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.
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