Critical fluctuations and conserved dynamics in a strange ferromagnetic metal

The origin of the strange metallic behavior observed in a wide range of quantum materials is an open challenge to condensed matter physics. Historically, strange metals were uniquely associated with antiferromagnetic quantum critical points (QCPs), but a new generation of materials reveals their association with uniform order parameters, such as ferromagnetism, valley or nematic order, suggesting a deeper common denominator. At a QCP, order parameter fluctuations are characterized by the dynamical critical exponent $z$, which quantifies the space-time scaling asymmetry. Here, we report the observation of a divergence in the Gr\"uneisen ratio at the QCP of the strange-metal ferromagnet CeRh$_6$Ge$_4$ with a dynamical critical exponent $z=3$, signaling that the underlying quantum singularity involves a conserved degree of freedom. Yet the magnetization of this easy-plane ferromagnet is not conserved. We argue that the $z=3$ strange criticality requires a description beyond the Landau paradigm, proposing a link with the gauge modes of the small-to-large Fermi surface transition and the associated gauge charge of the delocalizing heavy electrons.