We present here high-resolution magnetization measurements on high-quality BaFe 2(1−x) Co 2x As 2 , 0 x 0.046 as-grown single crystals. The results confirm the existence of a magnetic tricritical point in the (x,T ) plane at x m tr ≈ 0.022 and reveal the emergence of the heat-capacity anomaly associated with the onset of the structural transition at x s ≈ 0.0064. We show that the extrapolated T c onset doping could be close to the magnetic tricritical point x m tr .The 122 series (AFe 2 As 2 , A = Ba, Sr, Ca, Eu) is one of the most studied among the newly discovered iron arsenide high-temperature superconductors. One intriguing fact is that in this series, superconductivity can be induced by doping in any of the three atomic sites; the cobalt doped system BaFe 2−2x Co 2x As 2 1,2 is, for instance, one of the most studied systems. The antiferromagnetic (spin-density wave) (at T N ) and structural (tetragonal to orthorhombic) (at T = T s ) transitions that are near coincident in the parent compounds 3 are concomitantly and gradually suppressed upon doping. A large number of papers have been written on the thermodynamic nature of the transitions in 122s arguing for either firstorder or second-order phase changes. If we solely consider the BaFe 2 As 2 system, reports range from both second-order structural and magnetic phase transitions, 3 to both transitions second-order but with the possibility of a magnetic first-order transition within 0.5 K of T N , 4 to only a first-order magnetic transition, 5 to indiscernibility between the two scenarios for the magnetic phase transition (neither the abrupt change at T N of the magnetic order parameter that is expected for a first-order transition nor the divergence of the correlation length at T N that would suggest a second-order transition were seen). 6 More recent combined high-resolution x-ray diffraction and heat-capacity measurements on exceptionally high-quality BaFe 2 As 2 crystals revealed a first-order magnetic transition preceded by a structural transition that starts as a second-order transition at a slightly higher temperature but with a first-order jump in the orthorhombic distortion coincident with the firstorder magnetic transition. 7 Since data on some doped Ba122 samples show clear second-order magnetic and structural transitions, 8-10 it has been theoretically suggested that the magnetostructural transition in the parent is close to a tricritical point 11 that is tunable through doping. The only exception appears to be the case of the hole-doped Ba 1−x K x Fe 2 As 2 for which both the magnetic and structural transitions seem to be first order over the entire phase diagram. 12 Further, ARPES measurements on cobalt-doped Ba122 evidenced a Lifshitz transition at the onset of superconductivity, 13 while high-resolution x-ray diffraction and x-ray resonant magnetic scattering (XRMS) pointed to a magnetic tricritical point at x ≈ 0.022, but with a structural transition whose onset is second order across the whole cobalt doping range. 14 Magnetic and structural o...