Mott transition, spin-orbit effects, and magnetism in ${\mathrm{Ca}}_2{\mathrm{RuO}}_4$

In this work, we study the effects of spin-orbit and Coulomb anisotropy on the electronic and magnetic properties of the Mott insulator ${\mathrm{Ca}}_2{\mathrm{RuO}}_4$. We use the local-density approximation + dynamical mean-field approach and spin-wave theory. We show that, contrary to a recent proposal, the Mott metal-insulator transition is not induced by the spin-orbit interaction. We confirm that, instead, it is mainly driven by the change in structure from long to short $\mathbf{c}$-axis layered perovskite. We show that the magnetic ordering and the anisotropic Coulomb interactions play a small role in determining the the size of the gap. The spin-orbit interaction turns out to be essential for describing the magnetic properties. It not only results in a spin-wave gap, but it also enlarges significantly the magnon bandwidth.

Figure 1

The S-Pbca structure [8, 9] of ${\mathrm{Ca}}_2{\mathrm{RuO}}_4$. The pseudotetragonal axes are $\mathbf{x}\sim (\mathbf{a}+\mathbf{b})/2,\mathbf{y}\sim (\mathbf{b}-\mathbf{a})/2$, and $\mathbf{z}=\mathbf{c}$. Ru sites $i=2,3,4$ transform into the equivalent site $i=1$ via the symmetry operations $\mathbf{a}\to -\mathbf{a}$ $\left(i=2\right)$, $\mathbf{b}\to -\mathbf{b}$ $\left(i=3\right)$, and $\mathbf{c}\to -\mathbf{c}$ $\left(i=4\right)$.

Figure 2

Total LDA+DMFT spectral function at $T=200$ K for the S-Pbca structure. Light lines (cRPA): $U=2.3$ eV and $J=0.4$ eV. Dark lines (cLDA): $U=3.1$ eV and $J=0.7$ eV.

Figure 3

LDA+DMFT (upper panels) and LDA+SO+DMFT (lower panels) $t_{2g}$ spectral-function matrix. Solid lines: $A_{1,1}$. Dashed and dotted lines: $A_{2,2}$ and $A_{3,3}$. Left: L-Pbca, $T=580$ K. Right: S-Pbca, $T=290$ K. Calculations performed with cLDA Coulomb parameters.

Figure 4

LDA+DMFT (upper panels) and LDA+SO+DMFT (lower panels) $t_{2g}$ spectral-function matrix. Solid lines: $A_{1,1}$. Dashed and dotted lines: $A_{2,2}$ and $A_{3,3}$. Left: L-Pbca, $T=580$ K. Right: S-Pbca, $T=290$ K. Calculations performed with cRPA Coulomb parameters.

Figure 5

Total LDA+DMFT $t_{2g}$ spectral function with anisotropic Coulomb interactions. Left panel: $\mathrm{\Delta }U=\mathrm{\Delta }{U}^{\prime }=0$. Right panel: $\mathrm{\Delta }U=3\mathrm{\Delta }{U}^{\prime }=-0.45$ eV. $T=290$ K. These calculations have been done with the full Coulomb vertex at $T=290$ K and for cLDA parameters.

Figure 6

The LDA+DMFT total $t_{2g}$ spectral function for the paramagnetic (full line) and antiferromagnetic (dashed line) phase. The AFM spectrum is calculated in the presence of a large staggered antiferromagnetic field yielding a magnetic moment ${\mu }_z\sim 1.96{\mu }_B$. Both spectra have been calculated at $T=290$ K and for cLDA (left panel) and cRPA (right panel) Coulomb parameters.

Figure 7

Magnon dispersion of ${\mathrm{Ca}}_2{\mathrm{RuO}}_4$. Points: Experimental points showing the maximum of intensity taken from Fig. 3 in Ref. [33]. Lines: Spin-wave dispersion calculated by us with (a) all exchange and single-ion anisotropy parameters, (b) setting ${\mathrm{\Gamma }}_z^a={\mathrm{\Gamma }}_z^b=0$, (c) setting $D_{aa}$ and $D_{bb}$ equal to the average value $(D_{aa}+D_{bb})/2$, and finally (d) setting to zero all single-ion anisotropy parameters but $D_{bb}$, redefined as $D_{bb}-D_{aa}$. All interactions have been calculated for the cRPA Coulomb parameters.