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

Abstract

Below 360 mK, Fe8 magnetic molecular clusters are in the pure quantum relaxation regime and we show that the predicted "square-root time" relaxation is obeyed, allowing us to develop a new method for watching the evolution of the distribution of molecular spin states in the sample. We measure as a function of applied field H the statistical distribution P (ξH) of magnetic energy bias ξH acting on the molecules. Tunneling initially causes rapid transitions of molecules, thereby "digging a hole" in P (ξH) (around the resonant condition ξH = 0). For small initial magnetization values, the hole width shows an intrinsic broadening which may be due to nuclear spins.PACS numbers: 75.45.+j, 75.60Ej Strong evidence now exists for thermally-activated quantum tunneling of the magnetization (QTM) in magnetic molecules such as Mn 12 ac and Fe 8 [1][2][3][4][5]. Crystals of these materials can be thought of as ensembles of identical, iso-oriented nanomagnets of net spin S = 10 for both Mn 12 ac and Fe 8 , and with a strong Ising-like anisotropy. The energy barrier between the two lowest lying spin states with S z = ±10 is about 60 K for Mn 12 ac and 25 K for Fe 8 [6,7]. Theoretical discussion of thermallyactivated QTM assumes that thermal processes (principally phonons) promote the molecules up to high levels, not far below the top of the energy barrier, and the molecules then tunnel inelastically to the other side. The transitions are therefore almost entirely accomplished via thermal excitations.At temperatures below 360 mK, Fe 8 molecular clusters display a clear crossover from thermally activated relaxation to a temperature independent quantum regime, with a pronounced resonance structure of the relaxation time as a function of the external field [5]. This can be seen for example by hysteresis loop measurements (Fig. 1). 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].In this letter, we focus on the low temperature and low field limits, where phonon-mediated relaxation is astronomically long and can be neglected. In this limit, the S z = ±10 spin states are coupled by a tunneling matrix element ∆ tunnel which is estimated to be about 10 −8 K [9]. In order to tunnel between these states, the magnetic energy bias ξ H = gµ B SH due to the local magnetic field H on a molecule must be smaller than ∆ tunnel implying a local field smaller than 10 −9 T for Fe 8 clusters. Since the typical intermolecular dipole fields are of the order of 0.05 T, it seems at first that almost all...

Ferrimagnetic cagelikeFe4O6cluster: Structure determination from infrared dissociation spectroscopy

“…Such energy would mean the Curie temperature of such clusters to be higher than that of the bulk material ͑ϳ950 K͒. This is many times higher than the exchange found in other small magnetic entities-magnetic molecules, 25,26 even though there are certain similarities with the oxide cores of such materials, in particular, typical ferrimagnetic spin configuration. Therefore such clusters are very interesting for fundamental studies of subnanometer magnetism and may be useful to create new materials with tailored magnetic properties.…”

Time relaxation of interacting single-molecule magnets

“…The time evolution of "holes" that, under suitable conditions, develop in a magnetization density function, have also been reported. 6,7 The existing theory at the time 5,8,9 predicted a universal √ t short time relaxation from a fully polarized system, but said little about relaxation from or into weakly polarized states. 10 Other theories 11 take hyperfine interactions into account but disregard dipole-dipole interactions.…”

“…[6]. In them, a crystalline sample of SMM's is first quenched from k B T ∼ U/S to k B T 0.1U/S in either (a) a weak applied magnetic field of a few mT, and later observed after the field is switched off at time t = 0 or (b) a zero field, and later observed after a weak field is applied at t = 0.…”

“…However, MC simulations have been performed for various fully occupied cubic lattices, which have given values of p that agree with our predictions. 13,14 This paper's first aim is to extract from our theory how the magnetization is supposed to relax in Fe 8 , compare this with experiment over the time span where published experimental data exists, 6 and make predictions for later times. It is also our purpose to predict, and check with MC simulations, how m relaxes with t for other spatial distributions, namely, under full spatial disorder, thus providing another test for our theory.…”

Molecular nanomagnet in periodic magnetic field

“…It was proven experimentally that they display quantum hysteresis and quantum tunneling at the molecular level [1], [2], [3], [4], nonexponential dynamic scaling of the magnetization relaxation [5] and tunneling rate variations due to Berry phase [6], [7], [8]. Many efforts have been made to observe the quantum coherence [9].…”