The nuclear polaron beyond the mean-field approximation

Abstract

In III-V semiconductors it was shown theoretically that under optical cooling the nuclear spin polaron bound to neutral donors would form below some critical nuclear spin temperature TC [I. A. Merkulov, Phys. Solid State 40, 930 (1998)]. The predicted critical behavior is a direct consequence of the use of the mean-field approximation. It is known however that in any finite size system a critical behavior must be absent. Here we develop a model of the optically cooled nuclear polaron, which goes beyond the mean-field approximation. An expression of the generalized free energy of the optically cooled nuclear polaron, valid for a finite, albeit large, number of spins, is derived. This model permits to describe the continuous transition from the fluctuation dominated regime to the saturation regime, as the nuclear spin temperature decreases. It is shown that due to the finite number of nuclear spins involved in the polaron, the critical effects close to TC are smoothed by the spin fluctuations. Particularly, instead of a divergence, the nuclear spin fluctuations exhibit a sharp peak at TC, before being depressed well below TC. Interestingly, the formation of the nuclear polaron can, in certain conditions, boost the nuclear polarization beyond the value obtained solely by optical pumping. Finally, we suggest that the nuclear polaron could be detected by spin noise spectroscopy or via its superparamagnetic behavior.

7 pages, 6 figures

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Cited by in corpus (7)

• Spin temperature concept verified by optical magnetometry of nuclear spins
• Nuclear Spin Noise in the Central Spin Model
• Electron-induced nuclear magnetic ordering in n-type semiconductors
• Unveiling the electron-nuclear spin dynamics in an n-doped InGaAs epilayer by spin noise spectroscopy
• Kinetic approach to the nuclear-spin polaron formation
• Subsecond nuclear spin dynamics in $n$-GaAs
• Nuclear spin polaron-formation: anisotropy effects and quantum phase transition