Master Equations for pulsed magnetic fields: Application to magnetic molecules

摘要

We extend spin-lattice relaxation theory to incorporate the use of pulsedmagnetic fields for probing the hysteresis effects and magnetization steps andplateaus exhibited, at low temperatures, by the dynamical magnetization ofmagnetic molecules. The main assumption made is that the lattice degrees offreedom equilibrate in times much shorter than both the experimental time scale(determined by the sweep rate) and the typical spin-lattice relaxation time. Wefirst consider the isotropic case (a magnetic molecule with a ground state ofspin $S$ well separated from the excited levels and also the general isotropicHeisenberg Hamiltonian where all energy levels are relevant) and then weinclude small off-diagonal terms in the spin Hamiltonian to take into accountthe Landau-Zener-St\"{u}ckelberg (LZS) effect. In the first case, and for an$S=1/2$ magnetic molecule we arrive at the generalized Bloch equation recentlyused for the magnetic molecule \{V$_6$\} in Phys. Rev. Lett. 94, 147204 (2005).An analogous equation is derived for the magnetization, at low temperatures, ofantiferromagnetic ring systems. The LZS effect is discussed for magneticmolecules with a low spin ground state, for which we arrive at a veryconvenient set of equations that take into account the combined effects of LZSand thermal transitions. In particular, these equations explain the deviationfrom exact magnetization reversal at $B\approx 0$ observed in \{V$_6$\}. Theyalso account for the small magnetization plateaus (``magnetic Foehn effect''),following the LZS steps, that have been observed in several magnetic molecules.Finally, we discuss the role of the Phonon Bottleneck effect at lowtemperatures and specifically we indicate how this can give rise to apronounced Foehn effect.