Charge-ordering in manganates

Ordering of Mn<SUP>3+</SUP> and Mn<SUP>4+</SUP> ions occurs in the rare earth manganates of the general composition Ln<SUB>1−x</SUB>A<SUB>x</SUB>MnO<SUB>3</SUB> (Ln=rare earth, A=Ca, Sr). Such charge-ordering is associated with antiferromagnetic and insulating properties. This phenomenon is to be contrasted with the ferromagnetic metallic behavior that occurs when double-exchange between the Mn<SUP>3+</SUP> and Mn<SUP>4+</SUP> ions predominates. Two distinct types of charge-ordering can be delineated. In one, a ferromagnetic metallic (FMM) state transforms to the charge-ordered (CO) state on cooling. In the other scenario, the CO state is found in the paramagnetic ground state and there is no ferromagnetism down to the lowest temperatures. Magnetic fields transform the CO state to the FMM state, when the average radius of the A-site cations is sufficiently large (&lt;r<SUB>A</SUB>&gt;&gt;1.17Å). Chemical melting of the CO state by Cr<SUP>3+</SUP> substitution in the Mn site is also found only when &lt;r<SUB>A</SUB>&gt;≳1.17Å. The effect of the size of the A-cations on the Mn-O-Mn angle is not enough to explain the observed variations of the charge-ordering temperature as well as the ferromagnetic Curie temperature T<SUB>c</SUB>. An explanation based on a competition between the Mn and A-cation orbitals for σ-bonding with the oxygen ρ<SUB>σ</SUB> orbitals is considered to account for the large changes in T<SUB>c</SUB> and hence the true bandwidth, with &lt;r<SUB>A</SUB>&gt;. Effects of radiation, electric field, and other factors on the CO state are discussed along with charge-ordering in other manganate systems. Complex phase transitions, accompanied by changes in electronic and magnetic properties, occur in manganates with critical values of &lt;r<SUB>A</SUB>&gt; or bandwidth. Charge-ordering is found in layered manganates, Bi<SUB>x</SUB>Ca<SUB>1−x</SUB>MnO<SUB>3</SUB> and CaMnO<SUB>3−δ