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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classification ❄️ cond-mat.str-el

keywords relaxationcunbdistinctfastslowfrustratedmagneticmicroscopic

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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: (d) shows λLF as a function of applied longitudinal 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 describe λLF (µ… view at source ↗

**Figure 2.** Figure 2: (b), are estimated using the relation K = K0 + (Ahf /NAµB )χ(T), (3) where K0 represents the temperature-independent contribution to the Knight shift, NA is Avogadro’s number and χ(T) is the bulk magnetic susceptibility. The resulting values, A SC hf = 5.17 T/µB and A BC hf = 1.59 T/µB , imply an approximately 3.2-times enhancement of the hyperfine coupling for SC relative to BC, a factor that provides… view at source ↗

**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) β , (5) where C is a pre-factor and β, known as the stretched exponent, assumes a value less than 1, reflecting deviation from single-exponential relaxation. The temperature dependence 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.

Desk Editor's Note private letter to a colleague

The paper reports two distinct NMR relaxation channels with different power laws in Sr3CuNb2O9 but the RS/QSL coexistence claim depends on an unverified ILT separation that may not reflect real phases.

read the letter

The key takeaway is that the authors have identified two separate spin-lattice relaxation channels in the 93Nb NMR data for Sr3CuNb2O9, one fast with T to the 0.6 and one slow with T to the 1.1, and they link these to coexisting random singlet and quantum spin liquid like states, supported by muSR power laws. What stands out as new is the resolution of these two channels in a three-dimensional system with site disorder, along with the assignment based on spectral components. The muSR zero-field and longitudinal field data showing power-law divergences add concrete support for the RS aspect. This kind of microscopic probe data is scarce for 3D realizations. The softer part is the reliance on inverse Laplace transform to separate the relaxation rates. Without details on how they checked for stability under different noise levels or regularization parameters, it's hard to rule out that the two peaks are not just from the method splitting a broader distribution. The phase labels are also based on qualitative matching to expected behaviors rather than quantitative fits or theory comparisons. This work is for researchers in quantum magnetism who are looking at disorder effects in frustrated lattices. It provides experimental input on a candidate material that could help think about how RS and QSL states might mix in 3D. I would send it for peer review so that experts can examine the raw recovery curves and the ILT implementation to see if the bimodality holds up.

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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44 extracted references · 4 canonical work pages · 2 internal anchors

[1]

I. V . Gornyi, A. D. Mirlin, and D. G. Polyakov , Interacting elec- trons in disordered wires: Anderson localization and low- T transport, Phys. Rev . Lett.95, 206603 (2005)

2005
[2]

P . W . Anderson, Absence of diffusion in certain random lat- tices, Phys. Rev .109, 1492 (1958)

1958
[3]

Dasgupta and S

C. Dasgupta and S. K. Ma, Low-temperature proper- ties of the random heisenberg antiferromagnetic chain, Phys. Rev . B22, 1305 (1980)

1980
[4]

R. N. Bhatt and P . A. Lee, Scaling studies of highly disordered spin-½ antiferromagnetic systems, Phys. Rev . Lett.48, 344 (1982)

1982
[5]

R. N. Bhatt and P . A. Lee, A scaling method for low tem- perature behavior of random antiferromagnetic systems (in - vited), Journal of Applied Physics 52, 1703 (1981)

1981
[6]

Kimchi, J

I. Kimchi, J. P . Sheckelton, T . M. McQueen, and P . A. Lee, Scaling and data collapse from local mo- ments in frustrated disordered quantum spin systems, Nature Communications 9, 4367 (2018)

2018
[7]

J. Wang, W . Yuan, P . M. Singer , R. W . Smaha, W . He, J. Wen, Y . S. Lee, and T . Imai, Emergence of spin singlets with inhomogeneous gaps in the kagome lattice heisen- berg antiferromagnets zn-barlowite and herbertsmithite, 7 Nature Physics 17, 1109 (2021)

2021
[8]

C. Lee, W . Lee, S. Lee, T . Y amanaka, S. Jeon, J. Khatua, H. Nojiri, and K.-Y . Choi, Dirac spinons intermingled with singlet states in the random kagome antiferromagnet YCu 3(OD)6+x Br3−x (x = 0.5), Phys. Rev . B110, 064418 (2024)

2024
[9]

C. Lee, S. Lee, Y . Choi, C. Wang, H. Luetkens, T . Shiroka, Z. Jang, Y .-G. Y oon, and K.-Y . Choi, Coexistence of ran- dom singlets and disordered Kitaev spin liquid in H 3LiIr2O6, Phys. Rev . B107, 014424 (2023)

2023
[10]

Y . Chen, G. Duan, Y . Zhao, N. Xi, B. Pan, X. Xu, Z. Wu, K. Du, S. Li, Z. Hu, R. Bian, X. Wang, W . Li, L. Zhang, Y . Cui, S. Li, R. Yu, and W . Yu, Spinons, solitons and random singlets in the spin-chain com pound copper benzoate (2025), arXiv:2510.11551 [cond-mat.str-el]

work page arXiv 2025
[11]

S. M. Hossain, S. S. Rahaman, H. Gujrati, D. Bhoi, A. Matsuo, K. Kindo, M. Kumar , and M. Majumder , Evidence of random spin-singlet state in the three- dimensional quantum spin liquid candidate Sr 3CuNb2O9, Phys. Rev . B110, L020406 (2024)

2024
[12]

Y . J. Uemura, T . Y amazaki, D. R. Harshman, M. Senba, and E. J. Ansaldo, Muon-spin relaxation in aufe and cumn spin glasses, Phys. Rev . B31, 546 (1985)

1985
[13]

Y . J. Uemura, A. Keren, K. Kojima, L. P . Le, G. M. Luke, W . D. Wu, Y . Ajiro, T . Asano, Y . Kuriyama, M. Mekata, H. Kikuchi, and K. Kakurai, Spin ﬂuctuations in frustrated kagomé lat- tice system SrCr 8Ga4O19 studied by muon spin relaxation, Phys. Rev . Lett.73, 3306 (1994)

1994
[14]

Y oon, W

S. Y oon, W . Lee, S. Lee, J. Park, C. H. Lee, Y . S. Choi, S.-H. Do, W .-J. Choi, W .-T . Chen, F . Chou, D. I. Gor- bunov , Y . Oshima, A. Ali, Y . Singh, A. Berlie, I. Watan- abe, and K.-Y . Choi, Quantum disordered state in the J1−J2 square-lattice antiferromagnet Sr 2Cu(Te0.95W0.05)O6, Phys. Rev . Mater .5, 014411 (2021)

2021
[15]

Mustonen, S

O. Mustonen, S. V asala, E. Sadrollahi, K. P . Schmidt, C. Baines, H. C. Walker , I. T erasaki, F . J. Litterst, E. Baggio-Saitovitch, and M. Karppinen, Spin-liquid- like state in a spin-1 /2 square-lattice antiferromag- net perovskite induced by d 10 − d 0 cation mixing, Nature Communications 9, 1085 (2018)

2018
[16]

Kojima, A

K. Kojima, A. Keren, L. P . Le, G. M. Luke, B. Nachumi, W . D. Wu, Y . J. Uemura, K. Kiyono, S. Miyasaka, H. T akagi, and S. Uchida, Muon spin relax- ation and magnetic susceptibility measurements in the haldane system (Y2−x Cax )Ba(Ni1−y Mg y )O5, Phys. Rev . Lett.74, 3471 (1995)

1995
[17]

W . Lee, S. Do, S. Y oon, S. Lee, Y . S. Choi, D. J. Jang, M. Brando, M. Lee, E. S. Choi, S. Ji, Z. H. Jang, B. J. Suh, and K.-Y . Choi, Putative spin liquid in the triangle-based i ri- date Ba 3IrTi2O9, Phys. Rev . B96, 014432 (2017)

2017
[18]

Y aouanc and P

A. Y aouanc and P . D. D. Reotier ,Muon Spin Rotation, Relax- ation, and Resonance: Applications to Condensed Matter (Ox- ford University Press, 2011) pp. 247–259

2011
[19]

Živkovi ´c, V

I. Živkovi ´c, V . Favre, C. Salazar Mejia, H. O. Jeschke, A. Ma- grez, B. Dabholkar , V . Noculak, R. S. Freitas, M. Jeong, N. G. Hegde, L. T esta, P . Babkevich, Y . Su, P . Manuel, H. Luetkens, C. Baines, P . J. Baker , J. Wosnitza, O. Zaharko, Y . Iqbal, J. Reuther , and H. M. Rønnow , Magnetic ﬁeld in- duced quantum spin liquid in the two coupled tri...

2021
[20]

Bhattacharya, S

K. Bhattacharya, S. Mohanty , A. D. Hillier , M. T . F . T elling, R. Nath, and M. Majumder , Evidence of quantum spin liquid state in a Cu 2+-based S = 1 2 triangular lattice antiferromag- net, Phys. Rev . B110, L060403 (2024)

2024
[21]

Kundu, A

S. Kundu, A. Shahee, A. Chakraborty , K. M. Ranjith, B. Koo, J. Sichelschmidt, M. T . F . T elling, P . K. Biswas, M. Baenitz, I. Dasgupta, S. Pujari, and A. V . Mahajan, Gapless quantum spin liquid in the triangular system Sr 3CuSb2O9, Phys. Rev . Lett.125, 267202 (2020)

2020
[22]

Y . Li, D. Adroja, P . K. Biswas, P . J. Baker , Q. Zhang, J. Liu, A. A. Tsirlin, P . Gegenwart, and Q. Zhang, Muon spin relaxation evidence for the U (1) quantum spin-liquid ground state in the triangular antiferromagnet YbMgGaO 4, Phys. Rev . Lett.117, 097201 (2016)

2016
[23]

W . Hong, L. Liu, C. Liu, X. Ma, A. Koda, X. Li, J. Song, W . Y ang, J. Y ang, P . Cheng, H. Zhang, W . Bao, X. Ma, D. Chen, K. Sun, W . Guo, H. Luo, A. W . Sandvik, and S. Li, Extreme suppression of antiferromagnetic order and criti- cal scaling in a two-dimensional random quantum magnet, Phys. Rev . Lett.126, 037201 (2021)

2021
[24]

Khatua, M

J. Khatua, M. Gomilšek, J. C. Orain, A. M. Strydom, Z. Jagli ˇci´c, C. V . Colin, S. Petit, A. Ozarowski, L. Mangin- Thro, K. Sethupathi, M. S. R. Rao, A. Zorko, and P . Khuntia, Signature of a randomness-driven spin-liquid state in a fru s- trated magnet, Communications Physics 5, 99 (2022)

2022
[25]

Kancko, H

A. Kancko, H. Sakai, C. A. Corrêa, P . Proschek, J. Prokleška, T . Haidamak, M. Uhlarz, A. Berlie, Y . T oku- naga, and R. H. Colman, Random singlet physics in the S = 1 2 pyrochlore antiferromagnet NaCdCu 2F7, Phys. Rev . Res.8, 013344 (2026)

2026
[26]

A. T . Ogielski, Dynamics of three-dimensional ising spin glasses in thermal equilibrium, Phys. Rev . B32, 7384 (1985)

1985
[27]

I. A. Campbell, A. Amato, F . N. Gygax, D. Herlach, A. Schenck, R. Cywinski, and S. H. Kilcoyne, Dynamics in canonical spin glasses observed by muon spin depolarization, Phys. Rev . Lett.72, 1291 (1994)

1994
[28]

R. S. Hayano, Y . J. Uemura, J. Imazato, N. Nishida, T . Y a- mazaki, and R. Kubo, Zero-and low-ﬁeld spin relaxation studied by positive muons, Phys. Rev . B20, 850 (1979)

1979
[29]

F . L. Pratt, S. J. Blundell, T . Lancaster , C. Baines, and S. T ak- agi, Low-temperature spin diffusion in a highly ideal S = 1 2 heisenberg antiferromagnetic chain studied by muon spin re- laxation, Phys. Rev . Lett.96, 247203 (2006)

2006
[30]

Keren, J

A. Keren, J. S. Gardner , G. Ehlers, A. Fukaya, E. Se- gal, and Y . J. Uemura, Dynamic properties of a di- luted pyrochlore cooperative paramagnet (TbpY1−p)2Ti2O7, Phys. Rev . Lett.92, 107204 (2004)

2004
[31]

Kermarrec, A

E. Kermarrec, A. Zorko, F . Bert, R. H. Colman, B. Koteswararao, F . Bouquet, P . Bonville, A. Hillier , A. Amato, J. van T ol, A. Ozarowski, A. S. Wills, and P . Mendels, Spin dynamics and disorder effects in the S = 1 2 kagome heisenberg spin-liquid phase of kapellasite, Phys. Rev . B90, 205103 (2014)

2014
[32]

T . Dey , M. Majumder , J. C. Orain, A. Senyshyn, M. Prinz- Zwick, S. Bachus, Y . T okiwa, F . Bert, P . Khuntia, N. Büttgen, A. A. Tsirlin, and P . Gegenwart, Persistent low-temperatur e spin dynamics in the mixed-valence iridate Ba 3InIr2O9, Phys. Rev . B96, 174411 (2017)

2017
[33]

Bachhar , N

S. Bachhar , N. Pistawala, S. Kundu, M. Barik, M. Baenitz, J. Sichelschmidt, K. Y okoyama, P . Khuntia, S. Singh, and A. V . Mahajan, Gapless quantum spin liquid in the s = 14d 4 honeycomb material Cu 3LiRu2O6, Phys. Rev . B111, L100403 (2025)

2025
[34]

Khuntia, R

P . Khuntia, R. Kumar , A. V . Mahajan, M. Baenitz, and Y . Furukawa, Spin liquid state in the disor- dered triangular lattice Sc 2Ga2CuO7 revealed by nmr , Phys. Rev . B93, 140408 (2016) . 8

2016
[35]

Zheng, K

J. Zheng, K. Ran, T . Li, J. Wang, P . Wang, B. Liu, Z.-X. Liu, B. Normand, J. Wen, and W . Yu, Gapless spin excitations in the ﬁeld-induced quantum spin liquid phase of α−RuCl3, Phys. Rev . Lett.119, 227208 (2017)

2017
[36]

Y . Song, L. V enkataramanan, M. Hürlimann, M. Flaum, P . Frulla, and C. Straley , T 1 −T2 correlation spectra ob- tained using a fast two-dimensional laplace inversion, Journal of Magnetic Resonance 154, 261 (2002)

2002
[37]

P . M. Singer , A. Arsenault, T . Imai, and M. Fujita, 139La NMR investigation of the interplay between lattice, charge , and spin dynamics in the charge-ordered high- Tc cuprate La1.875Ba0.125CuO4, Phys. Rev . B101, 174508 (2020)

2020
[38]

S.-H. Baek, H. W . Y eo, S.-H. Do, K.-Y . Choi, L. Janssen, M. V ojta, and B. Büchner , Observation of a random singlet state in a diluted Kitaev honeycomb material, Phys. Rev . B102, 094407 (2020)

2020
[39]

Mahapatra, F

S. Mahapatra, F . D. Angelis, D. Rout, P . Tiwari, M. Etter , E. Welter , M. P . Saravanan, R. Rawat, S. Nishimoto, C. Meneghini, and S. Singh, Emergent random spin singlets in disordered spin-1 /2 perovskite BaCu 1/ 3Ta2/ 3O3 (2026), arXiv:2601.17455 [cond-mat.str-el]

work page arXiv 2026
[40]

F . Xu, R. Feyerherm, C. Glittum, T . J. Hicken, H. Luetkens, J. A. Krieger , C. Aguilar-Maldonado, S. Luther , L. K. Saunders, C. Ritter , P . Fouquet, M. Russina, K. Prokes, A. T . M. N. Islam, and B. Lake, Dynamical magnetism in the disordered cubic lattice materi al γ-Ba3CoNb (2026), arXiv:2604.18794 [cond-mat.str-el]

work page internal anchor Pith review Pith/arXiv arXiv 2026
[41]

S. Dash, V . Narang, and S. Kumar , V alence bond glass and glassy spin liquid in disordered frus trated magnets (2026), arXiv:2604.05501 [cond-mat.str-el]

work page internal anchor Pith review Pith/arXiv arXiv 2026
[42]

T arzia and G

M. T arzia and G. Biroli, The valence bond glass phase, Europhysics Letters 82, 67008 (2008)

2008
[43]

S. Lee, W . Lee, W . Guohua, J. Ma, H. Zhou, M. Lee, E. S. Choi, and K.-Y . Choi, Experimental evidence for a valence-bond glass in the 5 d 1 double perovskite Ba 2YWO6, Phys. Rev . B103, 224430 (2021)

2021
[44]

O. H. J. Mustonen, H. M. Mutch, H. C. Walker , P . J. Baker , F . C. Coomer , R. S. Perry , C. Pughe, G. B. G. Sten- ning, C. Liu, S. E. Dutton, and E. J. Cussen, V alence bond glass state in the 4 d 1 fcc antiferromagnet Ba 2LuMoO6, npj Quantum Materials 7, 74 (2022)

2022