Thermally assisted resonant quantum tunneling of magnetization in Fe8 clusters

Magnetic ac susceptibility of randomly arranged crystallites ~powder sample ! and well-oriented Fe 8 crystallites has been measured as a function of applied magnetic field, temperature, and frequency. The Fe8 clusters, made of eight iron ions and with formula @~tacn!6Fe8O2~OH!12# , have a ground state S510. From the magnetization data M (H) with the dc field, H, applied parallel and perpendicular to the easy axis of the aligned sample and x9(T) data for different frequencies, the anisotropy fieldHan;5 T and energy barrier U/kB526.9 K were obtained. Peaks in the curves of x8(H) were clearly observed at fields Hn5nH0 , with n50,61 for powder sample where H0 52.4 kOe; andn50, 61, 62, for an oriented sample where H052.2 kOe. These peaks appearing at Hn5nH0 in the curves ofx8(H) can be well described by the thermally assisted resonant quantum tunneling of magnetization. © 1999 American Institute of Physics. @S0021-8979 ~99!75708-7#

Magnetic ac susceptibility of randomly arranged crystallites ͑powder sample͒ and well-oriented Fe 8 crystallites has been measured as a function of applied magnetic field, temperature, and frequency.The Fe 8 clusters, made of eight iron ions and with formula ͓͑tacn͒ 6 Fe 8 O 2 ͑OH͒ 12 ͔ 8ϩ , have a ground state Sϭ10.From the magnetization data M (H) with the dc field, H, applied parallel and perpendicular to the easy axis of the aligned sample and Љ(T) data for different frequencies, the anisotropy field H an ϳ5 T and energy barrier U/k B ϭ26.9 K were obtained.Peaks in the curves of Ј(H) were clearly observed at fields H n ϭnH 0 , with nϭ0,Ϯ1 for powder sample where H 0 ϭ2.4 kOe; and nϭ0, Ϯ1, Ϯ2, for an oriented sample where H 0 ϭ2.2 kOe.These peaks appearing at H n ϭnH 0 in the curves of Ј(H) can be well described by the thermally assisted resonant quantum tunneling of magnetization.© 1999 American Institute of Physics.

͓S0021-8979͑99͒75708-7͔
Recently, resonant quantum tunneling of magnetization has been found in molecular magnet Mn 12 , 1-5 and antiferromagnetic ferritin particles, 6 which is different from the quantum tunneling of magnetization studied previously. 7,8The resonant tunneling of spins ͑or magnetization͒ is said to be thermally assisted, that is, the measured magnetization change ͑or susceptibility͒ caused by the resonant tunneling effect is governed not only by the tunneling rate of the dominant spin level͑s͒ but also by the thermal population of the very spin level͑s͒ simultaneously.It was found that the tunneling effect can be tuned by temperature and applied magnetic field, which resulted in the observation of some characteristic features ͓e.g., the jumps equally spaced in magnetization data M (H) [1][2][3][4] and peaks in the real part of susceptibility Ј(H)]. 5Although the effects of the applied dc field on tunneling have also been observed in magnetic nanoparticles, no fine features have been observed. 7In the studies of magnetic nanoparticles, 7 except the antiferromagnetic ferritin particles, there are a large number of spins ͑a sizable magnetic moment͒ in each particle involved in a tunneling event.This large number of spins and not very high anisotropy of the particles will normally lead to an almost continuous spectrum of the spin levels.Consequently no fine feature corresponding to the discrete levels will be observed.Resonant tunneling of magnetization has also been a subject of intensive theoretical studies. 9,10unneling of magnetization in a Fe 8 powder sample was recently observed by measuring the M (H) at very low temperatures. 11It was suggested that a possible source of tunneling in the Mn 12 system could be a small transverse magnetic field, perhaps of dipolar or hyperfine origin, 9 whereas the Fe 8 system is described by the spin Hamiltonian with the transverse anisotropy, which may require separate theoretical investigation. 10In this paper we report on the magnetization and ac-susceptibility study on the Fe 8 clusters to gain a deeper understanding of the physics underlying the resonant tunneling of magnetization.Fe 8 clusters with formula ͓͑tacn͒ 6 Fe 8 O 2 ͑OH͒ 12 ͔ 8ϩ , where tacn is the organic ligand trizacyclononane, 12 have approximate D 2 symmetry.Magnetic measurements showed that a Fe 8 cluster has a spin ground state Sϭ10, resulting from the competing antiferromagnetic coupling between eight Fe 3ϩ ions of spin sϭ5/2. 13The materials used in this experiment are pure Fe 8 crystallites with an average size of 0.2ϫ0.1ϫ0.1 mm.Since it is impossible to measure only one crystallite on the Quantum Design superconducting quantum interference device ͑SQUID͒ magnetometer, a sample composed of aligned crystallites embedded in a nonmagnetic matrix was used.After putting the mixture of Fe 8 crystallites and epoxy in a field of 9.6 T for 12 h, a solid cylinder with a diameter of 3 mm and length of 6 mm was obtained.The good alignment of the crystallites is confirmed by the dc-magnetization data shown in Fig. 1.
Magnetization as a function of temperature was measured in zero field cooled and field cooled processes in a small field of 5 Oe from 1.8 to 40 K, no blocking phenomenon was observed, in agreement with a previous article. 11a͒ Electronic mail: phxxz@ust.hkFigure 1 shows the magnetization as a function of dcmagnetic field, M (H), obtained at 1.8 and 2.5 K, with the field applied parallel and perpendicular to the axis of the cylindrical sample.It is clearly seen that the magnetization curves obtained at 1.8 and 2.5 K are almost superposed, indicating a very weak temperature-dependent behavior of M (H) near the blocking temperature 1.3 K. 11 Therefore, we can consider that the magnetization curves measured at 1.8 K should possess qualitatively the characteristics of that measured below the blocking temperature.As seen in Fig. 1, the behavior of M (H) for H parallel and perpendicular to the axis of the sample are completely different.For H parallel to the sample axis, M saturated at quite low field ͑at ϳ5 kOe͒; whereas, when H was applied perpendicularly to the sample axis, M just nearly saturated up to 50 kOe.The quality of alignment of the crystallites can be checked by the high field magnetization M (5 T) and the saturation magnetization M (0) which is obtained by extrapolating the magnetization curve ͑for H parallel to the axis of the sample͒ in the range of 5 and 1 T to Hϭ0.In Fig. 1, M (5 T)/M (0)Ϸ0.99 suggests a misorientation no more than 1°and an Ising-type anisotropy. 14The anisotropy field can be taken approximately to be 5 T. 15 Figure 2 shows the real part Ј(T) and imaginary part Љ(T) of the susceptibility versus temperature for f ϭ250, 499, 997, and 1490 Hz obtained on the aligned crystallites.It is evident that peaks in Ј(T) and Љ(T) shift to high temperatures with increasing f.For a system composed of identical magnetic clusters, Љ(T) shows a maximum at temperature T p when 2 f ϭ1.The relaxation time is given by ϭ 0 exp(U/k B T), where U is the anisotropy energy barrier for flipping the magnetic moment of the particle; 0 is the characteristic time of the system or the reciprocal of attempt frequency f 0 .Therefore, by fitting T p obtained from Fig. 2 for different frequencies to ln fϭln(f 0 /2)Ϫ(U/k B T p ), f 0 ϭ1.54ϫ10 8 Hz, and U/k B ϭ26.94 K were obtained.The energy barrier U/k B ϭ26.72 K and the attempt frequency f 0 ϭ1.39ϫ10 8 Hz have also been obtained from the temperature-dependent susceptibility measured on the powder sample, consistent with the values obtained on the oriented sample.
The ac susceptibility as a function of dc field has been measured at different temperatures ͑1.8-4 K͒ with different frequencies ͑1-1500 Hz͒ for the aligned sample and the powder sample.Figures 3͑a͒ and 3͑b͒ show the fielddependent Ј(H) obtained at 2.5 K for the powder sample and aligned sample, respectively.It is evident that two peaks at Hϭ0 and ϳ2400 Oe and three peaks at H n ϭnH 0 with nϭ0, 1, 2 and H 0 ϭ2.2 kOe appear in Ј(H) for the random and aligned sample, respectively.
These peaks indicate that the relaxation rate increases markedly at regular intervals of the magnetic field when field is applied parallel to the easy axis of magnetization.The similar phenomenon observed in Mn 12 is attributed to resonant tunneling between energy levels in opposite well of the double-well potential.This interpretation is based on a single spin of Sϭ10 model with strong uniaxial anisotropy ͑Hϭ ϪDSz 2 Ϫg B S•H, where D is the anisotropy energy͒ for which energy levels corresponding to the spin-up and spindown in the opposite wells coincide at fields H n ϭnD/g B BϭnH 0 .As illustrated in Fig. 4, pairs of levels become degenerate at regular intervals of field, and tunneling occurs between states near the top of barrier.In this process, spins first populate to the high energy levels by thermal activation, then tunnel to the opposite side of the double well through the particular level͑s͒, and decay to the bottom of the well.The particular level which dominates the magnetic transition ͑susceptibility͒ determines the effective energy barrier ͑Fig.4͒ involved in the relaxation process.This effective energy barrier oscillates with applied magnetic field along the easy axis.Consequently, the relaxation rate will oscillate with the applied field.
As known that Fe 8 clusters have a spin Sϭ10 and an Ising-type anisotropy ͑the anisotropy field H a ϳ5 T͒ indicated by Fig. 1, we can apply the above model to Fe 8 clusters.For the Fe 8 cluster, the resonant field H n ϭnH 0 with H 0 ϭD/g B ϭH a /2Sϭ2.5 kOe which are in agreement with the H 0 observed in Fig. 3 and the values obtained in the ac-susceptibility measurements. 11 optimizing the parameters which govern the tunneling susceptibility such as temperature, ac-field frequency, and magnetic field, the peak corresponding to H 3 ϭ3H 0 ϭ6.6 kOe is observed at Hϭ6.56 kOe in Ј(H) measured at Tϭ2 K with f ϭ500 Hz.The only peak ͑except the peak at Hϭ0͒ observed in the powder sample might be caused by the random distribution of easy axis which leads to a broad distribution of the resonant tunneling fields.The broad distribution might smear out the higher order resonant tunneling peaks, say, for nу2.Another feature that should be noted is that the resonant field H 0 ϭ2.4 kOe in the powder sample is higher than that in the aligned sample.This is due to the fact that the position of resonance in (H) only depends on the field applied along the easy axis of magnetization.The field along the easy axis is H cos , where is the angle between the applied field and easy axis, therefore the resonance should always appear at a higher total applied field in a powder sample than in aligned samples. 4e, therefore, conclude that the peaks appearing in Ј(H) at fields H n ϭnH 0 can be ascribed to thermally assisted resonant tunneling of spins.The anisotropy field of Fe 8 clusters has been extracted from the dc-magnetization data, which is agreement with the electron paramagnetic resonance experiment. 14

FIG. 1 .
FIG.1.Magnetization as a function of dc-magnetic field applied parallel and perpendicular to the easy axis of the sample, obtained at 1.8 and 2.5 K.