Experimental determination of the dipolar field in Mn12-acetate
S. McHugh, R. Jaafar, M. P. Sarachik, Y. Myasoedov, H. Shtrikman, E. Zeldov, R. Bagai, G. Christou
aa r X i v : . [ c ond - m a t . o t h e r] O c t Experimental determination of the dipolar field in Mn -acetate S. McHugh, R. Jaafar, and M. P. Sarachik ∗ Department of PhysicsCity College of New York, CUNYNew York, New York 10031, USA
Y. Myasoedov, H. Shtrikman, and E. Zeldov
Department of Condensed Matter PhysicsThe Weizmann Institute of ScienceRehovot 76100, Israel
R. Bagai and G. Christou
Department of ChemistryUniversity of FloridaGainesville, Florida 32611, USA
Crystals of the molecular magnet Mn -acetate are known to contain a small fraction of low-symmetry (minor) species with a small anisotropy barrier against spin reversal. The lower barrierleads to faster magnetic relaxation and lower coercive field. We exploit the low coercive fields ofthe minor species to make a direct determination of the dipole field in Mn -ac. We find that thedipolar field of a fully magnetized crystal is 51 . ± . Mn -acetate is one of the first synthesized and beststudied examples of a molecular magnet. Each moleculein a crystal of Mn -ac contains a cluster of twelveMn atoms surrounded by non-magnetic ligands. TheMn atoms are coupled antiferromagnetically by superex-change via oxygen bridges, forming a ferrimagnetic clus-ter at low temperatures with a large spin S = 10 and azero-field barrier to relaxation U ≈
60 K [1, 2]. Theoret-ical estimates and experimental observations have indi-cated that interactions between the molecules are weakand the system can be described by an effective Hamil-tonian [3] H = − DS z − gµ B B z S z + . . . + H ⊥ (1)where D = 0 . H ⊥ is a small symmetry-breakingterm that allows tunneling across the anisotropy bar-rier. The Mn -acetate molecule can thus be modeledby a double-well potential plotted as a function of an-gle, with (2 S + 1) discrete energy levels correspondingto the quantum-mechanical spin projections along theeasy, c-axis of the crystal, ( S z = 10 , , , . . . − , − T B ∼ µ H z ) = D/gµ B ,assuming B z = µ H z . The observation of these equally ∗ Electronic address: [email protected] spaced steps provided the first evidence for macroscopicquantum tunneling of the magnetization [3].Recent work has focused on circumstances where theassumption of independent spins breaks down in crystalsof molecular magnets. Thus, ferromagnetic ordering dueto magnetic dipole-dipole interactions has been demon-strated experimentally in high-spin molecular magnetsby Morello et al. [6] in Mn by Evangelisti et al.[7] inthe high-spin molecular magnet Fe . Based on neutronscattering experiments, Luis et al. [4] have claimed thatMn -ac also orders ferromagnetically provided a largetransverse field is applied to reduce the magnetic barrierand increase the relaxation rate. Recent detailed calcula-tions by Garanin and Chudnovsky[5] indicate that dipo-lar ferromagnetism in a transverse field should indeed befound in Mn -ac below a Curie temperature T c ∼ . -ac.It is well known that Mn -ac crystals contain a smallfraction of low- symmetry species molecules at a level ofroughly 5% [8]. This “minor” species, an isomer of the“major” species of Mn -ac, has a reduced energy barrierof ≈
42 K at zero field [9]. The magnetic relaxation rates,typically determined by AC susceptibility measurements,are fit with an Arrhenius equationΓ = Γ exp [ − U ( H ) /T ] . (2)For the major species, Γ ≈ . × s − and Γ ≈ . × s − for the fast-relaxing minor species[9].The different relaxation rates are also evident in mag-netization curves. Figure 1 shows a hysteresis loop fora single crystal of Mn -ac taken at 0 . ±
10 mT/s. Starting from zero
FIG. 1: (Color online) Magnetization versus magnetic fieldof a single crystal of Mn -ac measured for an external fieldsweep rate of ±
10 mT/s.FIG. 2: (Color online) Schematic of the procedure used toprepare Mn -ac with minor and major species magnetizedin opposite directions. (a) First, a +6 T field is applied toalign all spins. (b) Then, a − field, the total magnetization is constant as the field isincreased to 0 .
90 T. Small steps are observed at ∼ . .
28 T (see also Fig. 3) corresponding to the resonantrelaxation of the minor species magnetization. Above 1 . ≈ . . . FIG. 3: (Color online) (a) Magnetization of the minor speciesas a function of external magnetic field swept at +5 mT/swith the major species magnetization prepared following thethree protocols described in the text. The triangles (squares)are data taken with the major species aligned in the posi-tive (negative) direction. The circles are data taken with theminor species randomly oriented to yield zero magnetization.(b) The derivative of the curves shown in frame (a). same direction; and (C) major and minor species spinsaligned in opposite directions.(A) Starting with an unmagnetized (zero-field-cooled)crystal, and maintaining the temperature at 300 mK:a magnetic field of − − . − − -ac with typical dimensionsof 1 . × . × . immersed in He. Experimentaldetails can be found in Ref.[11].Fig. 3 (a) shows hysteresis curves for the minor speciestaken at 0 . M sat , the saturation value of the mi-nor species. The minor species hyteresis curves exhibita similar staircase structure as the major species. How-ever, the smaller anisotropy leads to a smaller spacingbetween steps. Fig. 3 (b) shows the derivative of themagnetization curve, which is useful for determining the location and widths of the tunneling resonances.It is clear that the externally applied magnetic fieldcorresponding to the tunneling resonances depends onthe direction of the magnetization of the major species.The circles of Fig. 3 are data taken with the net magne-tization of the major species equal to zero. Fully mag-netizing the major species in the positive direction shiftsthe location of the tunneling resonance fields by ≈ − . ≈ +0 .
05 T. In thiscase, the external field is larger to offset the dipolar fieldin the opposite direction. A close determination of theshift corresponding to the dipolar field associated withfull magnetization of the major species of Mn -ac yields51 . ± . -ac calculated in Ref. [5] was foundto be 52 . -ac and will be published elsewhere.This work was supported at City College by NSF grantDMR-00451605. E. Z. acknowledges the support of theIsrael Ministry of Science, Culture and Sports. Supportfor G. C. was provided by NSF grant CHE-0414555. [1] T. Lis, Acta Cryst. B69 , 2042 (1980).[2] R. Sessoli, D. Gatteschi, A. Caneschi, and M. A. Novak,Nature (London) , 141 (1993).[3] J. R. Friedman, M. P. Sarachik, J. Tejada, and R. Ziolo,Phys. Rev. Lett. , 3830 (1996).[4] F. Luis, J. Campo, J. Gmez, G. J. McIntyre, J. Luzn,and D. Ruiz-Molina, Phys. Rev. Lett. , 227202 (2005)[5] D. A. Garanin and E. M. Chudnovsky, preprinthttp://arxiv.org/abs/0805.1433[6] A. Morello, F. L. Mettes, F. Luis, J. F. Fernandez, J.Krzystek, G. Arom, G. Christou, and L. J. de Jongh,Phys. Rev. Lett. , 017206 (2003).[7] M. Evangelisti, A. Candini, A. Ghirri, M. Affronte, G.W. Powell, I. A. Gass, P. A. Wood, S. Parsons, E. K.Brechin, D. Collison, and S. L. Heath, Phys. Rev. Lett. , 167202 (2006)[8] A. Caneschi, T. Ohm, C. Paulsen, D. Rovai, C. Sangre- gorio and R. Sessoli, J. Magn. and Magn. Matt. 177-181,1330 (1998); Z. Sun, D. Ruiz, N. R. Dilley, M. Soler,J. Ribas, K. Folting, M. B. Maple, G. Christou and D.N. Hendrickson, Chem. Commun., 1973 (1999); Werns-dorfer, R. Sessoli, D. Gatteschi, Europhys. Lett. 47, 254(1999).[9] M. Soler, W. Wernsdorfer, Z. Sun, J. C. Huffman, D. N.Hendrickson and G. Christou, Chem. Commun. (Cam-bridge) 2003, 2672 (2003).[10] W. Wernsdorfer, N.E. Chakov, G. Christou,http://arxiv.org/abs/cond-mat/0405014.[11] Yoko Suzuki, M. P. Sarachik, E. M. Chudnovsky, S.McHugh, R. Gonzalez-Rubio, Nurit Avraham, Y. Mya-soedov, E. Zeldov, H. Shtrikman, N. E. Chakov, and G.Christou, Phys, Rev. Lett.95