Nuclear dipole magnetic moments have been measured for highly neutron deficient light rare-earth nuclei using the technique of on-line low temperature nuclear orientation. A novel pulsed implantation technique 139 has been used to set a limit of the relaxation times of both 139Eu and 139Sm isotopes in iron of < 3s. The measured moments are compared to calculations using a particle plus triaxial rotor model, and the ground-state configurations are discussed. The large magnetic moment for the nucleus 138Eu enables the assignment of the (pi5/2- [532] x nu7/2+ [404]) 6- Nilsson two-quasiparticle configuration. The measured moments for both 139Eu and 139Smm are explained in terms of the weak coupling of the respective odd-nucleon to a strongly triaxial rotating core.