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Comment on Tunneling in Mesoscopic Magnetic Molecules

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VOLUME 76, NUMBER 16 PHYSICAL REVIEW LETTERS 15A PRIL 19962 3Comment on “Tunneling in Mesoscopic Magnetic flip-flops with V , Sm yr (here DS › 61), or elsed zvia multimolecule (higher than binary) processes to gen-Molecules”erate transitions with DS › 62 (e.g., a four-moleculezIn a very interesting recent Letter [1] Politi et al. process could involve two neighboring molecules forstudied magnetic relaxation in Mn O acetate [2], which DS › 0, and two others having DS › 62).12 12 z zassuming a spin-phonon coupling mechanism. They Applying a magnetic field suppresses the flip-flop21 3predicted t , H for the relaxation rate in a high resonances. Increasing the field to hyA › 1 brings one21magnetic field, neglecting the dipolar interactions be- back to resonance, so t sHd will have a minimum [2]21tween molecules. We find the calculations in [1] to [there will also be a slow monotonic increase in t sHd21be entirely correct; however, the experimental t sHd due to barrier height reduction]. One would also expect21 3clearly disagrees with t , H , and shows nonmono- an increased propensity toward “avalanche” relaxation attonic behavior with a minimum at H › 0.2 T. In this this resonance field—this provides a natural explanation21Comment we argue that the minimum in t in the for the peak observed in such relaxation [2]. In any case21activation regime is due to the dipole-dipole interactions our picture clearly predicts maxima in t at resonantneglected in [1], which cause ...
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VOLUME76, NUMBER15 AH Y S I C A L16 PL E T T E R SR E V I E WPRIL1996 2 3 Comment on “Tunneling in Mesoscopic Magneticflip-flops withVd,Smyr( hereDSz61), or else Molecules”higher than binary) processes to gen-via multimolecule ( erate transitions withDSz62(e.g., a four-molecule In a very interesting recent Letter [1] Politiet al.process could involve two neighboring molecules for studied magnetic relaxation in Mn12O12acetate [2],whichDSz0, and two others havingDSz62). assuming a spin-phonon coupling mechanism.They Applyinga magnetic field suppresses the flip-flop 21 3 predictedt,Hresonances. Increasingthe field tofor the relaxation rate in a highhyA1brings one 21 magnetic field, neglecting the dipolar interactions be-back to resonance, sotsHdwill have a minimum [2] 21 tween molecules.We find the calculations in [1] to[there will also be a slow monotonic increase intsHd 21 be entirely correct; however, the experimentaltsHdOne would also expectdue to barrier height reduction]. 21 3 clearly disagrees witht,H, and shows nonmono-an increased propensity toward “avalanche” relaxation at tonic behavior with a minimum atH0.2 Tprovides a natural explanation— thisthis thisresonance field. In 21 Comment we argue that the minimum intin thefor the peak observed in such relaxation [2].In any case 21 activation regime is due to the dipole-dipole interactionsour picture clearly predicts maxima intat resonant neglected in [1], which cause flip-flop processes betweenfields — andwith no restriction onDSzbetween the reso-the molecules.We also believe these interactions play anating levels, these will be athyAinteger. role in the avalanche behavior at lowTvery recent experiment [3] has found a sequence. A 21 The argument goes as follows.The energy of theof regularly spaced maxima and minima intsHd, 12 12corresponding to transitions withhyAinteger. The Mn Omolecule in the magnetic field is authors explain the maxima in terms of phonon-assisted 2 22 E2AS1hSz;2AsSz2hy2Ad1hy4A,(1) z transitions, but this conflicts with Ref. [1], according to whereAø0.64 K,S10, andhmBH. Forhwhich phonon-assisted transitions would giveminimafor 0and also for the special valueshyA1, 2, . . .the matching levels.In fact we believe the violation of spectrum has doubly degenerate statesEshy2A,Sz# the selection ruleDS64provides further support for 10dEshyA2Szdall other values of. Forhthe our picture. degeneracy is absent, and, most importantly, none of the Finally, we note that nuclei will play a role.Nnuclei p transitionsEsSzd2EsSz11dforSz$hy2Amatches split each level into a multiplet of widthE0,v0N, EsSzd2EsSz21dforSz#hy2A. wherev0For Mn nuclei,is the hyperfine coupling.NWe consider theh0case, first, analyzing processes 12andv0is perhaps 300inhomogeneousMHz. This taking the molecule fromSz10toSz210, in the broadening, plus nuclear spin diffusion, will influence activation regime.The first molecule to climb the barrier both phonon and dipolar relaxation [4], as well as the does so at a rate21 position of the minimum int. 21 t,nexps2EAyTd,(2) 621A. L.Burin and N.V. Prokof'ev wheren,10 s[2]. Themolecule can then relax Russian Research Center “Kurchatov Institute” by phonon emission; the spin-phonon coupling is so Moscow 123182, Russia weak that this phonon is unlikely to be reabsorbed by another molecule.However, we donot needphonons to P. C. E.Stamp relax the excited molecule, because of resonant dipolar Physics Department,University of British Columbia flip-flop transitions between the molecules.The first 6224 Agricultural Rd., flip-flop transition (in this naive scheme neglecting line1Z1Vancouver, British Columbia, Canada V6T broadening, spin diffusion, etc.)brings another molecule to the top of the barrier, so the process may be repeated.Received 22 December 1995 One can have dipolar transitions withDSz64, as forPACS numbers: 75.20.Ck, 76.20.+q phonon-mediated transitions, with matrix elementsVd, [1] P.Politiet al.Phys. Rev. Lett.75, 537 (1995). 2 23 2 sSmyrdsK'yAdbetween two molecules separated by [2] C.Paulsenet al.J. Magn. Magn. Mater.140 – 144, r, incorporating the perpendicular anisotropyK'. If 379 (1995); inQuantum Tunneling of Magnetisation, K'yA,0.1[2], thenVd,n, for nearest neighbors. edited by L. Gunther and B. Barbara (Kluwer Publishing, Then dipolar and phonon processes have comparable Dordrecht, 1995). effects on relaxation in zero field (we have verified this by [3] J.R. Friedmanet al.(to be published); B. Barbaraet al. solving the rate equations withbothprocesses included). (to be published). More importantly, dipolar processes may proceed with [4] N.V. Prokof'ev and P.C. E.Stamp, Report No. cond-mat no restriction onDSz, either via the transverse dipolar9511011, 1995 and references therein; Report No. cond-coupling abovesDSz65,64,63d, via conventionalmat 9511016, 1995, and references therein).
© 1996 TheAmerican Physical Society