Quantum Critical Dynamics of a Heisenberg-Ising Chain in a Longitudinal Field: Many-Body Strings versus Fractional Excitations

Zhe Wang, M. Schmidt, A. Loidl, Jianda Wu, Haiyuan Zou, Wang Yang, Chao Dong, Y. Kohama, K. Kindo, D. I. Gorbunov, S. Niesen, O. Breunig, J. Engelmayer, and T. Lorenz

Phys. Rev. Lett. 123, 067202 – Published 6 August 2019

Abstract

We report a high-resolution terahertz spectroscopic study of quantum spin dynamics in the antiferromagnetic Heisenberg-Ising spin-chain compound ${BaCo}_{2} V_{2} O_{8}$ as a function of temperature and longitudinal magnetic field. Confined spinon excitations are observed in an antiferromagnetic phase below $T_{N} ≃ 5.5 K$ . In a field-induced gapless phase above $B_{c} = 3.8 T$ , we identify many-body string excitations as well as low-energy fractional psinon or antipsinon excitations by comparing to Bethe ansatz calculations. In the vicinity of $B_{c}$ , the high-energy string excitations are found to have a dominant contribution to the spin dynamics as compared with the fractional excitations.

Received 13 March 2019

DOI:https://doi.org/10.1103/PhysRevLett.123.067202

Physics Subject Headings (PhySH)

Magnetism Magnetocaloric effect Quantum phase transitions Spin dynamics

1-dimensional spin chains

Bethe ansatz Crystal growth Magnetization measurements Terahertz time-domain spectroscopy

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Zhe Wang^1,*, M. Schmidt², A. Loidl², Jianda Wu^3,†, Haiyuan Zou³, Wang Yang⁴, Chao Dong^5,6, Y. Kohama⁵, K. Kindo⁵, D. I. Gorbunov⁷, S. Niesen⁸, O. Breunig⁸, J. Engelmayer⁸, and T. Lorenz⁸

¹Institute of Radiation Physics, Helmholtz-Zentrum Dresden-Rossendorf, 01328 Dresden, Germany
²Experimental Physics V, Center for Electronic Correlations and Magnetism, Institute of Physics, University of Augsburg, 86135 Augsburg, Germany
³Tsung-Dao Lee Institute and School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
⁴Stewart Blusson Quantum Matter Institute, University of British Columbia, Vancouver, Canada
⁵Institute for Solid State Physics, University of Tokyo, Kashiwa, Chiba 277-8581, Japan
⁶Wuhan National High Magnetic Field Center and School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China
⁷Dresden High Magnetic Field Laboratory (HLD-EMFL), Helmholtz-Zentrum Dresden-Rossendorf, 01328 Dresden, Germany
⁸Institute of Physics II, University of Cologne, 50937 Cologne, Germany

^*zhewang@ph2.uni-koeln.de Present address: Institute of Physics II, University of Cologne, 50937, Cologne, Germany.
^†wujd@sjtu.edu.cn

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Vol. 123, Iss. 6 — 9 August 2019

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Images

Figure 1
Phase diagram of the antiferromagnetic $X X Z$ spin- $1 / 2$ chain with the anisotropy parameter $Δ$ in a longitudinal magnetic field. The different regimes (gapped or gapless) are separated by the critical field $B_{c}$ and saturation field $B_{s}$ and are characterized by distinct ground states (GS) and characteristic excitations due to a spin flip, as schematically illustrated by the insets.
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Figure 2
(a) Magnetocaloric-effect $T (B)$ , (b) magnetization $M (B)$ , and (c) differential susceptibility $d M / d H$ measured as a function of longitudinal field $B ∥ c$ . The critical field $B_{c} = 3.8 T$ and the characteristic fields $B_{h} = 19.5$ and $B_{s} = 22.9 T$ corresponding to half-saturated and saturated magnetizations, respectively, yield minima of $T (B)$ and peaks of $d M / d H$ at the lowest temperature, as marked by the dashed lines. In (a), the shaded area indicates the 3D Néel ordered phase [43]. In (b), the solid line is obtained from a Bethe ansatz (BA) solution of the Heisenberg-Ising model, in addition to a paramagnetic (PM) background.
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Figure 3
(a) Transmission spectra measured at 6.5 and 2 K, above and below $T_{N} ≃ 5.5 K$ , respectively, for the polarization $h^{ω} ⊥ c$ , $e^{ω} ∥ c$ . (b) The ratio of the transmission spectra at 6.5 and 2 K reveals absorption peaks, as indicated by the arrows, which signal the excitations of confined spinons below $T_{N}$ . (c) The energy hierarchy of these excitations linearly depends on $ζ_{i}$ , as expected for confined spinons in a linear confining potential [34].
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Figure 4
(a) Transmission spectra obtained at 2 K in the longitudinal fields above $B_{c}$ . Excitations of 2-string $χ_{π}^{(2)}$ , 3-string $χ_{π / 2}^{(3)}$ , psinon-antipsinon $R_{0}^{p a p}$ pairs, and psinon-psinon $R_{π / 2}^{p p}$ pairs are indicated, as identified by comparing to Bethe ansatz results. The weak wigglelike feature is due to multiple interference within the sample. (b) Contour plot of transmission at 2 K. For $B < B_{c}$ , confined-spinon levels $E_{i}$ are observed. For $B > B_{c}$ , different excitations with distinct slopes are observed, as for the string and fractional excitations. The symbols above $B_{c}$ show fitting of the theory results in (c) (see the text for details). A different color scale is adopted in the upper panel to highlight the weak 3-string mode. (c) Dynamic structure factors (DSF) $S^{+ -}$ and $S^{- +}$ as a function of the energy, obtained via Bethe ansatz for the magnetizations 4%, 6%, and 8% of the saturated value. The units are given by the Planck constant $ℏ$ and the exchange interaction $J$ . For clarity, the DSF for $p a p$ is multiplied by a factor of 10.
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