  High-precision frequency estimation is an ubiquitous issue in fundamental
physics and a critical task in spectroscopy. Here, we propose a quantum Ramsey
interferometry to realize high-precision frequency estimation in spin-1
Bose-Einstein condensate via driving the system through quantum phase
transitions(QPTs). In our scheme, we combine adiabatically driving the system
through QPTs with {\pi}/2 pulse to realize the initialization and
recombination. Through adjusting the laser frequency under fixed evolution
time, one can extract the transition frequency via the lock-in point. The
lock-in point can be determined from the pattern of the population measurement.
In particular, we find the measurement precision of frequency can approach to
the Heisenberg-limited scaling. Moreover, the scheme is robust against
detection noise and non-adiabatic effect. Our proposed scheme does not require
single-particle resolved detection and is within the reach of current
experiment techniques. Our study may point out a new way for high-precision
frequency estimation.
