Pressure-induced unconventional superconductivity in the heavy-fermion antiferromagnetCeIn3: AnIn115-NQR study under pressure

Abstract

We report on pressure-induced unconventional superconductivity (SC) in the heavy-fermion (HF) antiferromagnet ${\mathrm{CeIn}}_{3}$ by means of nuclear-quadrupole-resonance (NQR) studies conducted under a high pressure. The temperature $(T)$ and pressure $(P)$ dependences of the In-NQR spectra have revealed a first-order quantum-phase transition (QPT) from antiferromagnetism (AFM) to paramagnetism (PM) at a critical pressure ${P}_{\mathrm{c}}=2.46\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$ at which AFM disappears with a minimum value of ${T}_{\mathrm{N}}({P}_{\mathrm{c}})=1.2\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. High-energy x-ray scattering measurements under $P$ show a progressive decrease in the lattice density without any change in the crystal structure, whereas an increase in the NQR frequency $({\ensuremath{\nu}}_{\mathrm{Q}})$ indicates an increase in the hybridization between $4f$ electrons and conduction electrons, which stabilizes the HF-PM state. This competition between the AFM phase where ${T}_{\mathrm{N}}$ is reduced and the formation of the HF-PM phase triggers the first-order QPT at ${P}_{\mathrm{c}}=2.46\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$. Despite the lack of an AFM quantum critical point in the $P\text{\ensuremath{-}}T$ phase diagram, we highlight the fact that unconventional SC occurs in both phases of AFM and PM. The measurements of the nuclear spin-lattice relaxation rate $1∕{T}_{1}$ in the AFM phase have provided evidence for the uniformly coexisting $\mathrm{AFM}+\mathrm{SC}$ phase. Remarkably, the significant increase in $1∕{T}_{1}$ upon cooling in the AFM phase has revealed the development of low-lying magnetic excitations down to ${T}_{\mathrm{c}}$ in the AFM phase; it is indeed relevant to the onset of the uniformly coexisting AFM+SC phase. In the HF-PM phase where AFM fluctuations are not developed, $1∕{T}_{1}$ decreases without the coherence peak just below ${T}_{\mathrm{c}}$, followed by a power-law-like $T$ dependence that indicates an unconventional SC with a line-node gap. Remarkably, ${T}_{\mathrm{c}}$ has a peak around ${P}_{\mathrm{c}}$ in the HF-PM phase as well as in the AFM phase. In other words, an SC dome exists with a maximum value of ${T}_{\mathrm{c}}=230\phantom{\rule{0.3em}{0ex}}\mathrm{mK}$ around ${P}_{\mathrm{c}}$, indicating that the origin of the pressure-induced HF SC in ${\mathrm{CeIn}}_{3}$ is not relevant to AFM spin fluctuations but to the emergence of the first-order QPT in ${\mathrm{CeIn}}_{3}$. These phenomena observed in ${\mathrm{CeIn}}_{3}$ should be understood in terms of the first-order QPT because these new phases of matter are induced by applying $P$. When the AFM critical temperature is suppressed at the termination point of the first-order QPT, ${P}_{\mathrm{c}}=2.46\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$, the diverging AFM spin-density fluctuations emerge at the critical point from AFM to PM. The results with ${\mathrm{CeIn}}_{3}$ leading to a new type of quantum criticality deserve further theoretical investigations.