Direct measurement of the evolution of magnetism and superconductivity toward
the quantum critical point
W. Higemoto1,2,3), M. Yokoyama4), T.U. Ito1,3), T. Suzuki1,2), S. Raymond5), and Y. Yanase6)1): Res. Gr. for Surface and Interface Science, JAEA 2): Tokyo IT, 3): J-PARC Center4): Ibaraki Univ. 5): Univ. Grenoble Alpes 6): Kyoto Univ.

Quantum critical phenomena are one of the central issues incondensed matter physics. In the vicinity of the quantum criticalpoint (QCP), where two different interactions compete, quantum
fluctuations play a major role in realizing unconventional
superconductivity as well as other exotic ground states. Thisquantum critical phenomenon could be observed when the phasetransition occurs at T = 0 by tuning parameters other thantemperature, such as magnetic field, pressure, and chemical
substitutions. For instance, in a heavy fermion system, themagnetic Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction
conflicts with the nonmagnetic Kondo effect along with theDoniach phase diagram [1], and deviations from the Fermi
liquid theory, which is a basic concept of interacting fermions,are found in some systems. Such a “non-Fermi liquid” (NFL)state is observed in thermodynamic and transport properties.
Furthermore, unconventional superconductivity often appears ina region of the phase diagram enclosed by a dome-shaped
boundary near the QCP. The properties of the system in thesuperconducting (SC) dome are dominated by quantum
criticality, and the mechanism of the superconductivity isstrongly related to the quantum critical spin fluctuations.
Revealing the spin state in the SC dome where a strong impactof quantum critical fluctuations must be manifested. Therefore,
the direct measurements of the magnetic and superconducting
order parameters are thus significant to identify the physicalproperties near the QCP. From an experimental point of view,
the signals from the magnetic order in the SC dome are expected
to be very small compared with large SC signals, and a highly
sensitive magnetic probe is required.
As an example of the quantum critical compounds, tetragonal
CeCoIn5 is one of the extensively investigated heavy fermion
compounds, which exhibit superconductivity at ambientpressure (Tc = 2.3 K at B = 0) [2]. CeCoIn5 shows NFL
behaviors in various quantities just above the SC upper criticalfield Hc2 [3], suggesting that the magnetic field can induce
quantum critical fluctuations. Meanwhile, it is well known thatthe superconductivity of CeCoIn5 is strongly correlated withmagnetism. Recently, the coexistence of superconductivity andmagnetic ordering was also suggested in the case of the Zn
substitution system CeCo(In1-xZnx)5 [4,5]. By substituting In
with a tiny amount of Zn, a small modification in the system,
corresponding to the energy scale on the order of a few Kelvins,
occurs without any structural phase transition, and it is possible
to tune only magnetism and superconductivity. In this regard,CeCo(In1-xZnx)5 is one of the ideal systems to investigate therole of magnetic quantum criticality in the evolution ofsuperconductivity. In CeCo(In1-xZnx)5, the SC transition
temperature Tc continuously reduces from 2.3 K (x = 0) to 1.4 K(x = 0.07) upon Zn doping, and then, the antiferromagnetic(AFM) order, with a transition temperature of TN = 2.2 K, isfound for x > 0.05 at B = 0. However, in the doping range wherex < 0.05, TN becomes smaller than Tc, indicating that asignificant response due to superconductivity masks the weaksignal of the AFM state and its quantum critical fluctuations in
the SC dome, and it is unclear whether the quantum phasetransition and spin fluctuations exist even deeper inside the SC
phase. To reveal the possible weak magnetism and quantum
criticality both inside and outside the SC dome in CeCo(In1xZnx)5, we employed muon spin rotation/relaxation at J-PARC
and elastic neutron scattering measurements at ILL.
It was found that a magnetically ordered state develops at x ~0.03, coexisting with the superconductivity [6]. The obtainedphase diagram of CeCo(In1-xZnx)5 is shown in Fig. 1. The
magnitude of the ordered magnetic moment is continuously
reduced with decreasing x, and it disappears below x ~ 0.03,indicating a second-order phase transition and the presence of
the QCP at this critical Zn concentration. Furthermore, themagnetic penetration depth in the SC phase diverges toward theQCP. These facts provide evidence for the intimate coupling
between quantum criticality and Cooper pairing.
The present result indicates that magnetism due to quantum
effects plays a significant role in the emergence ofsuperconductivity, leading to the elucidation of the relationshipbetween the magnetic and possible mechanism of the emergenceof superconductivity.

Fig. 1 Obtained phase diagram of CeCo(In1-xZnx)5.

References[1] S. Doniach, Physica (Amsterdam) 91, 231 (1977).
[2] C. Petrovic et al., J. Phys.: Condens. Matter 13, L337 (2001).
[3] J. Paglione et al., Phys. Rev. Lett. 91, 246405 (2003).
[4] M. Yokoyama et al., J. Phys. Soc. Jpn. 83, 033706 (2014).
[5] M. Yokoyama et al., Phys. Rev. B 92, 184509 (2015).
[6] W. Higemoto et al., Proc. Natl. Acad. Sci. USA 119,e2209549119 (2022).