  We have investigated the nature of the competition between hidden order and
antiferromagnetic (AF) order in URu_2Si_2 by performing the neutron scattering
experiments under hydrostatic-pressure P, uniaxial-stress sigma, and
Rh-substitution conditions. Hidden order observed at ambient pressure in pure
URu_2Si_2 is found to be replaced by the AF order by applying P, sigma along
the tetragonal basal plane, and by doping Rh. We discuss these experimental
results on the basis of the crystalline strain calculations, and suggest that
this phase transition is generated by the 0.1% increase of the tetragonal c/a
ratio. We have also found that the magnetic excitation observed in the hidden
order phase vanishes in the AF phase. We show that this variation can be
qualitatively explained by assuming the hidden order parameter to be
quadrupole.
