Magnetic field-temperature competition and quantum criticality in a strange metal

Strange metals defy the quasiparticle description of conventional metals, exhibiting a linear in temperature ($T$-linear) resistivity in a broad temperature range. It has become increasingly clear that, together with $T$-linear resistivity, strange metals exhibit a characteristic response in strong magnetic fields, which might point to the quantum critical origin of the strange metal behavior. To explore the effects of strong magnetic fields on the dynamics of quantum fluctuations in a strange metal, here we report the thermodynamic study of electronic density of states on the Fermi surface in CeCoIn$_5$. Using ultrafast nanocalorimeters, we access the electronic density of states at low temperatures and high magnetic fields through two independent thermodynamic probes -- the nuclear spin-lattice relaxation rate and the electronic specific heat -- measured simultaneously on the same crystal. Both thermodynamic probes exhibit magnetic field and temperature competition, characteristic of quantum criticality, indicating that magnetic field acts as a cutoff for the dynamics of quantum critical fluctuations in CeCoIn$_5$. However, at low temperatures and high magnetic fields, the electronic specific heat and the nuclear spin-lattice relaxation rate cannot be understood solely in terms of a critical enhancement of the electronic density of states at the Fermi surface. This indicates that quantum criticality in CeCoIn$_5$ involves both local and itinerant fluctuating critical modes.