  We report magnetic-field-induced first-order phase transitions in the
ferro-quadrupole (FQ) ordered state of PrTi2Al20, in which non-Kramers Pr3+
ions with two 4f electrons have a non-magnetic Gamma3 doublet ground state in
the cubic Td crystalline electric field. For magnetic fields along [111],
27Al-NMR and magnetization experiments reveal Qz \propto 3z2-r2 type FQ order
below 2 K independent of field strength. Magnetic fields along [001] or [110],
however, induce discontinuous switching of order parameters within the two
dimensional space spanned by Qz and Qx \propto x2-y2 at small field values less
than a few tesla. A symmetry-based theoretical analysis shows that the
transitions can be caused by competition between the magnetic Zeeman
interaction and anisotropy in the quadrupole-quadrupole interactions, if the
latter dominates over the former in low fields and vice versa in high fields.
Furthermore, striking violation of proportionality between NMR Knight shift and
magnetic susceptibility is observed in the symmetry-broken FQ phases,
indicating significant influence of FQ order on the hybridization between
conduction and f electrons, which in turn mediates the RKKY-type quadrupole
interaction causing the FQ order. This feedback effect may be a specific
feature of quadrupole orders not commonly observed in magnetic phase
transitions and play a key role for inducing the discontinuous transitions.
