Phase diagram of a dilute ferromagnet model with antiferromagnetic next-nearest-neighbor interactions

TL;DR

This paper investigates the phase diagram of a dilute Heisenberg model with competing interactions, revealing multiple magnetic phases and reentrant transitions, which help explain experimental observations in dilute ferromagnets.

Contribution

It provides a detailed analysis of the phase diagram for a dilute ferromagnet with antiferromagnetic next-nearest interactions, highlighting the emergence of multiple phases and reentrant behavior.

Findings

Identification of ferromagnetic, spin glass, and mixed phases in the phase diagram.

Observation of reentrant spin glass transition near the ferromagnetic threshold.

The model reproduces experimental phase diagrams of certain dilute ferromagnetic materials.

Abstract

We have studied the spin ordering of a dilute classical Heisenberg model with spin concentration $x$, and with ferromagnetic nearest-neighbor interaction $J_1$ and antiferromagnetic next-nearest-neighbor interaction $J_2$. Magnetic phases at absolute zero temperature $T = 0$ are determined examining the stiffness of the ground state, and those at finite temperatures $T \neq 0$ are determined calculating the Binder parameter $g_L$ and the spin correlation length $\xi_L$. Three ordered phases appear in the $x-T$ phase diagram: (i) the ferromagnetic (FM) phase; (ii) the spin glass (SG) phase; and (iii) the mixed (M) phase of the FM and the SG. Near below the ferromagnetic threshold $x_{\rm F}$, a reentrant SG transition occurs. That is, as the temperature is decreased from a high temperature, the FM phase, the M phase and the SG phase appear successively. The magnetization which grows in the FM phase disappears in the SG phase. The SG phase is suggested to be characterized by ferromagnetic clusters. We conclude, hence, that this model could reproduce experimental phase diagrams of dilute ferromagnets Fe$_x$Au$_{1-x}$ and Eu$_x$Sr$_{1-x}$S.