Magnetic and orbital ordering of RuO2 planes in RuSr2(Eu,Gd)Cu2O8

TL;DR

This paper develops an effective Hamiltonian model for RuO2 planes in RuSr2(Eu,Gd)Cu2O8, revealing possible spin and orbital orderings and explaining magnetic properties through a double-exchange mechanism.

Contribution

It introduces a new effective Hamiltonian approach for RuO2 planes, including phase diagrams and a double-exchange model for doped systems, linking theory with experimental observations.

Findings

Identifies three possible spin and orbital orderings in undoped RuO2 planes.

Constructs a phase diagram constraining parameters based on experimental data.

Proposes a double-exchange model explaining magnetic properties in doped RuSr2(Eu,Gd)Cu2O8.

Abstract

We start from an effective Hamiltonian for Ru ions in a square lattice, which includes the on-site interactions between t_2g orbitals derived from Coulomb repulsion, and a tetragonal crystal-field splitting. Using perturbation theory in the hopping terms, we derive effective Hamiltonians to describe the RuO2 planes of RuSr2(Eu,Gd)Cu2O8. For undoped planes (formal valence Ru{+5}), depending on the parameters we find three possible orderings of spin and orbitals, and construct a phase diagram. This allows to put constraints on the parameters based on experimental data. When electron doping consistent with the hole doping of the superconducting RuO2 planes is included, we obtain (for reasonable parameters) a double-exchange model with infinite antiferromagnetic coupling between itinerant electrons and localized spins. This model is equivalent to one used before [H. Aliaga and A. A. Aligia, Physica B 320, 34 (2002)] which consistently explains the seemingly contradictory magnetic properties of RuSr2(Eu,Gd)Cu2O8.