Origin of Spin Stripes in Bilayer Nickelate La$_3$Ni$_2$O$_7$

Abstract

The bilayer nickelate La$_3$Ni$_2$O$_7$ has emerged as a new high temperature superconductor. We propose and study a microscopic Hamiltonian that addresses the interplay of lattice structure and magnetism in this system. Using state-of-the-art density matrix renormalization group calculations, we show that $(π/2,π/2)$ spin stripe order emerges in our model and exhibits a hidden quasi-one dimensionality. The spin stripe order occurs over a range of electron concentrations, but requires a sizable Hund's coupling $J_H$. Our model exhibits superconducting tendency only when the interlayer antiferromagnetic coupling $J_\bot$ becomes sufficiently large, which naturally occurs under pressure. Our study unveils the microscopic origin of both the unusual spin stripes and superconductivity in La$_3$Ni$_2$O$_7$, and highlights the indispensable role of Hund's coupling $J_H$ in this system.

Figures (5)

• Figure 1: (a) Illustration of a single Ni-O layer in the two phases which can be changed by strain. With tensile strain (and near zero strain), the positions of Ni atoms are distorted from a square lattice, while the O atoms are buckled either above or below the Ni-Ni plane. With large compressive strain, the Ni form a square lattice, with all O's buckled in the same direction. (b) In a minimal model that includes only the two $e_g$ orbitals from Ni, the strain effect can be modeled by adding some anisotropy into the $d_{x^2-y^2}$ hopping, resulting in both strong ($t$) and weak ($t'$) bonds. (c) Phase diagram of the model in Eq.\ref{['eq:model']} as a function of $t'$ and $U$, for a particular $J_H=4t$ and $J_\bot=0$ obtained from DMRG calculation. The $(\pi/2,\pi/2)$ and $(\pi,0)$ SSOs are shown in (d) and (e) respectively. Adding a small $J_\bot$ makes the spin pattern opposite between the two layers.
• Figure 2: (a) Representative spin correlation functions calculated from Eq. \ref{['eq:model2']} for the FM and $2k_F$-SDW phases, where the filled(hollow) markers in the data represent positive(negative) values. The inset shows the corresponding space patterns with the same color encoding as in Fig. \ref{['fig:model']}(d,e). (b) Phase diagram for the model in Eq. \ref{['eq:model2']} at quarter filling ($\braket{n}=1/2$) determined by the spin correlation. The FM and $2k_F$ orders can be adiabatically connected to the $(\pi/2,\pi/2)$ and $(0,\pi)$ SDW orders respectively in the 2D limit.
• Figure 3: Spin correlations from DMRG results where the decoupled 1D chains are in the ferromagnetic regime. The stars represent the reference sites. These correspond to a $(\pi/2,\pi/2)$ spin stripe in the 2D limit.
• Figure 4: (a-d)Four different possibilities of spin pattern in the coupled two-chain system when the decoupled 1D limit favors period-4 SDW tendency. Among them, (a) corresponds to another type of $(\pi/2,\pi/2)$ spin stripe, while (b) corresponds to a $(\pi,0)$ spin stripe. Our DMRG results suggest the pattern in (b) is more stable, which can be explained through a fourth-order perturbation term $J'\sim t^2t'^2/U^3$ that couples diagonal sites in each square plaquette. (e) DMRG result for the spin correlation with $J_H=4t$, $t'=0.3t$, and $U=2t$.
• Figure 5: Interlayer singlet pair correlation function $\Phi_s(\bm{r})$ calculated from Eq. \ref{['eq:model']} on a regular two layer, two leg and two orbital system for $J_H=4t, U=18t$.