Exploring electron spin dynamics in spin chains using defects as a quantum probe

TL;DR

This study provides a comprehensive experimental and theoretical evaluation of the relaxation and decoherence of quantum spin chain edge states (QSC-ES) in quasi-1D spin chains. By combining pulsed ESR measurements across multiple frequencies with DMRG simulations and moment-based analyses, it reveals how phonon processes (direct bottleneck, Orbach, Raman), phonon bottlenecks, and intra-chain exchange renormalize the dipolar decoherence landscape. A key finding is that intra-chain exchange strongly suppresses effective dipolar fields, with the dimerization parameter $\delta$ controlling edge-state localization and the strength of inter-edge coupling as $d_{\rm eff}/d \approx 3\delta$, offering concrete design rules for enhancing coherence. The results establish fundamental limits and design principles for nanoscale quantum devices that leverage topological edge states, and provide a framework applicable to related correlated quantum materials.

Abstract

We investigate the quantum dynamics of the electron spin resonance of topological defects (edge state) in dimerized chains. These objects are discontinuities of the spin chain protected by the properties of the global system leading to a quantum many-body multiplet protected from the environment decoherence. Despite recent achievements in the realization of isolated and finite spin chains, the potential implementation in quantum devices needs the knowledge of the relaxation and decoherence sources. Our study reveals that electron spin lattice relaxation is governed at lowest temperatures by phonon-bottlenecked process and at high temperature by the chain dimerization gap. We show that the inter edge-state effective dipolar field is reduced by the intrachain exchange coupling leading to a longer coherence time than isolated ions at equivalent concentration. Ultimately, we demonstrate that the homogeneous broadening is governed by the intra-chain dipolar field, and we establish design principles for optimizing coherence in future materials.

Figures (22)

• Figure 1: Local magnetization profiles obtained via DMRG simulations for open spin chains of length L=100 and L=101 spins. The simulations are performed using the spin-Peierls Hamiltonian (eq. \ref{['eq:HAFM-Hamiltonian']}) with a dimerization parameter $\delta=\pm0.08$. The different colored lines represent the expectation value of the Sz operator at each lattice site. The results illustrate how the open boundary conditions lead to a significant polarization of the spins at the chain ends, forming a cluster.
• Figure 2: Crystal structures of ($o$ -DMTTF)$_2$Br, ($o$ -DMTTF)$_2$I and($o$ -DMTTF)$_2$Cl . The left panels show the unit cell viewed along the c axis, while the right panels show the packing along the a axis. The crystallographic axes are indicated with colored arrows (red, green, and blue for a, b, and c, respectively). The $o$ -DMTTF molecules form stacks along the c-axis, with strong intra-stack interactions leading to 1D magnetic behavior. The packing and interactions are slightly different due to the different counter-anion.
• Figure 3: (a)-(b) Longitudinal magnetization as function of time after the inversion pulse. The semi-log scale is used to highlight the deviation from the monoexponential decay. The solid line is the best fit using eq. \ref{['eq:fit_relaxation']}. (a) At $T=7$ K, the stretched exponential parameter is $\beta=0.65$ and (b) at $T=14.5$ K $\beta=1$. (c) Temperature dependence of $\beta$ for ($o$ -DMTTF)$_2$Br and for the three microwave bands used.
• Figure 4: Temperature dependence of the inverse stretched relaxation time ($1/T_1^\text{str}$) for ($o$ -DMTTF)$_2$Br, obtained via inversion recovery experiments at three microwave frequencies: X-band (9.7 GHz), Q-band (34 GHz), and W-band (94 GHz). The data are plotted on a log-log scale. Dashed lines represent fits to a linear temperature dependence ($\alpha_D T$), reflecting the direct phonon process, which provides a poor fit. Black solid lines show fits to a square of temperature dependence ($\alpha_B T ^2$), indicative of a possible phonon bottleneck effect.
• Figure 5: Temperature dependence of the spin lattice relaxation rate corrected by the phonon bottleneck contribution with respect to (a) $1/T$ or (b) $T$ in log-scale. Plain and dash-doted lines are the best fit using Orbach and Raman model respectively.