Magnetization properties and vortex phase diagram of Cu${}_x$TiSe${}_2$ single crystals

We have investigated the magnetization properties and flux dynamics of superconducting Cu${}_x$TiSe${}_2$ single crystals within a wide range of copper concentrations. We find that the superconducting anisotropy is low and independent on copper concentration ($\gamma \sim 1.7$), except in the case of strongly underdoped samples ($x\le 0.06$) that show a gradual increase in anisotropy to $\gamma \sim 1.9$. The vortex phase diagram in this material is characterized by a broad region of vortex liquid phase that is unusual for such a low-$T_c$ superconductor with low anisotropy. Below the irreversibility line the vortex solid state supports relatively low critical current densities as compared to the depairing current limit ($J_c/J_0\sim {10}^{-7}$). All this points out that local fluctuations in copper concentration have little effect on bulk pinning properties in this system.

Figure 1

Magnetization hysteresis loops for Cu${}_{0.058}$TiSe${}_2$ sample for $H\parallel ab$ (top) and $H\parallel c$ (bottom) at different temperatures. The arrows indicate the transitions from superconducting to normal state, defining $H_{c2}$ points.

Figure 2

(a) Temperature dependence of the upper critical field $H_{c2}$ determined from magnetization measurements for Cu${}_x$TiSe${}_2$ samples with five different copper concentrations. Open symbols are for $H\parallel c$ and filled symbols are for $H\parallel ab$. The inset shows the values of the superconducting anisotropy $\gamma =H_{c2}^{ab}\left(0\right)/H_{c2}^c\left(0\right)$ for different copper concentrations $x$. (b) Normalized upper critical field dependence on the reduced temperature for all the samples in (a) with both directions of the applied field. The full line is a fit to Eq. (2).

Figure 3

Dependence of the upper critical fields and superconducting transition temperature on the Cu concentration $x$ in Cu${}_x$TiSe${}_2$.

Figure 4

Magnetic field dependence of the superconducting critical current density in Cu${}_{0.058}$TiSe${}_2$ for applied field $H\parallel c$ at $T=1.8$, 1.9, 2.0, 2.1, 2.2, and 2.3 K (upper panel) and for $H\parallel ab$ at $T=1.8$, 2.0, and 2.2 K (lower panel). The curves were fit with Eq. (3) and temperature dependence of parameters $J_{c0}$ and $H_0$ is shown in the inset.

Figure 5

Vortex phase diagram of Cu${}_x$TiSe${}_2$ for magnetic field applied $H\parallel c$ (upper panel) and $\parallel ab$ (lower panel).