Spin diffusion in the low-dimensional molecular quantum Heisenberg antiferromagnet Cu(pyz)(NO$_{3}$)$_{2}$ detected with implanted muons

TL;DR

This study uses muon-spin relaxation to investigate spin diffusion in a one-dimensional quantum antiferromagnet, revealing diffusive and ballistic regimes of spin transport and identifying muon sites with minimal perturbation.

Contribution

The paper combines experimental muon-spin relaxation measurements with density-functional theory to identify muon sites and characterize spin transport regimes in a low-dimensional quantum antiferromagnet.

Findings

Muon sites involve hydroxyl-type bonds with nitrate oxygen.

Spin excitations show diffusive transport between T_N and J.

A crossover to ballistic transport occurs at higher magnetic fields.

Abstract

We present the results of muon-spin relaxation measurements of spin excitations in the one-dimensional quantum Heisenberg antiferromagnet Cu(pyz)(NO$_{3}$)$_{2}$. Using density-functional theory we propose muon sites and assess the degree of perturbation the muon probe causes on the system. We identify a site involving the muon forming a hydroxyl-type bond with an oxygen on the nitrate group that is sensitive to the characteristic spin dynamics of the system. Our measurements of the spin dynamics show that in the temperature range $T_{\mathrm{N}}<T<J$ (between the ordering temperature $T_{\mathrm{N}}$ and the exchange energy scale $J$) the field-dependent muon spin relaxation is characteristic of diffusive transport of spin excitations over a wide range of applied fields. We also identify a possible crossover at higher applied fields in the muon probe's response to the fluctuation spectrum, to a regime where the muon detects early-time transport with a ballistic character. This behavior is contrasted with that found for $T>J$ and that in the related two-dimensional system Cu(pyz)$_2$(ClO$_4$)$_{2}$.