Understanding the dynamics of randomly positioned dipolar spin ensembles

TL;DR

This study investigates the spin dynamics in randomly positioned dipolar spin ensembles, revealing a significant discrepancy between observed and simulated time scales, and introduces an extended cluster-based mean-field theory to better explain these phenomena.

Contribution

The paper extends the spinDMFT to clusters (CspinDMFT), successfully capturing the large mismatch in spin correlation time scales caused by positional disorder.

Findings

Time scales in longitudinal and transversal channels differ by over an order of magnitude.

SpinDMFT fails to explain the observed mismatch, but CspinDMFT succeeds.

Positional disorder plays a pivotal role, indicating links to many-body localization.

Abstract

Dipolar spin ensembles with random spin positions attract much attention currently because they help to understand decoherence as it occurs in solid state quantum bits in contact with spin baths. Also, these ensembles are systems which may show many-body localization, at least in the sense of very slow spin dynamics. We present measurements of the autocorrelations of spins on diamond surfaces in a doubly-rotating frame which eliminates local disorder. Strikingly, the time scales in the longitudinal and the transversal channel differ by more than one order of magnitude which is a factor much greater than one would have expected from simulations of spins on lattices. A previously developed dynamic mean-field theory for spins (spinDMFT) fails to explain this phenomenon. Thus, we improve it by extending it to clusters (CspinDMFT). This theory does capture the striking mismatch up to two orders of magnitude for random ensembles. Without positional disorder, however, the mismatch is only moderate with a factor below 4. The pivotal role of positional disorder suggests that the strong mismatch is linked to precursors of many-body localization.