Magnetic relaxations in a Tb-based single molecule magnet studied by quasielastic neutron scattering

Chemical Physics 427 (2013) 147–152

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Magnetic relaxations in a Tb-based single molecule magnet studied by quasielastic neutron scattering Maiko Kofu a, Takashi Kajiwara b, Jason S. Gardner c, Giovanna G. Simeoni e, Madhusudan Tyagi c,d, Antonio Faraone c,d, Kenji Nakajima f, Seiko Ohira-Kawamura f, Motohiro Nakano g, Osamu Yamamuro a,⇑ a

Institute for Solid State Physics, University of Tokyo, Kashiwa, Chiba 277-8581, Japan Faculty of Science, Nara Women’s University, Nara, Nara 630-8506, Japan NIST Center for Neutron Research, National Institute of Standards and Technology, 100 Bureau Drive, Gaithersburg, MD 20899-6102, USA d Department of Materials Science, University of Maryland, College Park, MD 20742, USA e Technische Universität München, Forschungsneutronenquelle Heinz Maier-Leibnitz FRM II, D-85747 Garching, Germany f Neutron Science Section, J-PARC Center, Tokai, Ibaraki 319-1195, Japan g Graduate School of Engineering, Osaka University, Suita, Osaka 565-0871, Japan b c

a r t i c l e

i n f o

Article history: Available online 25 October 2013 Keywords: Single molecule magnet Magnetic relaxation Quasielastic neutron scattering Ac susceptibility

a b s t r a c t By using ac magnetic susceptibility and quasielatic neutron scattering (QENS) techniques, we have investigated a magnetization relaxation phenomenon of a rare-earth based single molecule magnet, TbCuC19H20N3O16. We clearly identified and characterized two magnetic relaxations. The slower relaxation observed in the ac susceptibility is at the ms timescale around T ¼ 2 K and its activation energy is 16 K. On the other hand, the faster relaxation in the QENS measurements occurs on the timescale between ns and ps with activation energy of 174 K. The slower relaxation may occur through thermally activated tunneling among magnetic substates. We discuss two possible origins for the faster relaxation; one is a thermally activated tunneling between the higher excited states, the other is the magnetic relaxation coupled with the motion of ligands around the magnetic ions. This is the first clear observation of magnetic relaxation on the single molecule magnet revealed by QENS. Ó 2013 Elsevier B.V. All rights reserved.

1. Introduction A single-molecule magnet (SMM) is an organic molecule that behaves as an individual nanomagnet. Each molecule, containing several metal centers with unpaired electrons, possesses a giant resultant spin. The bulky ligand isolates the molecule. Given that the giant spin exhibits easy-axis magnetic anisotropy (D < 0), the magnetization reversal between the ground states with Sz ¼ S is hindered by the potential barrier of DS2z . The barrier yields a slow relaxation of the magnetization reversal that is characteristic of SMMs. To date, SMMs containing transition metal atoms such as Mn, Fe, and Ni, have been intensively studied [1–14]. Recently a new series of rare-earth based SMMs attract much attention [15–20]. Owing to large contribution of angular momenta, lanthanide complexes can become SMMs containing only one or two magnetic atoms, being simpler than the transition metal SMMs consisting of many magnetic atoms. This is advantageous for fundamental studies. Another advantage of lanthanide SMMs is that

⇑ Corresponding author. Tel.: +81 4 7136 3494; fax: +81 4 7134 6069. E-mail address: [email protected] (O. Yamamuro). 0301-0104/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.chemphys.2013.10.004

the energy scale is expected to be larger and so they can be good candidates for magnetic devices [21]. One of the issues in SMMs is the quantum tunneling mechanism for the magnetization reversal [1–3,7–14]. In some cases, the activation energy of magnetization reversal observed in relaxation measurements is rather smaller than the energy barrier expected from DS2z . It implies that the relaxation occurs through tunneling path among excited substates, which is called thermally activated tunneling process. The possible origins of the tunneling, i.e. hybridization of the substates, are higher order magnetic anisotropy, hyperfine interaction between the nuclear spin and electron spin, interactions between molecules, and so on. In this work, we have investigated relaxation dynamics of a Tb–Cu dinuclear SMM [19] using ac magnetic susceptibility and quasielastic neutron scattering (QENS) techniques. The chemical formula of the sample studied is TbCuC19H20N3O16 and its molecular structure is schematically shown in Fig. 1. Only two magnetic ions, Tb3+ (J ¼ 6) and Cu2+ (S ¼ 1=2), are involved in a molecule. The Tb–Cu unit is isolated due to the bulky ligands and behaves as a nanomagnet. Neutron scattering techniques provide insight into the microscopic magnetic fluctuation. So far, inelastic neutron scattering (INS) studies have been reported for several types of molecular magnets [22-30] to investigate their energy schemes

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N O Tb

C Cu

resolution, Ho0.8Y1.2Ti2O7, which has no fluctuating spin in the measurement window, was used. The sample with the deuteration ratio of 97% was used for the measurements on TOFTOF, AGNES, and AMATERAS spectrometers, whereas the sample with the deuteration ratio of 99.3% was used for the HFBS and NSE instruments. The samples were loaded into cylindrical Al cans with He gas which facilitates thermal equilibration inside the cans. The cans were sealed with indium gasket and mounted in cryostats with closed cycle refrigerators (CCR). 3. Results and discussion 3.1. ac susceptibility

Fig. 1. Molecular structure of Tb–Cu dinuclear complex investigated in this work. The D atoms and the acetone molecule are omitted.

and spin Hamiltonians. However, clear QENS data has not been reported even though one of the characteristics of SMMs is the relaxation phenomenon. We aim at investigating the overall feature of the relaxation dynamics from QENS to ac susceptibility timeranges (from ps to ms).

In order to investigate the magnetization relaxation processes at the ms time scale, the ac susceptibility measurements were carried out. Fig. 2 (a) shows the ac susceptibility data of the protonated sample as a function of temperature at the frequencies ranging from 180 to 10000 Hz. We have also measured the sample with the deuteration ratio of 97 % and confirmed that there is no significant difference between the two samples. Both the real (v0 ) and imaginary (v00 ) signals exhibit clear dispersion for the frequency. In Fig. 2(b), the Cole–Cole plot of v0 and v00 are also shown. The Cole–Cole equation is described as follows;

2. Experimental

vðixÞ ¼ vS þ

1a

ð0 6 a < 1Þ;

ð1Þ

6

(a)

5

3 2

’

’’ 100 Hz 180 Hz 320 Hz 560 Hz 1000 Hz 1800 Hz 3200 Hz 5600 Hz 10000 Hz

-5

3

’’, ’ / 10 m mol

-1

4

1 10000 Hz

0 2 1 0 2

3

4

5

6

T/K 2.5 -1

(b)

2.0

2.0 K

1.5 2.0 K 2.5 K 3.0 K 3.5 K 4.0 K

-5

3

’’ / 10 m mol

Magnetic susceptibility measurements were performed on a hydrogenated sample, TbCuC19H20N3O16. For the QENS measurements, to reduce the contribution from strong incoherent scattering of H atoms, we have prepared deuterated samples. In this study, two samples with different deuteration ratio of 97% and 99.3% were prepared. The deuteration ratios were estimated by nuclear magnetic resonance (NMR) measurements. Magnetic susceptibility measurements were carried out with a Quantum Design PPMS-9 magnetometer. First, magnetic field (9T) was applied to a mixture of the powder sample and eicosane at 2 K. Next, the mixture was heated to 320 K to melt eicosane and then cooled to 300 K to bind the microcrystals. Ac measurements were performed at various frequencies from 10 to 10,000 Hz with oscillating field amplitude of 3  104 T under zero dc field. QENS experiments were performed using five spectrometers in order to investigate relaxations over a wide time range between 1 ps and 100 ns. For the measurements in the timescale between 1 ps and 1 ns, three time-of flight spectrometers were used: TOFTOF [31] (energy resolution, DE ¼ 8 leV) at Forschungsneutronenquelle Heinz Maier-Leibnitz (FRM II) in Germany, AGNES [32,33] (DE ¼ 49 leV) at JRR-3 in Japan Atomic Energy Agency (JAEA), AMATERAS [34] (DE ¼ 120 leV) at Japan Proton Accelerator Research Complex (J-PARC). The incident neutron energy used were 0.57 meV at TOFTOF, 2.7 meV at AGNES, and 4.9 meV at AMATERAS. A back scattering spectrometer HFBS [35] (DE ¼ 0:8 leV) installed at NIST Center for Neutron Research (NCNR) was used to investigate the relaxation dynamics in the timescale longer than 1 ns. Elastic fixed-window scans (EFWS) were also performed on HFBS. The final neutron energy was set to 2.08 meV and the energy window was 17 leV <  hx < 17 leV. The resolution data were taken at 3 K for all of these spectrometers. The above four spectrometers work in the energy domain. On the other hand, the neutron spin echo (NSE) works in the time domain, being advantageous for detecting relaxation phenomena. Another merit of NSE is that the polarization analysis enables us to separate experimentally the magnetic and nuclear scattering. The neutron spin echo measurements have been performed on the NSE instrument [36,37] at NCNR. The incident wavelength of neutron used was 6 Å, and the data were collected at Fourier times between 0.007 and 12 ns. To correct for the instrumental

vT  vS 1 þ ðixsÞ

1.0 0.5 0.0 0.0

1.0

4.0 K

2.0

3.0 -5

3

’ / 10 m mol

4.0

5.0

-1

Fig. 2. (a) Temperature dependence of the real (v0 ) and imaginary (v00 ) components of the magnetic susceptibility of the protonated sample. Solid lines are guides to the eye. (b) Cole–Cole plot at several temperatures from 2 K to 4 K. Solid curves represent the best fitting of the experimental data to Eq. (2). See text for details.

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00

v ¼

vS  vT

p 

a tan 2 2   vT  vS 2 n 2 p  o  0 vT þ vS 2 1=2 tan a þ1  v  : þ 2 2 2

25 -1

Q = 0.45 A

15

10

60 K 40 K

5

ð2Þ

The estimated a was about 0.03 in the whole temperature region. Thus, it is concluded that only a single relaxation process is observed in the ms timescale. It is noted that the vS =vT is 0.05 at T ¼ 2 K, which is indicative of the presence of a faster relaxation.

3.5 K 20 K 30 K 40 K 60 K

20

~ S (Q, ω) / arb.unit

where the isothermal susceptibility, vT , and the adiabatic one, vS , are the susceptibility observed in the two limiting cases for the ac frequency tending to zero and infinity, respectively. The parameter x is a frequency and s is a relaxation time. The Cole–Cole parameter a measures the broadness of the distribution of relaxation times. The equation with a ¼ 0 corresponds to the Debye formula with a single relaxation time, giving a semi-circle curve in the plot. The data were fitted to the following equation,

30 K

0 -0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

hω / meV Fig. 4. Dynamic structure factors observed at Q ¼ 0:45 Å1 and T ¼ 40 K. The data are taken on TOFTOF instrument with the energy resolution of 8 leV. The curves are the results of the fitting. See text for the details.

3.2. Quasielastic neutron scattering Firstly, we show the EFWS taken on the HFBS spectrometer. The EFWS enable us to determine the temperature at which a dynamical process activates within the time window of a given spectrometer. For the HFBS measurements with the energy resolution of 0.8 leV, the relaxational modes slower than  2 ns is detected as elastic intensity. Fig. 3 shows the logarithmic plot of normalized elastic scattering intensities as a function of temperature. For a harmonic oscillator, the data will lie on a line in the plot. When a relaxation process occurs, the intensity decreases and deviates from the straight line. It is clear that a relaxation gets activated at around 20 K in this time range. In order to examine the relaxation precisely, we have performed QENS measurements on TOFTOF, AGNES, AMATERAS, and HFBS spectrometers. Fig. 4 shows the observed dynamic structure factors, ~ SðQ ; xÞ at Q ¼ 0:45 Å1 at the temperatures ranging from 3.5 K to 60 K measured on the TOFTOF spectrometer. Clearly, the QENS broadening was observed above 30 K. The QENS spectrum was well fitted to the combination of delta and Lorentz functions given below,

~SðQ ; xÞ ¼ SðQ ; xÞ  RðQ ; xÞ þ BG; 1 C : SðQ ; xÞ ¼ C 1 dðxÞ þ C 2 p x 2 þ C2

ð3Þ

Here C1 and C 2 are prefactors for delta and Lorentz functions, respectively. C is the half width at half maximum (HWHM) of the Lorentz function. dðxÞ is attributed to the static component resulting from the incoherent nuclear scattering of H and D atoms. RðQ ; xÞ is the resolution function of each instrument,  represents the operator of the convolution, and BG is the background. The fittings were carried out by using a PAN program on the DAVE software [38]. The fits converged at all temperatures for all spectrometers. A good example is provided in Fig. 5, which shows the result of a fitting session for TOFTOF data. To obtain the space information on the relaxation, we investigated the Q-dependence of the relaxation. As seen in Fig. 6, C is almost independent of Q, indicating that the relaxation is of a local origin. In the measurements on AGNES, AMATERAS, and HFBS, similar behaviors were observed. We have also carried out NSE measurements to investigate the magnetic relaxation in the timescale longer than 1 ns. As mentioned above, we can extract the magnetic relaxation by performing the polarization analysis. Fig. 7 presents the normalized intermediate scattering function, IðQ ; tÞ=IðQ ; 0Þ at Q ¼ 0:4 Å1 which is free from nuclear Bragg peak positions, collected at temperatures from 3.7 K to 40 K. Apparent decay behavior was observed above 15 K. The curves were fitted to two exponential functions given below;

    t t IðQ ; tÞ=IðQ; 0Þ ¼ ð1  f Þ exp  þ f exp  ;

sfast

0.1

50

Iobs total delta Lorentzian

40

~ S (Q, ω) / arb.unit

ln[I (T) / I (T = 4 K)]

-1

0.0

-0.1

-0.2

-0.3 0

ð4Þ

sslow

20

40

60

80

100

T/K Fig. 3. Logarithmic plot of normalized elastic scattering intensities as a function of temperature. The data are taken on HFBS. The dashed line represents the behavior assuming a classical harmonic oscillator. Error bars throughout the text represent one standard deviation.

Q = 0.45 A T = 40 K

30

20

10

0 -0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

hω / meV Fig. 5. Dynamic structure factors observed at Q ¼ 0:45 Å1 and T ¼ 40 K. The data are taken on TOFTOF instrument with the energy resolution of 8 leV. The curves are the results of the fitting. See text for the details.

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0.015

-4

0.010

Ea(1) = 16 K

-6

-8

log (τ / s)

Γ / meV

T = 40 K

0.005

0.000 0.0

0.2

0.4

0.6

0.8

1.0

τ0(1) = 4.1 x 10 s -8

-10

-1

Q/A

Ea(2) = 174 K -12

τ0(2) = 1.5 x 10

Fig. 6. Q-dependence of C estimated from the fitting at T ¼ 40 K taken on the TOFTOF spectrometer. Dashed line is the guide to the eye.

-12 0.0

0.1

s

0.2

T

0.4

0.3 -1

/K

0.4

0.5

-1

Fig. 8. Arrhenius plots of the relaxation times observed on NSE, HFBS, TOFTOF, AMATERAS, and AGNES instruments. The results from the ac susceptibility measurements are also shown. The solid lines are the results of the fit. The dashed curve represents the calculated temperature dependence in the crossover scenario. See text for details.

0.3

I (Q, t) / I (Q, 0)

ac susceptibility NSE HFBS TOFTOF AMATERAS AGNES

0.2

0.1

3.7K 15K 20K 25K 30K 40K

0.0 0.01

0.1

1

10

t / ns Fig. 7. Normalized intermediate scattering functions observed at Q ¼ 0:4 Å1. Solid curves represent the results of the fit (see text for details).

estimated from the INS study, as a function of the z-component of the total angular momentum of the Tb ion, Jz . The relaxation 1 corresponds to the process that the magnetization reversal occurs through quantum tunneling between pairs of degenerated excited states at 1.7 meV, that is a thermally activated tunneling process. This process is also called an Orbach process. On the other hand, the relaxation 2 detected by QENS has quite different activation energy and s0 ; Ea ð2Þ = 174ð9Þ K, s0 ð2Þ ¼ 1:5ð5Þ  1012 s. Here two possible origins are considered

where f is the fraction of the slow relaxation and sfast and sslow are the relaxation times. The relaxation times of the fast motion, sfast , are so short that the decay behavior is not seen in this time region. Here we estimate sfast to be shorter than 1 ps and so practically fixed it to 0.1 ps in the fittings.

20

relaxation 2 15

Fig. 8 shows the Arrhenius plot of relaxation times estimated from QENS together with those from ac susceptibility. Here, the relaxation times ss are evaluated from the relation, s ¼ 1=C, where C is the HWHM of the Lorentz function. This provides a clear evidence of the existence of two distinct relaxation processes. We designate the slower relaxation as the relaxation 1 and the faster one as relaxation 2. Both relaxation processes were well fitted to the Arrhenius equation,

s ¼ s0 exp ðEa =kB T Þ;

E / meV

3.3. Overall feature of relaxation dynamics

10

5

relaxation 1

ð5Þ

where Ea is the activation energy of the relaxation process, s0 corresponds to the relaxation time at infinite temperature, and kB is the Boltzmann constant. The results of the fit are shown by the solid lines in Fig. 8. The Ea ð1Þ and s0 ð1Þ of the relaxation 1 are estimated to be 16.0(4) K and 4:1ð3Þ  108 s, respectively. It should be emphasized that the activation energy corresponds to the transition energy of 1.7 meV between the ground and the first excited states, revealed by our INS study [39]. Fig. 9 shows an energy diagram,

0

-8

-4

0

4

8

Jz Fig. 9. Calculated energy diagram as a function of the z-component of the total angular momentum of the Tb ion, Jz [39]. Dashed lines show possible relaxation processes.

M. Kofu et al. / Chemical Physics 427 (2013) 147–152

for the relaxation 2. One scenario is that the relaxation 2 takes place through the tunneling between higher excited states, as well as the relaxation 1. This is consistent with the Arrhenius behavior which is usually caused by an Orbach process. The process is drawn in Fig. 9. The activation energy of 174 K (= 15 meV) roughly corresponds to the calculated energy levels. However, it should be noted that the calculated energy diagram is not accurate in the high energy region, because the excitations are clearly observed only at 1.7 meV and 12.3 meV due to the selection rule (DS ¼ 0; 1) of INS. Other measurements, for instance electron paramagnetic resonance (EPR), and ab initio calculations are required to clarify the tunneling between the higher excited states. Another possible origin is that the magnetic relaxation is coupled with the motions of H atoms, more exactly the motions of ligands containing H atoms. The deuteration ratio of the samples and the polarization analysis suggest us that the relaxation obtained on TOFTOF, AGNES, AMATERAS, and HFBS contains the motion of hydrogen atoms. The ratio of magnetic scattering and incoherent scattering should be about 1:7.8 for the sample with the deuteration ratio of 97%, but we have observed 25% of QENS component in the TOFTOF, AGNES and AMATERAS measurements at the Q position without Bragg peaks. In addition, the s0 ð2Þ roughly corresponds to the inverse of the phonon frequency. We speculate that the motion of hydrogen atoms, corresponding to the fluctuation of the ligand field, affects the magnetic relaxation process. It is worthwhile to discuss whether the relaxations 1 and 2 have essentially the same origin and exhibit a crossover around 107 s, or they have different origins. The crossover scenario can be justified by the fact that IðQ ; tÞ=IðQ ; 0Þ relaxes to zero in the NSE measurements. In fact, if there is no crossover, the IðQ ; tÞ=IðQ ; 0Þ does not relax to zero owing to the component of the relaxation 1. Supposing the crossover scenario, we have calculated the Arrhenius plot of relaxation times by using

1

s

¼

1

þ

1

sð1Þ sð2Þ

;

ð6Þ

151

relaxation occurs through a quantum tunneling between the excited substates at 1.7 meV. On the other hand, the QENS works revealed another relaxation (relaxation 2) which is faster than the one observed in the ac susceptibility measurement. The absence of pronounced Q dependence of the relaxation times suggests that the relaxation 2 is of a local origin. Just like the relaxation 1, the relaxation 2 is of the Debye type and gets activated upon heating according to the Arrhenius law. The activation energy of the relaxation 2 is 174 K much larger than that of the relaxation 1. We consider two possible origins of the relaxation 2. One is that the relaxation occurs through the tunneling between the higher excited states. The other possibility is that the magnetic relaxation is coupled with the motion of the ligands containing hydrogen atoms. The two relaxation found in the present work exhibit a crossover around 107 s. Disclaimer The identification of commercial products does not imply endorsement by the National Institute of Standards and Technology nor does it imply that these are the best for the purpose. Acknowledgements We thank Dr. R. Paul (NCNR) for experimental supports on Prompt-c experiments and Prof. T. Yamamura (Tohoku University) for kind supports of the magnetic experiments. This work is financially supported by the Grant-in-Aid for Exploratory Research No. 24655127, JSPS, Japan. The NSE experiment at NCNR was financially supported by Institute for Solid State Physics, the University of Tokyo, through the Travel Expense Support for Overseas program. This work utilized facilities supported in part by the National Science Foundation under Agreement No. DMR-0944772. The experiment in the MLF at J-PARC was performed with the approval of J-PARC (proposal No. 2010A0044). References

where sð1Þ and sð2Þ are calculated from the Eq. (5) with Ea s and s0 s determined separately as described before. The calculated temperature dependence is shown by a dashed curve in Fig. 8. Thus the present results are consistent with the crossover scenario. For more conclusive discussion, however, the experimental data at the timescale of 107 s, for example muon spectroscopy, are required. Finally, we mention about the presence of the fast relaxation (s < 1 ps), which is much faster than the relaxation 2, observed in NSE. Sessolli et al. pointed out that the transverse component of susceptibility can give rise to the fast relaxation for the [Dy2Ni] system in which two Dy3+ ions are exchange-coupled through a paramagnetic 3d bridging ion [40]. In our system, only one lanthanide ion is in the molecule and its coordination is different from [Dy2Ni], but the transverse component can be induced by the Cu2+ spin (S ¼ 1=2). The mechanism of the fast relaxation is still an open question. 4. Conclusion We have investigated relaxation dynamics of a Tb–Cu dinuclear single molecule magnet from ps to ms time range, using the ac susceptibility and quasielastice neutron scattering (QENS) methods. In the ac susceptibility measurements, the magnetization relaxation at the ms timescale (relaxation 1) is observed between 2 and 4 K. This process is of the Debye type and its temperature dependence is well described by the Arrhenius law with the activation energy of 16 K. Combining the result of inelastic neutron scattering study reported before [39], it is concluded that the magnetization

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