Phase diagrams of $\mathrm{L}{\mathrm{a}}_{1-\mathrm{x}}\mathrm{C}{\mathrm{a}}_{\mathrm{x}}\mathrm{Mn}{\mathrm{O}}_3$ in Double Exchange Model with added antiferromagnetic and Jahn-Teller interaction

Abstract

The phase diagram of the multivalent manganites $\mathrm{L}{\mathrm{a}}_{1-\mathrm{x}}\mathrm{C}{\mathrm{a}}_{\mathrm{x}}\mathrm{Mn}{\mathrm{O}}_3$, 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 Néel 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 Néel 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 $x<0.5$.

13 pages, 5 figures

References in corpus (7)

• Unveiling New Magnetic Phases of Undoped and Doped Manganites
• Effects of the On-Site Coulomb Repulsion in Double Exchange Magnets
• Existence of a novel metallic ferromagnetic phase in models for undoped manganites
• Magnetic Phase Diagrams of Manganites-like Local-Moment Systems with Jahn-Teller distortions
• Effect of Jahn-Teller coupling on Curie temperature in the Double Exchange Model
• Curie temperature of the two band double exchange model for manganites
• Canted Ferromagnetism in Double Exchange Model with on-site Coulomb Repulsion