Influence of Intramolecular ff Interactions on Nuclear Spin Driven

Article pubs.acs.org/JPCA

Influence of Intramolecular f‑f Interactions on Nuclear Spin Driven Quantum Tunneling of Magnetizations in Quadruple-Decker Phthalocyanine Complexes Containing Two Terbium or Dysprosium Magnetic Centers Takamitsu Fukuda,* Kazuya Matsumura, and Naoto Ishikawa* Department of Chemistry, Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan S Supporting Information *

ABSTRACT: Nuclear spin driven quantum tunneling of magnetization (QTM) phenomena, which arise from admixture of more than two orthogonal electronic spin wave functions through the couplings with those of the nuclear spins, are one of the important magnetic relaxation processes in lanthanide single molecule magnets (SMMs) in the low temperature range. Although recent experimental studies have indicated that the presence of the intramolecular f-f interactions affects their magnetic relaxation processes, little attention has been given to their mechanisms and, to the best of our knowledge, no rational theoretical models have been proposed for the interpretations of how the nuclear spin driven QTMs are influenced by the f-f interactions. Since quadruple-decker phthalocyanine complexes with two terbium or dysprosium ions as the magnetic centers show moderate f-f interactions, these are appropriate to investigate the influence of the f-f interactions on the dynamic magnetic relaxation processes. In the present paper, a theoretical model including ligand field (LF) potentials, hyperfine, nuclear quadrupole, magnetic dipolar, and the Zeeman interactions has been constructed to understand the roles of the nuclear spins for the QTM processes, and the resultant Zeeman plots are obtained. The ac susceptibility measurements of the magnetically diluted quadruple-decker monoterbium and diterbium phthalocyanine complexes, [Tb−Y] and [Tb−Tb], have indicated that the presence of the f-f interactions suppresses the QTMs in the absence of the external magnetic field (Hdc) being consistent with previous reports. On the contrary, the faster magnetic relaxation processes are observed for [Tb−Tb] than [Tb−Y] at Hdc = 1000 Oe, clearly demonstrating that the QTMs are rather enhanced in the presence of the external magnetic field. Based on the calculated Zeeman diagrams, these observations can be attributed to the enhanced nuclear spin driven QTMs for [Tb−Tb]. At the Hdc higher than 2000 Oe, the magnetic relaxations become faster with increasing Hdc for both complexes, which are possibly ascribed to the enhanced direct processes. The results on the dysprosium complexes are also discussed as the example of a Kramers system.

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INTRODUCTION Slow magnetic relaxations observed in certain multinuclear transition metal clusters, and the resultant single molecule magnet (SMM) functions have recently attracted increasing attention because of their potential applications for ultrahighdensity data storage devices, quantum computations, spintronics devices, and so forth.1−14 The mechanism of slow magnetic relaxation processes of these compounds is generally interpreted by considering a double-well potential surface which originates from the uniaxial magnetic anisotropy and high spin multiplicity nature of the assembled metal centers in the molecule.15 On the other hand, as first demonstrated by utilizing lanthanide double-decker phthalocyanine derivatives (LnPc2, Ln = lanthanide), some lanthanide and actinide complexes exhibit slow magnetic relaxation phenomena in the presence of only a single metal center, giving rise to a concept of single-ion molecule magnets (SIMMs) or lanthanide SMMs.16−34 Because of a strong spin−orbit coupling, the total angular momentum of a free lanthanide ion having an © 2013 American Chemical Society

orbital angular momentum of L and a spin angular momentum of S can be described by the LS-couplings, leading to the (2J +1)-fold ground electronic states having the total angular momentum of J, where J = L + S for heavy lanthanide ions. For example, a terbium ion (Tb3+) has eight 4f-electrons and its ground states can be represented by the 7F6 atomic term, meaning that a free Tb3+ ion has the 13-fold degenerate ground states. The presence of crystal or ligand fields around the lanthanide ion, however, lifts the degeneracy through the electrostatic or ligand field (LF) potentials. In the case of a double-decker TbPc2 complex, the Tb3+ ion located midway between two phthalocyanine ligands is subject to a square antiprismatic LF with the D4d local symmetry. According to our preceding studies, the ground and the second lowest sublevels for the Tb3+ ion in the TbPc2 complexes have been determined Received: June 18, 2013 Revised: August 30, 2013 Published: September 4, 2013 10447

dx.doi.org/10.1021/jp406009m | J. Phys. Chem. A 2013, 117, 10447−10454

The Journal of Physical Chemistry A

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to be represented by |Jz⟩ = |±6⟩ and |±5⟩ basis functions, respectively, where Jz refers to the projection of J to the quantization axis, that is, the 4-fold symmetry axis in the present case, and the splitting energies between these reach several hundred cm−1. The slow magnetic relaxation phenomena observed for lanthanide SMMs in the high temperature range are attributed to their sublevel structures, and are rationally interpreted by assuming the dominant Orbach process.35−37 Therefore, the mechanism of slow magnetic relaxations in lanthanide SMMs is different from that of the conventional transition metal SMMs; that is, the presence of a strong uniaxial magnetic anisotropy arising from appropriate sublevel splittings gives the relatively large energy gap between the ground states with large |Jz| and the second lowest sublevels with small |Jz|, which results in the predominant population of the lowest sublevels even at the high temperature range, and the consequent slow magnetic relaxations. On the contrary, the magnetic relaxations in the lower temperature range involve more than one competitive mechanisms such as direct and Raman processes. In addition to the double-decker complexes, recent developments of synthetic strategies for extended stacked Pc complexes enable us to obtain a series of triple-, quadruple-, and quintupledecker Pc complexes containing two Ln centers with different Ln-Ln distances.38−42 Although the magnetic dipolar interactions between the two Ln centers in these multiple-decker complexes decrease inversely with the cubic power of the LnLn distance, we have demonstrated that the non-negligible ferromagnetic-like interactions are present between two Tb3+ centers at a distance of about 6.8 Å in the quadruple-decker Pc complex.43 Similar to the double-decker Pc complexes, the multiple-decker congeners also show the slow magnetic relaxations. The heteroleptic triple-decker Pc containing two Tb3+ ions surrounded by different LF potentials, in which two of the Pc ligands are unsubstituted Pc’s and the other is βoctabutoxyPc (Pc(OBu)8 = Pc*), exhibits two χ″M peaks in the alternating current (ac) magnetic susceptibility measurements irrespective of the presence of the external magnetic field (Hdc), indicating the presence of at least two magnetic relaxation paths corresponding to the two distinct Tb3+ sites, while dual magnetic relaxation processes have been reported for a series of homoleptic triple-, quadruple-, and quintuple-decker Pc*s containing two equivalent Tb3+ centers.44−46 Contrary to the magnetic relaxations arising from the energy exchanges between the paramagnetic ions and the phonon radiations, that is, the direct, Raman, and Orbach processes,47 magnetic relaxations caused by transitions between different spin states as a result of evolution of a two-level system in a time-varying magnetic field are referred to as a quantum tunneling of magnetizations (QTMs).15 Although the detailed mechanism of the QTM for lanthanide SMMs has not fully been understood yet, QTMs mediated by the presence of nuclear spin (I) of the lanthanide center, that is, nuclear spin driven QTM, are one of the pivotal QTM mechanisms for a lanthanide center having the nonzero nuclear spin quantum number as in the case of Tb3+ with I = 3/2.48,49 Because of the presence of hyperfine and nuclear quadrupole interactions between the 4f electrons and the nucleus, the lowest doublet with Jz = ±6 of Pc2Tb, that is, |±6⟩, splits into eight states denoted as |Jz, Iz⟩, where Jz = ±6 and Iz = ±3/2 or ±1/2. It should be noted that the estimated avoided level crossing points by calculating the numerical diagonalization of a [(2J + 1)(2I + 1) × (2J + 1)(2I + 1)] matrix which includes LF

potentials, hyperfine, nuclear quadrupole, and the Zeeman interactions rationally interpret the experimentally observed step structures appearing in the magnetic hysteresis loops of Pc2Tb.48,49 However, only a few attempts have so far been made to clarify the influence of the f-f interactions on nuclear spin driven QTMs. In the first part of the present paper, we discuss how the intramolecular f-f interactions in multiple-decker Pc complexes exert an influence on the nuclear spin driven QTM processes by constructing theoretical models. In the second part, the magnetic properties of the diluted mono- and diterbium quadruple-decker Pc complexes (Scheme 1) are compared with Scheme 1. Structures of Quadruple-Decker Phthalocyanines Used in This Study (2a−c and 3a−c), and Abbreviations of Their Diluted Samples, [Ln1−Ln2]

each other to relate the experimental data to the proposed model. Since two lanthanide centers are fairly separated from each other, but still exhibit the dipole−dipole f-f interactions, the quadruple-decker Pc’s are appropriate in a series of multiple-decker Pc’s for the purpose of this study. In the paper, magnetic properties of the Dy3+ congeners are also shown as the example of a Kramers system.

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EXPERIMENTAL SECTION The homonuclear quadruple-decker Pc’s, 2a-c, were synthesized according to our original methods with some modifications.39,40 A mixture of 2a or 2b and diamagnetic 2c are chromatographed followed by reprecipitation to yield the diluted [Tb−Tb] and [Dy−Dy] samples, respectively. The quadruple-decker formations by using 1a or 1b with an excess amount of 1c gave the magnetically diluted [Tb−Y] or [Dy−Y] samples, respectively. The abundance ratio of each complex in the samples was estimated by using a MALDI-TOF-Mass analysis (Shimadzu 10448



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of the double-decker complexes, 1a and 1b, respectively.43 For the construction of the model chemistry, therefore, the quadruple-decker Pc’s can be regarded as two longitudinally stacked double-decker Pc’s with the presence of magnetic dipole−dipole interactions between two lanthanide centers. It should be noted that the local symmetries of the lanthanide centers of the quadruple-decker Pc’s are lowered to C4 point group compared to that of the ideal double-decker Pc having the D4d symmetry because of the presence of the coordinated double-decker counterpart and the deviation of the skewed angle between two Pc ligands from 45°, leading to nonzero A44⟨r4⟩ and A46⟨r6⟩ LF parameters.44−46 While the O0k terms are predominant for determining the energy order of the |Jz⟩ states, the O44 and O46 terms are responsible for generating avoided level crossings through the couplings of the |Jz⟩ and |Jz ± 4⟩ basis wave functions. To obtain the Zeeman diagram for the ground substates of the quadruple-deckers, the Hamiltonian given in eq 4 was numerically diagonalized. The A20⟨r2⟩, A40⟨r4⟩, and A60⟨r6⟩ parameters determined for 1a or 1b in our previous study were employed, while the off-diagonal A44⟨r4⟩ and A46⟨r6⟩ parameters were set to arbitrarily assumed 300 and 0 cm−1, respectively, so that the avoided level crossing points can be visually enhanced.36,37 The external magnetic field (H) was applied along the C4(z) axis, and the hyperfine (Ahf) and nuclear quadrupole (P) coupling constants were set to those employed in ref 48. The distance of the two magnetic centers, R, for 2a and 2b were assumed to be 6.8 Å on the basis of the density functional theory (DFT, B3LYP/LanL2DZ) optimized structure for 2c. In the case of monoterbium 3a, the 16 = 42 crossing points appear in the Zeeman diagram (Supporting Information, Figure S2), at which the occurence of QTM is potentially possible in the presence of a transverse magnetic field. At four of these points, the |+6⟩ and |−6⟩ states are coupled through the off-diagonal LF parameters to give the avoided crossing points, and the energy gaps become larger as the A44⟨r4⟩ or A46⟨r6⟩ increase, indicating that the QTM processes take place more efficiently irrespective of the presence of a transverse field as the LF symmetry is lowered. In the case of diterbium 2a, two Tb3+ ions are coupled by the magnetic dipole−dipole interaction, and the wave functions are expressed by using the |JzA, IzA, JzB, IzB⟩ notation, where the indices A and B are used to distinguish the two Tb3+ sites. Consequently, the calculated Zeeman diagram becomes crowded, and the number of the crossing points increases (Figure 1 and Supporting Information, Figure S3 for enlarged view). Although the energies of |+6, IzA, −6, IzB⟩ and |−6, IzA, +6, IzB⟩ states are not affected by the external magnetic field because the Zeeman effects exert oppositely on each Tb3+ center, the intramolecular magnetic dipole−dipole interactions (V12) destabilize these states energetically. There are 2 × 162 = 512 crossing points in total between the |+6, IzA, +6, IzB ⟩ (or |−6, IzA, −6, IzB ⟩) and |±6, IzA, ∓6, IzB⟩ states (the bluehatched regions in Supporting Information, Figure S3), at which the QTM processes are anticipated in the presence of a transverse magnetic field. In this case, the number of the avoided-crossing points is 32, and importantly, the centers of the blue-hatched regions (Supporting Information, Figure S3) are shifted from the Hz = 0, indicating that the QTM between the |+6, IzA, +6, IzB⟩ (or |−6, IzA, −6, IzB ⟩) and |±6, IzA, ∓6, IzB⟩ states are rather promoted in the presence of a moderate external magnetic field than Hz = 0. As an example, the avoided crossing point arising from the |JzA, IzA, JzB, IzB⟩ = |+6, +1/2 −6,

AXIMA-CFR) using dithranol as a matrix (see Supporting Information for the details). The ac magnetic susceptibility measurements were carried out on a Quantum Design MPMS LX7AC SQUID (superconducting quantum interference device) magnetometer by employing an oscillating magnetic field of 3.9 Oe at indicated frequencies. All the powder samples for SQUID measurements were dispersed and fixed in eicosane.

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RESULTS AND DISCUSSION Theoretical Models. The Hamiltonian of the lanthanide ion with a nuclear spin of I for the monolanthanide quadrupledeckers, 3a and 3b, in the presence of an external magnetic field (H) can be written as ĤLn = F + μB (L + 2S) ·H + Ahf J·I

{

+ P Iz2 −

1 I(I + 1) 3

}

(1)

where F, L, and S are operator equivalents of the LF potential on the f-system, orbital angular momentum, and spin angular momentum operators, respectively, and μB is the Bohr magneton. The third and fourth terms of the right-hand side represent the hyperfine and nuclear quadrupole interactions, respectively, in which the Ahf and P are coupling constants. The LF term for the quadruple-decker Pc’s is written as: F = A 20⟨r 2⟩αO02 + A40⟨r 4⟩β O04 + A44 ⟨r 4⟩β O44 + A 60⟨r 6⟩γ O60 + A 64 ⟨r 6⟩γ O64

Aqk⟨rk⟩

(2)

The five parameters and the operators in eq 2 are LF parameters and polynomials of the total angular momentum matrices, J2, Jz, J−, and J+, respectively.47 The α, β, and γ coefficients are the Stevens parameters.50 For the dilanthanide derivatives, 2a and 2b, the Hamiltonian should also include the f-f interaction term, V12, in addition to the Ĥ Ln terms for each lanthanide site, that is, Ĥ Ln1 and Ĥ Ln2: Oqk

Ĥ Ln1Ln2 = Ĥ Ln1 + Ĥ Ln2 + V12

(3)

Although the V12 term includes both the magnetic dipolar (V12dip) and the exchange interactions in principle, our previous studies have demonstrated that the latter contribution is negligible for the quadruple-decker Pc’s.43 Therefore, the total Hamiltonian for the two lanthanide centers of 2a and 2b can be rewritten as Ĥ Ln1Ln2 = Ĥ Ln1 + Ĥ Ln2 + V12dip

(4)

where V12dip =

⎞ 1⎛ 3 ⎜M · M − (M1·R)(M 2 ·R)⎟ 1 2 ⎠ R3 ⎝ R2

(5)

M1 = μB (L1 + 2S1)

(6)

M 2 = μB (L 2 + 2S2)

(7)

Each lanthanide site is distinguished by the subindices in eqs 5−7. R is the vector connecting the two lanthanide sites, and R is the length of R. The estimated LF parameters by means of the theoretical simulations of the dc magnetic susceptibility data for 2a and 3a, and 2b and 3b indicate that the lowest substates of these complexes are the Jz = ±6 and ±13/2 states similarly to those 10449



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Supporting Information, Figure S6. As a consequence, less significant QTMs are theoretically expected for 2b and 3b. Magnetic Properties. To reduce the intermolecular magnetic interactions to the extent possible, the quadrupledecker samples used for the magnetic measurements were diluted with diamagnetic 2c.52 Since 3a and 3b can be obtained only by the reaction using a mixture of 1a or 1b and diamagnetic 1c, an excess amount of 1c was employed so that the formation of dilanthanide 2a or 2b can be suppressed. The ratios of each derivative contained in the sample were determined by using a MALDI mass analysis. The detailed sample preparation procedures are provided in the Supporting Information. The diluted samples are denoted as [Tb−Tb] and [Tb−Y] hereinafter. Figure 2 shows the temperature dependencies of ac susceptibilities for [Tb−Y] (left) and [Tb−Tb] (right) in the presence of the external magnetic field, Hdc, of 0, 500, and 1000 Oe (from top to bottom). At Hdc = 0, the χM″ values are near zero in the temperature range higher than 15 K when the ac magnetic field frequencies, f, of 10 and 1 Hz are applied for both [Tb−Y] and [Tb−Tb], while the threshold temperatures shift to about 25 and 35 K for the f = 100 and 997 Hz conditions, respectively. The corresponding χM′T values are close to that expected for one or two free Tb3+ ions (11.81 and 23.62 emu K mol−1, respectively). With decreasing temperature from the threshold temperatures, the χM″ plot starts to rise moderately, indicating the presence of slow magnetic relaxations. The [Tb−Y] and [Tb−Tb] samples show different behaviors in the χM″ plots at Hdc = 0, that is, [Tb−Tb] shows the peak temperature at about 20 and 10 K for f = 997 and 100 Hz, respectively, while no clear peaks are observed for [Tb−Y]. The different magnetic relaxation behaviors are more noticeable in the lower temperature range. As the temperature approaches 1.8 K, the χM′T values of [Tb−Tb] drop down, while the corresponding χM′T changes for [Tb−Y] are suppressed. As a consequence, the diminution ratios of the χM′T values for [Tb−Y] at 1.8 K are smaller than those of [Tb−Tb], implying more significant retardations of the oscillating magnetizations in phase with respect to the applied ac magnetic fields are observed for [Tb−Tb] than [Tb−Y]. In other words, the magnetic relaxation processes are more suppressed for [Tb−Tb] than [Tb−Y] in the lower temperature range at Hdc = 0. These observations are clearly demonstrated also in the plots of χM″ against f at Hdc = 0 (Figure 3, top). At 2 K, [Tb−Y] exhibits the peak frequency at about 50−70 Hz, which shifts to the higher frequency side with increasing temperature. On the other hand, the peak frequencies for [Tb−Tb] appear at as low as 1 Hz at 2 K, and at 5 Hz even at 5 K. Therefore, the magnetic relaxations occur more slowly for [Tb−Tb] than [Tb−Y] because of suppression of the possible relaxation processes by the presence of intramolecular f-f interactions. These facts are consistent with the calculated Zeeman diagrams, in which the efficient nuclear spin driven QTMs are anticipated for monoterbium 3a at Hdc = 0 (Supporting Information, Figure S2). On the contrary, the nuclear spin driven QTMs are suppressed in principle for diterbium quadruple-decker 2a (Figure 1) because of the spin-forbidden nature of the crossing points. It should be noted that undiluted 2a shows quite different χM″ vs f profiles at low temperatures (Supporting Information, Figure S8), in which the peak frequency at 2 K appears at much higher frequency (out of the measurement range). Contrary to the intramolecular f-f

Figure 1. Zeeman diagram for the Jz = ±6 states of 2a. Employed ligand parameters, Aqk⟨rk⟩, hyperfine (Ahf) and nuclear quadrupole (P) coupling constants are as follows: A02⟨r2⟩ = 414, A04⟨r4⟩ = −228, A44⟨r4⟩ = 300, A06⟨r6⟩ = 33, Ahf = 0.0173, and P = 0.01 cm−1.

−1/2⟩ and |+6, +1/2, +6, −1/2⟩, or |−6, −1/2, +6, +1/2⟩ and | +6, −1/2, +6, +1/2⟩ states is highlighted in Supporting Information, Figure S3. On the contrary, the 256 crossing points between the |+6, IzA, +6, IzB⟩ and |−6, IzA, −6, IzB⟩ states are distributed symmetrically with respect to the Hz = 0 point (the red-hatched region in Supporting Information, Figure S3). For the QTM to occur in this region, two quantum numbers, that is, JzA and JzB, must be flipped at the same time. However, these transitions are generally forbidden, and the lower QTM probabilities are expected in this region. As demonstrated in Supporting Information, Figure S4, the variation of the A44⟨r4⟩ values affects the energy separation at the avoided crossing regions, while it has little effects on the other regions. In summary, on the basis of the Zeeman diagram including the hyperfine and nuclear quadrupole interactions, the QTM processes for diterbium 2a are suppressed in the region where Hz = 0 compared to monoterbium 3a. In the case of the dysprosium complexes, 2b and 3b, there are seven naturally occurring isotopes for dysprosium, namely, 156 Dy, 158Dy, 160Dy, 161Dy, 162Dy, 163Dy, and 164Dy, with a natural abundance of 0.06, 0.01, 2.34, 18.91, 25.51, 24.90, and 28.18%, respectively. Of these, I = 5/2 for 161Dy and 163Dy and I = 0 for the other nuclear species. Therefore, Zeeman plots of 2b depend on the combination of isotopes of the two Dy3+ ions in the molecule, making the situation rather complicated. Some examples of the calculated Zeeman plots for 2b are given in Supporting Information, Figures S5 and S6. Although the Kramers theorem of spin parity says that no avoided crossings due to the LF are expected for 2b and 3b, an integer total spin arising from two coupled half-integer spin, that is, J = 15/2 and I = 5/2, allows partial admixing of more than two wave functions through the hyperfine interactions (AhfJ·I).51 However, the mixing of wave functions of this kind is generally limited in extent, and therefore the resultant avoided crossings exhibit quite small energy separations as demonstrated in 10450



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Figure 2. Plots of χM′T (top) and χM″ (bottom) against temperature T for [Tb−Y] (left) and [Tb−Tb] (right) at Hdc = 0, 500, and 1000 Oe (from top to bottom). Ac magnetic fields oscillating at 997 (black squares), 100 (red circles), 10 (blue triangles), and 1 (green upsidedown triangles) Hz are employed. See Supporting Information, Figure S6 for the data under higher Hdc’s.

interactions, therefore, it is conjectured that the intermolecular f-f interactions promote the magnetic relaxations, which cannot be neglected for the undiluted samples especially at Hdc = 0. At Hdc = 500 Oe, the χM′T values drop by about 60% with decreasing temperature at f = 1 Hz for both [Tb−Y] and [Tb− Tb] samples, indicating that the magnetic relaxation processes are suppressed in the presence of the external magnetic fields. In the χM″ vs f plots at Hdc = 500 Oe, the differences in magnetic relaxations between [Tb−Y] and [Tb−Tb] are obscured, and both samples show the peak frequencies at about 0.2 Hz at 2 K. In the Zeeman plots, these conditions correspond to the fringe of the crossing region for 3a

Figure 3. Plots of χM″ against applied ac frequency f at various external magnetic fields (Hdc, ranging from 0 to 3000 Oe) and temperatures (from 2 to 25 K) for [Tb−Y] (left) and [Tb−Tb] (right).

(Supporting Information, Figure S2), and to the crossing region between the |+6, IzA, +6, IzB⟩ and |±6, IzA, ∓6, IzB⟩ states for 2a (Figure 1 and Supporting Information, Figure S3), respectively. Therefore, the observed similar χM″ vs f profiles for [Tb−Y] and [Tb−Tb] at Hdc = 500 Oe can be ascribed to the comparable contribution from the QTMs to the magnetic 10451



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relaxations, although the responsible crossing regions of these complexes are different in origin. Interestingly, the clear differences in the relaxation properties can be perceived between [Tb−Y] and [Tb−Tb] in the presence of Hdc of 1000 Oe (Figure 3). The peak frequency remains at 0.2 Hz for [Tb−Tb] at 2 K, while it shifts to about 0.1 Hz for [Tb−Y]. Similar trends are observed even at the higher temperatures up to 5 K. Contrary to the results obtained at Hdc < 500 Oe, the faster magnetic relaxations are observed for [Tb−Tb] rather than [Tb−Y] at Hdc = 1000 Oe. In the temperature range lower than 5 K, the larger rate of decline in the χM′T values, or larger rate of increase in the χM″ values, are observed for [Tb−Y] than [Tb−Tb], also being consistent with the faster magnetic relaxations for [Tb−Tb] (Figure 2). In the Zeeman plots, the external magnetic field of 1000 Oe corresponds to the area outside of the crossing region for 3a (Supporting Information, Figure S2), while the corresponding region still remains inside the crossing region between the |+6, IzA, +6, IzB⟩ and |±6, IzA, ∓6, IzB⟩ states for 2a (Figure 1 and Supporting Information, Figure S3). Therefore, the Zeeman plots predict that the QTMs are of an ignorable level for 3a at Hdc = 1000 Oe, while those of 2a are rather enhanced by the presence of the external magnetic field. At Hdc higher than 2000 Oe, the χM′T vs T, χM″ vs T, and χM″ vs f plots of [Tb−Y] and [Tb−Tb] exhibit similar magnetic properties to each other (Supporting Information, Figures S7, and Figure 3), since the corresponding regions are away from the crossing regions in the Zeeman plots, leading to sufficient suppressions of the QTM processes for both cases. Interestingly, the peak frequencies in the χM″ vs f plots shift to the higher frequency side with increasing Hdc, which cannot be interpreted by the suppressions of the QTMs. It is known that the inverse of the relaxation time (τ) for the direct process of a non-Kramers system varies as H3coth(gβH/2kT) or as H2T when (gβH/2kT) ≪1, while no such evident field dependencies are included in the formalism of a Raman process.47 Therefore, the observed peak shifts could be attributed to the field dependencies of the direct process. The peak frequencies in Figure 3 are about 0.22, 0.32, and 0.45 Hz at 2K and 0.38, 0.50, and 0.60 Hz at 3 K at Hdc = 2000, 2500, and 3000 Oe, respectively, which approximately obeys the f ∝ H2dc relationships, also supporting the importance of the direct process in the lower temperature range in the presence of Hdc larger than 2000 Oe. The dysprosium samples also show the effect of f-f interactions on the magnetic relaxation processes. At Hdc = 0 Oe, [Dy−Dy] shows slower magnetic relaxations than [Dy−Y] (Figure 4). At Hdc = 2000 Oe, [Dy−Y] and [Dy−Dy] exhibit similar data profiles to each other. As discussed above, the presence of the external magnetic fields suppresses the QTM, and enhances the direct process at the same time. Therefore, it can be considered that the total effect of the Hdc on the QTM and direct process affects the experimental results, leading to the faster magnetic relaxations for [Dy−Dy] at Hdc = 2000 Oe. In the χM′T vs T and χM″ vs T plots (Supporting Information, Figure S10), the χM′T values of [Dy−Y] and [Dy−Dy] decrease by about 60 and 80% from the high temperature limits, respectively, at Hdc = 0 Oe and f = 997 Hz, while the diminution ratios of both samples are comparable at Hdc = 2000 Oe. These observations indicate that the magnetic relaxations are slower for [Dy−Dy] at 1.8 K at Hdc = 0 Oe, which on the other hand, becomes comparable at Hdc = 2000 Oe, being consistent with the conclusion derived from Figure 4. In the

Figure 4. Plots of χM″ against applied ac frequency f at the temperatures ranging from 1.8 to 4.0 K for [Dy−Y] (left) and [DyDy] (right) at Hdc = 0 (top) and 2000 Oe (bottom).

presence of intermediate magnetic fields, that is, Hdc = 1000 Oe, a slightly larger drop ratio is observed for [Dy−Y] than [Dy−Dy] due plausibly to the presence of a possible QTM path as demonstrated in Supporting Information, Figure S5.

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CONCLUSIONS In the present paper, we have constructed a theoretical model for interpreting nuclear spin driven QTM phenomena in lanthanide SMMs by assuming the moderate dipolar magnetic f-f interactions as in the case of quadruple-decker phthalocyanine complexes. By including the ligand field (LF) potentials, hyperfine, nuclear quadrupole, f-f, and the Zeeman interactions in the Hamiltonian, the Zeeman diagrams for diterbium or didysprosium systems have been obtained. The ac susceptibility measurements have demonstrated the slower magnetic relaxations for diterbium or didysprosium quadruple-decker phthalocyanine complexes compared to the monolanthanide congeners in the low temperature range in the absence of the external magnetic fields (Hdc), indicating that the QTMs are effectively suppressed by the f-f interactions. On the contrary, the presence of the intramolecular f-f interactions are found to enhance the QTMs at Hdc = 1000 Oe, and consequently, faster magnetic relaxations have been observed for the diterbium quadruple-decker than the monoterbium derivative. Based on the calculated Zeeman diagrams, these observations can be attributed to the enhanced nuclear spin driven QTMs for [Tb− Tb]. At the Hdc higher than 2000 Oe, the magnetic relaxations become faster with increasing the Hdc for both complexes, which are possibly ascribed to the enhanced direct processes. It has been widely known that an external magnetic field suppresses the QTM in general, and this magic spice makes a variety of lanthanide complexes function as SMMs. The results of the present study, however, demonstrate that the QTMs are not suppressed unconditionally by the external magnetic field, when moderate dipolar f-f interactions are present in the molecule.

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ASSOCIATED CONTENT

S Supporting Information *

Sample preparation procedures, MALDI mass spectra of [Ln1− Ln2] samples, Zeeman plots, and supplemental magnetic 10452



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properties. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] (T.F.). *E-mail: [email protected] (N.I.). Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Notes

The authors declare no competing financial interest.

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REFERENCES

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