Tracking the evolution from isolated dimers to many-body entanglement in ${\mathrm{NaLu}}_{x}{\mathrm{Yb}}_{1\text{\ensuremath{-}}x}{\mathrm{Se}}_{2}$

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Tracking the evolution from isolated dimers to many-body entanglement in ${NaLu}_{x} {Yb}_{1 − x} {Se}_{2}$

Luke Pritchard Cairns, Ryan Day, Shannon Haley, Nikola Maksimovic, Josue Rodriguez, Hossein Taghinejad, John Singleton, and James Analytis

Phys. Rev. B 106, 024404 – Published 7 July 2022

Abstract

We synthesize homogeneous compositions of $Na {Lu}_{x} {Yb}_{1 − x} {Se}_{2}$ , connecting nonmagnetic $Na Lu {Se}_{2}$ to the triangular lattice spin liquid candidate $Na Yb {Se}_{2}$ . Thermal and magnetic properties are studied as the system evolves from one with dilute magnetic defects to one of a dense magnetic lattice. The field- and temperature-dependent heat capacity show the carriers of entropy cross over from isolated magnetic ions to a correlated lattice born from spin dimers. For the dilute system we estimate the single-ion anisotropy $(g_{⊥} / g_{∥} = 3.13)$ and also the dimer exchange couplings $J_{∥} (= 5.4 K)$ and $J_{⊥} (= 9.6 K)$ , in order to draw comparison to the half-doped and full magnetic compounds.

Received 1 April 2022
Revised 5 June 2022
Accepted 6 June 2022

DOI:https://doi.org/10.1103/PhysRevB.106.024404

Physics Subject Headings (PhySH)

Crystal growth Magnetic anisotropy Magnetic susceptibility Magnetism Quantum spin liquid Specific heat Spin-orbit coupling

Raman spectroscopy

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Luke Pritchard Cairns ^1,2,*, Ryan Day^1,2, Shannon Haley ^1,2, Nikola Maksimovic^1,2, Josue Rodriguez^1,2, Hossein Taghinejad¹, John Singleton ³, and James Analytis ^1,2,4

¹Department of Physics, University of California, Berkeley, California 94720, USA
²Materials Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
³National High Magnetic Field Laboratory, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
⁴CIFAR Quantum Materials, CIFAR, Toronto, Canada

^*lpc@berkeley.edu

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Vol. 106, Iss. 2 — 1 July 2022

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Figure 1
(a) Raman spectra of the materials $Na {Lu}_{x} {Yb}_{1 − x} {Se}_{2}$ , where $x = 0$ , 0.5, and 1, obtained at 300 K in all cases. The solid lines show a sum of Gaussians fitted through the data, while the dot-dash lines show the position of the $E_{g}$ peak. The inset shows the crystal structure of $Na Yb {Se}_{2}$ ( $R \bar{3} m$ , space group 166). (b) Magnetic susceptibility per mole of Yb for $Na {Lu}_{x} {Yb}_{1 − x} {Se}_{2}$ , where $x = 0$ , 0.5, 0.9, and per mole of material for $Na Lu {Se}_{2}$ , plotted as a function of temperature for both in-plane and out-of-plane fields. All data were obtained in a field of 0.1 T. The inset shows the linear evolution of the Curie-Weiss temperature as a function of Yb content [estimated from fits in the region $T < 50$ K, shown in Fig. S4(a)].
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Figure 2
(a) Magnetization as a function of field for $Na {Lu}_{0.9} {Yb}_{0.1} {Se}_{2}$ , plotted for both field directions. Both data sets were taken at 1.9 K. The black line shows the linear Van Vleck contribution for in-plane fields, estimated by fitting to the $H > 12$ T data. The green line shows the in-plane magnetization with this contribution subtracted. (b) Zero-field heat capacity per mole of material for $Na {Lu}_{0.9} {Yb}_{0.1} {Se}_{2}$ and $Na Lu {Se}_{2}$ . The inset shows the magnetic heat capacity of the former, and also the released entropy. The solid line is a fit to a two-level system, with $Δ でるた E = 5.4$ K and 37% of the sites contributing. (c) Specific heat as a function of temperature and field for $Na {Lu}_{0.9} {Yb}_{0.1} {Se}_{2}$ . The applied field was out-of-plane. The solid/dotted lines show the approximate positions of the lowest-energy single ion and isolated dimer peak, respectively. The color bar is on a logarithmic scale for clarity.
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Figure 3
(a) Entropy released by $Na {Lu}_{0.9} {Yb}_{0.1} {Se}_{2}$ between 0.4–8 K, plotted as a function of field. The dotted line is at $R ln 2$ . (b) Field evolution of the energy levels for both an isolated single ion (red) and isolated dimer (black) calculated from the parameters estimated by the magnetization ( $g_{∥} = 1.04$ ), in-field specific heat ( $J_{∥} = 5.4$ K and $J_{⊥} = 9.6$ K), and susceptibility ( ${α あるふぁ}_{⊥} = 0.016 {μ みゅー}_{B} T^{- 1}$ ; see SM).
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Figure 4
(a) Magnetization of $Na {Lu}_{0.5} {Yb}_{0.5} {Se}_{2}$ and $Na Yb {Se}_{2}$ as a function of field, taken at 1.9 K in both cases. (b) Zero-field specific heat of both compounds, compared to the nonmagnetic analog $Na Lu {Se}_{2}$ . The inset shows the magnetic specific heat and also the released entropy. The solid blue line is a fit of the $Na {Lu}_{0.5} {Yb}_{0.5} {Se}_{2}$ data to a Gaussian broadened two-level system, and the dashed black line is at $R ln 2$ , the upper bound for a spin-1/2 system.
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Figure 5
Schematic to show the proposed evolution of correlations as a function of doping in $Na {Lu}_{x} {Yb}_{1 − x} {Se}_{2}$ , from isolated single ions and dimers ( $x = 0.9$ , left), through larger, finite magnetic clusters at the percolation threshold ( $x = 0.5$ , middle), to the full magnetic, many-body entangled state ( $x = 0$ , right).
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Physical Review B

covering condensed matter and materials physics

Tracking the evolution from isolated dimers to many-body entanglement in ${NaLu}_{x} {Yb}_{1 − x} {Se}_{2}$

Luke Pritchard Cairns, Ryan Day, Shannon Haley, Nikola Maksimovic, Josue Rodriguez, Hossein Taghinejad, John Singleton, and James Analytis

Phys. Rev. B 106, 024404 – Published 7 July 2022

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Physical Review B

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Tracking the evolution from isolated dimers to many-body entanglement in NaLuxYb1−xSe2

Luke Pritchard Cairns, Ryan Day, Shannon Haley, Nikola Maksimovic, Josue Rodriguez, Hossein Taghinejad, John Singleton, and James Analytis

Phys. Rev. B 106, 024404 – Published 7 July 2022

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Tracking the evolution from isolated dimers to many-body entanglement in ${NaLu}_{x} {Yb}_{1 − x} {Se}_{2}$