Microwave spin resonance in epitaxial thin films of spin liquid candidate TbInO3

Minimizing the energy of a many body system tends to favor order, but classical frustration and quantum fluctuations destabilize that order. The tension between these effects can produce exotic quantum states of matter. Quantum spin liquid (QSL) states emerge in models of localized magnetic moments where the crystal lattice connectivity frustrates ordering, and the exchange interaction of neighboring spins strengthens quantum fluctuations. Experimentally identifying a QSL in a real material is challenging from the lack of an order parameter. Piecing together evidence from varied techniques is necessary for diagnosing the nature of the ground state - QSL or otherwise - of a frustrated spin system. In this work, we use coplanar superconducting resonators to probe magnetic excitations in epitaxially grown thin films of a spin liquid candidate TbInO3. Adapting microwave techniques from the field of circuit quantum electrodynamics, we measure responses of these thin films whose volume is too low for applying conventional bulk techniques. In-plane susceptibility extracted from the spin resonance signal indicates extreme frustration of magnetic order down to 20 mK, over two orders of magnitude lower than the Curie-Weiss energy scale. Through a crystal field analysis, we identify the doublet eigenstates comprising the ground state. As a consequence of improper ferroelectricity, Tb moments split into two flavors with distinct g-factors reflecting the local crystal field environment of each site. Spin-orbit coupling, crystal fields, magnetic frustration and improper ferroelectricity distinctively combine to shape the magnetic ground state of TbInO3. This work establishes a measurement technique using superconducting resonators to probe thin films of frustrated magnets, and applies this technique towards building a coherent understanding of the magnetic properties of TbInO3.