Self-Organized Patterns of Macroscopic Quantum Tunneling in Molecular Magnets

We study low temperature resonant spin tunneling in molecular magnets induced by a field sweep with account of dipole-dipole interactions. Numerical simulations uncovered formation of self-organized patterns of the magnetization and of the ensuing dipolar field that provide resonant conditions inside a finite volume of the crystal. This effect is robust with respect to disorder and should be relevant to the dynamics of the magnetization steps observed in molecular magnets.

Figure 1

Thermally assisted tunneling.

Figure 2

Moving wall of resonant spin tunneling induced by a slow sweep, $\epsilon =10$. There are well-developed spatially quasiperiodic, time independent structures behind the wall.

Figure 3

Spatial profiles of the metastable population $n_{-S}$ and the reduced bias $\tilde{W}$ at ${\tilde{W}}_{\mathrm{ext}}=4.3$ and ${\tilde{E}}_D=200$. Everywhere in the wall the system is near the resonance, $\tilde{W}\approx 0$.

Figure 4

Time dependence of the average metastable population ${\overline{n}}_{-S}=⟨n_{-S}⟩$.

Figure 5

Spatial profiles of the metastable population $n_{-S}$ and the reduced bias $\tilde{W}$ in the presence of a relatively strong disorder. The condition $\tilde{W}\approx 0$ inside the wall is not affected by disorder.