Phase diagrams of $\rm La_{1-x}Ca_xMnO_3$ in Double Exchange Model with added antiferromagnetic and Jahn-Teller interaction

TL;DR

This paper models the phase diagram of La_{1-x}Ca_xMnO_3 using an extended Double Exchange Model with Jahn-Teller and antiferromagnetic interactions, successfully reproducing experimental phase transitions and critical temperatures.

Contribution

It introduces a directional-dependent effective Heisenberg model incorporating Jahn-Teller and antiferromagnetic effects to accurately predict phase transitions in manganites.

Findings

Reproduces phase transitions from A-type to ferromagnetic and C-type to G-type antiferromagnetism.

Calculates Curie and Néel temperatures in good agreement with experiments.

Provides parameter values that best fit the critical temperature behavior for x<0.5.

Abstract

The phase diagram of the multivalent manganites $\rm La_{1-x}Ca_xMnO_3$, in space of temperature and doping $x$, is a challenge for the theoretical physics. It is an important test for the model used to study these compounds and the method of calculation. To obtain theoretically this diagram for $x<0.5$, we consider the two-band Double Exchange Model for manganites with added Jahn-Teller coupling and antiferromagnetic Heisenberg term. In order to calculate Curie and N\'{e}el temperatures we derive an effective Heisenberg model for a vector which describes the local orientation of the total magnetization of the system. The exchange constants of this model are different for different space directions and depend on the density of $e_g$ electrons, antiferromagnetic constants and the Jahn-Teller energy. To reproduce the well known phase transitions from A-type antiferromagnetism to ferromagnetism at low $x$ and C-type antiferromagnetism to G-type antiferromagnetism at large $x$, we argue that the antiferromagnetic exchange constants should depend on the lattice direction. We show that ferromagnetic to A-type antiferromagnetic transition results from the Jahn-Teller distortion. Accounting adequately for the magnon-magnon interaction, Curie and N\'{e}el temperatures are calculated. The results are in very good agreement with the experiment and provide values for the model parameters, which best describe the behavior of the critical temperature for $x<0.5$.