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arxiv: 2604.20337 · v1 · submitted 2026-04-22 · ❄️ cond-mat.str-el

Disorder-driven coexistence of distinct dynamical states in frustrated Sr₃CuNb₂O₉: a microscopic μSR and ⁹³Nb NMR study

M. Biswas , K. Bhattacharya , K. M. Ranjith , S. M. Hossain , S. S. Islam , M. Naskar , R. Sarkar , B. B\"uchner
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T. Shiroka H.-J. Grafe M. Majumder
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The pith

μSR and ⁹³Nb NMR data show microscopic coexistence of random singlet and quantum spin liquid-like dynamical states in disordered Sr₃CuNb₂O₉.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The material Sr₃CuNb₂O₉ has magnetic copper ions arranged with disorder and geometric frustration. Muon spin relaxation measurements detect a relaxation rate that grows as a power law both with falling temperature and with applied magnetic field. This pattern matches expectations for a random singlet phase in which spins pair into singlets in a disordered fashion. The niobium NMR spectra split into two distinct lines, indicating two different local magnetic surroundings. An inverse Laplace transform applied to the magnetization recovery curves separates the relaxation into a fast channel and a slow channel. The fast channel relaxes with temperature to the power 0.6 while the slow channel follows a power of 1.1. The authors assign the fast channel to random-singlet-like dynamics and the slow channel to quantum-spin-liquid-like dynamics. The data therefore indicate that disorder produces microscopic regions or domains hosting these two distinct behaviors within the same crystal.

Core claim

The combined spectral and relaxation data demonstrate that the fast channel qualitatively represents an RS-like state, whereas the slow channel exhibits quantum spin liquid (QSL) like behavior, thereby establishing the microscopic coexistence of RS and QSL-like phases in Sr₃CuNb₂O₉.

Load-bearing premise

That the two well-separated relaxation channels identified by inverse Laplace transform correspond to distinct coexisting phases rather than a broad continuous distribution of environments or artifacts of the transform and fitting procedure.

Figures

Figures reproduced from arXiv: 2604.20337 by B. B\"uchner, H.-J. Grafe, K. Bhattacharya, K. M. Ranjith, M. Biswas, M. Majumder, M. Naskar, R. Sarkar, S. M. Hossain, S. S. Islam, T. Shiroka.

Figure 1
Figure 1. Figure 1: (d) shows λLF as a function of applied longitu￾dinal magnetic fields, which was inadequate to fit using the well-known Redfield fit [28] as in low-temperature the auto-correlation function S(t) ∼ (τ/t) x exp(−νt) (where x is the critical exponent, τ and 1/ν are the early and late time cutoffs respectively) develops differently with x 6= 0 rather a simple exponential function with x = 0. To de￾scribe λLF (µ… view at source ↗
Figure 2
Figure 2. Figure 2: (b), are estimated using the relation K = K0 + (Ahf /NAµB )χ(T), (3) where K0 represents the temperature-independent contri￾bution to the Knight shift, NA is Avogadro’s number and χ(T) is the bulk magnetic susceptibility. The resulting val￾ues, A SC hf = 5.17 T/µB and A BC hf = 1.59 T/µB , imply an ap￾proximately 3.2-times enhancement of the hyperfine cou￾pling for SC relative to BC, a factor that provides… view at source ↗
Figure 3
Figure 3. Figure 3: (a)] described by the equation [32], 1 − M(t)/M(∞) = C € 0.006e −(t/T1,str) β + 0.0335e −(6t/T1,str ) β + 0.0925e −(15t/T1,str) β + 0.215e −(28t/T1,str) β + 0.653e −(45t/T1,str) ⠊ , (5) where C is a pre-factor and β, known as the stretched ex￾ponent, assumes a value less than 1, reflecting deviation from single-exponential relaxation. The temperature de￾pendence of β, shown in the inset of [PITH_FULL_IM… view at source ↗
read the original abstract

Despite recent progress in identifying the exotic random singlet (RS) state in disordered frustrated magnets as a distinct correlated phase, three-dimensional (3D) realizations remain scarce. Sr$_3$CuNb$_2$O$_9$ was proposed to be one of such 3D frustrated systems with magnetic site disorder hosting an RS ground state. Here, we report a detailed microscopic investigation of Sr$_3$CuNb$_2$O$_9$ employing muon spin relaxation ($\mu$SR) and $^{93}$Nb nuclear magnetic resonance (NMR) techniques. The $\mu$SR zero-field relaxation rate reveals a power-law divergence of the relaxation rate as a function of temperature. Also, a power-law divergence is present in the relaxation rate as a function of applied longitudinal field, consistent with the formation of an RS phase. The $^{93}$Nb NMR spectra unambiguously resolve two components with distinct local magnetic environments, whose nature is further elucidated through spin-lattice relaxation measurements analyzed via an inverse Laplace transform (ILT) of the nuclear magnetization recovery. The relaxation-rate distribution obtained from ILT reveals two well-separated channels: a fast component, $(1/T_1)_{\mathrm{fast}}$, and a slow component, $(1/T_1)_{\mathrm{slow}}$. Both components follow distinct power-law temperature dependences ($T^{\alpha}$), with $\alpha = 0.6$ and $1.1$ for the fast and slow channels, respectively. The combined spectral and relaxation data demonstrate that the fast channel qualitatively represents an RS-like state, whereas the slow channel exhibits quantum spin liquid (QSL) like behavior, thereby establishing the microscopic coexistence of RS and QSL-like phases in Sr$_3$CuNb$_2$O$_9$.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

Based on abstract only; the central claim rests on standard domain interpretations of μSR power-law behavior and on the assumption that ILT-separated channels map to distinct phases.

free parameters (1)
  • power-law exponents = 0.6 (fast), 1.1 (slow)
    Fitted values 0.6 and 1.1 for fast and slow NMR relaxation channels
axioms (2)
  • domain assumption Power-law divergence of μSR relaxation rate signals random singlet phase
    Invoked to link observed temperature and field dependence to RS state
  • ad hoc to paper ILT-separated fast and slow channels represent distinct coexisting phases
    Central mapping used to conclude microscopic coexistence

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