Quantum Magnetic Deflagration in Mn12 Acetate

We report controlled ignition of magnetization reversal avalanches by surface acoustic waves in a single crystal of Mn12 acetate. Our data show that the speed of the avalanche exhibits maxima on the magnetic field at the tunneling resonances of Mn12. Combined with the evidence of magnetic deflagration in Mn12 acetate (Suzuki et al., cond-mat/0506569) this suggests a novel physical phenomenon: deflagration assisted by quantum tunneling.


Magnetic properties of Mn
-acetate have been intensively studied after the magnetic bi-stability of this molecular cluster below 3.5 K was demonstrated [1]. The bi-stability is caused by a large spin of the cluster, S = 10, and by strong uniaxial magnetic anisotropy that provides a 65 K energy barrier between spin-up and spin-down states. At low temperature a magnetized Mn 12 crystal exhibits two modes of magnetic relaxation. The first mode is a slow one. It manifests itself in a staircase hysteresis curve which is due to thermally assisted quantum tunneling of the magnetization [2]. The second relaxation mode, exhibited by sufficiently large crystals, is a much more rapid magnetization reversal that typically lasts less than 1 ms. It was initially studied by Paulsen and Park [3] and attributed to a thermal runaway or avalanche (see also Ref. 4). In the avalanche, the initial relaxation of the magnetization towards the direction of the field results in the release of heat that further accelerates the magnetic relaxation. Recent local magnetic measurements of Mn 12 crystals [5] have demonstrated that during an avalanche the magnetization reversal occurs inside a narrow interface that propagates through a crystal at a constant speed of a few meters per second. It has been argued that this process is analogous to the propagation of a flame front (deflagration) through a flammable chemical substance. The conventional theory of deflagration, in the first approximation, yields the following expression for the velocity of the flame front [5,6,7]: Here U, τ 0 , and T f are the energy barrier, the attempt frequency, and the temperature of the "flame" in the expression τ = τ 0 exp (U/k B T f ) for the "chemical reaction" time, and κ is thermal diffusivity. In the case of Mn 12 , κ ∼ 10 −5 m 2 /s, τ 0 ∼ 10 −7 s, and the field dependence of the energy barrier, U(H), is well known.
In a flammable chemical substance the potential barrier is a constant determined by the nature of the chemical reaction that transforms a metastable chemical into a stable chemical (e.g. a mixture of hydrogen and oxygen transforms into water). On the contrary, for the staircase hysteresis curve in Mn 12 and other molecular magnets. Due to this effect, one also should expect that the velocity of the avalanche, given by Eq. (1), increases at the resonant values of the magnetic field.
In the experiment of Suzuki et al. [5] avalanches were ignited in a stochastic way on sweeping magnetic field between −5 T and 5 T. In such an experiment one cannot control the ignition process. Consequently, the probability that the avalanche occurs at a tunneling resonance is low, which may explain why no oscillation of v on H due to resonant spin tunnelling has been observed. In this Letter we report a novel method of controlled ignition of avalanches in Mn 12 acetate at constant magnetic field by means of surface acoustic waves (SAW). We demonstrate that the velocity of the deflagration front, and the ignition rate, oscillate on the magnetic field in accordance with the expectation that quantum spin tunneling lowers the barrier for the deflagration. Thus, in effect, Mn 12 acetate exhibits a phenomenon which has not been seen in any other substance: slow burning (deflagration) To study magnetic avalanches, we first saturated the sample at −2 T and 2.1 K. The field was then varied at a constant rate of 300 Oe/s until a desired value of H was reached.
Maintaining this field value, we delivered to the sample the SAW pulses of increasing duration until the avalanche was triggered. This way, for each value of the magnetic field, a threshold duration of the SAW pulse needed to ignite the avalanche (that is, the threshold energy delivered to the sample) has been established. The required duration of the pulse was found to decrease with the magnetic field in accordance with the expectation that the "flammability" of the Mn 12 crystal increases on increasing H. These measurements have established a new method of igniting magnetization avalanches in molecular magnets. The advantage of using SAW is a total control over the field at which the avalanche takes place. to the specific heat, C(T ), through the relation where H is the field at which the avalanche occurs, ∆M is the total change of magnetization, and T i is the initial temperature. T f was found to be in the range between 6 K and 9 K, depending on the magnetic field. The only fitting parameter was √ κτ 0 for which the value of 2 × 10 −6 m was obtained. This agrees with κ ∼ 10 −5 m 2 /s and τ 0 ∼ 10 −7 s, known from independent measurements.
Vertical lines in Fig. 4  This observation is a clear evidence of the quantum aspect of the deflagration. To be precise, the magnetic deflagration corresponding to the avalanche is, of course, a thermal phenomenon, driven by thermal conductivity. However, the speed of the deflagration is also determined by the speed of "chemical reaction", which, in our case, is the rate of the transition between the two wells shown in Fig. 1. This rate is determined by both thermal activation to the excited spin levels and quantum tunneling between the levels. It is actually the thermally assisted quantum tunneling that accelerates deflagration at tunneling resonances. To our knowledge, slow burning (deflagration) assisted by quantum tunneling has never been observed in any chemical substance. In a crystal of molecular nanomagnet it becomes observable due to the possibility to control the speed of the deflagration by the magnetic field.
In conclusion, a new method of igniting magnetization reversal in molecular magnets by surface acoustic waves has been developed. We have observed a fundamentally new phenomenon: magnetic deflagration assisted by quantum tunneling. We have demonstrated that quantum tunneling can be seen not only in slow relaxation of molecular magnets (through staircase hysteresis loop) but also in the fast relaxation, that is avalanche, which is a process equivalent to slow burning. This observation opens a new way for the study of quantum phenomena in molecular magnets, as well as for the experimental study of the complex deflagration physics. We