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Ni-impurity effects on the superconducting gap of La$_{2-x}$Sr$_{x}$CuO$_4$ studied from the magnetic field and temperature dependence of the electronic specific heat

The magnetic field and temperature dependence of the electronic specific heat $C_{\rm el}$ have been systematically investigated in $\rm La_{2-{\it x}}Sr_{\it x}Cu_{1-{\it y}}Ni_{\it y}O_4$ (LSCNO) in order to study Ni-impurity effects on the superconducting (SC) gap. In LSCNO with $x$=0.15 and $y$=0.015, the value of $γ$ ($\equiv C_{\rm el}/T$) at $T$=0 K, $γ_0$, is enhanced under the magnetic field $H$ applied along the $\bm c$-axis. The increment of $γ_0$, $Δγ_0$, follows the Volovik relation $Δγ_0$=$A\sqrt{H}$, characteristic of the SC gap with line nodes, with prefactor $A$ similar to that of a pure sample. The $C_{\rm el}/T$ vs. $T$ curve under $H$=0 shows a d-wave-like SC anomaly with an abrupt increase at $T_{\rm c}$ and $T$-linear dependence at $T$$\ll$$T_{\rm c}$, although the $γ_0$-value in the $C_{\rm el}/T$ vs. $T$ curve increases with increasing Ni concentrations. Interestingly, as the SC part of $C_{\rm el}/T$, $C_{\rm el}/T$$-$$γ_0$$\equiv$$γ_{\rm s}$, decreases in LSCNO, $T_{\rm c}$ is reduced in proportion to the decrease of $γ_{\rm s}$. These findings can be explained phenomenologically by a simple model in which Ni impurities bring about strong pair breaking at the edges of the coherent nodal part of the Fermi surface but in the vicinity of the nodes of the SC gap. The reduction of the SC condensation energy $U_0$ in LSCNO, evaluated from $C_{\rm el}$ at $T$ {0.3em}\raisebox{0.4ex}{$<$} {-0.75em}\raisebox{-.7ex}{$\sim$} {0.3em}$T_{\rm c}$, is also understood by the same model.