# 1/f^2 spectra of decoherence noise on ^75^As nuclear spins in bulk GaAs

## TL;DR

This study investigates the spectral characteristics of decoherence noise on ^75^As nuclear spins in GaAs, revealing a consistent 1/f^2 dependence across various substrates and linking it to nuclear spin fluctuations.

## Contribution

The paper introduces a theoretical framework to accurately define spectral intensities from multiple-echo decays and incorporates Hahn-echo T_2 into noise spectra analysis.

## Key findings

- Nuclear spins exhibit 1/f^2 noise dependence over two orders of magnitude.
- Characteristic frequencies are identified for different substrates: 170 Hz, 210 Hz, and 460 Hz.
- Decoherence is attributed to fluctuations of next-nearest-neighboring nuclear spins.

## Abstract

To identify the decoherence origin, frequency spectra using multiple {\pi}-pulses have been extensively studied. However, little has been discussed on how to define the spectral intensities from multiple-echo decays and how to incorporate the Hahn-echo T_2 in the noise spectra. Here, we show that experiments based on two theories solve these issues. With the previous theory clarifying that the spectral intensity should be given as the decay in the long-time limit, the intensity can be deduced without experimental artifacts usually entailed in the initial process. The other is the fluctuation-dissipation theory, with which the Hahn-echo T_2 is utilized as the zero-frequency limit of the noise spectrum and as an answer to the divergent issue on the 1/f^n noises. As a result, arsenic nuclear spins are found to exhibit 1/f2 dependences over two orders of magnitude in all the substrates of un-doped, Cr-doped semi-insulating and Si-doped metallic GaAs at 297 K. The 1/f^2 dependence indicates single noise source that is characterized by the characteristic frequency f_c_^un^=170 Hz, f_c_^Cr^=210 Hz and f_c_^Si^ =460 Hz. These f_c values are explained by a model that the decoherence is caused by the fluctuations of next-nearest-neighboring nuclear spins.

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Source: https://tomesphere.com/paper/1905.12906