# Microscopic Aspects of Magnetic Lattice Demagnetizing Factors

## TL;DR

This paper investigates how microscopic details like spin type, orientation, and shape influence the demagnetizing factor N in magnetic lattices, combining theory, simulations, and experiments for a comprehensive understanding.

## Contribution

It reveals that N depends on microscopic spin and shape details, challenging the common ellipsoid approximation in magnetic systems with long-range interactions.

## Key findings

- N varies with spin dimensionality and orientation
- Monte Carlo simulations confirm theoretical predictions
- Experimental N for Dy2Ti2O7 matches calculations closely

## Abstract

The demagnetizing factor N is of both conceptual interest and practical importance. Considering localized magnetic moments on a lattice, we show that for non-ellipsoidal samples, N depends on the spin dimensionality (Ising, XY, or Heisenberg) and orientation, as well as the sample shape and susceptibility. The generality of this result is demonstrated by means of a recursive analytic calculation as well as detailed Monte Carlo simulations of realistic model spin Hamiltonians. As an important check and application, we also make an accurate experimental determination of N for a representative collective paramagnet (i.e. the Dy2Ti2O7 spin ice compound) and show that the temperature dependence of the experimentally determined N agrees closely with our theoretical calculations. Our conclusion is that the well established practice of approximating the true sample shape with "corresponding ellipsoids" for systems with long-range interactions will in many cases overlook important effects stemming from the microscopic aspects of the system under consideration.