Spontaneous Spin Textures in Multiorbital Mott Systems

Spin textures in $\mathbf{k}$-space arising from spin-orbit coupling in noncentrosymmetric crystals find numerous applications in spintronics. We present a mechanism that leads to the appearance of $\mathbf{k}$-space spin texture due to spontaneous symmetry breaking driven by electronic correlations. Using dynamical mean-field theory we show that doping a spin-triplet excitonic insulator provides a means of creating new thermodynamic phases with unique properties. The numerical results are interpreted using analytic calculations within a generalized double-exchange framework.

Figure 1

The hopping processes with corresponding amplitudes on the square lattice. The parameters used in the calculations: $t_a=0.4118$, $t_b=-0.1882$, $V_1=\pm V_2=0.05$, $\mathrm{\Delta }=3.4$, $U=4$, $U^{\prime }=2$, and $J=1$ in units of eV.

Figure 2

(a) and (c) Phase diagrams in the doping-temperature plane for even and odd cross hopping, respectively. Full lines mark continuous transitions, dotted lines mark the boundaries of phase coexistence regions. (b) and (d) The spin textures at the indicated points of the phase diagrams in the units of ${\mu }_B(a_0/2\pi {)}^2$ obtained for $n_h=0.14$ at $T=193\mathrm{K}$.

Figure 3

The $d$-wave spin texture in the ${\mathrm{SDW}}^{\prime }$ phase of a model with even cross hopping of opposite signs along the $x$ and $y$ axes. The results shown here were obtained for $n_h=0.16$ at $T=193\mathrm{K}$.

Figure 4

One-particle spectral density in the ${\mathrm{SCDW}}^{\prime }$ phase for the same parameters as Fig. 2: (a) Total spectral density $A(\mathbf{k},\omega )$ along high-symmetry lines in the Brillouin zone, (b) the Fermi surface $A(\mathbf{k},\omega =0)$, (c) in-plane magnetization spectral density $m_{\parallel }(\mathbf{k},\omega )$ along the same lines as in panel (a), (d) in-plane magnetization density at the Fermi level $m_{\parallel }(\mathbf{k},\omega =0)$ in the units of ${\mu }_B{\mathrm{eV}}^{-1}(a_0/2\pi {)}^2$.

Figure 5

A cartoon view of the orbital pattern (left) that gives rise to $t_a,t_b>0$ and $V_1=V_2$ on each bond with alternating signs between bonds (only half of the orbitals are shown for the sake of clarity). Zoomed out view of the texture on the ligand sublattice (right). The red square marks the crystallographic unit cell. The model can be transformed to the odd cross-hopping case with a single-atom unit cell by sublattice transformation $a_i\to (-1{)}^i{a}_i$.