The magnetic and magnetoelastic properties (third-order magnetic susce
ptibility and parastriction) of TbPO4, which has the zircon-type tetra
gonal structure, are analyzed in the paramagnetic phase. The susceptib
ility formalism is then used to describe all the symmetry-lowering mod
es in a rare-earth insulator. The dominant magnetoelastic coupling is
associated with the delta symmetry and is, at least partly, responsibl
e for the transition occuring at 2.15 K in the antiferromagnetic phase
and clearly dominates the gamma-symmetry mode. However, none of the d
ifferent symmetry-lowering modes can be completely neglected and we de
termine parameters for the alpha 1 and alpha 2 tetragonal modes and th
e epsilon monoclinic mode. Owing to the close vicinity of the first ex
cited singlet to the ground-state doublet, the alpha quadrupolar inter
actions play an important role in determining the temperature dependen
ce of the level spacing at low temperature, in particular in the order
ed phases. The determination of all the magnetoelastic modes of TbPO4
is an essential step towards the understanding of the complex magnetic
properties in the ordered phases, where numerous interactions coexist
.