Evidence from experimental nuclear magnetic resonance data concerning possible fundamental inadequacies of the conventional spin-wave theory (abstract)

Abstract

In the case of simple ferromagnets and antiferromagnets, the nuclear magnetic resonance data which had been used in the past to validate the applicability of conventional spin-wave theory, is shown to exhibit a simple pattern of functional forms, previously unrecognized. Special focus is given to the data of Narath et al. and deWijn et al. In all known cases (with minor qualifications) such data obey the equation ν=A(1−BT c) for the ‘‘low-temperature’’ region 0<ΔM≲10%. The experimentally found one-term power-law temperature dependences can be obtained in all cases from the first-term Heisenberg prediction, modified in a simple way: the exponent C=D/2d for ferromagnets and C=(D−1)/d for antiferromagnets, where d=1−( 1/2 )n, and n=1, 2, and 3 for 3D cases, and n=1 and 2 for 2D cases. (By contrast n=0, for conventional theory). In antiferromagnets the deviations from the simple power-law behaviors close to T=0 occur only below T≲Tgap, implying a far weaker influence of energy-gap effects than expected in conventional theory. The coefficients B (when T represents the reduced temperature) range between 0.3 and 0.5, clustering near the latter in most cases. A simple and coherent small-k spin-wave scheme can be constructed1 which reproduces the correct temperature dependences, if one assumes that the energies at the bottom of the spin-wave magnon spectrum are ‘‘renormalized’’ by a set of k-dependent (but temperature independent) renormalization factors in the following manner: for ferromagnets ωHeis(k), and for antiferromagnets ω2Heis(k) Tgap → 0), should be divided by k, k 1/2 , and k 1/4 for the 3D cases, and by k and k 1/2 for the 2D cases. Note in particular that such a renormalization gives a convergent result for ΔM for the 2D cases with no anisotropy forces, contrary to conventional theory (but in accord with experimental observations of 2D magnetic ordering). As is well known, non-integral exponents in the dispersion relations occur when the exchange interactions are long range. However, the above temperature dependences for the case of the antiferromagnets are inconsistent with such a possibility. Non-integral exponents in ω can also occur when there is a coupling of a long- and a short-range interaction (e.g., dipolar and exchange, for the 2D ferromagnet2). However, no known couplings reproduce the above effects correctly. Thus, the physical origins of the ‘‘renormalizations’’ still remain unidentified. Some difficulties may exist with regard to extending the above scheme to predict correctly the specific heats and susceptibilities of antiferromagnets, but the main difficulty so far has been in obtaining suitable data in numerical form.