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To track the formation and evolution links of the millisecond pulsars (MSPs)powered by accretion and rotation in the Galactic field, we investigate thespin period (P) and spin-down power (Edot) distributions of the MSPs observedat the wavebands of radio, X-ray, and {\gamma}-ray. We find that all but one(119/120) of the {\gamma}-ray MSPs have been detected with the radio signals(radio+{\gamma} MSPs); on the contrary, nearly half of the radio MSPs (118/237)have not been detected with {\gamma}-rays (radio-only MSPs). In addition, theradio+{\gamma} MSPs are shown to be the relative faster and more energeticobjects (<P> ~ 3.28 ms and <Edot> ~ 4.5 * 10^34 erg s^-1) compared with theradio-only MSPs (<P> ~ 4.70 ms and <Edot> ~ 1.0 * 10^34 erg s^-1), while thespin periods of these two MSP populations are compatible with the log-normaldistributions by the statistical tests. Most rotation-powered MSPs (RMSPs) withthe radio eclipsing (31/34) exhibit the radio+{\gamma} signals, which share thefaster spin (<P> ~ 2.78 ms) and larger spin-down power (<Edot> ~ 4.1 * 10^34erg s^-1) distributions than the non-eclipsing ones (<P> ~ 4.19 ms, <Edot> ~2.4 * 10^34 erg s^-1), implying the radio+{\gamma} MSPs to be younger than theradio-only MSPs. It is noticed that the spin distribution of theaccretion-powered X-ray MSPs shows a clustering phenomenon around ~ 1.6-2.0 ms,which is not observed in RMSPs, hinting that the RMSPs may experience themultiple possible origins. Particularly, all the three super-fast spinningRMSPs with P ~ 1.4-1.6 ms exhibit the non-eclipsing, and we argue that they maybe the distinctive sources formed by the accretion induced collapse (AIC) ofwhite dwarfs.

Investigation of the Millisecond Pulsar Origins by their Spin Periods at the Wavebands of Radio, X-Ray, and {\gamma}-Ray