Localized versus CollectivedElectrons and Néel Temperatures in Perovskite and Perovskite-Related Structures

Abstract

It is pointed out that a simple, localized-electron antiferromagnet having one electron per localized orbital interacting via 180° superexchange with similar orbitals on $z$ near-neighbor cations via an overlap integral $\Delta$ has a Néel temperature $k{T}_n\approx \frac{z\{q_{t}b_t^{}{}_{}{}^2+q_{e}b_e^{}{}_{}{}^2\}(S+1\mathrm{})\mathrm{}}{S},$ where $q_t$, $q_e$ are inversely proportional to electrostatic energies associated with electron transfers; $b_t\sim {\epsilon }_0{\Delta }_t$ and $b_e\sim \epsilon _0^{}{}_{}{}^{\prime }{\Delta }_e$ are the one-electron transfer integrals of states having $t_{2g}$ and $e_g$ symmetry, respectively. On the other hand, a collective-electron antiferromagnet having a half-filled band that is split in two by the magnetic ordering would have a $k{T}_N$ that decreased with increasing bandwidth, and hence increasing $\Delta$. This provides a criterion for distinguishing the two cases: $\frac{d{T}_N}{\mathrm{dp}}>0\mathrm{}$ for localized-electron antiferromagnetism and $\frac{d{T}_N}{\mathrm{dp}}<0\mathrm{}$ for collective-electron antiferromagnetism, where $p$ is the hydrostatic pressure. It is therefore surprising that $\frac{d{T}_n}{d{a}_0}>0\mathrm{}$, where $a_0$ is the cation-anion-cation separation, in the systems ${\mathrm{Ca}}_{1-x}{\mathrm{Sr}}_x\mathrm{Mn}{\mathrm{O}}_3$, $A^{3+}\mathrm{Fe}{\mathrm{O}}_3$, and $A^{3+}\mathrm{Cr}{\mathrm{O}}_3$, since independent data indicate that the $d$ electrons are localized. This fact is attributed to changes in $A-\mathrm{O}$ covalent bonding that cause $\Delta$ to increase with the more basic $A$ cation for a given lattice parameter. The relatively small changes in

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