the spin mixing conductance matrix and uncovers the unique
opportunities, such as level attraction, offered by van der Waals
antiferromagnet-normal metal hybrids.
