Electronic structure of CMR manganites (invited)

A “colossal” negative magnetoresistance (CMR) occurs in manganites at a first-order ferromagnetic transition. The ${\mathrm{Mn}}^{\text{4+}}$ and high-spin ${\mathrm{Mn}}^{\text{3+}}$ ions each contain localized $t^3$ configurations; the $t^3{\mathrm{–p}}_{\pi }{\mathrm{–t}}^3$ superexchange interactions are antiferromagnetic. The orbital degeneracy of localized ${\mathrm{Mn}}^{\text{3+}}{\mathrm{:t}}^3{e}^1$ , ${}^5{E}_g$ configurations is lifted by cooperative static or dynamic Jahn–Teller deformations. Strong $e$ -electron coupling to oxygen displacements, static or dynamic, introduces ferromagnetic $e^1{\mathrm{–p}}_{\sigma }{\mathrm{–e}}^0$ interactions either via superexchange or, for fast ${\mathrm{Mn}}^{\text{3+}}$ to ${\mathrm{Mn}}^{\text{4+}}$ electron transfer relative to the spin-relaxation time ${\mathrm{(\tau }}_h{\mathrm{<\tau }}_s)$ , via a stronger double exchange. At the first-order ferromagnetic transition, a change from ${\tau }_h{\mathrm{\approx \hslash /W}}_{\sigma }{\mathrm{>\omega }}_R^{\text{−1}}$ to ${\tau }_h{\mathrm{<\omega }}_R^{\text{−1}}$ occurs within mobile molecular units, where $W_{\sigma }$ is the bandwidth for states of $e$ -orbital parentage and ${\omega }_R^{\text{−1}}$ is the period of the optical-mode lattice vibration that traps a mobile hole as a small-polaron ${\mathrm{Mn}}^{\text{4+}}$ ion. $T_C$ increases with the fraction of double-exchange couplings, and this fraction increases with $W_{\sigma }$ and ${\omega }_R$ at the transition from polaronic to itinerant-electron behavior below $T_C.$ The bandwidth $W_{\sigma }{\mathrm{\sim \epsilon }}_{\sigma }{\lambda }_{\sigma }^2\hspace{0.17em}\cos \mathrm{\hspace{0.17em}\phi 〈}\cos {\mathrm{(\theta }}_{\mathrm{ij}}\text{/2)〉}$ depends on the covalent mixing parameter ${\lambda }_{\sigma },$ which increases with pressure, as well as on the Mn–O–Mn bond angle (180°−φ), which increases with the tolerance factor $t$ that measures the equilibrium bond-length mismatch, and on the angle ${\theta }_{\mathrm{ij}}$ between neighboring spins so that $W_{\sigma }$ increases with the spontaneous magnetization on cooling below $T_C.$ In the compositions ${\mathrm{Ln}}_{\mathrm{0.7}}{\mathrm{A}}_{\mathrm{0.3}}{\mathrm{MnO}}_{\mathrm{3}}$ with A=Ca or Sr, $T_C$ increases with $t$ over the range $\text{0.96⩽t⩽0.98}$ where the transition at $T_C$ is first order. The CMR is greatest near