Evolution of lattice coherence in the intermediate-valence heavy-fermion compound $\mathrm{Eu}{\mathrm{Ni}}_2{\mathrm{P}}_2$ studied by point contact spectroscopy

We performed a point contact spectroscopy study in an intermediate-valence heavy-fermion (HF) compound $\mathrm{Eu}{\mathrm{Ni}}_2{\mathrm{P}}_2$. Above the Kondo temperature $T_{\mathrm{K}}$, the differential conductance spectra show a broad peak due to the Kondo resonance at the Eu site. Below $T_{\text{K}}$, the broad peak splits into two peaks that can be reproduced by the summation of two Fano curves with the same parameters, indicating the emergence of the indirect hybridization gap in an Anderson lattice. With decreasing temperature, the separation between the two peaks increases and saturates at very low temperatures. The results reveal the evolution of the electronic structure in the HF state due to the development of the lattice coherence.

Figure 1

(a) Solid line: Differential conductance ($dI/dV$) of $\mathrm{Eu}{\mathrm{Ni}}_2{\mathrm{P}}_2/\mathrm{W}$ interface at 4.3 K; contact resistance is 60 $\mathrm{\Omega }$. Broken line: $\mathrm{Eu}{\mathrm{Ni}}_2{\mathrm{P}}_2/\mathrm{Pt}$ interface at 6.0 K; contact resistance is 6 $\mathrm{\Omega }$. (b) Differential resistance ($dV/dI$), which is the reverse of $dI/dV$ in (a). (c) Contact resistance dependence of differential conductance ($dI/dV$) of $\mathrm{Eu}{\mathrm{Ni}}_2{\mathrm{P}}_2/\mathrm{W}$ interface at 4.3 K. The spectra are measured with increasing contact resistance from 12 to 60 $\mathrm{\Omega }$. Broken lines provide visual guidance.

Figure 2

(a) The temperature dependence of differential conductance ($dI/dV$) $\mathrm{Eu}{\mathrm{Ni}}_2{\mathrm{P}}_2/\mathrm{W}$ interface below $T\sim 60$ K in run 1, for which the contact resistance is $R_C=17\mathrm{\Omega }$. (b) Differential conductance above $T\sim 60$ K at $R_C=17\mathrm{\Omega }$ in run 2. (c) Temperature variation of coefficient of determination $1-R^2$.

Figure 3

(a) Fitting of spectrum at T = 5.3 K due to the summation of two Fano curves, $f_1$ and $f_2$, as expressed in Eq. (2), where $f_1$ and $f_2$ have the same parameters for S, $q$, and $\mathrm{\Gamma }\left(eV\right)$ [42]. Two solid lines correspond to $f_1$ and $f_2$. (b) Temperature dependence of the spectra in Fig. 2 fitted by summation of two Fano curves. (c) Temperature dependence of the peak separation ${\mathrm{\Delta }}_p$ between two Fano curves. Dashed line shows $\sqrt{1-{(T/T_0)}^2}$ dependence.

Figure 4

(a) Fitting of $dI/dV$ spectra illustrated in Fig. 2 using the MDC model. (b) Temperature dependence of the indirect hybridization gap evaluated by the MDC model. Dashed line shows $\sqrt{1-{(T/T_0)}^2}$ dependence. (c) Temperature dependence of broadening parameter ${\mathrm{\Gamma }}_0$. Solid line represents fitting by ${\mathrm{\Gamma }}_0=\sqrt{{\left(\alpha k_{B}T\right)}^2+{\left(2k_B{T}_K\right)}^2}$, where $\alpha =3.4\pm 0.4$. (d) Temperature dependence of renormalized 4f-electron level $\lambda$.