Microwave measurement of energy gap and penetration depth of MgB₂ thin film

Using a dielectric resonator technique the magnetic field penetration depth λ and the energy gap Δ of two MgB₂ thin films were determined by measuring changes of resonance frequency with temperature. The exponential temperature dependence of λ is revealed at low temperatures (T < T_c/4, T_c is the critical temperature of the thin film). It indicates that a finite energy gap exists for thermal excitation of quasiparticles. From our measurements values of Δ/kT_c = 1.25 and λ₀ = 290 nm for sample A and Δ/kT_c = 1.20 and λ₀ = 160 nm for sample B give the best fit to the experimental results. The corresponding values for the energy gap Δ are 3.4 meV for sample A and 3.8 meV for sample B. In the high temperature region (T > T_c/2) the temperature dependence of λ can be well fitted by λ₀/[1-(T/T_c)²]^1/2. Our results strongly support the absence of nodes in the gap and a possible multigap scenario.