Interference effect in the Landau-Zener tunneling of the antiferromagnetically coupled dimer of single-molecule magnets

Two antiferromagnetically coupled tunneling systems compose a minimal model exhibiting the effect of the quantum-mechanical phase in the Landau-Zener effect. It is shown that the averaged staying probability oscillates versus the resonance shift between the two particles, as well as versus the sweeping rate. Such a resonance shift can be produced in ${\mathrm{Mn}}_4$ dimers by the gradient of the magnetic field.

Figure 1

Bare energy levels $(\Delta =0)$ for two antiferromagnetically coupled tunneling systems for $V<4J$.

Figure 2

Staying probabilities for a system of two antiferromagnetically coupled particles $a$ vs resonance shift $V$. Asymptotic values are shown by horizontal dased lines. $b$ vs sweep parameter $\epsilon$.