Unconventional Magnetic Oscillations in Kagome Mott Insulators

In conventional metals, electrons form Landau Levels in a magnetic field, leading to magnetic oscillations in their physical properties. In the absence of charged Fermi surfaces, a robust insulator is NOT expected to host any quantum oscillations. Therefore, the recent observations of Landau Level quantization in narrow-gap, correlated Kondo insulators Xiang2018; Li2020; Tan2015; Xiang2021; Senthil2019; Sodeman2018 have created a lot of excitement. These developments lead naturally to the next question: can quantum oscillations be observed in wide-gap correlated insulators, in particular, in nonmagnetic Mott insulators? In lattices with an odd number of electrons per unit cell, strong repulsion between electrons may result in a Mott insulator, where the electrons are localized on lattice sites, forming $S=\frac{1}{2}$ moments. The moments interact via antiferromagnetic (AF) interactions, and usually form an ordered AF state. In frustrated lattices, magnetic ordering may be suppressed due to frustration and quantum fluctuations, resulting in a novel state of matter called the quantum spin liquid (QSL) Anderson1973; Anderson1987. Some versions of the quantum spin liquid are predicted to host exotic particles such as gapless fermions which carry S=$\frac{1}{2}$ but no charge (called spinons), coupled to an emergent gauge field Savary; Zhou. Indeed it has been proposed that these low energy excitations can lead to quantum oscillations in certain spin liquid candidates which are charge insulators  Motrunich

The kagome lattice exhibits a high degree of frustration and is a strong candidate for hosting a spin liquid Ran2007; Hermele2008; Savary; Zhou; Norman. Experimentally, herbertsmithite is the most famous example of a kagome Mott insulator, leading to fascinating discoveries Han2012. Unfortunately, while the Cu ions in the kagome layers remain pristine Smaha2020; Freedman2010, a significant fraction of the Zn sites that lies between the kagome planes are substituted by Cu, creating impurity spins that can dominate the low temperature spectrum, thermodynamics, and magnetic properties Vries2008; Wei2021. A search for oscillations in this kagome Mott insulator was conducted but was unsuccessful Asaba2014. The recent discovery of YCu${}_{3}$(OH)${}_{6}$Br${}_{2}$[Br${}_{1-y}$(OH)${}_{y}$] (YCOB), in which Zn is replaced by Y, solves the site mixing problem thanks to the very different ionic sizes of Y and Cu JMMM; Zeng2022; Liu2022; Hong2022. These materials do not show magnetic order down to 50 mK, but there remains disorder in the exchange constants caused by the random replacement of Br above and below the Cu hexagons by OH Liu2022. It should also be mentioned that the so-called perfect Y-based kagome crystal YCu${}_{3}$(OH)${}_{6}$Cl${}_{3}$ with Cl instead of Br and without the OH disorder, was the first to be developed sun2016perfect and later found to order at 15 K zorko2019coexistence. This is not unexpected because the presence of a Dzyaloshinskii Moriya (DM) coupling is theoretically known to favor ordering Cepas2008; BernuPRB2020; Messio2010. On the other hand, the closely related Y-kapellasite Y${}_{3}$Cu${}_{9}$(OH)${}_{19}$Cl${}_{8}$ has a tripled inplane unit cell and orders at a lower temperature of 2.1 K ChatterjeePRB2023. Therefore, OH substitution and the subsequent disorder may play a role in suppression AF ordering, as discussed in a recent detailed study xu2024magnetic. The role of disorder is a complicated question and we will defer further comments to the Discussion section below. At this point we simply note this class of crystals exhibits a great deal of richness and complexity and we are motivated to study the magnetic behavior of YCOB under intense magnetic fields. We should also emphasize that while YCOB in zero field has been claimed to harbor Dirac spinons Zeng2022; Liu2022 and have been under intense studies xu2024magnetic; zeng2024spectral, the current paper focuses on the behavior under strong magnetic field, and the connection of the new state of matter that we uncover with the zero field case is left for future studies.