Application of a small oscillating magnetic field to reveal the peak effect in the resistivity of ${\text{Nb}}_3\text{Sn}$

By the application of a small oscillating magnetic field parallel to the main magnetic field and perpendicular to the transport current, we were able to unveil the peak effect in the resistivity data of ${\text{Nb}}_3\text{Sn}$ near the upper critical field $H_{c2}$. We investigated the dependence of this effect on the frequency and the amplitude of the oscillating magnetic field and show that the used technique can be more sensitive to detect the peak effect in a certain range of temperatures and magnetic fields than conventional magnetization measurements.

Figure 1

Schematic drawing of the configurations (a) $h_{ac}\parallel H$ plus a transport current $I_m$; (b) $h_{ac}\perp H$, with no transport current. The sheet current $J_c$ generates the diamagnetic response of the superconductor.

Figure 2

(a) Dc magnetization-hysteresis curve for $T=13\text{K}$. (b) Parts of the dc magnetization hysteresis curves for different temperatures (from left to right) : $T=15.5\text{K},15\text{K},14.5\text{K},14\text{K},13.5\text{K},13\text{K},12.5\text{K},12\text{K}$.

Figure 3

(Color online) $I_c\left(B\right)$ data as obtained from the magnetization measurements shown in Figs. 2.

Figure 4

(Color online) Resistance $R\left(T\right)$ of a ${\text{Nb}}_3\text{Sn}$ single crystal for different magnetic fields $H\parallel c$, measured with a transport current $I_m=5\text{mA}$. The temperature was swept downwards with $dT/dt=-50\text{mK}/\text{min}$. (a) Without an oscillating magnetic field, i.e., $h_{ac}=0$. (b) With an oscillating magnetic field $\left(f=1\text{kHz},{\mu }_0{h}_{ac}=0.58\text{mT}\right)$ superimposed.

Figure 5

(Color online) Resistance $R\left(T\right)$ of a ${\text{Nb}}_3\text{Sn}$ single crystal for different magnetic fields, measured with $I_m=0.5\text{mA}$. (a) Without an oscillating magnetic field, i.e., $h_{ac}=0$. (b) With an oscillating magnetic field ($f=1\text{kHz}$, ${\mu }_0{h}_{ac}=0.58\text{mT}$) superimposed.

Figure 6

(Color online) Temperature sweeps $R\left(T\right)$ for ${\mu }_{0}H=3\text{T}$, fixed $h_{ac}=0.29\text{mT}$, and $I_m=5\text{mA}$ but different “shaking” frequencies $f$.

Figure 7

(Color online) Temperature sweeps $R\left(T\right)$ for ${\mu }_{0}H=3\text{T}$, fixed frequency $f=1\text{kHz}$, $I_m=5\text{mA}$, but different amplitudes of the oscillating magnetic field $h_{ac}$.

Figure 8

Resistance $R$ for different amplitudes of the oscillating magnetic field $h_{ac}$ in ${\mu }_{0}H=3\text{T}$, $T=15.8\text{K}$, $I_m=5\text{mA}$, and fixed frequency $f=1\text{kHz}$.

Figure 9

(Color online) Temperature dependence of the resistance $R\left(T\right)$ for a fixed external magnetic field ${\mu }_{0}H=3\text{T}$, with an oscillating magnetic field $\left(f=1\text{kHz},{\mu }_0{h}_{ac}=0.58\text{mT}\right)$ superimposed and $I_m=5\text{mA}$.

Figure 10

(Color online) Part of the magnetic phase diagram of the ${\text{Nb}}_3\text{Sn}$ single crystal as derived from the data shown in Figs. 2, 4. Filled circles : upper critical field; open circles : $T_p$; open squares : center of the peak-effect region from $M\left(H\right)$ data. Inset : magnetic-field dependence of the width of the peak-effect region $\Delta H$. Circles represent data as deduced from the resistivity measurements of Fig. 4b, while squares stand for data extracted from the dc magnetization measurements shown in Figs. 2.