The quantum spin tunneling splitting also occurs for pairs of excited states with opposite magnetization.
As a consequence of quantum spin tunneling, the magnetization of a system can switch between states with opposite magnetization that are separated by an energy barrier much larger than thermal energy.
Thus, quantum spin tunneling provides a pathway to magnetization switching forbidden in classical physics.
In real systems containing Kramers ions, like crystalline samples of single ion magnets, the degeneracy of the ground states is frequently lifted through dipolar interactions with neighboring spins, and as such quantum spin tunneling is frequently observed even in the absence of an applied external field for these systems.
[citation needed] Initially discussed in the context of magnetization dynamics[2][3][4][5] of magnetic nanoparticles, the concept was known as macroscopic quantum tunneling, a term that highlights both the difference with single electron tunneling and connects this phenomenon with other macroscopic quantum phenomena.
It is customary to take z as the easy axis so that D<0 and |D|>> E. For E=0, this Hamiltonian commutes with
In the case of integer spins the second term of the Hamiltonian results in the splitting of the otherwise degenerate ground state doublet.
In this case, the zero field quantum spin tunneling splitting is given by:
From this result, it is apparent that, given that E/D is much smaller than 1 by construction, the quantum spin tunnelling splitting becomes suppressed in the limit of large spin S, i.e., as we move from the atomic scale towards the macroscopic world.
The magnitude of the quantum spin tunnelling splitting can be modulated by application of a magnetic field along the transverse hard axis direction (in the case of Hamiltonian [1], with D<0 and E>0, the x axis).
The modulation of the quantum spin tunnelling splitting results in oscillations of its magnitude,[6] including specific values of the transverse field at which the splitting vanishes.
Quantum tunneling of the magnetization was reported in 1996 for a crystal of Mn12ac molecules with S=10.
[7] Quoting Thomas and coworkers,[7] "in an applied magnetic field, the magnetization shows hysteresis loops with a distinct 'staircase' structure: the steps occur at values of the applied field where the energies of different collective spin states of the manganese clusters coincide.
At these special values of the field, relaxation from one spin state to another is enhanced above the thermally activated rate by the action of resonant quantum-mechanical tunneling".
Quantum tunneling of the magnetization was reported in ferritin[8] present in horse spleen proteins[9] A direct measurement of the quantum spin tunneling splitting energy can be achieved using single spin scanning tunneling inelastic spectroscopy, that permits to measure the spin excitations of individual atoms on surfaces.
Using the same technique other groups measured the spin excitations of S=1 Fe phthalocyanine molecule on a copper surface[12] and a S=1 Fe atom on InSb,[13] both of which had a quantum spin tunneling splitting of the
In the case of molecular magnets with large S and small E/D ratio, indirect measurement techniques are required to infer the value of the quantum spin tunneling splitting.
For instance, modeling time dependent magnetization measurements of a crystal of Fe8 molecular magnets with the Landau-Zener formula, Wernsdorfer and Sessoli [14] inferred tunneling splittings in the range of 10−7 Kelvin.