Emergence of Spinons in Layered Trimer Iridate ${\mathrm{Ba}}_{4}{\mathrm{Ir}}_{3}{\mathrm{O}}_{10}$

Emergence of Spinons in Layered Trimer Iridate ${Ba}_{4} {Ir}_{3} O_{10}$

Y. Shen, J. Sears, G. Fabbris, A. Weichselbaum, W. Yin, H. Zhao, D. G. Mazzone, H. Miao, M. H. Upton, D. Casa, R. Acevedo-Esteves, C. Nelson, A. M. Barbour, C. Mazzoli, G. Cao, and M. P. M. Dean

Phys. Rev. Lett. 129, 207201 – Published 10 November 2022

Abstract

Spinons are well known as the elementary excitations of one-dimensional antiferromagnetic chains, but means to realize spinons in higher dimensions is the subject of intense research. Here, we use resonant x-ray scattering to study the layered trimer iridate ${Ba}_{4} {Ir}_{3} O_{10}$ , which shows no magnetic order down to 0.2 K. An emergent one-dimensional spinon continuum is observed that can be well described by $X X Z$ spin- $1 / 2$ chains with a magnetic exchange of $\sim 55 meV$ and a small Ising-like anisotropy. With 2% isovalent Sr doping, magnetic order appears below $T_{N} = 130 K$ along with sharper excitations in $({Ba}_{1 - x} {Sr}_{x})_{4} {Ir}_{3} O_{10}$ . Combining our data with exact diagonalization calculations, we find that the frustrated intratrimer interactions effectively reduce the system into decoupled spin chains, the subtle balance of which can be easily tipped by perturbations such as chemical doping. Our results put ${Ba}_{4} {Ir}_{3} O_{10}$ between the one-dimensional chain and two-dimensional quantum spin liquid scenarios, illustrating a new way to suppress magnetic order and realize fractional spinons.

Received 4 January 2022
Accepted 17 October 2022

DOI:https://doi.org/10.1103/PhysRevLett.129.207201

Physics Subject Headings (PhySH)

Magnetism Quantum spin liquid

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Y. Shen ^1,*, J. Sears¹, G. Fabbris ², A. Weichselbaum¹, W. Yin ¹, H. Zhao ³, D. G. Mazzone⁴, H. Miao ^1,5, M. H. Upton², D. Casa², R. Acevedo-Esteves⁶, C. Nelson⁶, A. M. Barbour⁶, C. Mazzoli⁶, G. Cao ³, and M. P. M. Dean ^1,†

¹Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, New York 11973, USA
²Advanced Photon Source, Argonne National Laboratory, Argonne, Illinois 60439, USA
³Department of Physics, University of Colorado Boulder, Boulder, Colorado 80309, USA
⁴Laboratory for Neutron Scattering and Imaging, Paul Scherrer Institut, CH-5232 Villigen, Switzerland
⁵Material Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37830, USA
⁶National Synchrotron Light Source II, Brookhaven National Laboratory, Upton, New York 11973, USA

^*yshen@bnl.gov
^†mdean@bnl.gov

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Vol. 129, Iss. 20 — 11 November 2022

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Figure 1
(a) Crystal structure of ${Ba}_{4} {Ir}_{3} O_{10}$ . The material contains two symmetry-inequivalent Ir ions: Ir1 and Ir2, occupying the outer and middle sites of the trimers (black dashed ellipse), respectively. $J_{n}$ where $n = 1$ , 2, 3 denotes magnetic interactions for the first, second, and third nearest Ir neighbors. The barium ions are not shown. (b) Representative RIXS spectrum of ${Ba}_{4} {Ir}_{3} O_{10}$ at the Ir $L_{3}$ edge with a constant background subtracted. The circles represent the data and the different lines with shaded areas indicate the fitting results of different components, the summation of which gives the dark orange curve. Error bars represent 1 standard deviation based on Poisson statistics.
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Figure 2
One-dimensional spinons in undoped ${Ba}_{4} {Ir}_{3} O_{10}$ at 8 K. (a),(b) Magnetic excitations at different $Q$ along $H$ and $K$ directions, respectively, showing essentially dispersionless behavior. All the RIXS spectra in the text are presented with the constant background, quasielastic line and high-energy $d d$ excitations subtracted to highlight the magnetic contributions [43]. The vertical gray bars indicate the quasielastic regime, the widths of which represent the energy resolution. The values of $H / K$ are indicated for each curve and the spectra are shifted along the $y$ axis for clarity. (c) Color plot of the magnetic excitations along the $L$ direction. The dotted lines are the calculated excitation boundaries of an AFM spin- $1 / 2$ chain with $J_{chain} = 55 meV$ and $Δ = 1.3$ . The dashed lines are guides to the eye.
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Figure 3
Magnetic order and spin dynamics in doped $({Ba}_{1 - x} {Sr}_{x})_{4} {Ir}_{3} O_{10}$ ( $x = 0.02$ ) and comparison with undoped ${Ba}_{4} {Ir}_{3} O_{10}$ . (a) Background subtracted magnetic Bragg peaks at $Q = (0.5, 0, 0)$ , detected at the O $K$ edge with different temperatures in $({Ba}_{1 - x} {Sr}_{x})_{4} {Ir}_{3} O_{10}$ . The solid lines are the fitting results using pseudo-Voigt profiles [43]. (b) Temperature dependence of the fitted peak height. The magnetic transition takes place at $T_{N} = 130 K$ . The solid and dashed lines are guides to the eye. (c)–(e) Magnetic excitation spectra of $({Ba}_{1 - x} {Sr}_{x})_{4} {Ir}_{3} O_{10}$ at 8 K with different $Q$ along $L$ , $H$ , and $K$ directions, respectively. (f),(g) Magnetic excitation spectra at different temperatures for ${Ba}_{4} {Ir}_{3} O_{10}$ and $({Ba}_{1 - x} {Sr}_{x})_{4} {Ir}_{3} O_{10}$ samples. The intensities are normalized according to their maximum values. Note that $(3.5, 15.5, - 1)$ and $(7.5, - 7.5, 0)$ are symmetric regarding the chain direction. The observed phase shift in the spinon spectrum with respect to $L$ arises from zone folding caused by the interchain interactions and the sampling of different chains with changes in $Q$ [9]. The same applies to $(3.5, 15.5, - 0.6)$ and $(7.5, - 7.5, 0.4)$ . The dashed lines are guides to the eye and the quasielastic regime is indicated by the vertical gray bars.
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Figure 4
Effective chain decoupling. (a) Low-energy spectrum of the three-Ir-site cluster model as a function of intersite $d − d$ hopping [43]. The black arrow highlights the critical point where the $| S = 1 / 2 ⟩^{+}$ and $| S = 1 / 2 ⟩^{-}$ doublets are degenerate. (b) During the RIXS process, one Ir spin is flipped (cyan arrow), changing the trimer state at low energies and creating two spinons (domain walls). (c) The spinons can propagate in the zigzag chain along the $c$ direction by flipping the neighboring spins.
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Physical Review Letters

Emergence of Spinons in Layered Trimer Iridate Ba4Ir3O10

Y. Shen, J. Sears, G. Fabbris, A. Weichselbaum, W. Yin, H. Zhao, D. G. Mazzone, H. Miao, M. H. Upton, D. Casa, R. Acevedo-Esteves, C. Nelson, A. M. Barbour, C. Mazzoli, G. Cao, and M. P. M. Dean

Phys. Rev. Lett. 129, 207201 – Published 10 November 2022

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Emergence of Spinons in Layered Trimer Iridate ${Ba}_{4} {Ir}_{3} O_{10}$