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2009 MAGNETIC SYSTEMSHigh field torque magnetometry on a molecular Dysprosium triangleLanthanide based molecular nanomagnets have been attractingconsiderable attention due to their interesting magneticproperties. Mononuclear complexes of 4f ions haveshown slow relaxation of the magnetization at very hightemperatures compared to those observed in transition metals.Despite their out of phase ac signal observed above 40K, hysteresis curves were observed only at very low temperatures[Ishikawa et al., Angew. Chem. 117, 2991 (2005)].On cooling, deviations from the Arrhenius law predictedfor single molecule magnet behavior become more important,which indicates that tunnelling plays a crucial role inthe relaxation of the magnetization. It is therefore of crucialimportance to obtain information on the low lying sublevelsof the 4f electronic systems, in order to understand the magnetism,and especially the relaxation mechanisms of thesecompounds.We have performed high field torque magnetometry measurementson the recently investigated molecular Dy triangle[Luzon et al., Phys. Rev. Lett. 100 247205(2008)]. This compound shows an unprecedented magneticbehaviour having a non-magnetic ground doublet whichoriginates from the noncollinearity of the single-ion easyaxes of the Dy 3+ ions that lie in the plane of the triangleat 120 ◦ one from each other. This gives rise to a peculiarchiral nature of the ground nonmagnetic doublet and toslow relaxation of the magnetization which exhibits abruptaccelerations at the crossings of the discrete energy levels.The ground (|J = 15/2,m J = ±15/2〉) and the first excited(|J = 15/2,m J = ±13/2〉) doublets, were considered to describethe energy levels of the single ion assuming that theother excited states are very high in energy and do not contributeto the magnetic properties at low temperatures. Thesystem therefore mimics the behaviour of an S=3/2 spin.We have used the spin Hamiltonian approach to describethe low lying energy levels. The expression of the Hamiltonianused is,anisotropy in the system. The performed high field torquemeasurements at 50 mK enabled us to quantify the crystalfield splitting between the 15/2 and the 13/2 doubletsin Dy 3+ . Figure 109 (a) shows the measured torque signalat 50 mK up to 32 Tesla for the magnetic field applied atdifferent angles to the plane of the triangle. A peak in thetorque is evident at around 28 Tesla. Figure 109 (b) showsthe calculated torque signals for δ = 250 cm −1 , j = 0.064cm −1 , and g = 1.35 at 50 mK, which reproduce fairly wellthe experimentally observed curves. The observed peak inthe torque signal at around 28 Tesla for transverse magneticfields points towards the high anisotropy in the system. Thecrystal field splitting of δ = 250 ± 10 cm −1 is close to thatexpected from previously performed ab initio calculations[Chibotaru et al., Angew. Chem. Int. Ed. 47, 4126 (2008)].In a more general picture, this study has contributed to abetter understanding of lanthanide based systems. In particular,we have proven that high field torque magnetometrycan be a good substitute to spectroscopy in systems whichare spectroscopically inactive.Ĥ = − j(Ŝ 1 · Ŝ 2 + Ŝ 2 · Ŝ 3 + Ŝ 3 · Ŝ 1 )− gµ B ∑ B · Ŝ i + δ oi=1,314 ∑ (( 15i=1,32 )2 − Ŝ 2 z i)(16)The first term is the isotropic exchange between the Dy 3+ions, the second is the Zeeman term, and the last termdescribes the single-ion anisotropy where δ o is the zerofield splitting between |J = 15/2,m J = ±15/2〉 and |J =15/2,m J = ±13/2〉 states of each Dy 3+ ion. We have particularychosen torque magnetometry as it is a strong tool toinvestigate the anisotropy in high-spin clusters, especiallyin systems which are not accessible by spectroscopy. Apeak in the torque signal occurs at a characteristic fieldwhich depends on the temperature as well as the magneticFigure 109: (a) Torque signals for the magnetic field applied atdifferent angles close to 90 ◦ from the plane of the triangle at 50mK. (b) Similar calculated torque curves with the best fit parameters(δ = 250 cm −1 , j = 0.064 cm −1 , and g = 1.35). The temperatureand anisotropy dependent peak in the torque signal is evidentat around 28 Tesla. The inset shows the molecular structure of theDy 3 cluster.A. B. Antunes, I. SheikinF. El Hallak, J. van Slageren, M. Dressel (University of Stuttgart, Germany), M. Etienne, J. Luzon, R. Sessoli (Universityof Florence, Italy), C. Anson, A. Powell (University of Karlsruhe, Germany)81