Jahn-Teller mechanism of stripe formation in doped layered La${}_{2-x}$Sr${}_x$NiO${}_4$ nickelates

We introduce an effective model for $e_g$ electrons to describe quasi-two-dimensional layered La${}_{2-x}$Sr${}_x$NiO${}_4$ nickelates and study it using correlated wave functions on $8\times 8$ and $6\times 6$ clusters. The effective Hamiltonian includes the kinetic energy, on-site Coulomb interactions for $e_g$ electrons (intraorbital $U$ and Hund’s exchange $J_H$) and the coupling between $e_g$ electrons and Jahn-Teller distortions (static modes). The experimental ground state phases with inhomogeneous charge, spin and orbital order at the dopings $x=1\mathrm{/}3$ and $x=1\mathrm{/}2$ are reproduced very well by the model. Although the Jahn-Teller distortions are weak, we show that they play a crucial role and stabilize the observed cooperative charge, magnetic and orbital order in form of a diagonal stripe phase at $x=1\mathrm{/}3$ doping and a checkerboard phase at $x=1\mathrm{/}2$ doping.