Radio-Frequency Method for Detecting Superconductivity Under High Pressure

We introduce a contactless technique for probing superconductivity and magnetic ordering transitions in micron-sized samples under extreme pressure. Utilizing a multistage Lenz lens system, directly sputtered onto diamond anvils, we realize a radio-frequency (RF, 50 kHz - 200 MHz) transformer with a sample of 50-100 $\mu$m in diameter, as its core. This configuration enables efficient transfer and focusing of an electromagnetic field within the diamond anvil cell's chamber. Consequently, the transmitted RF signal exhibits high sensitivity to variations in the sample's surface conductivity and magnetic permeability. We validate this method by determining the critical temperatures ($T_{\text{c}}$) of known superconductors, including NbTi, MgB$_2$, Hg-1223, Bi-2212, YBCO, and REBCO in various magnetic fields, as well as the magnetic ordering temperatures of Gd and Tb. Notably, we apply this technique to the LaH$_{10-x}$, CeH$_{9-10}$, and (La,Ce)H$_{10-12}$ superhydrides at a pressure of about 1-1.5 Mbar. The observed superconducting transitions in Ce and La superhydrides at 90-110 K and 215-242 K, respectively, correlate with the $T_{\text{c}}$'s determined via traditional electrical-resistance measurements. Moreover, we show how multiple repetitions of the RF experiment with the La-Ce superhydride make it possible to detect the increase in $T_{\text{c}}$ over time up to $\approx$ 260-270 K. This finding indicates the possibility of reaching a critical $T_{\text{c}}$ around 0$^\circ$C in the La-based superhydrides.