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Register a new userTight-binding theory of lanthanum strontium manganate
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Authors
Walter A. Harrison
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An earlier analysis of manganese oxides in various charge states indicated that free-atom term values and universal coupling gave a reasonable account of the cohesion. This approach is here extended to LaxSr(1-x)MnO3 in a perovskite structure, and a wide range of properties, with comparable success, including the cohesion, as a function of x. Magnetic and electronic properties are treated in terms of the same parameters and the cluster orbitals used for cohesion. This includes an estimate of the Neel and Curie-Weiss temperatures for SrMnO3, an antiferromagnetic insulator, and the magnitude of a Jahn-Teller distortion in LaMnO3 which makes it also insulating with (100) ferromagnetic planes (due to a novel double-exchange for the distorted state), antiferromagnetically stacked, as observed. We estimate the Neel temperature and its volume dependence, and the ferromagnetic Curie-Weiss temperature which applies between the Neel and Jahn-Teller temperatures. We expect hopping conductivity when there is doping (0<x<1) and estimate it in the context of small-polaron theory. It is in accord with experiment between the Neel and Jahn-Teller temperatures, but below the Neel temperature the conduction appears to be band-like, for which we estimate a hole mass as enhanced in large-polaron theory. We see that above the Jahn-Teller temperature LaMnO3 should be metallic as observed, and paramagnetic with a ferromagnetic Curie-Weiss constant which we estimate. Many of these predictions are not so accurate, but are sufficiently close to provide a clear understanding of all of these properties in terms of a simple theory and parameters known at the outset. We provide also these parameters for Fe, Co, and Ca so that formulae for the properties can readily be evaluated for similar systems.
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We report on the magnetic, resistive, and structural studies of perovskite La$_{1/3}$Sr$_{2/3}$CoO$_{3-delta}$. By using the relation of synthesis temperature and oxygen partial pressure to oxygen stoichiometry obtained from thermogravimetric analysis, we have synthesized a series of samples with precisely controlled $delta=0.00-0.49$. These samples show three structural phases at $delta=0.00-0.15$, $approx0.25$, $approx0.5$, and two-phase behavior for other oxygen contents. The stoichiometric material with $delta=0.00$ is a cubic ferromagnetic metal with the Curie temperature $T_{rm C}=274$ K. The increase of $delta$ to 0.15 is followed by a linear decrease of $T_{rm C}$ to $approx$ 160 K and a metal-insulator transition near the boundary of the cubic structure range. Further increase of $delta$ results in formation of a tetragonal $2a_ptimes 2a_p times 4a_p$ phase for $deltaapprox 0.25$ and a brownmillerite phase for $deltaapprox0.5$. At low temperatures, these are weak ferromagnetic insulators (canted antiferromagnets) with magnetic transitions at $T_{rm m}approx230$ and 120 K, respectively. At higher temperatures, the $2a_ptimes 2a_p times 4a_p$ phase is $G$-type antiferromagnetic between 230 K and $approx$360 K. Low temperature magnetic properties of this system for $delta<1/3$ can be described in terms of a mixture of Co$^{3+}$ ions in the low-spin state and Co$^{4+}$ ions in the intermediate-spin state and a possible spin transition of Co$^{3+}$ to the intermediate-spin state above $T_{rm C}$. For $delta>1/3$, there appears to be a combination of Co$^{2+}$ and Co$^{3+}$ ions, both in the high-spin state with dominating antiferromagnetic interactions.
We consider the mapping of tight-binding electronic structure theory to a local spin Hamiltonian, based on the adiabatic approximation for spin degrees of freedom in itinerant-electron systems. Local spin Hamiltonians are introduced in order to describe the energy landscape of small magnetic fluctuations, locally around a given spin configuration. They are designed for linear response near a given magnetic state and in general insufficient to capture arbitrarily strong deviations of spin configurations from the equilibrium. In order to achieve this mapping, we include a linear term in the local spin Hamiltonian that, together with the usual bilinear exchange tensor, produces an improved accuracy of effective magnetic Weiss fields for non-collinear states. We also provide examples from tight-binding electronic structure theory, where our implementation of the calculation of exchange constants is based on constraining fields that stabilize an out-of-equilibrium spin configuration. We check our formalism by means of numerical calculations for iron dimers and chains.
The electronic structure is found to be understandable in terms of free-atom term values and universal interorbital coupling parameters, since self-consistent tight-binding calculations indicate that Coulomb shifts of the d-state energies are small. Special-point averages over the bands are seen to be equivalent to treatment of local octahedral clusters. The cohesive energy per manganese for MnO, Mn2O3, and MnO2, in which manganese exists in valence states Mn2+, Mn3+, and Mn4+, is very nearly the same and dominated by the transfer of manganese s electrons to oxygen p states. There are small corrections, one eV per Mn in all cases, from couplings of minority-spin states. Transferring one majority-spin electron from an upper cluster state to a nonbonding oxygen state adds 1.67 eV to the cohesion for Mn2O3, and two transfers adds twice that for MnO2 . The electronic and magnetic properties are consistent with this description and appear to be understandable in terms of the same parameters.
A method for incorporating electromagnetic fields into empirical tight-binding theory is derived from the principle of local gauge symmetry. Gauge invariance is shown to be incompatible with empirical tight-binding theory unless a representation exists in which the coordinate operator is diagonal. The present approach takes this basis as fundamental and uses group theory to construct symmetrized linear combinations of discrete coordinate eigenkets. This produces orthogonal atomic-like orbitals that may be used as a tight-binding basis. The coordinate matrix in the latter basis includes intra-atomic matrix elements between different orbitals on the same atom. Lattice gauge theory is then used to define discrete electromagnetic fields and their interaction with electrons. Local gauge symmetry is shown to impose strong restrictions limiting the range of the Hamiltonian in the coordinate basis. The theory is applied to the semiconductors Ge and Si, for which it is shown that a basis of 15 orbitals per atom provides a satisfactory description of the valence bands and the lowest conduction bands. Calculations of the dielectric function demonstrate that this model yields an accurate joint density of states, but underestimates the oscillator strength by about 20% in comparison to a nonlocal empirical pseudopotential calculation.
We extend a tight-binding total energy method to include f-electrons, and apply it to the study of the structural and elastic properties of a range of elements from Be to U. We find that the tight-binding parameters are as accurate and transferable for f-electron systems as they are for d-electron systems. In both cases we have found it essential to take great care in constraining the fitting procedure by using a block-diagonalization procedure, which we describe in detail.
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