The "LC resonator" method was greatly improved for high resolution measurements of magnetic-field penetration depth, λ, of radio frequency into thin films or plate-like high-Tc superconductors by replacing a solenoid testing coil by an open-flat coil (OFC) driven by a tunnel diode oscillator of a low power and a highly stable frequency. The assembled OFC magnetometer showed new technical advantages such as simplicity, convenience, and high resolution of Δλ ∼ 1 - 3 Å (Δλ/λ ∼ 10-6), ability of reliable operation in wide ranges of temperature (4.2-300 K) and magnetic field (up to 12 T), etc. This enables us to use it for studying peculiarities of the vortex dynamics with weak signal in small sample volume high-Tc cuprates. As a first test of the assembled 23 MHz measuring setup, the temperature dependence of the upper critical field, HC2(T), is determined from the magnetic transition curves at different temperatures for Y1Ba2Cu3O7 - δ thin-film ring. The HC2(T) data obey the formula: [1-(T/Tc)2]β with β = 1.22 ± 0.03 at temperatures close to Tc. The methods to increase the resolution of the OFC magnetometer by several orders of magnitude are suggested. It is believed to be feasible to reach the level of detection of the suppression of superconductivity in samples of size of a few micrometers by penetration of a few flux quanta by decreasing the size of the open-flat coil.
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