  Magnetic fields are crucial in shaping the non-thermal emission of the
TeV-PeV neutrinos of astrophysical origin seen by the IceCube neutrino
telescope. The sources of these neutrinos are unknown, but if they harbor a
strong magnetic field, then the synchrotron energy losses of the neutrino
parent particles---protons, pions, and muons---leave characteristic imprints on
the neutrino energy distribution and its flavor composition. We use high-energy
neutrinos as "cosmic magnetometers" to constrain the identity of their sources
by placing limits on the strength of the magnetic field in them. We look for
evidence of synchrotron losses in public IceCube data: 6 years of High Energy
Starting Events (HESE) and 2 years of Medium Energy Starting Events (MESE). In
the absence of evidence, we place an upper limit of 10 kG-10 MG (95% C.L.) on
the average magnetic field strength of the sources.
