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Coherent spin dynamics of solitons in the organic spin chain compounds (o-DMTTF)2X(X=Cl,Br)

J. Zeisner, O. Pilone, L. Soriano, G. Gerbaud, H. Vezin, O. Jeannin, M. Fourmigué, B. Büchner, V. Kataev, and S. Bertaina
Phys. Rev. B 100, 224414 – Published 16 December 2019
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  • INTRODUCTION
  • SAMPLES AND METHODS
  • RESULTS AND DISCUSSION
  • CONCLUSIONS
  • ACKNOWLEDGMENTS
  • APPENDICES
    • References

    Abstract

    We studied the magnetic properties, in particular dynamics, of the correlated spins associated with natural defects in the organic spin chain compounds (o-DMTTF)2X(X=Br,Cl) by means of electron spin resonance (ESR) spectroscopy. Both materials exhibit spin-Peierls transitions at temperatures around 50 K [P. Foury-Leylekian et al., Phys. Rev. B 84, 195134 (2011)], which allow a separation of the properties of defects inside the chains from the magnetic response of the spin chains. Indeed, continuous-wave ESR measurements performed over a wide temperature range evidence the evolution of the spin dynamics from being governed by the spins in the chains at elevated temperatures to a low-temperature regime which is dominated by defects within the spin-dimerized chains. Such defects polarize the antiferromagnetically coupled spins in their vicinity, thereby leading to a finite local alternating magnetization around the defect site which can be described in terms of a soliton, i.e., a spin-12 quasiparticle built of many correlated spins, pinned to the defect. In addition, contributions of triplon excitations of the spin-dimerized state to the ESR response below the transition temperature were observed, which provides a spectroscopic estimate for the spin gap of the studied systems. Moreover, details of spin dynamics deep in the spin-Peierls phase were investigated by pulse ESR experiments which revealed Rabi oscillations as signatures of coherent spin dynamics. The latter is a prerequisite for a selective manipulation of the defect-induced soliton spin states which is, for instance, relevant in the context of quantum computation. From a comparison of the characteristic damping times of the Rabi oscillations with measurements of the spin relaxation times by means of primary-echo decay and Carr-Purcell-Meiboom-Gill methods, it becomes evident that inhomogeneities in local magnetic fields strongly contribute to the soliton decoherence.

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    • Received 30 September 2019
    • Revised 25 November 2019

    DOI:https://doi.org/10.1103/PhysRevB.100.224414

    ©2019 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    MagnetismPeierls transition
    1. Physical Systems
    Organic compoundsSolitonsStrongly correlated systems
    1. Techniques
    Electron paramagnetic resonanceSpin chains
    Condensed Matter, Materials & Applied Physics

    Authors & Affiliations

    J. Zeisner1,2,*, O. Pilone3, L. Soriano3, G. Gerbaud4, H. Vezin5, O. Jeannin6, M. Fourmigué6, B. Büchner1,2, V. Kataev1,†, and S. Bertaina3,‡

    • 1Leibniz Institute for Solid State and Materials Research IFW Dresden, D-01069 Dresden, Germany
    • 2Institute for Solid State and Materials Physics, TU Dresden, D-01062 Dresden, Germany
    • 3Aix-Marseille Université, CNRS, IM2NP UMR 7334, F-13397 Marseille, France
    • 4Aix-Marseille Université, CNRS, BIP UMR 7281, F-13402 Marseille, France
    • 5Université de Lille, CNRS, LASIR UMR 8516, F-59655 Villeneuve d'Ascq, France
    • 6Université de Rennes, CNRS, ISCR UMR 6226, F-35042 Rennes, France

    • *j.zeisner@ifw-dresden.de
    • †v.kataev@ifw-dresden.de
    • ‡sylvain.bertaina@im2np.fr

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    Vol. 100, Iss. 22 — 1 December 2019

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    • Figure 1
      Figure 1

      Schematic representation of the spin-Peierls transition and defect-induced soliton formation. (a) At temperatures above the spin-Peierls temperature TSP, the uniform Heisenberg chain consists of equidistant spins coupled by an isotropic nearest-neighbor exchange J. (b) For T< TSP the bond lengths within the chain lattice are modulated, eventually leading to the formation of spin dimers (indicated by blue circles). The antiferromagnetic intradimer interaction J1=J(1+δ) is larger than the interdimer interaction J2=J(1−δ) giving rise to the spin-singlet ground state of the dimerized chain. (c) A nonmagnetic defect (gray sphere) introduced into a dimerized spin system breaks the chains into finite segments and can be modeled, for instance, by two successive weak bonds J2′ and J2 (with J2′<J2) within the chain. The coupling constant J2′ describes the effective exchange coupling between two spins across the defect site. (d) As a result of such a defect, a finite local alternating magnetization is induced around the defect site. This can be described in terms of a quasiparticle, the pinned soliton, which involves many entangled spins in the vicinity of the defect but carries an overall spin of 12. The profile of the local alternating magnetization shown here was calculated using a density matrix renormalization group method (see Ref. [10] for further details) considering a defect at the center of a dimerized chain with a length of 201 sites and assuming J2′=J2 as well as a dimerization parameter δ=0.03.

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    • Figure 2
      Figure 2

      Crystallographic structure of the (o−DMTTF)2X single crystals. Top: view on the ab plane of the unit cell with four o−DMTTF molecules which are rotated by 90∘ with respect to each other. Bottom: stacks of o−DMTTF molecules along the c axis. Each double molecule of such a stack hosts one charge, thus effectively forming a spin chain along the c axis. Crystallographic data are taken from Ref. [21].

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    • Figure 3
      Figure 3

      Temperature dependence of the ESR parameters obtained from cw ESR measurements on (o−DMTTF)2X samples with the static field applied along the c axis. (a) ESR linewidth ΔH of (o−DMTTF)2Cl. Respective data for (o−DMTTF)2Br are shown in the inset. (b) Temperature dependence of the intensity of the ESR line for both compounds obtained from double integration of the spectra. Representative spectra measured on a (o−DMTTF)2Cl sample at 7, 20, and 200 K are presented in the inset together with fits to the experimental data (solid red lines). At these different temperature regimes, the ESR lines are governed by the magnetic response of the solitons (7 K), by a combination of soliton and triplon contributions (20 K), and by the response of the spins within the chains (200 K), respectively.

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    • Figure 4
      Figure 4

      Angular dependence of ESR parameters obtained from cw ESR studies at ∼9.6 GHz. In these measurements the field was rotated from H∥c to H⊥c. (a) Angular-dependent linewidth of (o−DMTTF)2Cl at three different temperatures below TSP showing the effects of different contributions to ΔH(α) below the transition. Solid lines show fits according to Eq. (4) (see text). (b) Angular dependence of the g factor measured on a (o−DMTTF)2Cl crystal at temperatures between 5 and 200 K. Within this temperature range no changes in the g anisotropy are observed. The solid black line denotes a representative fit to the angular dependence of the g factor at 5 K according to Eq. (3). Corresponding measurements carried out on (o−DMTTF)2Br yielded very similar results as in (a) and (b) and are not shown here. (c) Temperature dependence of the ratio A/B as a measure of the relative strength of the triplon contribution to the linewidth obtained from fits of Eq. (4) to the ΔH(α) curves of (o−DMTTF)2Cl and (o−DMTTF)2Br at various temperatures. Solid lines are guides to the eye.

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    • Figure 5
      Figure 5

      Rabi oscillations in (o−DMTTF)2X measured at a mw frequency of ∼9.7 GHz. (a) Time evolution of 〈Sx(t)〉 in the mw field for (o−DMTTF)2Cl at 2.7 K with the external magnetic field applied along the c axis and a mw magnetic field hmw of about 0.5 mT. (b) Time evolution of 〈Sz(t)〉 in the mw field for (o−DMTTF)2Br at 7 K with H∥c and hmw∼0.25mT. Solid red lines are simulations of the damped oscillations according to Eq. (5). (c) Rabi frequencies (ΩR/2π) obtained for (o−DMTTF)2Cl at 2.7 K and various mw powers, i.e., different hmw. Corresponding data for (o−DMTTF)2Br at 7 K are shown in the inset. Note that the mw magnetic fields are given in arbitrary units since hmw was not calibrated independently. Solid lines are linear fits to the data. (d) Temperature dependence of T2* determined from the damping of the Rabi oscillations measured on (o−DMTTF)2Cl and (o−DMTTF)2Br crystals with hmw∼0.4mT (ΩR/2π∼10.5MHz) and hmw∼0.6mT (ΩR/2π∼14.9MHz), respectively. The external magnetic field was applied perpendicular to c. The inset shows the dependence of T2* as a function of Rabi frequency (and thus hmw) for both compounds measured with H⊥c.

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    • Figure 6
      Figure 6

      Comparison of primary-echo decay (black squares) and CPMG (open blue squares) measurements on (o−DMTTF)2Br at 9 K with H⊥c. In both cases, a π/2 pulse of 36 ns was used. For the CPMG sequence the number of π pulses n was set to 50. For comparison, intensities of the spin echoes are normalized to the respective intensities at tob∼807 ns, the time at which the first echo in the CPMG measurement was detected. Dashed-dotted lines denote monoexponential fits to the data while the solid line represents the fit of a stretched exponential function to the CPMG data (see text). The measured data are shown on a semilogarithmic scale in the inset to emphasize the increase of decoherence times by the CPMG protocol as well as the deviation of the CPMG data from a monoexponential behavior.

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    • Figure 7
      Figure 7

      Fourier transform of Rabi oscillations with different excitation frequencies at 2.7 K and with H⊥c for (a) (o−DMTTF)2Cl and (b) (o−DMTTF)2Br, respectively. The intensity of the fast Fourier transform (FFT) is given as color code where blue corresponds to low and light colors represent high intensities. The external magnetic field was set to match a resonance frequency of about 9.765 GHz which is indicated by gray dashed lines. These measurements were performed with microwave powers which correspond to microwave magnetic fields of about 0.7 and 0.6 mT for (o−DMTTF)2Cl and (o−DMTTF)2Br, respectively.

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    • Figure 8
      Figure 8

      Analysis of the temperature-dependent normalized susceptibility as obtained from cw ESR measurements at 9.6 GHz on a (o−DMTTF)2Cl crystal with external field applied parallel to c. (a) Fit of a Curie law (blue solid line) to the low-temperature part of the ESR intensity to correct the data with respect to the soliton contribution. (b) Corrected data after subtraction of the fit shown in (a) from the data. Dashed-dotted line denotes a fit for T>50 K using the model of a Heisenberg AFM chain (δ=0) from Ref. [9] in order to determine the exchange coupling constant J. The fit in the low-temperature region for δ>0 and fixed J is shown by the blue solid line. For comparison, a fit within the same temperature range using the Bulaevskii model [42] is indicated by the orange dashed line.

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