Stability of Differentiator Circuit
With the ideal differentiator, there is a phase lag in the negative feedback network. Combined with the phase shift in a real opamp this can result in making the overall phase shift around the loop reach 360 deg and cause oscillation. Even if it doesn't cause oscillation it can reduce the phase margin at high frequencies.

To understand this imagine that Vin is grounded. The network R and C will give a phase shift that is asymptotic to 90 deg at high frequency.

A typical opamp is designed with dominant pole compensation to provide stability - this adds another 90 deg of phase shift at high frequencies. In addition, there are usually one or two additional poles internal to the opamp that can give more phase shift.

Note from the diagram that although the phase shift is ~90 deg over much of the operating range it goes beyond that above ~100kHz while the gain is still >1. This can cause instability when combined with the phase-shift of the negative feedback network. (note: the curve that is horizontal for much of the graph is the phase shift, the sloping line is the open-loop gain).



OPA227 Datasheet