In-plane next-nearest-neighbour exchange coupling in uniaxial metamagnets: its influence on the low-temperature self-energy

Abstract

The ladder approximation is performed for metamagnets with uniaxial and exchange anisotropy and the following exchange couplings: in-plane nearest-neighbour ferromagnetic coupling J1, in-plane, next-nearest-neighbour antiferromagnetic coupling J2, and small interplane antiferromagnetic coupling J'. Taking J2 into account encounters non-trivial difficulties but the authors have tackled this problem because a suitable lattice-dependent value of J2=J2 causes the long-wavelength magnon dispersion curve to become a quartic power of the wavevector instead of a quadratic one, so one can expect dramatic consequences. In effect this is the case: the results the authors obtain for FeBr2, which has just the convenient ratio J2/J1 to fit the situation described above, give weak renormalisation and damping for the uniform mode, while for FeCl2 dramatic variances, at least from a quantitative point of view, do not arise with respect to previous approaches, where J2 was neglected. Such a result cannot be inferred on the basis of a finite-order perturbation theory which, on the contrary, would suggest a heavier renormalisation when the dispersion curve is more flat for small wavevectors, as in FeBr2.