Coexistence and Interaction of Spinons and Magnons in an Antiferromagnet with Alternating Antiferromagnetic and Ferromagnetic Quantum Spin Chains

H. Zhang, Z. Zhao, D. Gautreau, M. Raczkowski, A. Saha, V. O. Garlea, H. Cao, T. Hong, H. O. Jeschke, Subhendra D. Mahanti, T. Birol, F. F. Assaad, and X. Ke

Phys. Rev. Lett. 125, 037204 – Published 17 July 2020

Abstract

In conventional quasi-one-dimensional antiferromagnets with quantum spins, magnetic excitations are carried by either magnons or spinons in different energy regimes: they do not coexist independently, nor could they interact with each other. In this Letter, by combining inelastic neutron scattering, quantum Monte Carlo simulations, and random phase approximation calculations, we report the discovery and discuss the physics of the coexistence of magnons and spinons and their interactions in Botallackite- ${Cu}_{2} {(OH)}_{3} Br$ . This is a unique quantum antiferromagnet consisting of alternating ferromagnetic and antiferromagnetic spin- $1 / 2$ chains with weak interchain couplings. Our study presents a new paradigm where one can study the interaction between two different types of magnetic quasiparticles: magnons and spinons.

Received 16 April 2020
Accepted 18 June 2020

DOI:https://doi.org/10.1103/PhysRevLett.125.037204

Physics Subject Headings (PhySH)

Magnons Spin dynamics Spinon

Antiferromagnets Magnetic systems

Monte Carlo methods Neutron scattering

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

H. Zhang¹, Z. Zhao², D. Gautreau³, M. Raczkowski ⁴, A. Saha³, V. O. Garlea ⁵, H. Cao⁵, T. Hong⁵, H. O. Jeschke⁶, Subhendra D. Mahanti ¹, T. Birol ³, F. F. Assaad^4,7, and X. Ke ^1,*

¹Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, USA
²State Key Laboratory of Structural Chemistry, Fujian Institute of Research on the Structure of Matter, Chinese Academy of Sciences, Fuzhou, Fujian 350002, People’s Republic of China
³Department of Chemical Engineering and Materials Science, University of Minnesota, Minnesota 55455, USA
⁴Institut für Theoretische Physik und Astrophysik, Universität Würzburg, 97074 Würzburg, Germany
⁵Neutron Scattering Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
⁶Research Institute for Interdisciplinary Science, Okayama University, Okayama 700-8530, Japan
⁷Würzburg-Dresden Cluster of Excellence ct.qmat, Am Hubland, D-97074 Würzburg, Germany

^*Corresponding author. kexiangl@msu.edu

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Vol. 125, Iss. 3 — 17 July 2020

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Images

Figure 1
Crystal structure and magnetic structure of ${Cu}_{2} {(OH)}_{3} Br$ . Crystal structure of ${Cu}_{2} {(OH)}_{3} Br$ in the $a c$ (a) and $a b$ (b) plane showing a quasi-two-dimensional, distorted triangular lattice of Cu atoms. (c) Temperature dependence of neutron diffraction intensity of an ordering wave vector (0.5 0 0). The inset shows the temperature dependence of heat capacity and magnetic susceptibility measurements. (d) Schematics of spin structure of ${Cu}^{2 +}$ ions with Cu2 spins pointing along the $a$ axis while Cu1 spins point nearly along the diagonal direction in the $a c$ plane. Exchange interactions of Cu1-Cu1, Cu2-Cu2, and Cu1-Cu2 as well as DM interaction are denoted.
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Figure 2
Magnetic excitation spectra and the comparison to LSW calculations. (a) The momentum- and energy-resolved neutron scattering intensity map $I (E, H)$ ( $K = - 0.5$ and with all measured $L$ values integrated). (b) Intensity map $I (E, L)$ ( $K = - 0.5$ and with all measured $H$ values integrated). These two intensity maps show nearly dispersionless magnetic excitations along both $H$ and $L$ directions. (c) Intensity map $I (E, K)$ with both $H$ and $L$ integrated over all measured values to enhance the statistics of the signal. These intensity maps were obtained after using the data measured at $T = 100 K$ as background and subtracting it from the data measured at $T = 5 K$ . (d) The calculated $I (E, K)$ spectra using LSW theory. The white curves in all panels are the calculated dispersions using LSW theory.
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Figure 3
Electronic structure calculated via first-principles DFT. (a) The ground state spin density of the half-filled $e_{g}$ orbital of ${Cu}^{2 +}$ ions and p orbitals of O and Br atoms. Yellow denotes spin-up and cyan denotes spin-down. Cu1 ions with ferromagnetic spin alignment show antiferro-orbital orientational order while Cu2 ions with antiferromagnetic spin alignment show ferro-orientational order. (b) The projected density of states (PDOS) of Cu1, Cu2, Br, and O ions.
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Figure 4
Magnetic excitation spectra via quantum Monte Carlo simulations. Simulated magnetic excitation spectra (with $H = 1$ ) of a system consisting of alternating ferromagnetic and antiferromagnetic quantum spin chains with the inter-chain coupling $J_{3} = 0$ (a), $J_{3} = 0.1 J_{2}$ (b), and $J_{3} = 0.2 J_{2}$ (c). (d) Constant energy cuts at $E = [8.7 9.7] meV$ showing the asymmetric spectral intensity about $K = 1$ induced by nonzero $J_{3}$ . Note that the Bose factor but not magnetic form factor of ${Cu}^{2 +}$ ions has been taken into account in the simulation.
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Figure 5
Magnetic excitation spectra and the comparison with RPA calculations. (a) $I (E, K)$ intensity map obtained after background subtraction with $H$ integrated over [0.85 1.1] and $L$ integrated over all measured values. (b) The RPA calculation of $I (E, K)$ spectra for comparison. Constant energy cuts at $E = 10.75$ meV (c) and at $E = 7.75 meV$ (d) and their comparison with RPA calculations.
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