Radio-frequency magnetic response of vortex lattices undergoing structural transformations in superconducting borocarbide crystals

We report a clear anomaly in the rf response of tunnel-diode resonator measured in rare earth nickel borocarbide crystals with dc applied magnetic field along the crystallographic $c$ axis. We associate the anomaly in the dynamic magnetic susceptibility $\chi$ with a structural transition in the vortex lattice. $\chi$ is sensitive to the Campbell penetration depth ${\lambda }_C$ of the rf perturbation into the mixed state. ${\lambda }_C$ depends on the vortex lattice elastic moduli, which in turn depend on the vortex lattice structure. Using this technique, we map the high-field transition line for the square-to-rhombic transformation of the vortex lattice and provide a qualitative argument in favor of thermal vortex fluctuations as a major cause driving the transition.

Figure 1

(Color online) $\chi \left(T\right)$ of Y1221 measured in fixed fields with $1\mathrm{kOe}$ step. The anomaly is clearly seen in the upper left corner. Inset: $\chi \left(H\right)$ scans showing the same anomaly.

Figure 2

(Color online) $\chi \left(T\right)$ of Y1221 measured in $6.2\mathrm{T}$. Open symbols, FC-W; solid line, FC-C as described in the text. Inset: The dc magnetization $M\left(H\right)$ measured at $5\mathrm{K}$. Indicated are the irreversibility field, $H_{\mathrm{irr}}$, and approximate location of the anomaly, $H_{◻}$.

Figure 3

(Color online) Selected regions of $\chi (T,H)$ curves showing VL transition in Y1221 (top panel) and Lu1221 (bottom panel). At each field, the characteristic temperatures corresponding to $H_{c2}\left(T\right)$ line as well as $H_{◻}\left(T\right)$ are indicated by arrows at the lower frame.

Figure 4

(Color online) Phase diagram obtained from measurements of $H_{c2}\left(T\right)$ and $H_{◻}\left(T\right)$. The inset shows the same data in reduced units. Also shown are the results of Ref. 31 and the low-field results of Ref. 15.

Figure 5

(Color online) Relative change of $\chi$ at the anomaly in Y1221 as a function of $H{H}_{c2}\left(T\right)$. The solid line is a fit to Eq. (9). Inset: The definition of the anomaly size, $4\pi \Delta \chi$.