Comparative analysis of specific heat of ${\mathrm{YNi}}_2{\mathrm{B}}_2\mathrm{C}$ using nodal and two-gap models

The magnetic field dependence of low temperature specific heat in ${\mathrm{YNi}}_2{\mathrm{B}}_2\mathrm{C}$ was measured and analyzed using various pairing order parameters. At a zero magnetic field, the two-gap model, which has been successfully applied to ${\mathrm{MgB}}_2$ and the point-node model, appear to describe the superconducting gap function of ${\mathrm{YNi}}_2{\mathrm{B}}_2\mathrm{C}$ better than other models based on the isotropic $s$-wave, the $d$-wave line nodes, or the $s+g$ wave. The two energy gaps, ${\Delta }_L=2.67\mathrm{meV}$ and ${\Delta }_S=1.19\mathrm{meV}$, are obtained. The observed nonlinear field dependence of the electronic specific heat coefficient, $\gamma \left(H\right)\sim H^{0.47}$, is quantitatively close to the $\gamma \left(H\right)\sim H^{0.5}$ expected for nodal superconductivity or that can be qualitatively explained using a two-gap scenario. Furthermore, the positive curvature in $H_{c2}\left(T\right)$ near $T_c$ is qualitatively similar to that in the other two-gap superconductor ${\mathrm{MgB}}_2$.

Figure 1

(Color online) Temperature $\left(T\right)$ dependence of specific heat $\left(C\right)$ plotted as $C∕T$ vs $T^2$ at various magnetic fields for ${\mathrm{YNi}}_2{\mathrm{B}}_2\mathrm{C}$. The inset shows the deviation of the fit of $8\mathrm{T}$ data to $C_n\left(T\right)=A{T}^{-2}+{\gamma }_{n}T+\beta T^3+\alpha T^5$.

Figure 2

(Color online) A logarithmic plot of $C_e∕{\gamma }_n{T}_c$ vs $T_c∕T$ for ${\mathrm{YNi}}_2{\mathrm{B}}_2\mathrm{C}$ in its superconducting state. The solid line is the linear fit to the data for $T_c∕T$ between 4 $(T=3.7\mathrm{K})$ and 12 $(T=1.1\mathrm{K})$. The left-side inset shows the data fitted to the BCS model. In the right-side inset, the almost linear relation between $C_{\mathrm{e}}∕{\gamma }_{n}T$ and $(T∕T_c{)}^2$ indicates a nearly $T^3$ dependence of $C_e$.

Figure 3

(Color online) Various fitting of $C_e∕T$ vs $T$ using (a) line-node, (b) point-node, (c) $s+g$ wave, and (d) two-gap models. The quality of each fitting is shown in the respective inset, where DF represents the difference between the calculated values and actual data.

Figure 4

(Color online) Magnetic field dependence of electronic specific heat coefficient $\gamma \left(H\right)$ and the solid line representing $\gamma \left(H\right)\sim H^{0.47}$ is the best fit. The inset shows the determination of $\gamma \left(H\right)$ from the linear extrapolation of data for each field below $2\mathrm{K}$ in Fig. 1.

Figure 5

(Color online) Temperature dependence of upper critical field $H_{c2}$ $\left(T\right)$ of ${\mathrm{YNi}}_2{\mathrm{B}}_2\mathrm{C}$ obtained from Fig. 1. The crosses representing data from magnetization measurements provide a consistency check. The dashed line simply connects the data points, while the solid line is calculated from the WHH theory. The inset shows the determination of error bars.