Spin-spin correlations in ferromagnetic nanosystems

TL;DR

This paper investigates how finite size, surface effects, and anisotropy influence spin-spin correlations and critical temperatures in ferromagnetic nanosystems using various computational techniques.

Contribution

It introduces a comprehensive analysis of temperature-dependent spin correlations in finite ferromagnetic systems, highlighting surface effects and proposing methods to estimate critical temperatures.

Findings

Strong surface effects in small nanoparticles affect spin correlations.

Complex temperature-dependent behavior of spin correlations differs from simple models.

Methods to estimate critical temperatures of infinite systems from finite data.

Abstract

Using exact diagonalization, Monte-Carlo, and mean-field techniques, characteristic temperature scales for ferromagnetic order are discussed for the Ising and the classical anisotropic Heisenberg model on finite lattices in one and two dimensions. The interplay between nearest-neighbor exchange, anisotropy and the presence of surfaces leads, as a function of temperature, to a complex behavior of the distance-dependent spin-spin correlation function, which is very different from what is commonly expected. A finite experimental observation time is considered in addition, which is simulated within the Monte-Carlo approach by an incomplete statistical average. We find strong surface effects for small nanoparticles, which cannot be explained within a simple Landau or mean-field concept and which give rise to characteristic trends of the spin-correlation function in different temperature regimes. Unambiguous definitions of crossover temperatures for finite systems and an effective method to estimate the critical temperature of corresponding infinite systems are given.