Emergent spin-liquid-like state in the bond- disordered breathing pyrochlore Suheon Lee Chung-Ang University Seunghwan Do Chung-Ang University W.-J. Lee Chung-Ang University Y.-S. Choi Chung-Ang University Johan Van Tol NHMFL Arneil Reyes NHMFL https://orcid.org/0000-0003-2638-5474 Yurii Skourski Helmholtz-Zentrum Dresden-Rossendorf Wei-tin Chen Center for Condensed Matter Sciences, National Taiwan University K.-Y. Choi ( [email protected] ) Chung-Ang University https://orcid.org/0000-0001-8213-5395 Article Keywords: breathing pyrochlore system, spin-liquid-like state, spin liquids, bond disorder Posted Date: August 12th, 2020 DOI: https://doi.org/10.21203/rs.3.rs-50493/v1 License: This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License Emergent spin-liquid-like state in the bond-disordered breathing pyrochlore S. Lee1, S.-H. Do1, W. Lee1, Y. S. Choi1, J. van Tol2, A. P. Reyes2, Y. Skourski3, W.-T. Chen4,5, and K.-Y. Choi1,† 1 Department of Physics, Chung-Ang University, 84 Heukseok-ro, Seoul 06974, Republic of Korea 2 National High Magnetic Field Laboratory, Florida State University, Tallahassee, Florida 32310, USA 3 Dresden High Magnetic Field Laboratory, Forschungszentrum Dresden-Rossendorf, 01314 Dresden, Germany 4 Center for Condensed Matter Sciences, National Taiwan University, Taipei 10617, Taiwan 5 Center of Atomic Initiative for New Materials, National Taiwan University, Taipei 10617, Taiwan Abstract A breathing pyrochlore system is predicted to host a variety of quantum spin liquids. However, perturbations beyond nearest-neighbor Heisenberg interaction are an obstacle to identifying such exotic states. Here, we utilize a bond-alternating disorder to tune a magnetic ground state in the Cr-based breathing pyrochlore. By combining thermodynamic and magnetic resonance techniques, we provide experimental signatures 2 of a spin-liquid-like state in LiGa1-xInxCr4O8 (x=0.2), namely, a nearly T -dependent magnetic specific heat and a persistent spin dynamics by muon spin relaxation (μSR). Moreover, 7Li NMR, ZF-μSR, and ESR unveil the dichotomic nature of both temporal and thermal spin fluctuations: slowly fluctuating tetramer singlets at high temperatures and a fast fluctuating spin-liquid-like state at low temperatures. Our results suggest that a bond disorder in the breathing pyrochlore offers a new route to achieve an unexplored state of matter. Introduction Frustrated quantum magnets provide a fertile ground to discover exotic quantum and topological phenomena, ranging from quantum spin liquids to magnetic monopoles in spin ice to Majorana anyons in the Kitaev honeycomb lattice.1,2 A prominent instance is a pyrochlore lattice, which is a three-dimensional network of corner-sharing tetrahedra.3 The pyrochlore Heisenberg antiferromagnet is predicted to harbor a spin-liquid ground state in the absence of further neighbor interactions.4–6 In real materials, the macroscopic ground-state degeneracy can be lifted by a range of perturbations, including spin-lattice couplings, additional magnetic interactions, and quenched disorders.7–10 The lifting of the highly degenerate ground states gives rise to emergent phenomena such as zero-energy modes, quantum spin ice, quantum spin liquid, and moment fragmentations.11–15 By the same token, bond alternation as a perturbation to the pyrochlore system leads to a new structural motif called a breathing pyrochlore lattice. Its spin Hamiltonian is described as , where J and J' are the nearest-neighbor exchange interactionsℋ = 16,17 퐽for∑ 푖,푗∈Athe A퐒 푖and⋅ 퐒 푗B+ tetrahedra 퐽′ ∑푖,푗∈B 퐒 of푖 ⋅ two 퐒푗 alternating sizes, respectively. In the breathing pyrochlore, the breathing anisotropy Bf = J'/J gauges a degree of the bond alternation. Remarkably, the breathing pyrochlore can host Weyl magnons in an antiferromagnetically ordered phase, as well as a fracton spin liquid in the presence of Dzyaloshinskii-Moriya interactions not to mention a Coulomb spin liquid.18,19 3+ 3+ On the material side, the Cr-based breathing pyrochlore LiACr4O8 (A = Ga , In ; space group ) is a particularly interesting example because Bf can be tuned by varying the 17 퐹4composition3푚 of Li and A. LiGaCr4O8 , having the breathing anisotropy Bf = 0.6, behaves much like a uniform pyrochlore. On the other hand, LiInCr4O8 has the small Bf = 0.1, in which the A tetrahedra are weakly coupled through inter-tetrahedral interaction J'. Despite the large difference in Bf, both the LiACr4O8 compounds show commonly two-stage symmetry breaking: a magnetostructural phase transition at TS=16 (17) K with subsequent antiferromagnetic 20 ordering at TM=13 (14) K for A=In (Ga). The lasting magnetic orders suggest that the bond alternation alone is not sufficient to repress the effect of spin-lattice coupling that induces a cubic-to-tetragonal transition. In this situation, bond randomness can counteract the detrimental impact of the magnetoelastic transition. This raises the exciting prospect of tracing intrinsic spin dynamics of the breathing pyrochlore lattice to a putative spin-liquid ground state, not being interrupted by long-range magnetic order. In this work, we investigate spin dynamics and low-energy excitations of the bond-disordered breathing pyrochlore LiGa0.2In0.8Cr4O8 by combining multiple magnetic resonances with thermodynamic techniques. We observe a thermal and temporal dichotomy between a coupled tetramer singlet and a spin-liquid-like state. Spin fluctuations probed on the different time scales give evidence that the emergent spin-liquid state is pertinent to a correlated pyrochlore lattice with dimensional reduction. Results Fig. 1| Crystal structure, phase diagram, and magnetic properties. a Schematic structure of the uniform breathing pyrochlore LiACr4O8 (A = Ga, In) and the bond-disordered breathing pyrochlore LiGa0.2In0.8Cr4O8. b T-x phase diagram of LiGa1-xInxCr4O8. The inverse red triangle marks the investigated compound LiGa0.2In0.8Cr4O8. c Temperature dependence of the static magnetic susceptibility χdc(T) of LiGa0.2In0.8Cr4O8. χdc(T) is decomposed into the intrinsic χintr(T) and the orphan spin contribution χorp(T). d Real component of the ac magnetic susceptibility χ'ac(T) as a function of T and B measured with a fixed frequency of ν=100 Hz. e High-field magnetization measured at selected temperatures. The black dashed-dotted and green dashed lines indicate the orphan spin magnetization Morp(T) and the bulk magnetization Mintr(T). A linear extrapolation gives the spin gap of ΔM/kB ~ 20 K. Magnetic phase diagram As sketched in Fig. 1a, the A-site ordered LiACr4O8 (A = Ga, In) spinels are a nearly perfect realization of the breathing pyrochlore lattice due to the significant difference between the Li+ and A3+ valence states. The Ga-for-In substitution disrupts a uniform arrangement of the two alternating tetrahedra and leads to the rich magnetic phase 21 diagram of LiGa1-xInxCr4O8, as shown in Fig. 1b. The magnetic ordering vanishes for x>0.1 or x<0.95. A spin-glass phase occupies a wide range of x=0.1 - 0.625. For the Ga-rich 7 compound LiGa0.95In0.05Cr4O8, the Li NMR and neutron experiments revealed the spin 22 nematic transition at Tf = 11 K, driven by the small bond disorder. In the In-rich range of x=0.7 - 0.95, LiGa1-xInxCr4O8 exhibits a spin-gap behavior with the lack of magnetic ordering and spin freezing down to 2 K.21,23 However, little is known about an exact ground state. Here, we have chosen the x=0.8 compound (marked by the inverse triangle in Fig. 1b) to address this issue. Magnetic susceptibilities and magnetization Figure 1c presents the T dependence of dc magnetic susceptibility χdc(T) of LiGa0.2In0.8Cr4O8. On cooling, χdc(T) shows a broad hump at around 70 K, and a subsequent upturn below 10 K. Above 100 K, χdc(T) follows the Curie- Weiss law with the Curie-Weiss temperature ΘCW=-386(1) K and the effective magnetic moment μeff =3.873(4) μB (see Supplementary Note 1 and Supplementary Fig. 1) that are 21 consistent with the values in the previous report. The low-T upturn of χdc(T) is reminiscent of orphan spins. We attempt to single out the intrinsic χintr(T) by fitting the T<5 K data to χdc(T) = χintr(T) + χorp(T), where χorp(T)=Corph/(T+ Θorp). We obtain Θorp= -2.0(2) K, confirming the contribution of weakly interacting orphan spins. The orphan spin concentration is estimated to be 0.6 % of the Cr3+ spins, smaller than the value obtained from the high-field magnetization data (see below). After the subtraction of χorp(T) from χdc(T), we can identify a nearly constant χintr(T<5 K), indicative of the presence of abundant low-energy in-gap states. Exhibited in Fig. 1d is the real component of the ac magnetic susceptibility χ'ac(T, B) as a function of T and B at a fixed frequency ν=100 Hz. The low-T upturn of χ'ac(T, B) is systematically suppressed with increasing B. Remarkably, χ'ac(T, B=2 T) becomes nearly T independent below T*=10 K. This is attributed to the Zeeman splitting of the orphan s= 3/2 moments that weakly interact with an energy scale of . In addition, χ'ac(T) shows no apparent frequency dependence, ruling out the formation|Θorp |of ≈ spin 2 K freezing or spin glass state (see Supplementary Note 2 and Supplementary Fig. 2). We next turn to the high-field magnetization M(T, B) measured up to 58 T at selected temperatures (see Fig. 1e). With increasing field, M(T=1.8 K, B) shows an upward convex behavior at low fields and then switches to a concave curvature at high fields. The low-B convex M(H) is associated with the orphan spin contribution Morp (H).