Fate of soliton matter upon symmetry-breaking ferroelectric order

K. Sunami, R. Takehara, A. Katougi, K. Miyagawa, S. Horiuchi, R. Kato, T. Miyamoto, H. Okamoto, and K. Kanoda

Phys. Rev. B 103, 134112 – Published 16 April 2021

Abstract

In a one-dimensional (1D) system with degenerate ground states, their domain boundaries, dubbed solitons, emerge as topological excitations often carrying unconventional charges and spins; however, the soliton excitations are vital in only the nonordered regime. Then a question arises: How do the solitons conform to a three-dimensional (3D) ordered state? Here, using a quasi-1D organic ferroelectric, tetrathiafulvalene- $p$ -chloranil (TTF-CA), with degenerate polar dimers, we pursue the fate of spin-soliton charge-soliton composite matter in a 1D polar-dimer liquid upon its transition to a 3D ferroelectric order by resistivity, nuclear magnetic resonance (NMR), and nuclear quadrupole resonance (NQR) measurements. We demonstrate that the soliton matter undergoes neutral spin-spin soliton pairing and spin-charge soliton pairing to form polarons, coping with the 3D order. Below the ferroelectric transition, the former contributes to the magnetism through triplet excitations, which rapidly fade out on cooling, whereas the latter carries electrical current with paramagnetic spins that more moderately decrease with temperature. The nearly perfect scaling between NMR and NQR relaxation rates in the ferroelectric phase evidences that spin carriers diffuse with lattice distortion, namely, in the form of polarons. From the combined analyses of conductivity and NMR relaxation rate, we derive the excitation energies of polaron excitations and diffusion. Our results reveal the whole picture of soliton matter that condenses into the 3D ordered state.

Received 20 July 2020
Revised 15 February 2021
Accepted 2 April 2021

DOI:https://doi.org/10.1103/PhysRevB.103.134112

Physics Subject Headings (PhySH)

Polarons Spin dynamics Topological phases of matter

Ferroelectrics Topological materials

Nuclear magnetic resonance Nuclear quadrupole resonance Resistivity measurements

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

K. Sunami ^1,*, R. Takehara ¹, A. Katougi¹, K. Miyagawa ¹, S. Horiuchi ², R. Kato ³, T. Miyamoto⁴, H. Okamoto ^4,5, and K. Kanoda ^1,†

¹Department of Applied Physics, University of Tokyo, Bunkyo-ku, Tokyo 113-8656, Japan
²Research Institute for Advanced Electronics and Photonics, National Institute of Advanced Industrial Science and Technology, Tsukuba, Ibaraki 305-8565, Japan
³Condensed Molecular Materials Laboratory, RIKEN, Wako, Saitama 351-0198, Japan
⁴Department of Advanced Materials Science, University of Tokyo, Kashiwa, Chiba 277-8561, Japan
⁵AIST-UTokyo Advanced Operando-Measurement Technology Open Innovation Laboratory, National Institute of Advanced Industrial Science and Technology, Chiba 277-8568, Japan

^*sunami@mdf2.t.u-tokyo.ac.jp
^†kanoda@ap.t.u-tokyo.ac.jp

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Vol. 103, Iss. 13 — 1 April 2021

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Figure 1
Phase diagram and spin and charge excitations in TTF-CA. (a) Molecular structures of TTF and CA. The central double-bonded carbon atoms in the TTF molecule are enriched by ${}^{13}C$ isotopes for ${}^{13}C$ NMR measurements. The neutral state ( $ρ = 0$ for simplicity) is illustrated at the bottom, where D and A represent the donor and acceptor molecules, TTF and CA, respectively. (b) Pressure-temperature phase diagram of TTF-CA. The dashed arrow indicates the trace of measurements in the present study. Illustrations of spin and charge excitations in the ionic (c) paraelectric and (d) ferroelectric phases of TTF-CA ( $ρ = 1$ for simplicity), respectively.
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Figure 2
${}^{13}C$ NMR spectra, shift, and relaxation rate of TTF-CA. (a) Temperature dependence of ${}^{13}C$ NMR spectra at 14 kbar. The doublet structure arises from the ${}^{13}C - {}^{13}C$ nuclear dipolar coupling, and the NMR shift is given by the midpoint of the doublet. The shift origin corresponds to the resonance frequency of TMS (tetramethylsilane). (b) Plot of the midpoint of the doublet as a function of temperature. Left and right axes represent the total shift and the spin shift [total shift $-$ chemical shift (82 ppm)], respectively. Inset: Close-up of the behavior near $T_{c}$ . Estimates of the polaron contribution to spin shift are indicated by three green lines (upper and lower limits and their median; see text for the details of the estimation). (c) Temperature dependence of the ${}^{13}C$ NMR spin-lattice relaxation rate ${}^{13}T_{1}^{- 1}$ at 14 kbar. (d) Comparison between ${}^{13}T_{1}^{- 1}$ (blue solid circles; left axis) and $T$ times spin shift (orange open circles; right axis) plotted against inverse temperature. The blue dashed line is a fit of the single-exponential function to ${}^{13}T_{1}^{- 1}$ in the range 120 $< T <$ 200 K. The orange dashed line is a fit of the single-exponential function to $T$ times spin shift in the range 200 K $< T < T_{c}$ .
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Figure 3
${}^{35}{Cl}$ NQR spectra, frequency, and relaxation rate of TTF-CA. Temperature dependence of (a) ${}^{35}{Cl}$ NQR spectra and (b) frequency at 14 kbar. (c) Plot of line splitting width at 14 kbar. (d) Comparison between ${}^{35}{Cl}$ NQR spin-lattice relaxation rate ${}^{35}T_{1}^{- 1}$ (red solid diamonds; left axis) and ${}^{13}T_{1}^{- 1}$ (blue open circles; right axis) under 14 kbar. The dotted line indicates the $T^{2}$ law expected from the conventional phonons.
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Figure 4
Electrical resistivity of TTF-CA. (a) Temperature dependence of electrical resistivity at 14 kbar. Inset: Activation plot of electrical conductivity $σ$ . The dotted line represents the Arrhenius form with an activation energy of 2100 K. (b) Plot of ${(^{13} T_{1}^{- 1} σ T \sqrt{a})}^{0.5}$ , which is proportional to the density of polarons $n_{p}$ well below $T_{c}$ (see text). The dotted line represents the Arrhenius form with an activation energy of 2010 K estimated using the data below 250 K. (c) Temperature dependence of the diffusion constant evaluated through Eq. (3) using $σ$ and $n_{p}$ (see text); the value at $T_{c}$ is normalized to unity. The dotted line represents the Arrhenius form with an activation energy of 240 K estimated using the data below 220 K. (d) Comparison between the observed ${}^{13}C$ NMR spin-lattice relaxation rate ${}^{13}T_{1}^{- 1}$ and the contribution of polarons to ${}^{13}T_{1}^{- 1}, {(^{13} T_{1}^{- 1})}_{p}$ , calculated using $σ$ (see text). ${(^{13} T_{1}^{- 1})}_{p}$ is normalized to ${}^{13}T_{1}^{- 1}$ at 190 K. Inset: Behavior near $T_{c}$ in linear scale. The excess in ${}^{13}T_{1}^{- 1}$ from the ${(^{13} T_{1}^{- 1})}_{p}$ curve near $T_{c}$ is likely the contribution of the triplet excitations of the bound soliton pairs.
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Figure 5
Molecular principal axes of TTF ( $X$ = H) and TMTTF ( $X$ = ${CH}_{3}$ ) molecules.
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Figure 6
Temperature dependence of the ratio of conductivities along the $a$ and $b$ axes $σ_{a} / σ_{b}$ at 15 kbar.
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