In particular the key paper is published in 1938, A new method of measuring nuclear magnetic moment(3)
It is the purpose of this note to describe an experiment in which nuclear magnetic moment is measured very directly. The method is capable of very high precision and extension to a large number and variety of nuclei.A beam of particles, in the case of the first experiment they used molecules of LiCl, passed through a group of magnets, so that the nuclear spins is decoupled from each other and from the molecular rotation. At this point an additional magnetic field, this time slightly oscillating, is applied such that the spin and the nuclear magnetic moment are redirected, obtaining at the end a sort of frequency's precession(3).
At the end, Rabi and his colleagues were able to observe perfectly the separated resonance peaks of the two nuclei of lithium and chlorine and just a year later, as also promised in the conclusions of the first article, they were able to update the method using some new atoms, describing with more details the experimental apparatus used by the team:(4):
The apparatus consists of two magnets in succession which produce inhomogeneous magnetic fields of oppositely directed gradients. A molecular beam of the substance to be studied possesses a sigmoid path in these magnets and is focused on a suitable detector. A third magnet which produces a homogeneous field is placed in the region between the two deflecting magnets.(4)In these early works there are not any explicit reference to the applications for the construction of an atomic clock. The experiments of Rabi's team, indeed, had a much more specific goal: to understand the fine structure of the nucleus and if the nucleus interacts like a magnet with electrons(4). Of course in 1939 Rabu started informally the discussion about the atomic clocks(2), but only on the 20th Genuary of 1945, during a conference of the American Physical Society and the American Association of Physics Teachers he spoke explicitally about the construction of this device(2).
Following some sources(2), Rabi was waiting to measure the Cesium's transition, that it happened in 1940. The first atomic clock was built in 1948 by the a team from National Bureau of Standards leaded by Harold Lyons(5) and it is based on ammonia.
In this way Rabi awarded the Nobel Prize for the science behind the atomic clocks and Lyons became the inventor of the device, a record set by a small advertising cartoon:
(1) for his resonance method for recording the magnetic properties of atomic nuclei
(2) M.A. Lombardi, T.P. Heavner, S.R. Jefferts (2007). "NIST Primary Frequency Standards and the Realization of the SI Second". Journal of Measurement Science 2 (4): 74. (pdf)
(3) Rabi, I., Zacharias, J., Millman, S., & Kusch, P. (1938). A New Method of Measuring Nuclear Magnetic Moment Physical Review, 53 (4), 318-318 DOI: 10.1103/PhysRev.53.318
(4) Rabi, I., Millman, S., Kusch, P., & Zacharias, J. (1939). The Molecular Beam Resonance Method for Measuring Nuclear Magnetic Moments. The Magnetic Moments of Li63, Li73 and F199 Physical Review, 55 (6), 526-535 DOI: 10.1103/PhysRev.55.526 (pdf)
(5) Harold Lyons, The atomic clock