Spin-resolved quasiparticle interference patterns on altermagnets via non-spin-resolved scanning tunneling microscopy

We investigate quasiparticle interference on an altermagnetic Lieb-like lattice and show how a non-spin-polarized scanning tunneling microscopy measurement can yield effectively spin-resolved information. Within a four-site tight-binding model, which can be tuned between an antiferromagnetic and a Lieb-type altermagnetic state, we introduce on-site impurities at distinct sublattice sites and compute the real space local density of states (LDOS) via a Green's function approach. A Fourier transformation of the impurity-induced LDOS yields the characteristic $d$-wave spin-split Fermi surface contours of the altermagnetic phase. Notably, by choosing which sublattice the impurity is placed upon, we show that the scattering amplitudes effectively encode spin-dependent contrasts: Impurities on one of the magnetic sublattices highlights predominantly spin-up contributions along one crystallographic direction, while impurities on the other one favor the complementary spin-down channel and orientation.