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

We present a computational study of antiferromagnetic transition in ${\mathrm{RuO}}_2$. The rutile structure with the magnetic sublattices coupled with $\pi /2$ 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 in ${\mathrm{RuO}}_2$ 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.

Figure 1

(a) DFT+DMFT band structure, the spectral function $A_{\uparrow \uparrow }\left(\omega \right)+A_{\downarrow \downarrow }\left(\omega \right)$, along the high-symmetry lines in BZ. (b) The spin polarization of the band structure is calculated as $A_{\uparrow \uparrow }\left(\omega \right)-A_{\downarrow \downarrow }\left(\omega \right)$. (c) HF band structure: paramagnetic (black) and AFM ($\uparrow$ red; $\downarrow$ blue). The energy is measured from the Fermi level.

Figure 2

(a) Fermi surface of paramagnetic ${\mathrm{RuO}}_2$ obtained with HF method. The color codes the atomic polarization (difference of the ${\mathrm{Ru}}_1$ and ${\mathrm{Ru}}_2$ contributions to the wave function at a given k point). (b) Spin-polarized Fermi surface of the AFM state. (c) Crystal structure of ${\mathrm{RuO}}_2$ with global, $\mathbf{a}, \mathbf{b}, \mathbf{c}$, and local coordinates indicated.

Figure 3

(a) Paramagnetic and (b) antiferromagnetic band structure obtained with the HF method. Here the SOC is included. The color map shows simulated ARPES spectra. Lorentzian broadening of half-width 0.05 eV and Fermi-Dirac distribution at 300 K are included.

Figure 4

The contribution $\eta \left(k\right)$ (defined in the text) to the condensation energy along several cuts through BZ.

Figure 5

Band structures along $K_1{K}_2$ line of the HF model with (a) the paramagnetic (green) and (b) the AFM ($\uparrow$ red; $\downarrow$ blue) phase. The effect of SOC is represented with dashed (black) lines. (c) Paramagnetic band structure in the horizontal $K_1{K}_2{K}_3$ plane obtained with dominant $nn$ hopping. (d) The same as in panel (c) with a staggered potential.