The rare-earth oxide compound TmPO4 (tetragonal zircon structure) is i
nvestigated using the extended susceptibility formalism, which conside
rs at any temperature all of the features of the crystalline electric
field within the ground-state multiplet in the joint analysis of the m
agnetic, magnetoelastic and elastic properties. The magnetoelastic coe
fficients are determined from third-order magnetic susceptibility, par
astriction and elastic constant measurements for the different symmetr
y modes. The dominant magnetoelastic coupling is associated with the o
rthorhombic delta-symmetry; however, tetragonal and symmetry-lowering
modes are also observed to give rise to noticeable effects, in particu
lar in the thermal expansion. The close coherency between the magnetoe
lastic coefficients in TmPO4 and TbPO4 is then emphasized: the tetrago
nal magnetoelastic coefficients are sizeable and all of the magnetoela
stic couplings keep the same sign and order of magnitude in the two ph
osphates. This coherency appears to be valid throughout the large fami
ly of rare-earth zircons. Through these two examples, the occurrence o
f a quadrupolar ordering is then discussed as being governed by the cr
ystalline electric field, and the role of undercritical quadrupolar in
teractions is emphasized in TmPO4.