Local field dynamics in a resonant quantum tunneling system of magnetic molecules

Abstract

We observed non-exponential relaxation for a quantum tunneling molecular magnetic system at very low temperatures and argue that it results from evolving intermolecular dipole fields. At the very beginning of the relaxation, the magnetization follows a square-root time dependence. A simple model is developed for the intermediate time range that is in good agreement with the data over 4 decades in time. Detailed numerical calculations as well as measurements are presented which indicate unusual correlation effects in these systems. PACS. 75.45.+j Macroscopic quantum phenomena in magnetic systems -61.46.+w Clusters, nanoparticles, and nanocrystalline materials -75.60.Ej Magnetization curves, hysteresis, Barkhausen and related effects Recent experiments have shown evidence of quantum tunneling of the magnetization in the molecular nanomagnetic systems Fe8 [1] and Mn12ac [2,3]. General theoretical considerations for quantum tunneling of a giant spin through its anisotropy energy barrier have been proposed during the last 10 years [4]. Both Fe8 and Mn12ac can be thought of as an ensemble of identical, iso-oriented nanomagnets of net spin S = 10 with an Ising like anisotropy. Fe8 has the advantage in terms of tunneling measurements in that its anisotropy energy barrier is approximately 24 K compared to 63 K for Mn12ac, and its crystal symmetry affords a sizable transverse anisotropy, both of which greatly enhance tunneling effects [1,4].At low enough temperatures (below 400 mK and approximately 1.8 K, respectively) both systems display a crossover from a thermal activated (over barrier) relaxation to a temperature independent relaxation [1,2] with a remarkable resonant structure of the relaxation time as a function of the external field [1,3]. Below these crossover temperatures and after saturation in a high field, only the m S = +10 state is occupied and the only way relaxation can occur (at the first resonance field B = 0) is by under barrier quantum tunneling from the m S = +10 to the m S = −10 state.Ideally, the relaxation for non interacting, identical (giant) spins would be given by an exponential function M (t) ∝ exp(−t/τ ). However, for Fe8 the data in the low temperature regime is best approximated by a stretched exponential M (t) ∝ exp(−(t/τ stretch ) β ) a

Photon-induced magnetization reversal in theFe8single-molecule magnet

“…In our simulations, we used T 2 = 0.17 ns, a value that allowed us to reproduce most of the data curves well. This value is a lower bound for T 2 since it may reflect the effects of inhomogeneities from dipole fields, anisotropy parameters and g factors [15][16][17]. Our line widths are consistent with those found spectroscopically by others [18].…”

Observation of the Distribution of Molecular Spin States by Resonant Quantum Tunneling of the Magnetization

“…Indeed the predicted √ t relaxation (Eq. (1)) has been seen in preliminary experiments on fully saturated Fe 8 crystals [8]. We 1…”

“…The distributions become more broad as the initial magnetization becomes smaller reflecting the random fraction of reversed spins. The small satellite bumps are due to flipped nearest neighbor spins on the tri-clinic lattice as seen in computer simulations [8,13].…”

“…In this regime only the two lowest levels of each molecule are occupied, and only "pure" quantum tunneling through the anisotropy barrier can cause direct transitions between these two states. It was surprising however that the observed relaxation of the magnetization in the quantum regime was found to be non-exponential and the resonance width orders of magnitude too large [5,8]. The key to understanding this seemingly anomalous behavior now appears to involve the ubiquitous hyperfine fields as well as the (inevitable) evolving distribution of the weak dipole fields of the nanomagnets themselves [9].…”

“…Figure 2 shows a typical set of relaxation curves plotted against the square-root of time. However instead of saturating the sample before each relaxation measurement so that the initial magnetization M in = M s as described in [8], these measurements were made by rapidly quenching the sample from 2 K in zero field (ZFC), i.e. for an initial magnetization M in = 0.…”