# One-Component Order Parameter in URu$_2$Si$_2$ Uncovered by Resonant Ultrasound Spectroscopy and Machine Learning

## TL;DR

This study uncovers that the hidden order in URu$_2$Si$_2$ is a one-component order parameter using resonant ultrasound spectroscopy and machine learning, providing new insights into its nature and constraining theoretical models.

## Contribution

The paper introduces a machine learning framework that determines the order parameter's dimensionality from raw ultrasound data, even in small crystals, advancing experimental analysis methods.

## Key findings

- No anomalies in shear elastic moduli indicate a one-component order parameter.
- Machine learning confirms the one-component nature directly from raw data.
- Results rule out theories based on two-component order parameters.

## Abstract

The unusual correlated state that emerges in URu$_2$Si$_2$ below T$_{HO}$ = 17.5 K is known as "hidden order" because even basic characteristics of the order parameter, such as its dimensionality (whether it has one component or two), are "hidden". We use resonant ultrasound spectroscopy to measure the symmetry-resolved elastic anomalies across T$_{HO}$. We observe no anomalies in the shear elastic moduli, providing strong thermodynamic evidence for a one-component order parameter. We develop a machine learning framework that reaches this conclusion directly from the raw data, even in a crystal that is too small for traditional resonant ultrasound. Our result rules out a broad class of theories of hidden order based on two-component order parameters, and constrains the nature of the fluctuations from which unconventional superconductivity emerges at lower temperature. Our machine learning framework is a powerful new tool for classifying the ubiquitous competing orders in correlated electron systems.