| A novel heterodyne detection system determines the frequency and temperature dependence of the Hall transport in single crystal, optimally doped Bi 2Sr2CaCu2O8+δ. The frequencies measured are in the mid-infrared and correspond to the spectral lines of a CO2 laser between 900 and 1110 cm−1. The measured temperature range is continuous and extends from 35 to 330K. The sample is an approximately 200 nm thick film peeled from a bulk crystal grown by G. D. Gu of the Department of Physics, Brookhaven National Laboratory, Upton, NY. Infrared conductivity data from measurements performed by J. J. Tu (also of the Department of Physics, Brookhaven National Laboratory) on other bulk crystals from this batch supplied the real and imaginary parts of σ xx which were used in the analysis to isolate the Hall angle, σ xy, RH.; The experimental system uses a photoelastic modulator (PEM) to phase modulate the y polarization channel of the beam transmitted by the sample. A mercury cadmium telluride optical detector then mixes the modulated polarization of the y channel with the unmodulated polarization of the x channel, forming sidebands, whose amplitudes are proportional to the real and imaginary parts of the Faraday angle. Maxwell's equations and the contributed values of σ xx are used to convert the complex Faraday angle to the Hall angle.; The results for 2212 BSCCO show a significant disconnect from the behavior of the Hall angle in the existing data for YBCO in the far-infrared. The existing far-infrared data indicate a negative value for the real part of the Hall angle above 250 cm−1. That of the current work is positive. The current work when analyzed using an extended Drude formalism results in a Hall frequency and scattering rate almost constant in frequency. The scattering increases linearly with temperature from ∼100 cm−1 at 100 K to 560 cm−1 at 330 K. Sum rules when evaluated using extrapolations of the data do not indicate a significant difference between the f-sum, the sum for Re(&thetas;H), and the sum for ω Im(σxy). |
