We report the first measurement of the g factor of the first 2+ state of the radioactive neutronrich nucleus 72Zn using the High-Velocity Transient-Field (HVTF) technique. The neutron-rich N=40 region has long been discussed regarding the competition between single-particle-like structures in the Ni isotopes and the collective states in their immediate vicinity. Nuclear gyromagnetic factors, with their sensitivity to the single-particle properties of the nuclear states, can be one of the most sensitive probes of this interplay. Whereas the g factors of the 2+ states of the stable Ni isotopes show predominantly single particle behavior, consistent with relatively simple shell model structures [1], those of the nearby Zn and Ge isotopes show a trend consistent with the Z/A rule characteristic of collective states [2]. Particular interest in the Zn isotopes comes about because a number of theoretical calculations predict a change from collective to single-particle dominated behavior in the N=40 region. The main difference between the various models is related to the strength of this change and how sudden or gradual it is expected to be. The last known g factor of the stable isotope 70Zn still implies collective behavior. In the present experiment we have applied the HVTF technique for the first time to nuclei with Z>20 and A>40. As has been demonstrated in the previous measurement of this type [3], the technique can provide a very strong transient magnetic field (TF) for ions traversing ferromagnetic layers with velocities ~Zv0, which in the Z<20 case has been shown to increase the sensitivity of the TF method sufficiently for applications to low intensity radioactive beams. 72Zn was produced at GANIL by intermediate-energy projectile fragmentation (~60 MeV/A) of 76Ge on a 500 μg/cm² Be target, and selected using the LISE spectrometer. The 2+ state was populated via Coulomb excitation in a secondary Gd target, also used as the ferromagnetic layer for providing the TF. The scattered beam particles were detected in a plastic scintillator in coincidence with gamma-rays registered by 8 EXOGAM Clovers, positioned in the horizontal plane. The integral rotation of the angular distribution, monitored as a function of the external magnetic field (up vs. down), allows the determination of the g factor of the state of interest, provided that the strength of the TF field is known. The stable 76Ge beam, with known g(2+), was used for calibration [2]. The results of this experiment, which suggest that g(2+) in 72Zn is considerably smaller than g(2+) ≈ Z/A in 76Ge, will be presented and compared with theoretical models.