Controlled Frustration Release on the Kagome Lattice by Uniaxial-Strain Tuning

Jierong Wang, M. Spitaler, Y.-S. Su, K. M. Zoch, C. Krellner, P. Puphal, S. E. Brown, and A. Pustogow

Phys. Rev. Lett. 131, 256501 – Published 18 December 2023

Abstract

It is predicted that strongly interacting spins on a frustrated lattice may lead to a quantum disordered ground state or even form a quantum spin liquid with exotic low-energy excitations. However, a controlled tuning of the frustration strength, separating its effects from those of disorder and other factors, is pending. Here, we perform comprehensive ${}^{1}H$ NMR measurements on $Y_{3} {Cu}_{9} {(OH)}_{19} {Cl}_{8}$ single crystals revealing an unusual $\vec{Q} = (1 / 3 \times 1 / 3)$ antiferromagnetic state below $T_{N} = 2.2 K$ . By applying in situ uniaxial stress, we break the symmetry of this disorder-free, frustrated kagome system in a controlled manner yielding a linear increase of $T_{N}$ with strain, in line with theoretical predictions for a distorted kagome lattice. In-plane strain of $\approx 1 %$ triggers a sizable enhancement $Δ T_{N} / T_{N} \approx 10 %$ due to a release of frustration, demonstrating its pivotal role for magnetic order.

Received 14 July 2023
Revised 26 September 2023
Accepted 16 November 2023

DOI:https://doi.org/10.1103/PhysRevLett.131.256501

Physics Subject Headings (PhySH)

Antiferromagnetism Frustrated magnetism Magnetic order Magnetic phase transitions Magnetism Phase transitions Pressure effects Spin liquid Strain

Kagome lattice Layered crystals Mott insulators Single crystal materials Strongly correlated systems

Liquid helium cooling Nuclear magnetic resonance Nuclear magnetic resonance relaxation rate Strain engineering

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Jierong Wang¹, M. Spitaler ², Y.-S. Su¹, K. M. Zoch³, C. Krellner ³, P. Puphal ^3,4, S. E. Brown¹, and A. Pustogow ^1,2,*

¹Department of Physics and Astronomy, UCLA, Los Angeles, California 90095, USA
²Institute of Solid State Physics, TU Wien, 1040 Vienna, Austria
³Institute of Physics, Goethe-University Frankfurt, 60438 Frankfurt (Main), Germany
⁴Max-Planck-Institute for Solid State Research, 70569 Stuttgart, Germany

^*pustogow@ifp.tuwien.ac.at

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Vol. 131, Iss. 25 — 22 December 2023

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Images

Figure 1
Crystal structure of $Y_{3} {Cu}_{9} {(OH)}_{19} {Cl}_{8}$ (Y-kapellasite). (a) ${Cu}^{2 +}$ atoms (blue, cyan) arranged in layers. (b) Within the $a b$ plane, they form a slightly distorted $S = 1 / 2$ kagome lattice that preserves threefold rotational symmetry with AFM couplings $J_{⬡} / J \approx 1$ and $J / J^{'} \approx 18$ [30, 31, 33].
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Figure 2
(a) ${}^{1}H$ NMR spectra acquired for in-plane magnetic field ( $B ⊥ a$ , $B_{0} = 0.9789 T$ ). At elevated temperatures, the spectra consist of two peaks ( $H_{1}$ and $H_{2}$ ) separated by 30–40 kHz. The lines exhibit successive broadening upon cooling and exceed the experimental bandwidth below 4 K. (b) The spectra below 4 K, acquired by magnetic field sweeps at constant frequency $ν_{0} = 41.68 MHz$ , reveal a pronounced splitting into three peaks below $T_{N} = 2.2 K$ . The separation between the two outer peaks ( $B_{1}$ and $B_{2}$ ) increases to lower $T$ in a mean-field fashion (inset), while the central peak remains at $B_{0}$ . The gray line indicates the spectrum at 6 K, which follows the frequency scale at the top. (c) The false-color plot of the data from (b) illustrates the shifting of $B_{1}$ and $B_{2}$ as well as the strong broadening. The horizontal bar corresponds to a frequency $Δ ν = Δ B / {}^{1}γ = 1 MHz$ .
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Figure 3
(a) $Q = (1 / 3 \times 1 / 3)$ AFM order predicted for a distorted kagome lattice [33]. Colored circles indicate the location of ${}^{1}H$ nuclei in the crystal lattice of Y-kapellasite (cf. Fig. 1). The color corresponds to $δ B = | B_{0} + B_{loc} | - B_{0}$ ( $B_{0} = 0.9789 T$ ; see legend on the right). (b) The ${}^{1}H$ NMR spectrum (violet; measured at 1.70 K) consists of three main peaks $B_{0}$ , $B_{1}$ , and $B_{2}$ [cf. Fig. 2]. The experimental data agree well with the calculated NMR spectrum (black line) upon dipolar coupling of the ${}^{1}H$ nuclei to the local magnetic field of the ${Cu}^{2 +}$ spins in (a). The spin-lattice relaxation rate (orange diamonds) was measured at different fields: $T_{1}^{- 1}$ of the side peaks ( $B_{1}$ and $B_{2}$ ) is $\approx 50 %$ smaller than for the central peak at $B_{0} = 0.9789 T$ . (c) The full width at half maximum (FWHM), extracted for the ${}^{1}H$ NMR peaks $H_{1}$ and $H_{2}$ [ $T > T_{N}$ ; see Fig. 2] as well as for the three lines $B_{0}$ , $B_{1}$ , and $B_{2}$ emerging below $T_{N}$ [see Figs. 2 and 2], exceeds the homogeneous linewidth below 30 K and shows a steep increase at $T_{N}$ . Note the different units of the vertical scales.
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Figure 4
The ${}^{1}H$ NMR spin-lattice relaxation rate $T_{1}^{- 1}$ was probed for $B ∥ a b$ and $B ∥ c$ (inset). Upon cooling from room temperature, $T_{1}^{- 1}$ initially decreases toward a minimum around 32 K (orange double arrow). Below that, the increase of $T_{1}^{- 1}$ signals the onset of strong antiferromagnetic spin fluctuations [37], which result in a sharp maximum at $T_{N} = 2.2 K$ . Increasing the magnetic field yields a reduced peak value and broadening of the transition, consistent with specific heat results [30]. Above 4 K, $T_{1}^{- 1}$ does not exhibit pronounced field dependence or anisotropy. The pink dotted line indicates the ${}^{1}H$ relaxation rate of ${ZnCu}_{3} {(OH)}_{6} {Cl}_{2}$ [51].
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Figure 5
In situ strain tuning of frustrated magnetism in $Y_{3} {Cu}_{9} {(OH)}_{19} {Cl}_{8}$ . (a)–(c) For NMR experiments under uniaxial strain a single crystal was glued between the two arms of a piezoelectric strain cell (a), and, subsequently, an NMR coil was wound around it (b),(c). (d) $T_{1}^{- 1}$ was measured for $B ∥ a$ upon uniaxial compression of the kagome lattice parallel to the ${Cu}^{2 +}$ chains (sketched on the top right; cf. Fig. 1). Inset: in-plane strain $ϵ = - 1.6 %$ [44] results in a considerable enhancement of the transition temperature by $Δ T_{N} / T_{N} \approx 10 %$ .
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