Composite to Tilted Vortex Lattice Transition in ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+\delta }$ in Oblique Fields

Precision measurements of the vortex phase diagram in single crystals of the layered superconductor ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+\delta }$ in oblique magnetic fields confirm the existence of a second phase transition, in addition to the usual first-order vortex-lattice melting line $H_m(T)$. The transition has a strong first-order character, is accompanied by strong hysteresis, and intersects the melting line in a tricritical point ($H_m^{\perp }$, $H_{\mathrm{cr}}^{\parallel }$). Its field dependence and the changing character of the melting line at the tricritical point strongly suggest that the ground state for magnetic fields closely aligned with the superconducting layers is a lattice of uniformly tilted vortex lines.

Figure 1

(a) dc local magnetization loops recorded on an as-grown ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+\delta }$ single crystal ($T_c=88\mathrm{K}$) at 75 K, as function of the magnetic field component $H^{\perp }$ perpendicular to the superconducting layers, with the in-plane field $H_{\parallel }$ held constant. The inset shows a magnified view of the discontinuity at the vortex melting transition in $H^{\parallel }=0$. (b) The in-phase (screening) component of the ac response of the same crystal, recorded under the same conditions, with an ac magnetic field of amplitude $h_{\mathrm{ac}}=0.8\mathrm{Oe}$ and frequency $f=11\mathrm{Hz}$ applied along the $c$ axis. The melting transition shows up as a paramagnetic peak (see inset), the transition from combined to tilted vortex lattice is indicated by arrows. The ac response is plotted as the transmittivity $T^{\prime }\equiv [B^{\prime }(f,T)-B(f,T\ll T_c)]/[B(f,T>T_c)-B(f,T\ll T_c)]$.

Figure 2

Transmittivity $T^{\prime }$ of the same crystal as in Fig. 1, recorded at $T=70\mathrm{K}$ and constant $H^{\perp }=58\mathrm{Oe}$, as a function of $H^{\parallel }$ for various frequencies $f$ and amplitudes $h_{\mathrm{ac}}$ of the ac ripple field. A marked hysteresis of the ac screening is observed. This hysteresis disappears when $h_{\mathrm{ac}}$ is increased.

Figure 3

Two field-component vortex-lattice phase diagram, with the first-order melting transition $H_m^{\perp }$ (∘) determined from the paramagnetic peak in $T^{\prime }$, and the first-order transition to the tilted PV lattice at $B_t$ (•), determined from the “glitch” in $T^{\prime }$ [Fig. 1b]. The dashed line is a fit to the composite-to-tilted lattice transition, Eq. (2) with $C=0.030$; the continuous line is a fit of the high-field portion of the vortex-lattice melting line to Eq. (1).

Figure 4

Temperature dependence of the apparent anisotropy ${\gamma }_{\mathrm{eff}}$ extracted from the fits of the melting line to Eq. (1). The drawn line shows a fit to Eq. (4) with intrinsic $\gamma =500$.