[Paper Review] Comment on "Discovery of slow magnetic fluctuations and critical slowing down in the pseudogap phase of YBa$_2$Cu$_3$O$_y$"

J. E. Sonier|arXiv (Cornell University)|Jun 9, 2017

Physics of Superconductivity and Magnetism3 citations

TL;DR

This paper challenges the interpretation of muon spin relaxation (μSR) data in YBa₂Cu₃Oᵧ, arguing that Zhang et al.'s claim of critical slowing down near T* is invalid due to unaccounted nuclear dipole contributions and muon diffusion. The authors show that assuming a T-independent Gaussian Kubo-Toyabe function for nuclear dipolar fields and neglecting muon diffusion leads to misleading relaxation rate trends, especially above 160 K, where muon mobility distorts the signal and invalidates the detection of slow magnetic fluctuations.

ABSTRACT

A recent zero-field (ZF) and longitudinal-field (LF) muon spin relaxation ($μ$SR) study of YBa$_2$Cu$_3$O$_y$ [Jian~Zhang {\it et al.}, arXiv:1709.06799] claims to have detected critical slowing down of magnetic fluctuations near the pseudogap temperature $T^*$, and attribute this to the onset of slow fluctuating domains of intra-unit-cell magnetic order. Here it is argued that the relaxation data displayed in this study are misleading due to an improper account of the nuclear dipole contribution and a failure to acknowledge the occurrence of muon diffusion.

Motivation & Objective

• To challenge the interpretation of zero-field and longitudinal-field μSR data in YBa₂Cu₃Oᵧ as evidence for critical slowing down near T*.
• To demonstrate that the assumption of a T-independent nuclear dipole contribution via the static Gaussian Kubo-Toyabe function is invalid in this system.
• To show that muon diffusion above ~160 K significantly distorts μSR relaxation rates, rendering them unreliable for probing magnetic fluctuations.
• To argue that the observed peaks in relaxation rates near T* are artifacts of muon diffusion and detection limits, not genuine critical dynamics.
• To question the validity of LF-μSR fits to the Redfield formula due to low signal levels and potential extrinsic effects from beam geometry and fringe fields.

Proposed method

• Re-evaluates the ZF-μSR relaxation function G_z(t) = G_KT(Δ,t) × exp(−λ_ZF t), questioning the assumption that the nuclear dipole contribution is well described by a T-independent Gaussian Kubo-Toyabe (KT) function.
• Highlights that the KT function is a crude approximation in systems with strong electric field gradients (EFG), requiring inclusion of nuclear quadrupole interactions for accuracy.
• Analyzes prior ZF-μSR data on YBa₂Cu₃Oᵧ (Ref. Sonier:02) to show that Δ must vary with temperature due to CDW order and structural transitions near 60 K and 100 K.
• Demonstrates that muon diffusion above ~160 K reduces the observed relaxation rate λ_ZF, which can mimic or obscure true magnetic fluctuations.
• Evaluates the LF-μSR data by comparing λ_LF vs. B_LF to the Redfield formula, finding poor agreement and questioning the reliability of extracted correlation times.
• Considers extrinsic effects such as beam focusing and fringe fields in the magnet, which may cause artificial decreases in λ_LF with increasing B_LF.

Experimental results

Research questions

• RQ1 Is the assumption of a T-independent nuclear dipole contribution via the Gaussian Kubo-Toyabe function valid for YBa₂Cu₃Oᵧ in the pseudogap regime?
• RQ2 How do charge-density-wave order and structural transitions near 60 K and 100 K affect the nuclear dipole contribution to ZF-μSR?
• RQ3 To what extent does muon diffusion above ~160 K distort μSR relaxation rates and invalidate the detection of slow magnetic fluctuations?
• RQ4 Are the small peaks in λ_ZF and λ_LF near T* in underdoped samples real or artifacts of muon diffusion and detection noise?
• RQ5 Can the observed B_LF dependence of λ_LF in LF-μSR be reliably fitted to the Redfield formula, or are extrinsic effects such as beam focusing responsible?

Key findings

• The nuclear dipole contribution to ZF-μSR in YBa₂Cu₃Oᵧ is not T-independent and cannot be accurately described by a static Gaussian Kubo-Toyabe function due to EFG and CDW effects.
• The value of Δ in the KT function must vary with temperature, as shown by better fits when Δ is allowed to vary, especially below 100 K and near 60 K.
• Muon diffusion above ~160 K reduces the observed λ_ZF, which can mimic or obscure true magnetic relaxation, invalidating the use of λ_ZF as a probe of critical fluctuations.
• The small peaks in λ_ZF near 210 K and λ_LF near 160 K are likely artifacts of muon diffusion and trapping at defects, not evidence of critical slowing down.
• The LF-μSR data show poor agreement with the Redfield formula, and the extremely low relaxation rates (on the order of 10⁻³ μs⁻¹) are near the detection limit, raising concerns about reliability.
• Extrinsic effects such as beam focusing and fringe fields may cause an artificial decrease in λ_LF with increasing B_LF, and control experiments on Ag are insufficient to rule out this scenario without exact replication of sample geometry and position.