  Most macroscopic magnetic phenomena (including magnetic hysteresis) are
typically understood classically. Here, we examine the dynamics of a uniaxial
rare-earth ferromagnet deep within the quantum regime, so that domain wall
motion, and the associated hysteresis, is dominated by large-scale quantum
tunneling of spins, rather than classical thermal activation over a potential
barrier. The domain wall motion is found to exhibit avalanche dynamics,
observable as an unusual form of Barkhausen noise. We observe non-critical
behavior in the avalanche dynamics that only can be explained by going beyond
traditional renormalization group methods or classical domain wall models. We
find that this ``quantum Barkhausen noise'' exhibits two distinct mechanisms
for domain wall movement, each of which is quantum-mechanical, but with very
different dependences on an external magnetic field applied transverse to the
spin (Ising) axis. These observations can be understood in terms of the
correlated motion of pairs of domain walls, nucleated by co-tunneling of
plaquettes (sections of domain wall), with plaquette pairs correlated by
dipolar interactions; this correlation is suppressed by the transverse field.
Similar macroscopic correlations may be expected to appear in the hysteresis of
other systems with long-range interactions.
