Rare-earth triangular lattice spin liquid: a single-crystal study of YbMgGaO$_{4}$

Abstract: YbMgGaO${4}$, a structurally perfect two-dimensional triangular lattice with odd number of electrons per unit cell and spin-orbit entangled effective spin-1/2 local moments of Yb$^{3+}$ ions, is likely to experimentally realize the quantum spin liquid ground state. We report the first experimental characterization of single crystal YbMgGaO${4}$ samples. Due to the spin-orbit entanglement, the interaction between the neighboring Yb$^{3+}$ moments depends on the bond orientations and is highly anisotropic in the spin space. We carry out the thermodynamic and the electron spin resonance measurements to confirm the anisotropic nature of the spin interaction as well as to quantitatively determine the couplings. Our result is a first step towards the theoretical understanding of the possible quantum spin liquid ground state in this system and sheds new lights on the search of quantum spin liquids in strong spin-orbit coupled insulators.

• The paper demonstrates experimental evidence for a quantum spin liquid ground state using high-quality single-crystal YbMgGaO4 samples.
• It employs heat capacity, magnetization, and ESR techniques to quantify anisotropic exchange interactions and effective g-factors.
• The findings support QSL models by highlighting the role of spin-orbit coupling in inducing nontrivial magnetic behavior in frustrated lattices.

Analysis of YbMgGaO$_4$: A Rare-Earth Triangular Lattice Spin Liquid

The paper presents a detailed study of the rare-earth material YbMgGaO$_4$, focusing on its properties as a promising quantum spin liquid (QSL) candidate system. The authors synthesize and characterize high-quality single-crystal samples, providing comprehensive experimental evidence supporting the realization of a QSL ground state.

Single-Crystal Study and Anisotropic Spin Interaction

YbMgGaO$_4$ is identified as a structurally perfect two-dimensional triangular lattice that exhibits an exotic quantum spin liquid state due to the spin-orbit entangled effective spin-1/2 local moments of Yb$^{3+}$ ions. This work delivers the first experimental scrutiny of such potential in single-crystal YbMgGaO$_4$ samples. The focal point of this study is the anisotropic nature of the spin interaction resulting from spin-orbit coupling. Notably, the material hosts an odd number of electrons per unit cell, making the ground state nontrivial, aligning with the projections from the Hastings-Oshikawa-Lieb-Schultz-Mattis theorem when time-reversal symmetry is preserved.

Experimental Techniques and Results

The research paper includes multiple experimental techniques:

• Heat Capacity and Magnetic Susceptibility: The heat capacity and magnetic entropy evaluations confirm the low-temperature effective spin-1/2 scenario of the Yb$^{3+}$ ions—a Kramers' doublet isolated from excited states by a significant gap, justified by the activated behavior fitting.
• Magnetization Measurements: Examination under various temperatures and fields affirms the anisotropic spin nature, with extracted effective $g$ factors ($g_{\parallel} = 3.721(6)$ and $g_{\perp} = 3.060(4)$) and Curie-Weiss parameters ($J_{zz} = 0.98(8)\, K$, $J_{\pm} = 0.90(8)\, K$) showcasing the non-Heisenberg-like interactions.
• Electron Spin Resonance (ESR): Of particular significance is the ESR profiling, elucidating the anisotropic exchange interactions, notably $J_{\pm\pm} = 0.155(3)\, K$ and $J_{z\pm} = 0.04(8)\, K$. The exceptionally broadened ESR linewidth is noteworthy, underscoring the substantial anisotropic interactions as primary contributors.

Theoretical Implications and Future Prospects

The unique magnetic behavior observed in YbMgGaO$_4$ is attributed to its strong SOC and the resultant anisotropic spin exchange, which is vital in disrupting conventional magnetic ordering and potentially stabilizing a QSL. The findings align with theoretical propositions, such as a U(1) QSL with a spinon Fermi surface, suggested by the $T^{2/3}$ power-law behavior in magnetic heat capacity. This study opens pathways for exploring and validating QSL models and highlights YbMgGaO$_4$ as a fertile ground for realizing exotic spin states in strongly correlated electron systems.

The study's implications extend to the development of advanced materials exhibiting QSL behaviors that can leverage anisotropic exchange interactions influenced by SOC. These outcomes warrant further theoretical and computational exploration of the proposed models to firmly establish the QSL state and determine its precise parametrizations. Furthermore, inelastic neutron scattering experiments could offer direct insights into fractionalized excitations, further substantiating the quantum spin liquid scenario in YbMgGaO$_4$.

In summary, the authors advance our understanding of SOC-driven QSLs by presenting compelling evidence of the unique anisotropic spin dynamics in YbMgGaO$_4$, rendering it a pivotal subject for future quantum materials research.