# Cooling of the Nuclear Spin System of a Nanostructure by Oscillating Magnetic Fields

## Abstract

**:**

## 1. Introduction

## 2. Dynamic Spin Polarization by an Oscillating Magnetic Field in a Static External Field

## 3. “True Cooling” of Nuclear Spins by Oscillating Magnetic Fields

## 4. Limitations of the Method and Numerical Estimates

_{2}is:

## 5. Conclusions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Abragam, A. The Principles of Nuclear Magnetism; Clarendon Press: Oxford, UK, 1961. [Google Scholar]
- Goldman, M. Spin Temperature and Nuclear Magnetic Resonance in Solids—International Series of Monographs on Physics; Clarendon: Oxford, UK, 1970. [Google Scholar]
- EPurcell, M.; Torrey, H.C.; Pound, R.V. Resonance Absorption by Nuclear Magnetic Moments in a Solid. Phys. Rev.
**1946**, 69, 37. [Google Scholar] [CrossRef] - Litvyak, V.M.; Cherbunin, R.V.; Kalevich, V.K.; Lihachev, A.I.; Nashchekin, A.V.; Vladimirova, M.; Kavokin, K.V. Warm-up spectroscopy of quadrupole-split nuclear spins in n-GaAs epitaxial layers. Phys. Rev. B
**2021**, 104, 235201. [Google Scholar] [CrossRef] - Landau, L.D.; Lifshitz, E.M. Statistical Physics, 3rd ed.; Butterworth-Heinemann: Oxford, UK, 1980; Chapter 12. [Google Scholar]
- Zapasskii, V.S. Spin-noise spectroscopy: From proof of principle to applications. Adv. Opt. Photonics
**2013**, 5, 131–168. [Google Scholar] [CrossRef] - Dyakonov, M.I. Spin Physics in Semiconductors, 2nd ed.; Springer Series in Solid-State Sciences; Springer: Berlin/Heidelberg, Germany, 2017; Volume 157. [Google Scholar]
- Vladimirova, M.; Cronenberger, S.; Colombier, A.; Scalbert, D.; Litvyak, V.M.; Kavokin, K.V.; Lemai, A. Simultaneous measurements of nuclear-spin heat capacity, temperature, and relaxation in GaAs microstructures. Phys. Rev. B
**2022**, 105, 155305. [Google Scholar] [CrossRef] - Flisinski, K.; Gerlovin, I.Y.; Ignatiev, I.V.; Petrov, M.Y.; Yu, S.; Yakovlev, D.R.; Reuter, D.; Wieck, A.D.; Bayer, M. Optically detected magnetic resonance at the quadrupole-split nuclear states in (In, Ga)As/GaAs quantum dots. Phys. Rev. B
**2010**, 82, 081308. [Google Scholar] [CrossRef] - Chekhovich, E.A.; Kavokin, K.V.; Puebla, J.; Krysa, A.B.; Hopkinson, M.; Andreev, A.D.; Sanchez, A.M.; Beanland, R.; Skolnick, M.S.; Tartakovskii, A.I. Structural analysis of strained quantum dots using nuclear magnetic resonance. Nat. Nanotechnol.
**2012**, 7, 646. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Dzhioev, R.I.; Korenev, V.L. Stabilization of the electron-nuclear spin orientation in quantum dots by the nuclear quadrupole interaction. Phys. Rev. Lett.
**2007**, 99, 037401. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Meier, F.; Zakharchenja, B.P. (Eds.) Optical Orientation; North-Holland: Amsterdam, The Netherlands, 1984; Chapter 5. [Google Scholar]
- Vladimirova, M.; Cronenberger, S.; Scalbert, D.; Ryzhov, I.I.; Zapasskii, V.S.; Kozlov, G.G.; Lemaître, A.; Kavokin, K.V. Spin temperature concept verified by optical magnetometry of nuclear spins. Phys. Rev. B
**2018**, 97, 041301. [Google Scholar] [CrossRef] [Green Version] - Giri, R.; Cronenberger, S.; Glazov, M.M.; Kavokin, K.V.; Lemaître, A.; Bloch, J.; Vladimirova, M.; Scalbert, D. Nondestructive Measurement of Nuclear Magnetization by Off-Resonant Faraday Rotation. Phys. Rev. Lett.
**2013**, 111, 087603. [Google Scholar] [CrossRef] [PubMed] - Berski, F.; Hübner, J.; Oestreich, M.; Ludwig, A.; Wieck, A.D.; Glazov, M. Interplay of Electron and Nuclear Spin Noise in n-Type GaAs. Phys. Rev. Lett.
**2015**, 115, 176601. [Google Scholar] [CrossRef] - Ryzhov, I.I.; Poltavtsev, S.V.; Kavokin, K.V.; Glazov, M.M.; Kozlov, G.G.; Vladimirova, M.; Scalbert, D.; Cronenberger, S.; Kavokin, A.V.; Lemaître, A.; et al. Measurements of nuclear spin dynamics by spin-noise spectroscopy. Appl. Phys. Lett.
**2015**, 106, 242405. [Google Scholar] [CrossRef] - Ryzhov, I.I.; Kozlov, G.G.; Smirnov, D.S.; Glazov, M.M.; Efimov, Y.P.; Eliseev, S.A.; Lovtcius, V.A.; Petrov, V.V.; Kavokin, K.V.; Kavokin, A.V.; et al. Spin noise explores local magnetic fields in a semiconductor. Sci. Rep.
**2016**, 6, 21062. [Google Scholar] [CrossRef] [Green Version]

**Figure 1.**Scheme of the experiment on dynamic spin polarization in a constant magnetic field perpendicular to the structure axis. The red arrow shows the direction of the probe beam of linearly polarized light with fluence J. Fluctuations of its polarization plane induced by spin fluctuations in the sample, detected with the polarimetric device, form the spin noise signal ${u}_{sn}$ used to control the current in the magnetic coil that creates the time-dependent magnetic field ${B}_{1}\left(t\right)$.

**Figure 2.**Schematic explanation of the dynamics of the nuclear magnetic moment under the magnetic field ${B}_{1}\left(t\right)$, correlated with the nuclear spin fluctuation. Green and red arrows show magnetic fields and magnetic moment components, correspondingly. The field ${B}_{1}\left(t\right)$ turns the Z-component of the fluctuating part of the nuclear magnetic moment, $\delta {M}_{Z}$, so that it feeds the regular magnetization along X. At the same time, ${M}_{X}$ turns in the XZ plane, so that $\delta {M}_{Z}$ decreases.

**Figure 3.**Evolution of the mean spin polarization along the static field $p/{p}_{0}$ (solid curves) and of the mean squared transverse fluctuation in relation to its equilibrium value (dashed curves), after switching on the magnetic field ${B}_{1}\left(t\right)$, for different values of the transformation coefficient $\zeta $. Blue curves: $\zeta =0.5{\zeta}_{0}$; magenta curves: $\zeta =2{\zeta}_{0}$; red curves: $\zeta =10{\zeta}_{0}$.

**Figure 4.**Experimental arrangement for “true” nuclear spin cooling in an external field. The red arrow shows the direction of the probe beam of linearly polarized light with fluence J. The time-dependent field ${B}_{1}\left(t\right)$ is applied parallel to the probe beam, with the $-T/4=-\pi /\left(2\left|\gamma B\right|\right)$ phase shift between the field and the optical spin noise signal being provided by the electronics.

**Figure 5.**Spin polarization vs. the transformation coefficient $\zeta $ for different ratios of spectral power densities of spin noise ${W}_{sn}$ (at the peak) and of background photonic noise ${W}_{ph}$. Inset: typical spectrum of spin noise in a transverse magnetic field over the background of photonic noise.

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Kavokin, K.V.
Cooling of the Nuclear Spin System of a Nanostructure by Oscillating Magnetic Fields. *Nanomaterials* **2023**, *13*, 2120.
https://doi.org/10.3390/nano13142120

**AMA Style**

Kavokin KV.
Cooling of the Nuclear Spin System of a Nanostructure by Oscillating Magnetic Fields. *Nanomaterials*. 2023; 13(14):2120.
https://doi.org/10.3390/nano13142120

**Chicago/Turabian Style**

Kavokin, Kirill V.
2023. "Cooling of the Nuclear Spin System of a Nanostructure by Oscillating Magnetic Fields" *Nanomaterials* 13, no. 14: 2120.
https://doi.org/10.3390/nano13142120