Exploring the coexistence of antiferromagnetic ordering and superconducting in Ce$3$PtIn${11}$

The properties of the heavy fermion compound Ce$_3$PtIn$_{11}$ are certainly enigmatic. At ambient pressure the compound displays two consecutive magnetic transitions into antiferromagnetic (AFM) states at $T_{\mathrm{N1}} = 2.2$K and $T_{\mathrm{N}} = 2.0$K, respectively. Below $T_{\mathrm{c}} = 0.32$K superconductivity (SC) is found [1]. It has been speculated that the coexistence of AFM and SC results from the peculiar crystal structure. The compound crystallizes in the P4/$mmm$ and harbors two inequivalent Ce sites [2]. The Ce1-ion (2 atoms per f.u.) occupies the Wyckoff $2g$ position ($D_{4h}$ symmetry). Its surrounding is identical to Ce-atoms in Ce$_2T$In$_8$ with $T$ being a transition element. It is believed to be largely Kondo screened and responsible for SC. Ce2 (1 atom per f.u.) resides the Wyckoff $1a$ position which has local $C_{4v}$ symmetry. The ion experiences CeIn$_3$-like environment and hence, is assumed to order magnetically. Entropy analysis indeed conjectured this idea [1] and further support comes from recent $^{115}$In NQR experiments. These experiments found evidence for spin fluctuations, and which could only be affiliated to the Ce1-site [3]. In addition, they revealed that magnetic moment of Ce2 has to be 20 times larger than the moment of Ce1 [4].

In this presentation we will try to shed some light on the SC properties. A pressing question is what is at the origin of the Cooper-pairing as the critical point where the AFM transition temperature becomes zero is still far away (the critical pressure needed equals $p_{c} \approx 1.5$GPa). Intriguing, in our $^{115}$In NQR experiment a sudden drop of spin-relaxation rate $1/T_1$ emerges upon entering the superconducting state suggesting a first order type of transition from the AFM state into the SC one [3]. Such would indicate a breaking of symmetry and implies that magnetic order and superconductivity compete [5]. Far below $T_{\mathrm{c}}$ a Korringa-type of evolution of $1/T_1$ is observed pointing to the existence of a finite density of states deep inside the superconducting phase. Recent low temperature specific heat measurements confirm the presence of uncondenstated heavy quasi-particles down to lowest temperatures
In addition, we conducted zero-field (ZF) and longitudinal field (LF) $\mu$SR experiments. We observed a subtle oscillatory component in the spectra for $T<T_{\mathrm{N}}$ on top of the exponential relaxation decay indicating the presence of an ordered magnetic structure. A weak magnetic field in of only 1kG was enough to fully decouple the muon and resulting in a time dependence of the spectra which can be described by an exponential. This, combined with the ZF observation of an oscillatory component indicates the presence of a static or quasi-static internal field. For $T<T_{\mathrm{c}}$, the static field increases upon lowering the temperature suggesting that we are tracking an order parameter in the form of a static internal field. Our $\mu$SR data confirms the microscopic coexistence of AFM and SC in Ce$_3$PtIn$_{11}$ but also questions the presence of critical spin fluctuations in Ce$_3$PtIn$_{11}$ as source for Cooper pairing. Further study is needed to elucidate in detail the superconducting state.

$^*$This work was supported by the Czech Science Foundation (GAČR) Grant No. 18-23606S, the EU COST Action CA16218 and by the Czech Ministry of Education under the COST project scheme, project No. LTC18024.

[1] J. Prokleška, et al., Phys. Rev. B 92, 161114(R) (2015). https://doi.org/10.1103/PhysRevB.92.161114
[2] M. Kratochvílová, et al., J. Cryst. Growth 397, 47 (2014). https://doi.org/10.1016/j.jcrysgro.2014.04.008
[3] S. Kambe et al., Phys. Rev. B 101, 081103(R) (2020). https://doi.org/10.1103/PhysRevB.101.081103
[4] H. Fukazawa et al., Phys. Rev. B 102, 165124 (2020). https://doi.org/10.1103/PhysRevB.102.165124
[5] M. Kato and K. Machida, Phys. Rev. B 37, 1510 (1988). https://doi.org/10.1103/PhysRevB.37.1510