Comparative study between charge and spin thermoelectric figure of merits in an antiferromagnetic ring.

Considering the unique and diverse characteristic features of antiferromagnetic (AFM) systems, here in our work, we explore spin-dependent
thermoelectric behavior in an antiferromagnetic ring geometry. A reasonably large ($>>1$) spin figure of merit, referred to as $Z_ST$,
is obtained under suitable input conditions. Two important prerequisites are (i) breaking the symmetry among up and down spin
sub-Hamiltonians and (ii) generating different asymmetric transmission line shapes across a Fermi energy for two opposite spin
electrons. Describing the physical system within a tight-binding framework, where spin-dependent scattering occurs due to the interaction
of itinerant electrons with local magnetic moments via the usual spin-moment exchange interaction, we compute all the thermoelectric
quantities based on Landauer integrals following the Green's function technique. The behavior of charge figure of merit, denoted as
$Z_CT$, is also discussed along with $Z_ST$. Though $Z_CT$ reaches above unity, it is much smaller compared to $Z_ST$. This is the key
finding of our investigation. To make the present communication a self-contained one, we compare the results with another
arrangement of magnetic moments in a ring-like geometry and in a chain-like one. Our analysis gives a suitable hint that in the presence
of spin-dependent scattering, much more favorable energy conversion can be substantiated.