The Magnetic Ordering of the 3d Wigner Crystal

TL;DR

This study uses Path Integral Monte Carlo to analyze magnetic ordering in a 3D Wigner crystal, revealing pair exchange dominance and estimating the critical temperature for antiferromagnetic transition.

Contribution

It provides the first detailed calculation of exchange frequencies in a 3D Wigner crystal, highlighting the dominance of pair exchange over multi-electron exchanges.

Findings

Pair exchange dominates in the 3D Wigner crystal.

Estimated critical temperature for antiferromagnetic transition is roughly 1e-8 Ry.

The 3D Wigner crystal differs from 2D and solid helium in exchange behavior.

Abstract

Using Path Integral Monte Carlo, we have calculated exchange frequencies as electrons undergo ring exchanges of 2, 3 and 4 electrons in a ``clean'' 3d Wigner crystal (bcc lattice) as a function of density. We find pair exchange dominates and estimate the critical temperature for the transition to antiferromagnetic ordering to be roughly $1 \times 10^{-8}$Ry at melting. In contrast to the situation in 2d, the 3d Wigner crystal is different from the solid bcc 3He in that the pair exchange dominates because of the softer interparticle potential. We discuss implications for the magnetic phase diagram of the electron gas.