Effect of a quartic anisotropy energy on the ‘‘spiral magnetic’’ coexistence state of superconductivity and ferromagnetism

Abstract

The effect of three types of ‘‘quartic’’ anisotropy energy (i.e., in the M4 term of the magnetic Ginzburg-Landau free energy) on the polarization of the ‘‘spiral magnetic’’ state of Blount and Varma is studied near the onset temperature. For a quartic anisotropy with uniaxial symmetry, we find continuous polarization transitions from circular to elliptical and then to linear as the strength of a uni-easy-axis anisotropy is increased. (No transition is found for the uni-hard-axis case.) If the quartic anisotropy has cubic symmetry, we find a discontinuous transition directly between circular and linear, without going through an elliptic stage, when the sign of the anisotropy energy is to favor the cubic axes. (The polarization stays circular at all strengths of the anisotropy energy if the sign of the latter is to favor the body diagonals.) Finally, we model the anisotropy in primitive tetragonal ErRh4B4 with a quadratic anisotropy giving a hard c axis, plus a quartic anisotropy in the basal plane with a square symmetry. A first-order polarization transition directly between circular and linear is also obtained for this case, when the quartic anisotropy favors the principal axes in the basal plane. This last case studied provides a plausible explanation for the linear polarization observed in the coexistence state of ErRh4B4. .AE

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