Spin Waves in Doped Manganites

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In our study1 3 of the DE model in one dimension, we found that while the SWD differs drastically from Heisenberg shape (HS) for some carrier concentrations, x, there is a range where the shapes are very close. The example La1 xCax MnO3 defines x. Since this range included the value x = 0.3, we offered our result as an explanation for the surprising experimental finding2 that the SWD shape for La. 7 Pb. 3MnO3 at low temperature is HS throughout the Brillouin zone. (We define HS as that of the nearest-neighbor Heisenberg model.) But quite recently there appeared an experimental study6 of Pr. 6 3Sr. 3 7MnO3 that found SWD of drastically different shape from Heisenberg, in contrast to the situation for the La-Pb compound. And since our calculations within the DE model also showed essentially Heisenberg shape for x=.37, we are forced to ask what is the source of the observed shapes. The change in shape of the SWD accompanies changes in dopant and rare earth ions. There is evidence that magnetic properties are correlated with the size of these ions, resulting from a size-dependence of the bandwidth or hopping integral t.1 6 There are three presently pursued corrections to the usual DE model, all of which might possibly be involved in the effects of interest here. Namely, there is orbital degeneracy1 7 2 1 , there are We focus here on the spin waves in the low-temperature ferromagnetic-metal phase of doped manganites. While the experimental discovery of essential remarkable characteristics of these materials occurred as long ago as 19501 , experiments on the fundamental low-lying excitations called magnons or spin waves only appeared within the last 2 years.2 8 The first theoretical consideration of these excitations was in the work of Kubo and Ohata (1972)9 , who presented a semi-classical approximation within the double exchange (DE) model 11 1 0 . This approximation was emphasized recently by Furukawa (1996). The first exact calculations, Zang et al 2 and the present authors1 3, didn’t appear until 1997. An important result of these exact calculations is that the shape of the spin wave dispersion (SWD) curve, energy vs. wave vector, differs in general from that of the famous Heisenberg spin model (with nearest neighbor interactions). In fact such a difference was not at all unexpected in view of fundamental differences found earlier1 4 , 1 5 between the magnetic behavior of the two models. We note though that the semiclassical DE model happens to give precisely Heisenberg shape for the SWD. 9, 11