The Magnetic Ordering of the 3d Wigner Crystal

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.

References in corpus (7)

• Zero Temperature Phases of the Electron Gas
• Striped phase in a quantum XY-model with ring exchange
• Spin Polarization of the Low Density 3D Electron Gas
• Diffusion quantum Monte Carlo study of three-dimensional Wigner crystals
• Exchange Frequencies in the 2d Wigner crystal
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• Phase Diagram of the BCC S=1/2 Heisenberg Antiferromagnet with First and Second Neighbor Exchange

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