  We study Landau-Zener macroscopic quantum transitions in ferromagnetic metal
nanoparticles containing on the order of 100 atoms. The model that we consider
is described by an effective giant-spin Hamiltonian, with a coupling to a
random transverse magnetic field mimicking the effect of quasiparticle
excitations and structural disorder on the gap structure of the spin collective
modes. We find different types of time evolutions depending on the interplay
between the disorder in the transverse field and the initial conditions of the
system. In the absence of disorder, if the system starts from a low-energy
state, there is one main coherent quantum tunneling event where the
initial-state amplitude is completely depleted in favor of a few discrete
states, with nearby spin quantum numbers; when starting from the highest
excited state, we observe complete inversion of the magnetization through a
peculiar ``backward cascade evolution''. In the random case, the
disorder-averaged transition probability for a low-energy initial state becomes
a smooth distribution, which is nevertheless still sharply peaked around one of
the transitions present in the disorder-free case. On the other hand, the
coherent backward cascade phenomenon turns into a damped cascade with
frustrated magnetic inversion.
