Understanding the quantum behavior of electrons at extremely low temperatures is a central challenge in condensed-matter physics. Many quantum phenomena, including unconventional superconductivity, quantum criticality, frustrated magnetism, and heavy-fermion behavior, emerge only under small thermal fluctuations. Specific-heat measurement is a unique experimental technique that directly probes entropy and low-energy excitations.

Ironically, these measurements are more difficult at low temperatures. At temperatures below approximately 1 K, atomic nuclei contribute nuclear specific heat, which increases approximately as , eventually overwhelming the electronic contributions of interest. In many materials, the nuclear contribution is hundreds of times larger than the electronic one.

The recently developed initial slope method (ISM) calorimetric technique overcomes this long-standing experimental obstacle by using a new thermal model. The conventional thermal model for calorimetric systems consists of a sample comprising two thermally coupled subsystems (nuclear and electron–phonon subsystems), sample platform, and thermal bath.

The nuclear and electron–phonon subsystems are treated as a single thermal component and the specific heat is determined from the complete thermal-relaxation curve, which includes both nuclear and electronic contributions, and is time-consuming.

In contrast, the ISM considers the nuclear and electron–phonon subsystems separately. Rather than measuring the complete thermal-relaxation curve of the sample, the ISM focuses only on the first fraction of a second immediately after the application of a small heat pulse.

This seemingly simple idea exploits a fundamental difference in relaxation times. Electrons and phonons equilibrate almost instantaneously, whereas nuclear spins respond slowly. During the initial stage of relaxation, the nuclei remain frozen; only the electronic and lattice degrees of freedom contribute to the observed temperature change. By analyzing this initial slope, the electronic specific heat can be obtained without subtracting the nuclear contribution.

To verify this method, high-purity copper was measured using the conventional method and ISM under magnetic fields of 0 and 7 T. Under 7 T, the nuclear contribution was more than 250 times larger than the electronic specific heat, at temperatures below 0.1 K. The conventional relaxation measurements under this condition were dominated almost entirely by nuclear contribution. However, the ISM measurements were the same as the electronic specific heat measured at 0 T, demonstrating that the nuclear contribution had been eliminated during measurement.

ISM also dramatically improved the measurement efficiency. Conventional measurements often required waiting for nuclear spins to relax, which could take up to 10³ s. In contrast, the ISM typically required less than one second, substantially speeding up measurement.

Beyond improving calorimetry, the ISM opens new opportunities for studying quantum materials. Nuclear specific heat has long hindered thermodynamic studies of quantum phenomena. The ISM provides researchers with direct access to the intrinsic low-energy physics that has long remained hidden behind nuclear heat.

(Written by Noriyuki Kabeya on behalf of all authors.)

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