T. A. Kaplan

Frustrated classical Heisenberg model in one dimension with nearest-neighbor biquadratic exchange: Exact solution for the ground-state phase diagram

The ground state phase diagram is determined for the frustrated classical Heisenberg chain with added nearest-neighbor biquadratic exchange interactions. There appear ferromagnetic, incommensurate-spiral, and up-up-down-down phases; a lock-in transition occurs at the spiral boundary. The model contains an isotropic version of the ANNNI model; it is also closely related to a model proposed for some manganites. The Luttinger-Tisza method is not obviously useful due to the non-linear weak-constraint problem; however the ground state is obtained analytically by the exact cluster method of Lyons and Kaplan. The results are compared to the model of Thorpe and Blume, where the Heisenberg part of the energy is not frustrated.

Valence fluctuation in samarium compounds—A theoretical approach

A theoretical approach to the problem of configuration fluctuation in Sm chalcogenides is presented. Properties of the fluctuating valence phase (also referred to as the collapsed phase) are discussed within an essentially localized model (ELM) in which most of the Sm 5d electrons are localized and only a small number (?0.1 electrons per Sm) occupy the free‐electron‐like states at the bottom of a d‐band. We argue that the ELM for the collapsed phase of SmS can account for almost all and, as far as we know, is inconsistent with none of the available experimental data.

Theoretical Approach to the Configuration Fluctuation in Sm-Chalcogenides

We present a theoretical approach to the problem of configuration mixing in Sm chalcogenides. Properties in the collapsed phase of SmS are discussed in terms of an essentially localized or excitonic picture of most of the Sm 5d-electrons, with a small number (≃.1 electrons per Sm) occupying the free-electron-like states at the bottom of a broad 5d-band. We review how such an essentially localized model for the 5d-electrons can lead to the observed results on volume and degree of mixing vs. pressure, low-T specific heat, dc electrical conductivity, plasma frequency, XPS intensities and magnetism. We also present new calculations of phase boundaries in the T-p plane, obtaining for SmS both a first order and a second order boundary within a simplified model. The latter boundary, which occurs e.g. at high p and low T makes contact with a recent experimental result of Guntherodt et al. The unusual shape of the observed first-order boundary is shown to be in accord with our general model, A new evaluation of the low frequency dielectric constant (ħω⋝.lev) shows behavior very similar to the unusual experimental results obtained recently by Batlogg et al. and by Allen. We compare the above picture with the more common models where all the 5d-electrons (~.7 per Sm in SmS) occupy free-electron like states, and give a critique of the latter.

Theory of electronic properties of SmS, SmSe, SmTe, SmB6

Optical absorption data in semiconducting Sm chalcogenides suggest1 the existence of low energy excitations from f6 to f5(d−t2g) localized configurations (Frenkel excitons) with a weak f6 to f5 (ds) ‐band excitation2 starting from a lower energy. Based on this picture, Kaplan and Mahanti3,4 suggested that such excitons are created in pairs via an intersite Coulomb interaction W. Within a mean field theory they found a second order phase transition from an unmixed f6 to a coherently mixed (Af6+Bf5d) localized state (CMLS) as a function of decreasing volume. We have now investigated the effect of lattice energy on the transition. With reasonable values of W we can semiquantiatively reproduce the PV curves for SmS, (discontinuity in V vs. P), SmSe and SmTe (smooth behavior). We can also reproduce the amount of mixing of f6 and f5d configurations in collapsed SmS. In addition, the case of SmB6 fits naturally into our general picture.The metallic behavior in collapsed SmS is interpreted in terms of partial low...

Spin Waves in Doped Manganites

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