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We present first specific-heat data of the alloy Yb(Rh_(1-x)Co_x)_2Si_2 atintermediate Co-contents x=0.18, 0.27, and 0.68. The results already point to acomplex magnetic phase diagram as a function of composition. Co-doping ofYbRh_2Si_2 (T_N^{x=0}=72 mK) stabilizes the magnetic phase due to the volumedecrease of the crystallographic unit cell. The magnetic phase transitions areclearly visible as pronounced anomalies in C^{4f}(T)/T and can be suppressed byapplying a magnetic field. Going from x=0.18 to x=0.27 we observe a change fromtwo mean-field (MF) like magnetic transitions at T_N^{0.18}=1.1 K andT_L^{0.18}=0.65 K to one sharp \lambda-type transition at T_N^{0.27}=1.3 K.Preliminary measurements under magnetic field do not confirm the field-inducedfirst-order transition suggested in the literature. For x=0.68 we find twotransitions at T_N^{0.68}=1.14 K and T_L^{0.68}=1.06 K.

Magnetic field dependence of the antiferromagnetic phase transitions in Co-doped YbRh_2Si_2