A single layer of Mn in a GaAs quantum well: a ferromagnet with quantum fluctuations

TL;DR

This paper demonstrates that a single Mn layer in a GaAs quantum well can exhibit ferromagnetism due to magnetic frustration, despite the Mermin-Wagner theorem, with quantum fluctuations reducing the ordered magnetic moment.

Contribution

It shows that magnetic frustration stabilizes ferromagnetism in a single Mn layer in GaAs quantum wells, and compares Heisenberg and Kohn-Luttinger models to estimate quantum fluctuations.

Findings

Single Mn layer can be ferromagnetic in GaAs quantum wells.

Quantum fluctuations suppress the magnetic moment from saturation.

Heisenberg model is valid at low Mn concentrations.

Abstract

Some of the highest transition temperatures achieved for Mn-doped GaAs have been in delta-doped heterostructures with well-separated planes of Mn. But in the absence of magnetic anisotropy, the Mermin-Wagner theorem implies that a single plane of magnetic ions cannot be ferromagnetic. Using a Heisenberg model, we show that the same mechanism that produces magnetic frustration and suppresses the transition temperature in bulk Mn-doped GaAs, due to the difference between the light and heavy band masses, can stabilize ferromagnetic order for a single layer of Mn in a GaAs quantum well. This comes at the price of quantum fluctuations that suppress the ordered moment from that of a fully saturated ferromagnet. By comparing the predictions of Heisenberg and Kohn-Luttinger models, we conclude that the Heisenberg description of a Mn-doped GaAs quantum well breaks down when the Mn concentration becomes large, but works quite well in the weak-coupling limit of small Mn concentrations. This comparison allows us to estimate the size of the quantum fluctuations in the quantum well.