Non-equilibrium Muon Dynamics Imitating Fractional Spin Excitations in a Quantum Spin Chain

The gist The study investigates spin dynamics in AgCuVO4 using muon spectroscopy and reveals that field-resilient muon polarization decay can arise from non-equilibrium muon dynamics, specifically a two-state model involving random hopping between sites rather than intrinsic sporadic spin fluctuations

Background and Motivation

Unconventional magnetic ground states like quantum spin liquids are of significant interest due to phenomena such as fractional spin excitations The study focuses on the amplitude-modulated magnetic ground state of AgCuVO4, a spin-1/2 chain compound with competing intrachain interactions Muon spin spectroscopy (µSR) is a powerful technique for probing sporadic spin dynamics, which is often associated with a monotonic quasistatic (Gaussian) decay of muon polarization that remains weakly affected by applied magnetic fields

Experimental Findings on Muon Dynamics

The extended µSR measurements on AgCuVO4 demonstrated that the muon randomly hops between two nearby stopping sites and eventually equilibrates across both via quantum delocalization on a microsecond timescale This dynamic behavior provides a natural explanation for the characteristic Gaussian decay of the muon polarization and its observed resilience to an applied magnetic fields, which does not involve exotic sporadic spin dynamics of the spin chains

Modeling and Interpretation

The temperature dependence of the muon polarization is modeled as a sum of a GBG function, representing low-temperature electron magnetism, and a KT function accounting for nuclear fields The two-state model successfully reproduces the full field dependence of the µSR signal by assuming that the muon transitions between two distinct magnetic environments This transition is interpreted as muon hopping between two nearby sites, followed by thermalization and quantum delocalization across both sites, resulting in a static magnetic field distribution

Microscopic Mechanism Identification

Density functional theory (DFT) calculations identified five candidate stopping sites for the muon Site number 2 was determined to be the most likely site because it exhibited a much lower classical-muon DFT energy (by ∼0.2 eV) and a much more extended potential minimum Furthermore, calculations of the QLCR spectrum showed that the best agreement between the experiment and calculations is found for the muon stopping sites 2 The analysis supports a mechanism where the muon hops between two nearby sites, separated by just ∼0.5 ˚A, which are related by a local inversion center

Conclusion on Physical Origin

The two-state model is compatible with muon hopping between two physical sites or delayed magnetic ordering at the muon site The most consistent explanation is that the muon hops between nearby sites, and upon thermalization, it becomes delocalized over both sites, experiencing a broad KT-like field distribution with a mean value consistent with experimental results This mechanism offers an alternative to sporadic relaxation processes which often lack a clear microscopic justification

Methods Summary

The study employed extended µSR measurements on a powder sample of AgCuVO4 to extend sensitivity to smaller magnetic fields DFT calculations were used with the MuFinder program and CASTEP code to determine classical muon sites, identifying site number 2 as the most probable location QLCR spectra were calculated for each candidate site and compared with experimental LF decoupling data at 2.4 K, confirming the best fit for site number 2 The final analysis utilized a two-state model to explain the field resilience, concluding that the muon transitions from a fast-fluctuating regime to a fully static state

Acknowledgments

This work has been funded by the Slovenian Research Agency (ARIS), and computing resources were provided by local clusters at the Jožef Stefan Institute and STFC Scientific Computing Department The paper cites numerous foundational works in frustrated magnetism, muon spin rotation, and DFT calculations for magnetic materials

References

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Supplementary Materials

Fig. S1 shows calculated effect of QLCR on the muon polarization in AgCuVO4 Fig. S2 shows longitudinal field decoupling of the muon polarization in AgCuVO4 at 0.09 K The paper uses a modified Gaussian line to fit the field-dependent muon relaxation λ(B) The derived parameters for site number 2 are consistent with experimental data, including a two-state transition rate r = 1.

1. The AI system can accurately model emergent sporadic spin dynamics by incorporating a two-state model instead of assuming intrinsic spin fluctuations, as this provides a microscopic explanation for the field-resilient muon polarization.

2. The system can predict the nature of magnetic ground states in frustrated systems by utilizing the findings that suggest the muon randomly hops between two nearby sites and eventually equilibrates across both via quantum delocalization, offering an alternative perspective on the µSR response in frustrated spin systems.

3. The AI can identify specific, energetically favorable muon stopping sites for complex materials by performing density functional theory (DFT) calculations and selecting the site with the much more extended potential minimum as the most likely location.

4. The system can distinguish between different physical scenarios for field suppression by contrasting them against experimental data, specifically ruling out Muon diffusion between two physical sites because it is inconsistent with the paramagnetic response at 2.4 K.

5. The AI can predict the magnetic structure of a material by correlating calculated fields with experimental results; for instance, it can determine that the configuration with moments along b yields an average field of ∼4(1) mT near the identified muon site, consistent with the experimentally determined √2∆2-state KT /γµ = 2.8(2) mT.

Fractional spin excitations in low-dimensional and frustrated magnets are commonly associated with sporadic spin fluctuations, as observed in quantum spin liquids, spin ices, and other complex magnetic states. In this study, we investigate the spin dynamics in the amplitude-modulated magnetic ground state of AgCuVO 4, a spin-1/2 chain compound with competing intrachain interactions, by muon spectroscopy. Our data reveal a Gaussian decay of muon polarization that remains remarkably resilient against applied magnetic fields---a behavior often interpreted as evidence of emergent sporadic spin dynamics. However, density functional theory calculations of muon stopping sites and their quadrupolar level-crossing resonance spectra suggest an alternative mechanism: a two-state model where the muon randomly hops between two nearby sites, eventually equilibrating across both on a microsecond timescale via quantum delocalization. These findings provide a microscopic explanation for the field-resilient muon polarization and indicate that such behavior may not always stem from intrinsic spin fluctuations, but can also arise from non-equilibrium muon dynamics.