Deflagration, fronts of tunneling, and dipolar ordering in molecular magnets

Although there is no exchange interaction in crystals of molecular magnets characterized by a giant effective spin $S$ ($S$ =10 for Mn$_{12}$, and Fe$_{8})$, magnetic field $B^{(D)}$ generated by magnetic moments \textit{g$\mu $}$_{B}S$ of magnetic molecules creates energy bias $W^{(D) }$=2\textit{Sg$\mu $}$_{B} B^{(D)}$ on a molecule that largely exceeds the tunnelling splitting $\Delta $ of matching quantum states on different sides of the anisotropy barrier. Thus the dipolar field has a profound influence on the processes of tunnelling and relaxation in molecular magnets. Both theoretical and experimental works showed a slow non-exponential relaxation of the magnetization in both initially ordered and completely disordered states since most of the spins are off tunneling resonance at any time. Recently a new mode of relaxation via tunneling has been found, the so-called fronts of tunneling, in which (within a 1$d$ theoretical model) dipolar field adjusts so that spins are on resonance within the broad front core. In this ``laminar'' regime fronts of tunnelling are moving fast at speeds that can exceed that of the temperature-driven magnetic deflagration, if a sufficiently strong transverse field is applied. However, a ``non-laminar'' regime has also been found in which instability causes spins to go off resonance and the front speed drops. In a combination with magnetic deflagration, the laminar regime becomes more stable and exists in the whole dipolar window 0$\le W \quad \le W^{(D)}$ on the external bias $W$, where the deflagration speed strongly increases. Another dipolar effect in molecular magnets is dipolar ordering below 1 K that has recently been shown to be non-uniform because of formation of magnetic domains. An object of current research is possible non-uniformity of magnetic deflagration and tunneling fronts via domain instability that could influence their speed.