0.1 0.2 0.3 0.4 0.5 0.6 ndash;15 ndash;10 ndash;5 0 5 10 15 K / T In (1 / t) Resonant magnetization tunnelling in the half-integer-spin single-molecule magnet PPh4Mn12O12(O2CEt)16(H2O)4 Sheila M. J. Aubin,a Stefano Spagna,b Hilary J. Eppley,c Ronald E. Sager,b George Christou*c and David N. Hendrickson*a a Department of Chemistry and Biochemistry-0358, University of California at San Diego, La Jolla, CA 92093, USA b Quantum Design, 11578 Sorrento Valley Road, Suite 30, San Diego, CA 92121, USA c Department of Chemistry, Indiana University, Bloomington, IN 47405-4001, USA Steps are observed on the magnetization hysteresis loop for an oriented crystal sample of PPh4Mn12O12(O2CEt)16- (H2O)4 and these are taken as evidence for field-tuned resonant magnetization tunnelling between quantum levels of the S = 19/2 ground state.The interest in single-molecule magnets (SMM) is growing.1,2 A SMM has a large spin ground state with such a large magnetic anisotropy that an individual molecule exhibits hysteresis in its magnetization vs.external field response. The first SMM reported3ndash;5 is neutral Mn12O12(O2CMe)16- (H2O)4middot;2(HO2CMe)middot;4H2O 1 (denoted Mn12-acetate), which has an S = 10 ground state. Molecules possessing Mn12,6 Mn4,7 Fe8,8 and V4 9 metal contents have been found to function as SMM. Recently, Friedman et al.10 reported the initial observation of resonant magnetization tunnelling for Mn12-acetate; steps were observed at regular intervals of magnetic field in the magnetization hysteresis loop for oriented crystals.Here, we report the observation of steps in the hysteresis loop for oriented crystals of the salt PPh4Mn12O12(O2CEt)16(H2O)4 2. In previous work we have shown11 the Mn122 anions in 2 have an S = 19/2 ground state. The observation of resonant quantum tunnelling in this salt is of considerable interest since a halfinteger- spin system should not tunnel coherently in the absence of a magnetic field.12,13 In solution, it is possible to add a single electron to a Mn12 molecule, and the X-ray crystal structure11 for complex 2 shows that the added electron is localized on an outer (originally Mn3+) ion rather than an inner (cubane) Mn4+ ion, producing a trappedvalence Mn2+, Mn3+ 7, Mn4+ 4 anion in the crystal.The Mn122 anion has an S = 19/2 ground state with the double-well potential energy diagram shown in Fig. 1. There are 20 different states with ms = plusmn;19/2, plusmn;17/2 .. ., plusmn; 1/2. The double well represents the change in potential energy of one Mn122 anion in zero field as the anion changes the direction of its magnetic moment from lsquo;spin uprsquo; (parallel to z-axis) where ms = +19/2 to lsquo;spin downrsquo; (antiparallel to z-axis) where ms = 219/2. The barrier height U is 90yacute;Dyacute;, where D is the parameter characterizing the axial zero-field splitting (DSz 2) in the S = 19/2 ground state. The rate of relaxation of the magnetization was measured for a polycrystalline sample of 2 equilibrated at one of five temperatures in the range 1.8ndash;2.5 K in an external magnetic field of 3.5 T; the latter was then quenched to zero.The decrease in the magnetization measured at each temperature was fitted to a distribution of single exponentials to give the relaxation rate. Relaxation rates were also determined in the range 3.2ndash;7.2 K by means of ac magnetic susceptibility measurements in zero dc field. At a fixed temperature, the in-phase (cMA) and out-ofphase (cMB) components of magnetic susceptibility were measured as the frequency of the ac field (0.05 Oe) was varied from 0.01 to 1500 Hz.The relaxation time (t) at a given temperature was determined by fitting the data to eqn. (1),14 where w is the angular frequency (2pn), cS is the adiabatic susceptibility (i.e. w ? H) and cT is the isothermal cMA = cS + (cT 2 cS)/(1 + w2t2) (1) susceptibility (i.e. w ? 0). The relaxation rates vary from 3.94 3 104 s21 at 7.2 K to 6.19 3 1026 s21 at 1.8 K.Fig. 2 shows an Arrhenius plot of ln(1/t) vs. 1/T. These data were fit to the Arrhenius law to give a barrier height, U, of 60.2 K with a preexponential (1/t0) of 1.31 3 108 s21. This compares with U = 61ndash;67 K and 1/t0 ~ 107 s21 found4,5 for the S = 10 molecule, Mn12-acetate. Fig. 1 Plot of potential energy vs. the magnetization direction for a single molecule with an S = 19/2 ground state in zero magnetic field. Axial zerofield interactions split the S = 19/2 state into m = plusmn;19/2, plusmn;17/2, .. ., plusmn;1/2 levels. Fig. 2 Plot of the logarithm of the rate of relaxation vs. the inverse absolute temperature for PPh4Mn12O12(O2CEt)16(H2O)4 2 Chem. Commun., 1998 803ndash;20 ndash;10 0 10 20 ndash;1 0 1 2 3 ndash;8 ndash;4 0 4 8 106 (dM / d H ) / emu (kOe)ndash;1 103 M / emu H / kOe Five small crystals (3 3 0.1 3 0.1 mm) of 2, grown from CH2Cl2ndash;hexanes, were suspended in eicosane held at 40 deg;C and the suspension introduced into a 5.5 T field, whereupon the five crystals were oriented each with its easy axis parallel to the field.The eicosane was then cooled to room temperature, to give a solid wax cube with the five crystals oriented with parallel easy axes. Fig. 3 shows the hysteresis loop taken at 1.85 K with the magnetic field applied along the easy axes of the crystals. The sample was first saturated in a field of +2.0 T, and the field then swept down to 22.0 T, and cycled back to +2.0 T. The rate of change of the field was 25 Oe s21 and each data point was measured within a few milliseconds.The whole hysteresis loop was collected in 1 h. Steps can clearly be seen on the hysteresis loop, as was reported10 for the neutral molecule, Mn12-acetate. In the lower part of Fig. 3 is shown the first derivative of the hysteresis plot. As the field is decreased from +2.0 T, the first step is seen at zero field, followed by steps at 20.4686, 20.9022 and 21.262 T. The steps correspond to increases in the rate of change of the magnetization, and are attributable to resonant tunnelling between quantum spin states.With reference to Fig. 1, a +2.0 T field leads to a stabilization in energy of the ms = 219/2 and a destabilization of the ms = +19/2 state. When there is saturation, all of the molecules are in the ms = 219/2 state. As the field is decreased, the first step in the hysteresis loop is seen at zero field. Resonant tunneling occurs because the ms levels on the right-hand side of the double well have the same energies as the ms levels on the left.The simplest Hamiltonian for PPh4Mn12O12(O2CEt)16- (H2O)4 2 is given by eqn. (2). �H = 2D�S z 2 2 gmB�S middot; �H (2) If the field is applied along the easy axis, then the eigenstates are IS, ms . The first term in the Hamiltonian gauges the axial zerofield splitting of the S = 19/2 ground state. Physically, this zerofield splitting of the ground state is largely due to the single-ion zero-field splitting at the Mn3+ ions in the Mn122 anion.With the above Hamiltonian, it can be shown that the spacings between the steps in the hysteresis loop are given as DH = 2Dn/gmB, where n = 0, 1, 2, 3, . . . . From Fig. 3, we calculate the average step size to be DH = 0.42 T, which gives a value of D/g of 0.20 cm21, identical to the value obtained for 2 by fitting variable-field magnetization data,11 and high-field EPR data more recently. Friedman et al.10 observed six steps for the neutral Mn12- acetate, including the step at zero field, as the field was swept from zero to 23 T after saturation in a +3 T field.We have observed only four steps for the salt 2, presumably due to the faster relaxation rate of the latter complex. At lower temperatures, more steps should be seen since the relaxation rate will decrease. For both molecular systems, each successive step is seen. This is interesting because the Mn12-acetate molecule has an integer spin ground state with S = 10, whereas the Mn122 anion has a half-integer-spin ground state with S = 19/2.There have been several papers12,13 addressing the fact that a molecule with an odd number of unpaired electrons (such as S = 19/2) should not exhibit resonant tunnelling in the absence of a magnetic field.h a molecule, each pair of plusmn;ms levels in zero-field exhibits Kramers degeneracy. An S = 19/2 molecule should not be able to tunnel coherently between the ms = 219/2 and ms = +19/2 levels, or for that matter, between any ms and 2ms pair in the absence of a magnetic field.However, clearly the salt of Mn122 shows steps on the hysteresis loop. A possible mechanism for resonant tunneling in this S = 19/2 molecule centers around the nuclear spins in the molecule. The 55Mn and 1H nuclei have spins of I = 5/2 and I = 1/2, respectively, and this will give rise to a small internal magnetic field (10ndash;200 G) in the molecule. A transverse component of this internal magnetic field may lead to resonant tunnelling for an oriented collection of Mn122 molecules in zero external field.This work was supported by the National Science Foundation. The W. M. Keck Foundation provided funds for the SQUID magnetometer used in the ac susceptibility experiments. Notes and References dagger; E-mail: christou@indiana.edu 1 B. Schwarzschild, Physics Today, January 1997, 17. 2 E. M. Chudnovsky, Science, 1995, 274, 938. 3 R. Sessoli, D.Gatteschi, A. Caneschi and M. A. Novak, Nature, 365, 141; D. Gatteschi, A. Caneschi, L. Pardi and R. Sessoli, Science, 1994, 265, 1054. 4 R. Sessoli, H.-L. Tsai, A. R. Schake, S. Wang, J. B. Vincent, K. Folting, D. Gatteschi, G. Christou and D. N. Hendrickson, J. Am. Chem. Soc., 1993, 115, 1804. 5 F. Lionti, L. Thomas, R. Ballou, B. Barbara, A. Sulpice, R. Sessoli and D. Gatteschi, J. Appl. Phys., 1997, 81, 4608. 6 S. M. J. Aubin, Z. Sun, I. A. Guzei, A. L. Rheingold, G.Christou and D. N. Hendrickson, Chem. Commun., 1997, 2239. 7 S. M. J. Aubin, M. W. Wemple, D. M. Adams, H.-L. Tsai, G. Christou and D. N. Hendrickson, J. Am. Chem. Soc., 1996, 118, 7746. 8 C. Sangregorio, T. Ohm, C. Paulsen, R. Sessoli and D. Gatteschi, Phys. Rev. Lett., 1997, 78, 4645. 9 S. L. Castro, Z. Sun, C. M. Grant, J. C. Bollinger, D. N. Hendrickson and G. Christou, J. Am. Chem. Soc., in press. 10 J. R. Friedman, M. P. Sarachik, J. Tejada and R. Ziolo, Phys. Rev. Lett., 1996, 76, 3830. 11 H. J. Eppley, H.-L. Tsai, N. de Vries, K. Folting, G. Christou and D. N. Hendrickson, J. Am. Chem. Soc., 1995, 117, 301. 12 D. Loss, D. P. Di Vincenzo, G. Grinstein, D. Awschalom and J. F. Smyth, Physica B, 1993, 189, 189. 13 D. P. Di Vincenzo, Physica B, 1994, 197, 109. 14 R. L. Carlin, Magnetochemistry, Springer-Verlag, Berlin, 1986. Received in Bloomington, IN, USA, 21st January 1998; 8/00586I Fig. 3 The top plot shows the magnetization hysteresis loop measured at 1.85 K for five crystals of PPh4Mn12O12(O2CEt)16(H2O)4 2 oriented in an eicosane wax matrix. In the lower plot is shown a plot of the first derivative of the magnetization hysteresis loop. 804 Chem. Commun., 1998
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