The idea of stimulating a cooperative Jahn-Teller effect in undercriti
cal electronic systems using an external stress, which does not belong
to the symmetry of the quadrupolar ordering, was recently suggested t
heoretically. The rare-earth oxide compound TmPO4 (tetragonal zircon s
tructure) is discussed here. The role of the external stress, a magnet
ic field applied along the [100] axis, is to bring the delta-symmetry
quadrupolar component to criticality by the reconstruction of both the
levels spacings and the eigenfunctions. The thermodynamical propertie
s are obtained by considering all the characteristics of the magnetoel
astic couplings and of the crystalline electric field. The structural
phase diagram exhibits reentrant transitions between the tetragonal an
d orthorhombic symmetries. The measurements of the magnetic vector and
of the magnetostriction induced by the magnetic field are well descri
bed within this model. The simultaneous measurement of the components
of the magnetic moment parallel and perpendicular to the field is an i
nteresting experimental technique, efficient for the investigation of
quadrupolar interactions.