Multi-modal spectroscopy of phase transitions

Stephen Carr, Ilija K. Nikolov, Rong Cong, Adrian Del Maestro, Chandrasekhar Ramanathan, V. F. Mitrović

Published 2022-08-23Version 1

To understand a phase transition, independent measurement of the value and variation in each physical parameter of a material's Hamiltonian is vital. Conventional one-dimensional spectroscopy, which studies responses to fields as a function of an experiment time ($t$), struggles to distinguish between different sources of noise, but multi-dimensional spectroscopy can directly probe individual Hamiltonian parameters by varying an integration time ($\tau$). In this work, we present a spectroscopic technique based on the multi-dimensional paradigm, and show it can probe the distribution of a quadrupolar interaction strength ($\mathcal{S}_z^2$) even in the presence of large magnetic noise ($\mathcal{S}_z$). Inversion symmetric combinations of spin operators are found to give clear sinusoidal responses in $\tau$ due to periodic refocusing. The time-scale on which the magnetization partially decays in $\tau$ provides a direct measure of the distribution of interaction strengths, even when the average value of the interaction is zero across a sample. A derivation of this effect for general spin magnitudes is included. This provides an ideal method for assessing the distribution and source of different forms of disorder, helping elucidate which microscopic physics and symmetry dominates near a phase transition.