Peak Effect and Dynamic Melting of Vortex Matter in ${\mathrm{NbSe}}_2$ Crystals

We present a mode locking (ML) phenomenon of vortex matter observed around the peak effect regime of $2\mathrm{H}\mathrm{\text{−}}{\mathrm{NbSe}}_2$ pure single crystals. The ML features allow us not only to trace how the shear rigidity of driven vortices persists on approaching the second critical field, but also to demonstrate a dynamic melting transition of driven vortices at a given velocity. We observe the velocity dependent melting signatures in the peak effect regime, which reveal a crossover between the disorder-induced transition at small velocity and the thermally induced transition at large velocity. This uncovers the relationship between the peak effect and the thermal melting.

Figure 1

(a) Peak anomaly of critical current $I_c$ measured by varying magnetic field $H$ at 4.2 K. The peak field $H_p$ is denoted by an arrow. A dotted line marks the dynamic melting field measured at high velocity. The inset displays how differential resistance $R_d$ measured at a large dc current of 30 mA $(\gg I_c)$ depends on field. The definition of the second critical field $H_{c2}$ is given in text. (b) Phase diagram of ${\mathrm{NbSe}}_2$. Both $H_{c2}$ and $H_p$ are plotted. See text for arrows.

Figure 2

ML phenomenon of driven vortices. (a) Differential conductance ($dI/dV$)-voltage ($V$) curves measured in 1.90 T with superimposing 3 MHz rf current of various amplitudes. For clarity, the origin for each curve is shifted vertically. ML conditions are denoted. (b) Frequency, $f$, dependence of ML voltages for the fundamental and higher harmonics. (c) rf current $I_{\mathrm{rf}}$ vs the fundamental ML current width $\Delta I$ obtained by integrating the fundamental ML peak shown in (a) with respect to the flux-flow baseline (see the inset). See text for a broken curve. (d) $\Delta I$ for 3 MHz vs $I_{\mathrm{rf}}$ observed in 1.995 T between $H^{*}$ and $H_{\mathrm{on}}$.

Figure 3

(a) Magnetic field dependence of the fundamental ML voltage $V_{1/1}$ measured with superimposing a 7 MHz rf current. A solid curve represents the fundamental ML-voltage condition (see text). (b) Differential conductance curves measured with a 7 MHz rf current in fields from 1.96 T to 2.02 T by a constant field step of 0.01 T. For clarity the origin for each curve is vertically shifted.

Figure 4

(a) Magnetic field vs the maximized fundamental ML current width $\Delta I_{\max }$ for 3 and 9 MHz. For clarity, the origin for 9 MHz data is shifted vertically. Onset $H_{\mathrm{on}}$ and vanishing $H^{*}$ fields are indicated by arrows. Their velocity dependencies are given in (b). A broken line represents the saturation field. See text for solid and dotted curves.