  We have performed elastic and inelastic neutron scattering experiments on the
solid solutions U(Ru_{1-x}Rh_x)_2Si_2 for the Ru rich concentrations: x=0,
0.01, 0.02, 0.025, 0.03, 0.04 and 0.05. Hidden order is suppressed with
increasing x, and correspondingly the onset temperature T_m (~ 17.5 K at x=0)
of weak antiferromagnetic (AF) Bragg reflection decreases. For x=0.04 and 0.05,
no magnetic order is detected in the investigated temperature range down to 1.4
K. In the middle range, 0.02 <= x <= 0.03, we found that the AF Bragg
reflection is strongly enhanced. At x=0.02, this takes place at ~ 7.7 K (=T_M),
which is significantly lower than T_m (~ 13.7 K). T_M increases with increasing
x, and seems to merge with T_m at x=0.03. If the AF state is assumed to be
homogeneous, the staggered moment \mu_o estimated at 1.4 K increases from
0.02(2) \mu_B/U (x=0) to 0.24(1) \mu_B/U (x=0.02). The behavior is similar to
that observed under hydrostatic pressure (\mu_o increases to ~ 0.25 \mu_B/U at
1.0 GPa), suggesting that the AF evolution induced by Rh doping is due to an
increase in the AF volume fraction. We also found that the magnetic excitation
observed at Q=(1,0,0) below T_m disappears as T is lowered below T_M.
