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Phonon anomalies and critical scaling in the spin-12 trimer chain Na2Cu3Ge4O12

P. Srikanth Patnaik1, A. K. Bera2,3, Srishti Bhardwaj4, Tulika Maitra4, Buddhananda Banerjee5, Anushree Roy1,*, and S. M. Yusuf2,3,6,†

  • *Contact author: anushree@phy.iitkgp.ac.in
  • †Contact author: smyusuf@barc.gov.in
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Phys. Rev. B 114, 074403 – Published 3 August, 2026

DOI: https://doi.org/10.1103/bt1k-q2cb

Abstract

Low-dimensional quantum magnets provide an ideal platform to explore spin-lattice coupling-mediated quantum correlations, which give rise to emergent quasiparticle excitations. The antiferromagnetically coupled spin-1/2 trimer chain of copper ions in Na2Cu3Ge4O12 (NCGO) hosts high-energy spin excitations of different species, whose energy scales overlap with those of lattice vibrations. Here, we report a comprehensive temperature-dependent Raman spectroscopic study performed between 80 and 400 K. The dynamic spin susceptibility, as obtained from the analysis of the broad spectral background, reveals the emergence of quasiparticle excitations below 170 K. We further identify an unusual crossover of phonon dynamics when the material transits from a normal paramagnetic state to a correlated quantum magnetic state. A power law dependence of the integrated Raman susceptibility of the phonon modes, Iχ″i∼|T−Tc|β, is observed with the critical temperature Tc=167±1K, and critical exponent β=0.24±0.02. The combined results obtained from the broad spectral background and sharp phonon peaks further indicate that the phonon renormalization observed across the crossover is driven by dynamic spin states. Additionally, statistical correlations among phonon energy eigenvalues, quantified through matrix-norm and power-test analyses of 200 spectra recorded at 80 K, reveal an unexpected linear correlation among phonon modes, also indicating that the collective lattice response is governed by spin correlations. These findings establish NCGO as a model system for investigating cooperative spin-lattice coupling and critical scaling behavior of phonon dynamics in low-dimensional magnetic materials.

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Phys. Rev. B 114, 074403– Published 3 August, 2026
  • Received 25 November 2025
  • Revised 11 June 2026
  • Accepted 13 July 2026
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