Abstract
A microscopic theory of metaelasticity is derived and applied to Jahn-Teller crystals with $x\text{\ensuremath{-}}y$ ordered octahedron distortions. The theory explains the interrelation of the elastic and magnetic properties of those crystals and with modifications, could be applied to other systems. The consequences of the application of pressure along the $z$-axis and a $z$-axis magnetic field are explored. Both, the pressure and the magnetic field applications lead to phase transitions. As a manifestation of the field-induced phase transition giant dynamic magnetostriction in colossal magnetoresistance manganite-type crystals is calculated.
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