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The spin-wave spectrum of the antiferromagnet with the garnet structure has been studied by inelastic neutron scattering on the triple-axis spectrometers IN12 and IN14 at ILL. Magnon dispersion curves were measured along and directions up to energies of 0.3 THz. The spin-wave symmetry analysis, which reduced the number of independent exchange parameters to six, was performed to ensure correct description of the spin-wave branches. As determined by the fitting, five of the parameters are statistically significant and have been found to be , and . This quite unusual sequence of exchange parameters clearly demonstrates the importance of the superexchange chain geometry.

In terms of the generalized Bardeen-Cooper-Schrieffer model for a superconductor with degenerate orbital electron states, we derive a Ginzburg-Landau energy functional with a microscopic deciphering of the coefficients involved. The superconducting order parameter is separated out by expanding the wave function of a Cooper pair in the basis functions of crystal point group irreducible representations. It is shown that a many-component superconducting order parameter may arise from the degeneracy of the electron states on the Fermi surface—either owing to the degeneracy of the orbital states or owing to the degeneracy over the arms of the star, or as a result of both degeneracies simultaneously. Allowance for the orbital degeneracy extends the physical basis on which superconducting modes are realized and perturbs the classification of singlet and triplet states according to even and odd point group representations. It is also shown that allowance for the orbital degeneracy may alter the conditions for the superconducting gap to go to zero in individual Fermi surface points or lines as compared with the conditions that follow from arm degeneracy alone.

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