Doping dependence of spin and orbital correlations in layered manganites

TL;DR

This study explores how doping influences spin and orbital correlations in layered manganites using an effective model, revealing phase stability and transitions consistent with experimental observations.

Contribution

It introduces a comprehensive spin-orbital model that explains doping-dependent magnetic and orbital phases in layered manganites, including CE, C-type, and G-type antiferromagnetic states.

Findings

The model explains the stability of the CE phase at doping x=0.5.

It predicts C-AF and G-AF phases at high doping levels.

Orbital and spin correlations show complementary behaviors depending on doping and crystal field effects.

Abstract

We investigate the interplay between spin and orbital correlations in monolayer and bilayer manganites using an effective spin-orbital t-J model which treats explicitly the e_g orbital degrees of freedom coupled to classical t_{2g} spins. Using finite clusters with periodic boundary conditions, the orbital many-body problem is solved by exact diagonalization, either by optimizing spin configuration at zero temperature, or by using classical Monte-Carlo for the spin subsystem at finite temperature. In undoped two-dimensional clusters, a complementary behavior of orbital and spin correlations is found - the ferromagnetic spin order coexists with alternating orbital order, while the antiferromagnetic spin order, triggered by t_{2g} spin superexchange, coexists with ferro-orbital order. With finite crystal field term, we introduce a realistic model for La_{1-x}Sr_{1+x}MnO_4, describing a gradual change from predominantly out-of-plane 3z^2-r^2 to in-plane x^2-y^2 orbital occupation under increasing doping. The present electronic model is sufficient to explain the stability of the CE phase in monolayer manganites at doping x=0.5, and also yields the C-type antiferromagnetic phase found in Nd_{1-x}Sr_{1+x}MnO_4 at high doping. Also in bilayer manganites magnetic phases and the accompanying orbital order change with increasing doping. Here the model predicts C-AF and G-AF phases at high doping x>0.75, as found experimentally in La_{2-2x}Sr_{1+2x}Mn_2O_7.