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 $pi/2$-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.