Second ac screening step as a probe for the first-order melting transition in layered vortex matter at intermediate temperatures

TL;DR

The paper tackles the challenge of locating the first-order melting transition in highly anisotropic layered vortex matter within an intermediate temperature range where standard dc and ac magnetometry lose sensitivity. It introduces a two-step ac screening protocol and a remote, crossed transmittivity measurement to probe nonlocal responses, revealing a second screening step whose temperature is independent of the excitation frequency and amplitude and aligns with the first-order transition line. The findings show that the second screening step serves as a robust proxy for the first-order transition in the intermediate regime, and that remote measurements echo this behavior, indicating nonlocal propagation of elasticity and rigidity across the vortex lattice. These results enable more reliable mapping of the first-order transition in Bi-2212 and reveal nonlocal coupling mechanisms that underlie rigidity transfer in vortex matter.

Abstract

We present a new probe for the first-order transition for layered vortex matter: A second step in the screening of an ac field that is independent of the frequency and amplitude of the excitation. This second step is observed in the intermediate temperature and field ranges where detecting the jump in induction associated with the transition is rather elusive with standard magnetometry techniques. We observe this second step following a novel experimental protocol where the screening of a locally-generated ac field is remotely detected in another region of the sample. The coincidence of the typical temperature of the second step in direct and remote measurements strongly supports this feature is a probe of the first-order transition. This nonlocal effect detected at distances of thousands of vortex lattice spacings away indicates that a very efficient mechanism propagates the change in rigidity of the structure from the more (liquid) to the less (solid) symmetric vortex phases.

Figures (7)

• Figure 1: (a) Pair of Hall sensors and on-chip coils (1 and 2) used for performing Hall magnetometry measurements. The dc field $H$, as well as the $h_{\rm ac}$ excitation, are applied perpendicular to the plane of the chips where lay the sensors. In the global excitation mode, $h_{\rm ac}$ is generated by a coil external to the chips (see blue lines on the schematics), while in the local excitation mode $h_{\rm ac}$ is generated by one of the smaller on-chip coils. Insert: Centered inside each one of the on-chip coils there is a Hall probe with a $9\times9$$\mu$m$^2$ detection area, that measures the stray field of the sample. (b) Large Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ single crystal studied, mounted on top of the two probes with its $c$-axis parallel to the applied fields.
• Figure 2: Typical dc magnetization loops of vortex matter in Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ measured by local Hall magnetometry at different temperature ranges. (a) In the high-temperature range, $T>60$ K, the reversible magnetization presents a sub-Gauss jump in induction, $\Delta B$, a manifestation of the first-order vortex melting transition. This jump is zoomed in the insert for the negative $H$ branches. (b) In the low temperature range, $T<30$ K, irreversibility is important and the magnetization loops widen. The order-disorder transition manifests as a local increase in the widening of the loop indicated as $H_{\rm SP}$. (c) Loop at intermediate temperatures for the regular and dithering measurement protocols (in-plane alternating pulsed field of 30 Oe during 3 msec, 0 during 7 msec and -30 Oe during 3 msec, repeated cyclically during the whole measurement). In the latter case hysteresis is suppressed and the magnetization jump associated with the first-order transition is made evident also in the intermediate temperature range.
• Figure 3: ac transmittivity $T'$ as a function of temperature in the low-field range. The so-called paramagnetic peak entailing values of $T'>1$ is a signature of the jump in $B$ produced at the first-order melting transition. The measurements were performed at the dc fields indicated in the legend, using an ac ripple field of 0.4 Oe$_{\rm rms}$ and 17.1 Hz.
• Figure 4: Transmittivity measurements in Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ on decreasing temperature following a field-cooling process at a field $H$. (a) Main: data for $H$ in the high-field range from 150 to 300 Oe showing a first and a second screening response. Insert: Comparison between data obtained at high and low fields. All data in this panel come from measurements performed at a ripple field of 17.1 Hz and 0.4 Oe$_{\rm rms}$. (b) Transmittivity when field-cooling at 200 Oe applying a ripple field with various frequencies and 0.4 Oe$_{\rm rms}$. The temperature location of the first screening shifts with frequency while that of the second screening remains unchanged.
• Figure 5: Normalized third harmonic signal $|T_{\rm{h3}}|$ (left axis) and transmittivity (right log-scale axis) as a function of temperature, recorded simultaneously while following a field-cooling protocol. Data for an applied dc field of 300 Oe and a ripple field of 17.1 Hz and 0.4 Oe rms. The midpoints of both screening steps are indicated with red arrows. The midpoint in the first screening in transmittivity coincides with the location of the larger peak in $|T_{\rm{h3}}|$ while the midpoint in the second screening is within a faint and broad peak registered at smaller temperatures. A horizontal dashed blue line indicates the upper noise level in the third harmonic signal. The irreversibility temperature $T_{\rm irr}$ at which the magnetic signal becomes non-linear is estimated from the onset of $|T_{\rm{h3}}|$ above the upper noise level on cooling, see blue arrow.