The spin-lattice relaxation rate $T_{1}^{-1}$ and NMR spectra of $^1$H in
single crystal molecular magnets of Fe8 have been measured down to 15 mK. The
relaxation rate $T_1^{-1}$ shows a strong temperature dependence down to 400
mK. The relaxation is well explained in terms of the thermal transition of the
iron state between the discreet energy levels of the total spin S=10. The
relaxation time $T_1$ becomes temperature independent below 300 mK and is
longer than 100 s. In this temperature region stepwise recovery of the
$^1$H-NMR signal after saturation was observed depending on the return field of
the sweep field. This phenomenon is attributed to resonant quantum tunneling at
the fields where levels cross and is discussed in terms of the Landau-Zener
transition.Comment: 13 pages, 5 figure

A. Lascialfari

C. Delfs

C. Sangregorio

C. Zener

D. Gatteschi

J. R. Friedman

J. Villain

K. Wieghardt

L. Landau

L. Thomas

M. Ueda

Miki Ueda

S. Miyashita

Satoru Maegawa

Susumu Kitagawa

T. Ohm

W. Wernsdorfer

English

arXiv

Ueda, M

Maegawa, S

Kitagawa, S

Kyoto University Research Information Repository

Physical Review B

Proton spin relaxation induced by quantum tunneling in Fe8 molecular nanomagnet

Crossref

Title Proton spin relaxation induced by quantum tunneling in Fe8molecular nanomagnetAuthor(s)Ueda, M; Maegawa, S; Kitagawa, SCitationPHYSICAL REVIEW B (2002), 66(7)Issue Date2002-08-15URL http://hdl.handle.net/2433/39854RightCopyright 2002 American Physical SocietyType Journal ArticleTextversionnone; publisherKyoto UniversityProton spin relaxation induced by quantum tunneling in Fe8 molecular nanomagnetMiki Ueda and Satoru MaegawaGraduate School of Human and Environmental Studies, Kyoto University, Kyoto 606-8501, JapanSusumu KitagawaFaculty of Engineering, Kyoto University, Kyoto 606-8501, Japan~Received 19 April 2002; published 26 August 2002!The spin-lattice relaxation rate T121 and NMR spectra of 1H in single crystal of molecular magnets Fe8 havebeen measured down to 15 mK. The relaxation rate T121 shows a strong temperature dependence down to400 mK. The relaxation is well explained in terms of the thermal transition of the iron state between thediscreet energy levels of the total spin S510. The relaxation time T1 becomes temperature independent below300 mK and is longer than 100 s. In this temperature region stepwise recovery of the 1H-NMR signal aftersaturation was observed depending on the return field of the sweep field. This phenomenon is attributed to theresonant quantum tunneling at the fields where levels cross and is discussed in terms of the Landau-Zenertransition.DOI: 10.1103/PhysRevB.66.073309 PACS number~s!: 76.60.2k, 75.45.1jRecently, molecular nanomagnets have attracted muchattention to study quantum mechanical phenomena inthe macroscopic system owing to their identical size,the well-defined structure and a well-characterizedenergy structure.1–3 The molecular magnet@(C6H15N3)6Fe8O2(OH)12#Br7(H2O)Br8H2O, abbreviatedFe8, is a representative compound in which quantum tunnel-ing of magnetization ~QTM! has been observed as thetemperature-independent recovery of magnetization below400 mK.4–7The molecular magnet Fe8 consists of eight Fe31 ionswith spin s55/2 in each molecule. The magnetic interactionsbetween the spins in the molecule are antiferromagnetic andtheir magnitudes are 22–170 K,8 while the magnetic interac-tions between the molecules are negligibly small. The mag-netic properties of this compound at low temperatures havebeen described by a total spin of S510 for each molecule, inwhich six spins are parallel to each other and the remainingtwo spins are antiparallel to the six spins.8,9 The spin Hamil-tonian in the field H is expressed byH5DSz21E~Sx22Sy2!1gmBS"H, ~1!where D and E are the easy axis and the in-plane aniso-tropy, respectively.4 We have determined the values ofD520.276 K and E520.035 K by magnetization mea-surement on a single crystal.9 When there is no magneticfield, the anisotropy stabilizes the degenerate spin states ofm5610 at low temperatures. These states correspond to op-posite directions of the magnetization in the classical sense.The energy barrier caused by the anisotropy for reversal ofthe magnetization between m5610 is reported to be 25 K.4Quantum tunneling of magnetization in Fe8 has been ob-served only by magnetization measurements.4–7 In order tostudy the spin dynamics in Fe8 from a microscopic point ofview we performed NMR experiments and found a stepwiserecovery of the 1H spin echo signal due to resonant quantumtunneling at the level crossing fields.We synthesized single crystals of Fe8, following themethod reported previously.10 The sizes of the crystals usedfor the experiments were about 43231 mm3. The NMRspectrum and the spin-lattice relaxation rate T121 of 1H inFe8 were measured by the coherent pulsed NMR method inexternal magnetic fields up to 5.4 T. The spectra were ob-tained by measuring the spin-echo intensity with sweepingthe field at a fixed frequency. The relaxation rate was ob-tained by measuring the recovery of the spin echo intensityas a function of the time after saturation of the 1H spinsusing comb pulses. The experimental temperature was low-ered down to 15 mK using a 3He-4He dilution refrigerator.The samples were sealed with 4He gas in a cell made ofPCTFE plastic~polychlorotrifluoroethylene!. The cell was setin the mixing chamber of the dilution refrigerator.The NMR spectrum at room temperature is narrow withthe width smaller than 50 Oe, while the spectrum becomesbroader and shows structure at lower temperatures. Thestructure is caused by freezing of the iron magnetization andthe existence of many 1H sites.Figure 1 shows the temperature dependence of the relax-ation rate T121. The rate T121 decreases steeply over six de-cades with lowering the temperature from 10 K to 400 mK,and decreases with increasing field. Below 300 mK T121 isalmost temperature independent and has a strong site depen-dence, as is found in Fig. 1.Figure 2 shows NMR spectra of the single crystal at150 mK. The field was applied so as to make an angle u of50° from the easy axis and to be within the ab plane. In thisexperiment we first saturated the 1H spin system by thecomb pulses at a fixed frequency, sweeping the field up anddown between 0.1 and 1.5 T for more than three times, untilthere was no observation of the echo signals. Then the fieldwas decreased to a certain field Hr with a constant sweeprate dH/dt . Immediately after arriving at Hr , the field wasincreased with the same sweep rate and the spectrum wastaken at a fixed repetition time. No signals were expected tobe observed, because the returning duration after the satura-tion was planned to be enough shorter than the relaxationtime that is longer than 100 s. Indeed no signals except fromPHYSICAL REVIEW B 66, 073309 ~2002!0163-1829/2002/66~7!/073309~4!/$20.00 ©2002 The American Physical Society66 073309-119F in the material of the sample cell and 3He in the mixingchamber were observed when the field was returned at0.05 T, as shown in the lowest spectrum in Fig. 2. However,signals were observed when the return fields were negative.FIG. 3. Return field Hr dependence of echo intensity at field of~a! 0.45 T, u550° and ~b! 0.60 T, u50°. Broken lines show calcu-lated level crossing fields. The echo intensity at 60 mK in ~a! isnormalized with that for 150 mK at Hr522.0 T.FIG. 4. Sweep rate dH/dt dependence of echo intensity at0.60 T when ~a! Hr520.1 T and ~b! Hr520.3 T. The field isapplied parallel to the easy axis. The solid and broken lines showcalculated values by Eqs. ~8! and ~9!, respectively.FIG. 1. Temperature dependence of relaxation rate T121 for thesamples composed of plural single crystals and for a single crystal.Lines denote calculated values.FIG. 2. NMR spectra of single crystal Fe8, which were takenwith increasing the field from Hr after the saturation. T5150 mK,f 529 MHz, dH/dt50.9 T/min, and u550°. Broken lines show thelevel crossing fields.BRIEF REPORTS PHYSICAL REVIEW B 66, 073309 ~2002!073309-2The intensities of the signals increased with decreasing re-turn field.Figures 3~a! and 3~b! show the return field dependence ofthe echo intensity. Figure 3~a! was obtained in the case whenthe field was applied with u550° within the ab plane. Fig-ure 3~b! is the case when the field was parallel to the easyaxis (u50°). The echo intensities were picked up at fields of0.45 and 0.60 T for Figs. 3~a! and 3~b!, respectively. Theintensity increases sharply with steps at 0, 20.31, 20.63,and 21.00 T for Fig. 3~a!, while for Fig. 3~b! the steps are at10.02 and 20.20 T. The increase in the intensity at the stepscannot be explained by recovery due to the spin-lattice re-laxation time shown in Fig. 1. Moreover the intensity is de-pendent on the sweep rate of the field, but independent ontemperature. Figure 4 shows the sweep rate dependence ofthe intensity at a field of 0.60 T when the field was appliedparallel to the easy axis and the return fields were 20.1 Tand 20.3 T. The intensity is large when the sweep rate isslow.First we analyze the relaxation rate. The temperature de-pendent relaxation rates of a molecular magnet Mn12 werefirst discussed by Lascialfari et al.11 In general T121 is givenby the Fourier transform of the correlation function for fluc-tuating transverse local fields h6(t) at nuclear sites, and isexpressed as1T15gN22 E ^$h6~ t !h7~0 !%&eivLtdt , ~2!where gN is the nuclear gyromagnetic ratio and vL is theLarmor frequency. When the correlation is assumed to bedescribed by an exponential function with a lifetime tm inthe m state, the correlation can be expressed as^$h6~ t !h7~0 !%&5 (m5210110^Dh62 &e2t/tme2Em /kBTZ , ~3!where Em is the energy of the eigenstate m and Z is thepartition function. The lifetime tm for the m state is governedby the spin-phonon interaction Hsp and is expressed by theprobabilities pm→m21 for the transition from the m to them21 state and pm→m11 for that from the m to the m11state, as follows:121tm5pm→m211pm→m1155CDEm3eDEm /kBT211CDEm11312e2DEm11 /kBT~for m.0 !,CDEm312e2DEm /kBT1CDEm113eDEm11 /kBT21~for m,0 !,~4!where DEm5uEm212Emu. The parameter C is given byC532prv5\4u^muHspum61&u2, ~5!where v is the phonon velocity and r is the specific mass.Thus the spin-lattice relaxation rate is obtained as1T15AZ (m5210110tme2Em /kBT11vL2tm2 , ~6!where A5gN2 ^Dh62 & .The relaxation rates calculated by using Eq. ~6! with fit-ting parameters A5431012 rad/s2 and C553105 Hz/K3are shown for several fields in Fig. 1. The experimental re-sults of the temperature and field dependence above 400 mKare well reproduced over six decades by this calculation.This means that relaxation above 400 mK is dominated bythermal fluctuations resulting from the transitions of ironspins between neighboring states due to spin-phonon inter-actions. The deviations at high temperatures must be causedby the contribution from higher energy levels which are notdescribed by the simplified spin model with S510.The observed T121 below 300 mK deviates from the cal-culated values and becomes temperature independent. Thismay be related to the temperature independent recovery ofmagnetization that has been observed in SQUID below400 mK at nonlevel crossing fields,4 and may be attributed tothe quantum effect.Next we discuss the stepwise behavior of the echo inten-sity, shown in Fig. 3. Figure 5 shows schematically the fielddependence of the energy levels of the iron spin system de-scribed by Eq. ~1! and the transitions of the states when thefield is decreased. In the experiment, when the field is posi-tive at low temperatures, all the spins are in the m5210state. When the field is decreased to zero, the level of them5210 state crosses with that of the m510 state, and thespins in the m5210 state would change to the m510 stateby quantum tunneling with a probability P210,10 . Furtherdecrease of the field causes the energy levels to cross againand the transition to occur again. The transition at the pointwhere the levels cross has been calculated by Landau andZener, and the probability from the m state to the m8 state inthis case is expressed13–15 asPm ,m8512expS 2 pDm ,m822\gmBum2m8udH/dt D , ~7!FIG. 5. Schematic energy level diagram of the spin system andthe transitions.BRIEF REPORTS PHYSICAL REVIEW B 66, 073309 ~2002!073309-3where Dm ,m8 is the tunneling gap at the level crossing. Thesetransitions would induce fluctuations of the local field atproton sites and cause extra relaxation of the nuclear spins.After quantum tunneling, the spin state rapidly relaxesto the lower energy levels, following the Boltzmann distri-bution. The lifetime tm below 300 mK estimated is to beless than 1027 sec from the measured relaxation time andEq. ~6!. It should be noted that these thermal transitions canoccur only between states with the same sign of m, whilequantum tunneling occurs between states with opposite signof m.The measured period of the stepwise behavior for u550°was 0.32 T, while that for u50° was 0.22 T. The period oflevel crossing fields is expressed approximately as DH5D/gmB cos u and the values are 0.31 and 0.21 T for u550°and 0°, respectively. The values coincide fairly well with theexperimental results. These results clearly indicate that thesudden recovery of the 1H spins is caused by resonant quan-tum tunneling of the iron magnetization at the level crossingfields.When the iron spin state in a certain molecule changesthrough tunneling, the 1H spins in the molecule would berapidly relaxed. The iron spins which have tunneled in zeroor negative fields arrive at the m510 state and have possi-bility to tunnel again in the zero or positive fields. If it isassumed that the iron spins which have experienced tunnel-ing once at least contribute to the proton relaxation, the echointensities I i at the monitoring field after the field returningwould be expressed asI15I01$12~12P210,10!2%, ~8!for H210,9,Hr,0, andI25I02$12~12P210,10!2~12P210,9!2%, ~9!for H210,8,Hr,H210,9 , where Hm ,m8 is the crossing fieldof the states m and m8. The measured sweep rate dependenceof echo intensities was fitted to Eqs. ~8! and ~9! with Eq. ~7!,D210,1053.5231027 K and D210,959.6631027 K, asshown in Fig. 4. The agreement between calculated and ex-perimental values is reasonably good and these values forD210,10 and D210,9 are close to those reported from magne-tization measurements.6,7As is found in Fig. 3~b!, the echo intensities for Hr,20.25 T at a sweep rate of 0.9 T/min remain constant andsmaller than those for dH/dt50.08 T/min. The stepwise re-covery was not observed for the lower crossing fields. Anintensity of the signals which were measured at the slowsweep rate of 0.08 T/min with Hr less than 20.6 T corre-sponds to the intensity of the signal which recovered com-pletely. This intensity was obtained for the fast rate of0.9 T/min by sweeping the field up and down three timesbetween 20.1 and 20.6 T. However, the intensity aftersweeping up and down three times at lower fields between20.6 and 21.0 T with dH/dt50.9 T/min remained small.This suggests that tunneling does not occur at fields lowerthan 20.6 T, though the reason is not clear.In conclusion, the proton relaxation rate T121 of Fe8 above400 mK is dominated by the thermal fluctuation of the ironmagnetization with spin S510. The transition of magnetiza-tion between the states split by DSz2 is caused by the spin-phonon interaction, and induces the fluctuation at nuclearsites. The rate becomes temperature independent below300 mK. In this temperature region the stepwise recovery ofthe echo intensity caused by quantum tunneling at the levelcrossing fields was observed in the 1H-NMR spectrum. Thisindicates that the internal field at proton sites fluctuates dueto the resonant quantum tunneling of iron spins, which isdescribed by the Landau-Zener transition. The temperatureindependent relaxation rates themselves measured below 300mK are governed by the temperature independent correlationtimes possibly related to the quantum effect, however, thisquantum process is another one than the resonant quantumtunneling.We would like to thank Prof. S. Miyashita and Dr. K.Saito for valuable discussions. We also thank Dr. H. Mi-yasaka and Dr. H. -C. Chang for their helpful advice onsynthesis of the samples.1 D. Gatteschi, A. Caneschi, L. Pardi, and R. Sessoli, Science 265,1054 ~1994!.2 L. Thomas, F. Lionti, R. Ballou, D. Gatteschi, R. Sessoli, and B.Barbara, Nature ~London! 383, 145 ~1996!.3 J. R. Friedman, M. P. Sarachik, J. Tejada, and R. Ziolo, Phys.Rev. Lett. 76, 3830 ~1996!.4 C. Sangregorio, T. Ohm, C. Paulsen, R. Sessoli, and D. Gatteschi,Phys. Rev. Lett. 78, 4645 ~1997!.5 T. Ohm, C. Sangregorio, and C. Paulsen, J. Low Temp. Phys. 113,1141 ~1998!.6 W. Wernsdorfer, R. Sessoli, A. Caneschi, D. Gatteschi, and A.Cornia, Europhys. Lett. 50, 552 ~2000!.7 W. Wernsdorfer and R. Sessoli, Science 284, 133 ~1999!.8 C. Delfs, D. Gatteschi, L. Pardi, R. Sessoli, K. Wieghardt, and D.Hanke, Inorg. Chem. 32, 3099 ~1993!.9 M. Ueda, S. Maegawa, H. Miyasaka, and S. Kitagawa, J. Phys.Soc. Jpn. 70, 3084 ~2001!.10 K. Wieghardt, K. Pohl, I. Jibril, and G. Huttner, Angew. Chem.Int. Ed. Engl. 23, 77 ~1984!.11 A. Lascialfari, Z.H. Jang, F. Borsa, P. Carretta, and D. Gatteschi,Phys. Rev. Lett. 81, 3773 ~1998!.12 J. Villain, F. H-Boutron, R. Sessoli, and A. Rettori, Europhys.Lett. 27, 159 ~1994!.13 L. Landau, Phys. Z. Sowjetunion 2, 46 ~1932!.14 C. Zener, Proc. R. Soc. London, Ser. A 137, 696 ~1932!.15 S. Miyashita, J. Phys. Soc. Jpn. 64, 3207 ~1995!.BRIEF REPORTS PHYSICAL REVIEW B 66, 073309 ~2002!073309-4

Proton Spin Relaxation Induced by Quantum Tunneling in Fe8 Molecular
  Nanomagnet

Proton Spin Relaxation Induced by Quantum Tunneling in Fe8 Molecular Nanomagnet

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