  Magnetoelastic properties in field-induced magnetic ordered phases are
studied theoretically based on a Ginzburg-Landau theory. A critical field for
the field-induced ordered phase is obtained as a function of temperature and
pressure, which determine the phase diagram. It is found that magnetic field
dependence of elastic constant decreases discontinuously at the critical field,
Hc, and that it decreases linearly with field in the ordered phase (H>Hc). We
found an Ehrenfest relation between the field dependence of the elastic
constant and the pressure dependence of critical field. Our theory provides the
theoretical form for magnetoelastic properties in field- and pressure-induced
ordered phases.
