Evolution of ground state and upper critical field in $R_{1-x}{\text{Gd}}_x{\text{Ni}}_2{\text{B}}_2\text{C}$ $\left(R=\text{Lu},\text{Y}\right)$: Coexistence of superconductivity and spin-glass state

We report effects of local magnetic moment, ${\text{Gd}}^{3+}$, doping $\left(x\lesssim 0.3\right)$ on superconducting and magnetic properties of the closely related ${\text{Lu}}_{1-x}{\text{Gd}}_x{\text{Ni}}_2{\text{B}}_2\text{C}$ and ${\text{Y}}_{1-x}{\text{Gd}}_x{\text{Ni}}_2{\text{B}}_2\text{C}$ series. The superconducting transition temperature decreases and the heat capacity jump associated with it drops rapidly with Gd doping; qualitative changes with doping are also observed in the temperature-dependent upper critical field behavior, and a region of coexistence of superconductivity and spin-glass state is delineated on the $x\text{−}T$ phase diagram. The evolution of superconducting properties can be understood within Abrikosov-Gor’kov theory of magnetic impurities in superconductors taking into account the paramagnetic effect on upper critical field with additional contributions particular for the family under study.

Figure 1

(Color online) Gd concentration evaluated from a Curie-Weiss fit of the high-temperature susceptibility vs nominal Gd concentration in $R_{1-x}{\text{Gd}}_x{\text{Ni}}_2{\text{B}}_2\text{C}$, $R=\text{Lu},\text{Y}$. Dashed lines are linear fits with intercept fixed to zero. (See text for details.)

Figure 2

(Color online) Normalized resistivity, $\rho /{\rho }_{300\text{K}}$ for (a) ${\text{Lu}}_{1-x}{\text{Gd}}_x{\text{Ni}}_2{\text{B}}_2\text{C}$ $\left(x=0,0.055,0.13,0.19,0.27\right)$ and (b) ${\text{Y}}_{1-x}{\text{Gd}}_x{\text{Ni}}_2{\text{B}}_2\text{C}$ $\left(x=0,0.10,0.14,0.21,0.26,0.30\right)$. Arrows show the direction of increasing $x$, insets: low-temperature part of the data. Panel (c): normalized (to the values for the parent compounds) $T_c$ as a function of Gd concentration $x$ for $R_{1-x}{\text{Gd}}_x{\text{Ni}}_2{\text{B}}_2\text{C}$, $R=\text{Lu},\text{Y}$; data for $\text{Lu}{\left({\text{Ni}}_{1-x}{\text{Co}}_x\right)}_2{\text{B}}_2\text{C}$ from Ref. 34 are included for comparison. Inset: RRR vs $x$ for the same three series.

Figure 3

(Color online) Temperature-dependent heat capacity for (a) ${\text{Lu}}_{1-x}{\text{Gd}}_x{\text{Ni}}_2{\text{B}}_2\text{C}$ $\left(x=0,0.055,0.13,0.19,0.27,0.33\right)$ and (b) ${\text{Y}}_{1-x}{\text{Gd}}_x{\text{Ni}}_2{\text{B}}_2\text{C}$ $\left(x=0,0.10,0.14,0.21,0.26,0.30\right)$. Arrows show examples of how $T_{max}$ and $T_c$ are determined.

Figure 4

(Color online) Normalized jump in heat capacity at $T_c$ vs normalized $T_c$ for the ${\text{Lu}}_{1-x}{\text{Gd}}_x{\text{Ni}}_2{\text{B}}_2\text{C}$ and ${\text{Y}}_{1-x}{\text{Gd}}_x{\text{Ni}}_2{\text{B}}_2\text{C}$ series (for pure ${\text{LuNi}}_2{\text{B}}_2\text{C}$ and ${\text{YNi}}_2{\text{B}}_2\text{C}$ $\Delta C_p$ at $T_c$ values are $665\text{mJ}/\text{mol}\text{K}$ and $460\text{mJ}/\text{mol}\text{K}$, respectively). Dashed lines correspond to BCS law of corresponding states, Abrikosov-Gor’kov magnetic scattering and $\gamma =0$ (strong spin-dependent scattering) limit of Shiba’s theory (Ref. 43). See text for more details.

Figure 5

(Color online) $T\text{−}x$ phase diagram for the ${\text{Lu}}_{1-x}{\text{Gd}}_x{\text{Ni}}_2{\text{B}}_2\text{C}$ (filled and partially filled symbols) and ${\text{Y}}_{1-x}{\text{Gd}}_x{\text{Ni}}_2{\text{B}}_2\text{C}$ (open symbols) series. Symbols: squares $T_c$ from onset and offset of the resistive transitions; circles—$T_c$ from heat capacity; triangles—$T_{max}$ from heat capacity. Dashed lines are guides for the eyes. Dotted-dashed line approximates spin-glass phase (crossover) line.

Figure 6

(Color online) (a) Examples of magnetic field-dependent resistance of ${\text{Lu}}_{0.81}{\text{Gd}}_{0.19}{\text{Ni}}_2{\text{B}}_2\text{C}$ single crystal measured at several constant temperatures for $H\parallel c$. Onset and offset criteria of superconducting transition are illustrated. (b) Examples of temperature-dependent resistance of the same sample measured in different applied magnetic fields. (c) Temperature-dependent upper critical field of ${\text{Lu}}_{0.81}{\text{Gd}}_{0.19}{\text{Ni}}_2{\text{B}}_2\text{C}$ for $H\parallel c$. Circles—onset, triangles—offset, open symbols are from $R\left(T\right){\mid }_H$ scans, filled symbols are from $R\left(H\right){\mid }_T$ scans.

Figure 7

(Color online) Temperature-dependent upper critical field $\left(H\parallel c\right)$ for (a) ${\text{Lu}}_{1-x}{\text{Gd}}_x{\text{Ni}}_2{\text{B}}_2\text{C}$ $\left(x=0,0.055,0.13,0.19\right)$ and (b) ${\text{Y}}_{1-x}{\text{Gd}}_x{\text{Ni}}_2{\text{B}}_2\text{C}$ $\left(x=0,0.10,0.14,0.21,0.26\right)$. Circles and triangles correspond to the onset and offset criteria, respectively. Insets show the same data on a semilog scale.

Figure 8

(Color online) Normalized to $H_{c2}\left(T=0\right)$ temperature-dependent upper critical field for (a) ${\text{Lu}}_{1-x}{\text{Gd}}_x{\text{Ni}}_2{\text{B}}_2\text{C}$ $\left(x=0,0.055,0.13,0.19\right)$ and (b) ${\text{Y}}_{1-x}{\text{Gd}}_x{\text{Ni}}_2{\text{B}}_2\text{C}$ $\left(x=0,0.10,0.14,0.21,0.26\right)$ as a function of normalized to $T_c\left(H=0\right)$ temperature. Data for $H\parallel c$ obtained using onset criteria are shown.

Figure 9

(Color online) $d{H}_{c2}/dT$ in the $H\to 0$ limit as a function of $T_c$ in zero field for the ${\text{Lu}}_{1-x}{\text{Gd}}_x{\text{Ni}}_2{\text{B}}_2\text{C}$ (circles) and ${\text{Y}}_{1-x}{\text{Gd}}_x{\text{Ni}}_2{\text{B}}_2\text{C}$ (triangles) series. Dashed line is a guide to the eyes.