Rearrangement of Uncorrelated Valence Bonds Evidenced by Low-Energy Spin Excitations in YbMgGaO4

Abstract

dc-magnetization data measured down to 40 mK speak against conventional freezing and reinstate YbMgGaO4 as a triangular spin-liquid candidate. Magnetic susceptibility measured parallel and perpendicular to the c-axis reaches constant values below 0.1 and 0.2 K, respectively, thus indicating the presence of gapless low-energy spin excitations. We elucidate their nature in the triple-axis inelastic neutron scattering experiment that pinpoints the low-energy (E ≤ J0 ∼ 0.2 meV) part of the excitation continuum present at low temperatures (T < J0/kB), but completely disappearing upon warming the system above T J0/kB. In contrast to the high-energy part at E > J0 that is rooted in the breaking of nearest-neighbor valence bonds and persists to temperatures well above J0/kB, the low-energy one originates from the rearrangement of the valence bonds and thus from the propagation of unpaired spins. We further extend this picture to herbertsmithite, the spin-liquid candidate on the kagome lattice, and argue that such a hierarchy of magnetic excitations may be a universal feature of quantum spin liquids.Introduction.-Quantum spin liquids (QSLs) have a special place in condensed-matter physics as states with unconventional excitations solely driven by spin degrees of freedom in the absence of charge and orbital fluctuations. The QSL physics may be behind many intriguing phenomena studied over the last decades, including the high-temperature superconductivity [1,2]. Exotic properties of the QSLs are also central to new technologies, such as topological quantum computing [3]. The prototype of a QSL was proposed by Anderson back in 1973 as a resonating-valence-bond (RVB) state, a superposition of many different partitions of the triangular spin network into valence bonds (VBs, spin-0 singlets), 1

YbMgGaO4: A Triangular‐Lattice Quantum Spin Liquid Candidate

“…While, at T << H << J 0 the scaling law is a little hard to be measured, because the lowest available temperature is only about 40 mK and the magnetic coupling is small for the rare‐earth magnet of YbMgGaO 4 , J 0 /k B ≈ 2 K. Using the zero‐ T limits ( T ≈ 0.04 K at least) of the magnetization reported in ref. [], we get M ║ ≈ H 0.81(1) and M ┴ ≈ H 0.83(1) (see Figure d), which may be not far away from the scaling law prediction, M ≈ H 1 − γ . These observed universal scaling law features should further confirm the formation of the uncorrelated/random VBs and the quantum paramagnetic phase in YbMgGaO 4 …”

“…Quantitatively, the measured Q ‐dependence can be well fitted by the high‐energy uncorrelated VB model (see Figure c–e), where the neutron breaks NN VBs and thus produces unpaired spins (see Figure a) where f (| Q |) is the magnetic form factor of free Yb 3+ in the dipole approximation for | Q | ≤ 2.5 Å −1 , and N is the number of NN VBs involved in the INS process. N is temperature‐dependent nearly according to the Boltzmann distribution between the GS spin singlet and the excited quasi‐triplet …”

“…Therefore, the weak anomaly observed at ≈0.1 K is more like a crossover to the GS region with a nearly T ‐independent susceptibility, instead of a conventional magnetic transition. Inspired by the above points, we carried out the low‐ T dc‐magnetization (susceptibility) measurements on the single‐crystal sample along both the c axis and ab plane, by applying various magnetic fields (see Figure c) . The broad hump is indeed observed at T s || ≈ 0.1 K when the measuring field of 0.01 T (≈1% J 0 /μ B / g ave ) is applied along the c axis, but it shifts to T s ┴ ≈ 0.2 K when the field is along the ab plane (see Figure c): T s || / T s ┴ ≈ J zz / J xx , where J xx = 2 J ± .…”

“…Inspired by the above points, we carried out the low‐ T dc‐magnetization (susceptibility) measurements on the single‐crystal sample along both the c axis and ab plane, by applying various magnetic fields (see Figure c) . The broad hump is indeed observed at T s || ≈ 0.1 K when the measuring field of 0.01 T (≈1% J 0 /μ B / g ave ) is applied along the c axis, but it shifts to T s ┴ ≈ 0.2 K when the field is along the ab plane (see Figure c): T s || / T s ┴ ≈ J zz / J xx , where J xx = 2 J ± . If there is a transition, the critical temperature must keep direction independent .…”

“…At low transfer energies below ≈ J 0 , this high‐energy continuum should be fully gapped, as a finite energy of ≥ J 0 is required to break at least one NN VB. And the gapped nature can be well characterized on the cold triple‐axis INS spectrometer, PANDA, owing to the extremely low instrumental background of its point detector (see below) …”