Energy minima and ordering in ferromagnets with quenched randomness

TL;DR

This work probes ordering in ferromagnets with quenched randomness by combining $T=0$ energy minimization and finite-$T$ Monte Carlo across 2D/3D RF and RA models. It finds that 3D RA systems can order as temperature lowers, though strong RA suppresses magnetization and induces glassy features, while 3D RF systems fail to order and instead freeze into correlated spin glasses with a cusp in the heat capacity. In 2D RA, the ground state is magnetized, but finite-temperature order is blocked by topological defects and anisotropy barriers, leading to no true LRO. Overall, RA tends to support partial ordering under certain conditions, whereas RF promotes glassy freezing, with implications for soft magnetic materials and the physics of quenched randomness.

Abstract

Energy minimization at T=0 and Monte Carlo simulations at T>0 have been performed for 2D and 3D random-field and random-anisotropy systems of up to 100 million classical spins. The main finding is that 3D random-anisotropy systems magnetically order on lowering temperature, contrary to the theoretical predictions based on the Imry-Ma argument. If random-anisotropy is stronger than the exchange, which can be the case in sintered materials, the system still orders but the magnetization is strongly reduced and there is a large spin-glass component in the spin state, the heat capacity having a cusp instead of a divergence. 3D random-field systems do not magnetically order on lowering temperature but rather freeze into the correlated spin-glass state. Here, although magnetized local energy minima have lower energies than non-magnetized ones, magnetic ordering is prevented by singularities pinned by the random field.

Figures (13)

• Figure 1: Adaptive Monte Carlo: MCS vs $T$ for the 3D $xy$ model.
• Figure 2: Local energy minima of 2D models with quenched randomness sampled by the RIC-CIC crossover, random dropping, and simulated annealing. Upper panel: 2D RA model. Lower panel: 2D RF model.
• Figure 3: Local energy minima of 3D models with quenched randomness sampled by the RIC-CIC crossover. Upper panel: 3D RA model. Lower panel: 3D RF model. States on the left with lower magnetization and higher energies contain singularities (hedgehogs).
• Figure 4: Local energy minima of 3D models with quenched randomness sampled by the RIC-CIC crossover: $D_{R}/J=3$ and 10. Energy minima with smaller magnetization and higher energy contain singularities (hedgehogs).
• Figure 5: $D_{R}$ and $H_{R}$ scans with energy minimization of 3D Heisenberg systems at $T=0$. Upper panel: RA model. Lower panel: RF model.