  We demonstrate detection of a weak alternate-current magnetic field by
application of the spin echo technique to F = 2 Bose-Einstein condensates. A
magnetic field sensitivity of 12 pT/Hz^1/2 is attained with the atom number of
5*10^3 at spatial resolution of 99 \mu m^2. Our observations indicate magnetic
field fluctuations synchronous with the power supply line frequency. We show
that this noise is greatly suppressed by application of a reverse phase
magnetic field. Our technique is useful in order to create a stable magnetic
field environment, which is an important requirement for atomic experiments
which require a weak bias magnetic field.
