  We have investigated the critical conditions required for a steady propeller
effect for magnetized neutron stars with optically thick, geometrically thin
accretion disks. We have shown through simple analytical calculations that a
steady-state propeller mechanism cannot be sustained at an inner disk radius
where the viscous and magnetic stresses are balanced. The radius calculated by
equating these stresses is usually found to be close to the conventional Alfven
radius for spherical accretion, r_A. Our results show that: (1) a steady
propeller phase can be established with a maximum inner disk radius that is at
least \sim 15 times smaller than r_A depending on the mass-flow rate of the
disk, rotational period and strength of the magnetic dipole field of the star,
(2) the critical accretion rate corresponding to the accretion-propeller
transition is orders of magnitude lower than the rate estimated by equating r_A
to the co-rotation radius. Our results are consistent with the properties of
the transitional millisecond pulsars which show transitions between the
accretion powered X-ray pulsar and the rotational powered radio pulsar states.
