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arXiv:2504.21616

Fermionic Band Dispersions and an Evidence of Cooperon Excitations in a Spin-$1/2$ Trimer Chain

P. Srikanth Patnaik, Sen, Snehasish, Anup Kumar Bera, Sudhansu S. Mandal, Anushree Roy, Seikh Mohammad Yusuf

Published Apr 30, 2025• 0 citations
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Abstract

We obtain the solution of the Hamiltonian of an antiferromagnetically coupled spin-$1/2$ trimer chain in terms of three bands that host three different species of fermions. While the lowest two bands correspond to spin-$1/2$ fermions, the fermions in the highest band are of spin-$3/2$. Because the bands are for different species of fermions, the particle-hole excitation channel across the bands is closed. However, fractionalized excitations as spin-$1/2$ and spin-$3/2$ fermions in pairs open a cooperon channel of excitations in Raman scattering. The background spectral intensity profile obtained by Raman scattering measurements in Na$_2$Cu$_3$Ge$_4$O$_{12}$ having a trimer chain consisting of spin-$1/2$ Cu ions, has comprehensively been shown to be consistent with these excitations.

DOI
10.48550/arxiv.2504.21616

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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 Na2_22​Cu3_33​Ge4_44​O12_{12}12​ (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∣βI_{χ^{\prime\prime}}^{i}\sim|T-T_{c}|^βIχ′′i​∼∣T−Tc​∣β, is observed with the critical temperature TcT_cTc​=167$\pm$1 K, and critical exponent β=0.24±0.02β= 0.24\pm 0.02β=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.
Cu 2 Fe 2 Ge 4 O 13 is a quantum magnet consisting of Cu spin dimers and Fe spin chains. It shows an antiferromagnetic phase transition at low temperatures due to the magnetic moment of Fe. Since the two parts are weakly coupled, magnetic excitations are well separated into high-energy Cu dimer part and low-energy Fe chain part. We study the magnetic excitations in the ordered phase of Cu 2 Fe 2 Ge 4 O 13 based on a theory used for coupled spin dimer systems such as TlCuCl 3 . Analyzing the dynamical spin correlation functions, we find several high-energy modes with longitudinal spin fluctuations peculiar to the coupled spin dimer and spin chain system. This is consistent with the recent experimental result of inelastic neutron scattering. A possibility to detect such longitudinal modes is discussed by means of magnetic Raman scattering.