Ferromagnetic Curie Temperature in Cubic Lattices with Next-Nearest-Neighbor Interaction

Abstract:

The Curie temperature for a Heisenberg ferromagnet with nearest-neighbor interaction JT and nextnearest-neighbor interaction J2 is calculated by a Green's-function technique. The J2/J& dependence is found to be significantly different from that given by molecular field theory. The Curie temperature approaches zero when J2/J& ~ —1 in a face-centered cubic magnetic lattice, and when J2/J1 ~0.6799 in a bodycentered cubic lattice. The face-centered cubic magnetic lattice is relevant to the chalcogenides of europium.

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 l. INTRODUCTION ~

  While most of the present theories of ferromagnetism and antiferromagnetism are based on the assumption of the nearest-neighbor exchange interaction only, the recent studies' ' of the magnetic properties of the europium chalcogenides indicate that in addition to the nearest-neighbor exchange the next-nearest-neighbor interaction is also appreciable. This picture has now been analyzed in the spin-wave theory. ' However, the spin-wave theory adequately describes the behavior of magnetic systems only in the limit of low temperatures. Close to the transition temperature, the spin-wave picture becomes inappropriate' and therefore other approximate theories, such as the Weiss molecular field theory and the various cluster theories, are usually employed. The results of these theories are at best qualitatively satisfactory while sometimes they can be quite misleading. '" The most reliable estimates of the critical properties are, of course, those obtained by extrapolating the exact high-temperature series-expansion results to the transition region. ' ' This, however, is a very tedious procedure and the only systems adequately analyzed so far are those including a single exchange parameter. 8