We developed far-IR spectroscopic ellipsometer at the U4IR beamline of the National Synchrotron Light Source in Brookhaven National Laboratory. This ellipsometer is able to measure both, rotating analyzer and full-Mueller matrix spectra using rotating retarders, and wire-grid linear polarizers. We utilize exceptional brightness of synchrotron radiation in the broad spectral range between about 20 and 4000 cm(-1). Fourier-transform infrared (FT-IR) spectrometer is used for multi-wavelength data acquisition. The sample stage has temperature variation between 4.2 and 450 K, wide range of θ-2θ angular rotation, χ tilt angle adjustment, and X-Y-Z translation. A LabVIEW-based software controls the motors, sample temperature, and FT-IR spectrometer and also allows to run fully automated experiments with pre-programmed measurement schedules. Data analysis is based on Berreman's 4 × 4 propagation matrix formalism to calculate the Mueller matrix parameters of anisotropic samples with magnetic permeability μ ≠ 1. A nonlinear regression of the rotating analyzer ellipsometry and∕or Mueller matrix (MM) spectra, which are usually acquired at variable angles of incidence and sample crystallographic orientations, allows extraction of dielectric constant and magnetic permeability tensors for bulk and thin-film samples. Applications of this ellipsometer setup for multiferroic and ferrimagnetic materials with μ ≠ 1 are illustrated with experimental results and simulations for TbMnO3 and Dy3Fe5O12 single crystals. We demonstrate how magnetic and electric dipoles, such as magnons and phonons, can be distinguished from a single MM measurement without adducing any modeling arguments. The parameters of magnetoelectric components of electromagnon excitations are determined using MM spectra of TbMnO3.

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Forward models for the Mueller Matrix (MM) components of materials with relative magnetic permeability tensor 1 µ ≠ are studied. 4 4 × matrix formalism is employed to produce general solutions for the complex reflection coefficients and MMs of dielectric-magnetic materials having arbitrary crystal symmetry and arbitrary laboratory orientation. For certain orientations of materials with simultaneously diagonalizable ε and µ tensors (with coincident principal axes), analytic solutions to the Berreman equation are available. For the single layer thin film configuration of these materials, analytic formulas for the complex reflection and transmission coefficients are derived for orthorhombic or higher crystal symmetry. The separation of the magnetic and dielectric contributions to the optical properties of a material are demonstrated using measurements of the MM at varying angles of incidence.

Far-infrared spectra of ferrimagnetic Dy 3 Fe 5 O 12 single crystals have been studied in the spectral range between 12 and 700 cm -1 and in a wide temperature range between 5 K and 300 K using transmission spectroscopy and rotating analyzer ellipsometry. In the temperature range below T C =16 K for the magnetic ordering of Dy 3+ spins, a number of ligand field (LF) and Kaplan-Kittel (KK) exchange resonance modes have been found. Temperature dependences of their frequencies allowed us to estimate the ratio between the Fe−Dy and Dy−Dy exchange constants.We found that variation of the oscillator strength of the KK modes correlates with the magnetic field induced changes of magnetic permeability. The low temperature peak in the static value of the dielectric function at T C =16 K may be related to the observed temperature-induced variation of the oscillator strength of the optical phonons.

We have measured the in-phase component of the low-frequency ac impedance of the dc current-induced intermediate state in indium-lead alloywires. The specimens were mounted in a specific configuration that allowed a proper calculation of their dynamic resistances following the theory developed by Gauthier and Rochon, which is based on London's theory of the intermediate state. The theoretical values are considerably larger than our measurements, particularly near the critical current. We have modified the Gauthier-Rochon theory, to a first approximation, to take account of the Baird-Mukherjee model of the intermediate state and we find reasonably good agreement between the modified theoretical values and our observations.