  An extremely weak circularly polarized signature was recently discovered in
spectral lines of the chemically peculiar Am star Sirius A. A weak surface
magnetic field was proposed to account for the observed polarized signal, but
the shape of the phase-averaged signature, dominated by a prominent positive
lobe, is not expected in the standard theory of the Zeeman effect. We aim at
verifying the presence of weak circularly polarized signatures in two other
bright Am stars, beta UMa and theta Leo, and investigating the physical origin
of Sirius-like polarized signals further. We present here a set of deep
spectropolarimetric observations of beta UMa and theta Leo, observed with the
NARVAL spectropolarimeter. We analyzed all spectra with the Least Squares
Deconvolution multiline procedure. To improve the signal-to-noise ratio and
detect extremely weak signatures in Stokes V profiles, we co-added all
available spectra of each star (around 150 observations each time). Finally, we
ran several tests to evaluate whether the detected signatures are consistent
with the behavior expected from the Zeeman effect. The line profiles of the two
stars display circularly polarized signatures similar in shape and amplitude to
the observations previously gathered for Sirius A. Our series of tests brings
further evidence of a magnetic origin of the recorded signal. These new
detections suggest that very weak magnetic fields may well be present in the
photospheres of a significant fraction of intermediate-mass stars. The strongly
asymmetric Zeeman signatures measured so far in Am stars (featuring a dominant
single-sign lobe) are not expected in the standard theory of the Zeeman effect
and may be linked to sharp vertical gradients in photospheric velocities and
magnetic field strengths.
