Scaling Breakdown as a Signature of Spinon-Gauge Interaction in the Quantum Spin Liquid YbZn$_2$GaO$_5$

Abstract

Scaling behavior in magnetization has been reported in a wide range of quantum spin liquid (QSL) candidates and is often interpreted as evidence for scale-free spin liquid physics. Here we present a comprehensive scaling analysis of high-field magnetization measurements on the QSL material YbZn$_2$GaO$_5$. Between 5 K and 70 K, $M(H)$ displays scale invariance resembling that of a zero-field quantum critical point. Below 3 K, we observe a breakdown of this scale invariance that cannot be recovered by simply changing the critical exponents. This temperature coincides with the onset of enhanced spin correlations observed in $\mu$SR measurements. Moreover, the form of the deviation from scaling is consistent with collective spinon excitations coupled via emergent gauge interactions. These results indicate that the breakdown of scaling reflects the emergence of intrinsic low-energy excitations upon entering the QSL regime. Our work clarifies that magnetic scaling is associated with quantum critical fluctuations rather than with the spin liquid phase itself, and establishes magnetization scaling as a sensitive thermodynamic probe of emergent energy scales in QSL systems.