Antiferromagnetism in RuO${}_2$ as $d$-wave Pomeranchuk instability

We present a computational study of antiferromagnetic transition in RuO${}_2$. The rutile structure with the magnetic sublattices coupled by $\pi \mathrm{/}2$-rotation leads to a spin-polarized band structure in the antiferromagnetic state, which gives rise to a $d$-wave modulation of the Fermi surface in the spin-triplet channel. We argue a finite spin conductivity that changes sign in the $ab$ plane is expected RuO${}_2$ because of this band structure. We analyze the origin of the antiferromagnetic instability and link it to presence of a nodal line close to the Fermi level.