Coexistence of Altermagnetic and Compensated Ferrimagnetic Motifs in a Noncollinear Multiferroic

Collinear compensated magnets with nonrelativistic spin splitting comprise altermagnets (ALMs), whose rotation- or mirror-related opposite-spin sublattices produce momentum-selective splitting that vanishes at $\mathrm{\Gamma }$, and compensated ferrimagnets (CFIMs), whose symmetry-inequivalent sublattices allow splitting throughout the Brillouin zone, including at $\mathrm{\Gamma }$. Here, we show that the coplanar noncollinear magnetic state of multiferroic boracite Ni${}_3$B${}_7$O${}_{13}$Cl hosts both motifs on distinct Ni sublattices in real space. The electronic structure and spin texture exhibit coexisting $d$-wave-like and $s$-wave-like spin-polarization components associated with the ALM and CFIM motifs, respectively. Opposite ferroelectric states exhibit reversed band-resolved spin polarizations, indicating magnetoelectric coupling, and sign reversals of linear shift and circular injection currents.