Aggregation‐induced suppression of quantum tunneling by manipulating intermolecular arrangements of magnetic dipoles

The relaxation time under zero field reflects the memory retention capabilities of single‐molecule magnets (SMMs) when used as storage devices. Intermolecular magnetic dipole interaction is ubiquitous in aggregates of magnetic molecules and can greatly influence relaxation times. However, such interaction is often considered harmful and challenging to manipulate in molecular solids, especially for high‐performance lanthanide single‐ion magnets (SIMs). By an elaborately designed combination of ion pairing and hydrogen bonding, we have synthesized two pseudo‐D5h SIMs with supramolecular arrangements of magnetic dipoles in staggered and side‐by‐side patterns, the latter of which exhibits a 104‐fold slower zero‐field relaxation time at 2 K. Intriguingly, the side‐by‐side complex exhibits a significantly accelerated magnetic relaxation upon diamagnetic dilution, contrary to the general trend observed in the staggered complex. This strongly reveals the presence of aggregation‐induced suppression of quantum tunneling in a side‐by‐side arrangement, which has not been observed in mononuclear SMMs. By leveraging ion‐pairing aggregation and converting to a side‐by‐side pattern, this study successfully demonstrates an approach to transform a harmful intermolecular dipole interaction into a beneficial one, achieving a τQTM of 980 s ranking among the best‐performance SMMs.

Although these indeed extend S C H E M E 1 Ising-limit mononuclear SMM (plum) in an internal magnetic dipole field generated from the neighboring molecule (blue).The plum arrow represents the magnetic moment of the magnetic molecule.The small blue arrow is the magnetic dipole field generated from the neighboring molecules, and the dashed arrows are longitudinal (blue) and transversal (red) components of the dipole field.the zero-field relaxation time by weakening harmful dipole interaction, they also greatly reduce the density of information storage.More strikingly, magnetic dipole interaction is inevitable in high-density storage and requires studies to turn waste into wealth.
Simple dipole field models are sufficient to explain mononuclear systems with only pure dipole interaction (Scheme 1).Each molecule is a small magnet with dipole fields and "feels" the dipole fields imposed by adjacent molecules. [52,53]When the magnetic axis is perfectly parallel, the transversal component produced by the dipole field is related to the relative arrangement of magnetic dipoles.If adjacent molecules are arranged side-by-side (θ = 90 • ) or head-to-tail (θ = 0 • ), the transversal component of the dipole field vanishes and the QTM process is strongly suppressed. [22]But most mononuclear compounds are in a staggered arrangement, and thus the transverse dipole field cannot be ignored, often resulting in fast QTM processes.
Molecular arrangements can be influenced by many supramolecular interactions in crystal engineering.It is very challenging to design and manipulate the arrangements of magnetic dipoles in molecular solids.The head-to-tail arrangement of the mononuclear complex is only found in a case of one-dimensional column [LnNcPc] 0 (Ln = Dy, Tb) as π-π stacking, where the QTM is effectively suppressed by intermolecular ferromagnetic (FM) coupling. [40,41][44][45] To date, the side-by-side intermolecular arrangement of magnetic dipoles in SIMs has not been reported.
The Ln-SIM constructed from pentadentate thiosemicarbazone ligands has been shown to possess a pseudo-D 5h symmetric charge distribution, making them suitable for building pentagonal bipyramidal SIMs. [54]Here, we selected the thiosemicarbazone ligand with supramolecular active sites and successfully synthesized two SIMs with staggered and side-by-side arrangements driven by ion pairing and hydrogen bonding between anions and cations.By changing the cation from the mono-hydrogen-bonding donor to a dual one, the anionic SIM aggregates from a staggered to side-by-side arrangement.By manipulating the arrangements of supramolecular ion pairs and the aggregation of magnetic dipoles, the zero-field relaxation has been greatly improved based on magnetic studies.By elaborately design-ing supramolecular interaction, we successfully realize the transformation of harmful dipoles into beneficial dipoles in a unique system of side-by-side arrangement of magnetic dipoles in SIMs.
Single-crystal X-ray diffraction reveals that complex 1-Dy crystallizes in the triclinic space group P−1, while complex 2-Dy crystallizes in the monoclinic space group P2 1 /n.The asymmetric unit of both complexes contains one [Dy(DABT)( t Bu-DDTP) 2 ] − anion and one cation ([HNEt 3 ] + in 1-Dy and [HTMG] + in 2-Dy), forming a supramolecular ion pair (Figures S12 and S14).In both complexes, the Dy(III) is encapsulated in the S2N3 pocket of a planar ligand and axially coordinated by two phenoxy atoms from H t Bu-DDTP (Figure 1A).As a result, Dy(III) is seven-coordinated and possesses a distorted and compressed pentagonal bipyramidal geometry, as further confirmed by the calculations of continuous shape measures (CShM). [56]Compared to ).These differences in the primary coordination sphere of both complexes are hints of stronger axial magnetic anisotropy for complex 1-Dy, which contrasts with their magnetic properties and highlights the crucial role played by their distinct supramolecular assembly arrangements (vide infra).It is worth mentioning that despite the difference in their space groups, the presence of an inversion center between two neighboring ion pairs leads to the perfect parallel of their magnetic axes.
For complex 1-Dy, the [HNEt 3 ] + cation contains one proton and can donate one hydrogen bond to the S acceptor from the anion.The neighboring two dysprosium atoms are separated by [HNEt 3 ] + at a distance of 9.85 Å (Figure S18) and staggered at an O2−Dy1−Dy1a angle of 72.68 • (Figure 1C).In contrast, the [HTMG] + cation in complex 2-Dy has two protons and two V-shaped [HTMG] + on upper and lower positions bridge two neighboring [Dy(DABT)( t Bu-DDTP) 2 ] − anions with totally four hydrogen bonds (Figure 1C).These supramolecular interactions act like "staples", bringing two neighboring Dy(III) closer with a distance of 7.62 Å (Figure S19) and arranged side-byside with an O2−Dy1−Dy1a angle of 91.97 • .Their anions are stable in solution, as confirmed by high-resolution mass spectrometry (Figures S7-S10).Therefore, by mixing 1-Dy with tetramethylguanidine in acetonitrile, the cation can be exchanged and co-crystallized as 2-Dy (Figures 1B and  S6).This transformation is a supramolecular rearrangement process driven by ion-pairing aggregation.

Magnetic characterization
The variable-temperature magnetic susceptibilities were measured on polycrystalline samples of 1-Dy and 2-Dy from 2 to 300 K under a 0.1 T direct-current (DC) field (Figure S21).The χ M T values for 1-Dy and 2-Dy are 13.57and 13.87 cm 3 K mol −1 at 300 K, respectively, slightly lower than the expected value for a free Dy(III) (14.17 cm 3 K mol −1 ), mainly attributed to the large splitting of the 6 H 15/2 ground term.For both complexes, the steady decrease upon cooling in χ M T can be mainly attributed to the depopulation of excited Stark sublevels.Subsequently, a rapid decline occurs below 12 K, which can be attributed to magnetic blocking and intermolecular antiferromagnetic (AFM) coupling.The field-cooled (FC) and zero-field-cooled (ZFC) magnetic susceptibilities at 0.15 T were measured (Figures S22 and S23), with the curve of 1-Dy diverging at 8.0 K (8.5 K for 2-Dy) and the ZFC maximum located at 6.1 K (7.2 K for 2-Dy), which are clearly indicative of magnetization blocking.Magnetic hysteresis loops of 1-Dy and 2-Dy were collected up to 2 T and down to 2 K.At a sweep rate of 0.02 T s −1 , 1-Dy shows butterfly shaped hysteresis loops and gradually vanishing until 12 K (Figures S24 and S26).Notably, the hysteresis of 1-Dy is completely closed around zero DC field but open at external fields, which means there is a fast QTM process under zero DC field.The hysteresis of 2-Dy remains open not only under external fields but also at zero field up to 10 or 12 K, based on the coercive field or the remanent magnetization, respectively (Figures S25 and S26).This implies that the magnetic relaxation of 2-Dy around zero field is much slower than that of 1-Dy.Interestingly, a pair of steps can be observed around −0.02/+0.02T for the hysteresis of 2-Dy, which does not depend on sweep rates (Figures S27 and S28) and thus confirms their QTM origin.This "bias field effect" suggests that the hysteresis loop can be successfully switched from closed to open by manipulating the easily tailored supramolecular arrangements from 1-Dy to 2-Dy.
Variable-temperature and variable-frequency alternatingcurrent (AC) magnetic susceptibilities were measured to study the magnetic relaxation behaviors.In the absence of an applied DC field, an obvious temperature-dependence of AC magnetic susceptibilities is observed with a maximum of χ M ″ (999 Hz) located at 56 K for 1-Dy and 55 K for 2-Dy (Figures S31 and S36).The frequency dependence of AC magnetic susceptibilities shows typical characteristics of SMMs, with the peaks of χ M ″ shifting to the lower frequency region on cooling.
1-Dy exhibits a constant peak position around 6 Hz at low-temperature ranges (2−10 K), which arises from the hindrance of a fast temperature-independent QTM process.Whereas for 2-Dy, the peak position continuously shifts to lower frequencies as the temperature decreases and exceeds the lower limit of the measured AC frequency (0.1 Hz) below 11 K, indicating the much slower magnetic relaxation for 2-Dy.
The relaxation times (τ) with narrow-to-moderate distributions at variable temperatures were extracted using the generalized Debye model (Figures S33 and S37), and the much slower relaxation times of 2-Dy below 11 K were obtained by DC magnetization decay (Figure S38).The logarithm of τ versus T shows linear Orbach-like processes at high temperatures, with Raman-like and QTM processes deviating from the linearity upon cooling (Figure 2C).The relaxation times are fitted well by using the equation τ 26 and τ QTM = 0.045(5) s for 1-Dy, and 33 and τ QTM = 980(175) s for 2-Dy.From 1-Dy to 2-Dy, the U eff has increased ca.200 K, and the QTM rate is ca.20,000 times slower under zero field.][19] The exponent for Kramers ion is n = 9 in the long-wavelength approximation and will be smaller (n = 1−6) when optical and acoustic phonons are taken into account. [57]In addition, the exponent of 1-Dy is also close to the exponent of the phonon bottleneck process (n = 2). [58]This suggests that the relaxation process of 1-Dy at low temperatures may be dominated by the bottleneck or Raman process.It is worth noting that the direct process (n = 1) should be absent under a zero magnetic field (τ −1 ∼ H m , where m = 4 for a Kramers ion). [57]he field-dependent AC magnetic susceptibilities were measured at 15 K, and relaxation times were extracted for different fields ranging from 0 to 0.5 T (Figures 2D, S29, and  S30).1-Dy shows field-sensitive magnetic relaxation, with τ increasing over 50 times under the external field. [21,49,50]he peak of χ M ″ quickly switches from 11 to 0.3 Hz as the external magnetic field increases from 0.02 to 0.08 T (Figure S29), and clearly shows dual relaxation components.In contrast, at higher or lower AC frequencies, χ M ″ displays single peaks with only one relaxation component.This indicates that the fast relaxation process switches abruptly, rather than gradually, to a slow relaxation process when an external field exceeds a critical point. [49]For 2-Dy, τ is much less sensitive to external fields and only ranges from 0.25 to 0.45 s. τ decreases first and then increases with the applied field and a valley can be observed near 0.02−0.03T (Figure S30).The opposite field-dependent relaxation behavior can be attributed to the staggered or side-by-side arrangements of magnetic dipoles (vide infra).Under an optimal field of 0.08 T for 1-Dy and 0.15 T for 2-Dy (Figures S32 and  S39), the relaxation processes are dominated by Ramanlike and Orbach-like processes for both complexes, giving U eff /k B = 945(40) K for 1-Dy, and U eff /k B = 1062(68) K for 2-Dy (Figures S34 and S41).The slight enhancement of the effective energy barrier under applying the optimal field is attributed to the decreased contribution of QTM, which is commonly observed in other SMMs. [59,60]

Theoretical analysis
To further understand the magnetic properties of 1-Dy and 2-Dy, CASSCF/SO-RASSI/SINGLE_ANISO ab initio calculations were performed using the OpenMOLCAS program [61] (see more detailed information in Supporting Information) for a single [Dy(DABT)( t Bu-DDTP) 2 ] − anion.
For both complexes, the quantization axes are approximately along the phenol groups of the axial ligands (Figure 4).The ground and first excited Kramers doublets (KDs) are well described as | ± 15/2 > and | ± 13/2 > (> 99%), respectively (Tables S12 and S13).These states are largely separated by 399.3 cm −1 in 1-Dy and 390.3 cm −1 in 2-Dy.The magnetic relaxation is expected to primarily proceed through higher KD like third KD (Figure S48, 1-Dy: 648.8 cm −1 , ca. 934 K; 2-Dy: 630.6 cm −1 , ca. 908 K), which is close to experimental values (1-Dy: 828 K; 2-Dy: 1018 K).The small deviation could arise from the contributions from other relaxation pathways and/or the inherent dipole fields in the magnetic molecular solid.In fact, the temperature dependence of their magnetic relaxation times can also be well fitted by fixing the U eff as the Stark sublevel energy of the third KD, combined with QTM and spin-lattice relaxation processes, which gives the similar results to those obtained by free fitting, n = 1.48 (11), C = 0.7(3) s −1 K −1. 48and τ QTM = 0.0386(4) s for 1-Dy, and n = 4.30(4), C = 2.1(2) × 10 −5 s −1 K −4. 30 and τ QTM = 1011(196) s for 2-Dy (Figure S53).This further validates the thermally activated process for both compounds and suggests that the molecular arrangements in magnetic aggregates may also affect the spin-lattice relaxation process that is related to low-energy phonons, [57,58,62] in addition to quantum tunneling.It is noteworthy that 1-Dy and 2-Dy possess high similarity in the energy splitting of Stark sublevels, probability of state transitions (Figure S50), and weights of crystal-field parameters B k q (Tables S12-S14).Meanwhile, the electrostatic potential and charge distribution of the coordination sphere of Dy(III) in 1-Dy and 2-Dy are also quite similar and very close to D 5h symmetry (Figures S49-S51), [54] which suggest that the magnetic properties of [Dy(DABT)( t Bu-DDTP) 2 ] − in 1-Dy and 2-Dy should have been very similar.The significant differences observed in their experimental relaxation cannot be attributed to inherent differences in their molecular or electronic structures, but rather to intermolecular differences in cation-driven arrangements of magnetic dipoles.
Owing to the presence of intermolecular hydrogenbonding interactions and the absence of bridging ligands, the magnetic dipolar interaction is almost the only source of intermolecular magnetic coupling.Therefore, it is sufficient to study this system without considering direct or superexchange interactions that require orbital overlap.For a pair of magnetic molecules separated by a distance of d, the dipolar interaction can be considered to arise from the "magnetic dipole field" ( ⃗ B dip , as shown in Equation 1) generated by magnetic moment (⃗ ) of neighboring Dy(III). [22,52]ince the ground KD of both complexes is very close to the Ising limit (g x,y = 0.001, g z = 19.98), the magnetic moment can be taken as |⃗ | ≈ 1 / 2 g z μ B .In addition, the angle θ between ⃗  and the unit vector ⃗ u from Dy1 to Dy1a is 69.5 • in 1-Dy and 86.3 • in 2-Dy (Figure 3A).The magnitude of | ⃗ B dip | (Table 1) can be estimated using Equation (2).
The dipole fields | ⃗ B dip | of 1-Dy and 2-Dy, generated by a neighboring molecule, are calculated to be 11.4 and 21.1 mT, respectively.The larger dipole field in 2-Dy is attributed to its shorter Dy⋅⋅⋅Dy distance.The value for 2-Dy closely aligns with the steepness of the hysteresis loop (Figure 4C) and the valley of the field-dependent relaxation time around 20−30 mT (Figure 2D), at which the external field is resonant with the internal dipole field, resulting in field-induced fast QTM.This consistency between experimental observations and theoretical calculations implies that the ultraslow zero-field magnetic relaxation in 2-Dy is due to its dipole field preventing resonance in the absence of an applied field.In terms of a dimeric Dy(III) with anti-paralleled/parallel alignments, the AFM ground states do not contribute to the variation of magnetization, and thus the observed slower relaxation stems from the thermal population of FM excited states (0.057 cm −1 for 1-Dy and 0.193 cm −1 for 2-Dy) with stronger anisotropy, as is the case with 2-Dy.However, no hysteresis platforms for 1-Dy are observable in the range of ± 0.1 T; instead, ultrafast relaxation appears at zero field.
In complex 2-Dy, two Ising-like Dy(III) anionic molecules are bridged by a dual-hydrogen-bonding [HTMG] + cation.This results in a side-by-side arrangement that leads to a small φ between the dipole field and magnetic axis (Figure 3B).Notably, the smaller φ in 2-Dy results in a stronger axial dipole field (B axial ) and weaker transversal dipole field (B trans ), which is very helpful in suppressing QTM.In addition, the valley of field-dependent relaxation times around B axial (ca.20 mT) is attributed to the fast tunneling through the strongly mixed FM and AFM states.This is consistent with the experimental magnetic relaxation mentioned above.In contrast, the staggered arrangement in complex 1-Dy exhibits a large deviation of φ = 57.4• , giving rise to a smaller B axial of 6.12 mT but a larger B trans of 9.56 mT.The presence of a non-negligible transversal dipole field perpendicular to the local magnetic axis accelerates the QTM process accompanied by transverse crystal fields (CFs).This is in line with the fast relaxation rates and rapid decline of the hysteresis loops at zero DC field.
To better depict a more accurate simulation of the dipole field in both molecular solids, we consider the contribution of magnetic molecules far away from each other, as well as the closest pairs.In Tables S15 and S16, it is shown that further considering other pairs with larger distances only results in slight changes to B axial and B trans and the angle between the dipole field and magnetic axis, which can be attributed to the fact that ⃗ B dip is inversely proportional to the third power of d, thus only relatively close dipole pairs play dominant roles (Figures S54 and S55).This again solidifies that complex 2-Dy experiences a weaker transversal dipole field and a stronger longitude dipole field than complex 1-Dy.
To obtain favorable supramolecular arrangements and magnetism, both the linkage of supramolecular assembly and the orientation of magnetic easy axis are crucial.The linkage between the central metal ion and the supramolecular sites associated with donor/acceptor atoms should be located at the "parallel" or "perpendicular" position relative to magnetic easy axis, which can enable the assembly to adopt head-to-tail (θ = 0 • ) or side-by-side (θ = 90 • ) patterns, respectively.The orientation of magnetic easy axis can be estimated by using an electrostatic model.And the supramolecular assembly of individual molecules involves various aspects of supramolecular chemistry, such as hydrogen bonding, [63,64] ion pair receptors, [65] cation/anion-π interactions, [66] and so on.This work is designed based on well-defined magnetic axes and the linkage of supramolecular assembly through hydrogen bonding and ion pairing, which can be suitable to other systems.
To further improve our approach, the orientation of magnetic easy axis can also be fine-tuned by modifying the coordination sphere of Dy(III) ion, and the arrangement of supramolecular assembly can also be altered by the choice of peripheral ligands and counterions, thus regulating the angles of θ and φ.For instance, a near-perfect head-to-tail (θ = 0 • ) or side-by-side (θ = 90 • ) pattern can be achieved by introducing electron-withdrawing or -donating groups or substituents of varying sizes to adjust the coordination sphere and the angles between hydrogen bonds.

Magnetic dilution characterization
To further understand the role of staggered/side-by-side arrangements of magnetic dipoles on relaxation behavior, diamagnetic isomorphic lutetium compounds were doped with a Dy:Lu ratio of 1:19 to obtain diluted samples of 1-Dy@Lu (ca.3% Dy) and 2-Dy@Lu (ca.5% Dy).The relaxation times at low temperatures are obtained using the DC relaxation measurements (Figures 4A, S42, and Table S9).Phenomenological relaxation times can be obtained using a stretched exponential function, over the first 2000 s, during which time most of the magnetic molecules have completed the relaxation process, giving 38.6( 14) s for 1-Dy@Lu and 30.1(3) s for 2-Dy@Lu at 2 K, respectively (Figure S44).The similar relaxation time of 1-Dy@Lu and 2-Dy@Lu further indicates that the magnetization dynamics of [Dy(DABT)( t Bu-DDTP) 2 ] − are very similar as suggested by ab initio calculations.The relaxation time of 1-Dy@Lu is much longer than the aggregated sample (0.043 s), which is consistent with common observations in many lanthanide SIMs where the removal of homogeneous dipolar fields leads to slower magnetic relaxation.Interestingly, the relaxation time of 2-Dy (675.6(3)s) observed for the aggregated sample is much longer than that of the diluted 2-Dy@Lu (30.2(2) s).As far as we know, such aggregation-induced suppression of QTM has not been observed in pure lanthanide SIMs, especially in a side-byside arrangement, although it has been reported in many polynuclear SMMs as well as in a chain-like arrangement of [TbNcPc] 0 with delocalized radical. [24,38,45,67][70] However, the opposite magnetization dynamics in aggregation/dilution between 1-Dy and 2-Dy indicates that their magnetic behavior is more than an exchange-biased effect since it is strongly dependent on how they aggregate-staggered or side-by-side pattern, which leads to the distinct contributions of B axial and B trans .This anomaly highlights the significance of the side-by-side arrangement of AFM dipoles in 2-Dy, which indeed plays a critical role in suppressing QTM and slowing down the magnetic relaxation.
It should be noted that all magnetization decays in 2000 s give very small exponent β values (0.27 for 1-Dy@Lu and 0.38 for 2-Dy@Lu, see Table S9).This suggests a broad distribution of relaxation times due to the inevitable inhomogeneity in doping.Magnetization decays were measured over longer times up to 7000 s, but the fits of a stretched exponential function are much worse and the β values are much smaller (Figure S45 and Table S10).
To understand the distributions of relaxation times in inhomogeneous doping samples, the time-dependent relaxation time can be obtained through the Bloch equation of longitudinal relaxation at zero field, As time increases, τ Bloch also extends and approaches τ Bloch(7000s) = 24,000 s for 2-Dy@Lu.It should be mentioned that the 1-Dy@Lu is more diluted than that of 2-Dy@Lu (3% vs. 5%).Therefore, such extremely long τ Bloch(7000s) could represent the limit of the slowest magnetic relaxation for an isolated side-by-side dimer, rather than the faster-relaxing monomer demonstrated in the τ Bloch(7000s) of 1-Dy@Lu (ca.15,000 s).

CONCLUSIONS
Using thiosemicarbazone as a pentadentate ligand for highperformance pseudo-D 5h SIMs and as a hydrogen-bonding acceptor for supramolecular dimers, two aggregates have been isolated with staggered and side-by-side supramolecular arrangements for 1-Dy and 2-Dy, respectively.Additionally, 1-Dy can be converted to 2-Dy through ion-pairing aggregation due to adapted supramolecular interactions.Although ab initio calculations on single molecules suggest very similar electronic structures and SMM behaviors, experimental measurements indicate huge differences in their magnetic relaxation of molecular solids.This arises from the switching roles of intermolecular AFM dipoles from harmful to beneficial along with the change of intermolecular arrangement of magnetic dipoles from staggered to side-by-side pattern, as revealed by the analysis of magnetic dipole interactions.The butterfly shaped hysteresis in 1-Dy is successfully opened at zero fields up to 12 K, and the relaxation time at 2 K has increased over four orders of magnitude, reaching τ QTM as large as 980 s among the longest reported SMMs.Furthermore, the side-by-side aggregation on QTM suppression in 2-Dy is further evidenced by relaxation acceleration upon dilution, which has not yet been found in molecules with only one spin center.With the assistance of suitable supramolecular binding sites and judiciously induced aggregation of ion pairs, the side-by-side arrangement of magnetic dipoles highlights a neglected but feasible and well-designed approach toward slowing zero-field relaxation time and suppressing QTM.The aggregation-induced suppression of QTM is an effective strategy to enhance the capabilities of nonvolatile data storage without altering the molecular storage medium or lowering the storage density by magnetic dilution.By combining it with magnetic molecules that possess inherently high anisotropy, we believe it will expedite the development of SMMs with high capabilities.

Materials and physical measurements
H 2 DABT was synthesized as described in the previous literature. [55]Metal salts and other reagents were commercially available and used as received without further purification.The C, H, N, and S elemental analyses were carried out with an Elementar Vario-EL CHNS elemental analyzer.Powder X-ray diffraction patterns were performed on RIGAKU D-MAX 2200 VPC (Cu-K α , λ = 1.54056Å).Thermogravimetric analysis (TGA) was carried out on a NETZSCH TG209-F3 thermogravimetric analyzer.Mass spectra for the methanol solution of samples were measured on UltiMate3000-timsTOF mass spectrometer.Magnetic susceptibility measurements were performed with a Quantum Design MPMS-3.Polycrystalline samples were embedded in vaseline to prevent torquing.Data were corrected for the diamagnetic contribution calculated from Pascal constants.

X-ray crystallography
Single-crystal X-ray measurements of ligand H t Bu-DDTP were collected on XtaLAB Synergy R, DW system with Rigaku (Cu) X-ray Source at 293 K.

Synthesis
All reactions were carried out at room temperature.The metal salts and reagents were commercially available and used as received without further purification.

Dysprosium-doped lutetium materials 1-Lu@Dy
The magnetically dilute sample, 1-Dy@Lu, was obtained by combining accurately measured amounts of Dy(CF 3 SO 3 ) 3 and Lu(CF 3 SO 3 ) 3 in a 1:19 molar ratio, following the procedure described as compound 1-Dy.The final crystalline product with dysprosium content (molar ratio of Dy/Lu ∼2.9%) was determined by the inductively coupled plasma atomic emission spectroscopy (ICP-AES) analyzed by a TJA IRIS(HR) spectrometry.

Dysprosium-doped lutetium materials 2-Lu@Dy
The magnetically dilute sample, 2-Dy@Lu, was obtained by combining accurately measured amounts of Dy(CF 3 SO 3 ) 3 and Lu(CF 3 SO 3 ) 3 in a 1:19 molar ratio, following the procedure described as method 1 of 2-Dy.The final crystalline product with dysprosium content (molar ratio of Dy/Lu ∼5.2%) was determined by the ICP-AES analyzed by a TJA IRIS(HR) spectrometry.

C O N F L I C T O F I N T E R E S T S TAT E M E N T
The authors declare no conflict of interest.

D ATA AVA I L A B I L I T Y S TAT E M E N T
The data that support the findings of this study are available from the corresponding author upon reasonable request.

F
I G U R E 2 (A,B) Frequency-dependent (0.1−999 Hz) out-of-phase χ M ″ AC susceptibility signals for 1-Dy (A) at 2−65 K and 2-Dy (B) at 11−60 K under zero applied field.(C) Temperature dependence of the relaxation time τ of 1-Dy (green circle) and 2-Dy (blue circle).The solid lines are the best fits described in the text.(D) Field dependence of the relaxation time τ at 15 K, and the Inset displays an enlarged view of the range from 0 to 0.12 T, with the error bars inside the circles.

F I G U R E 3
The easy axis of magnetization (plum vectors) of 1-Dy (A) and 2-Dy (B), and the magnetic dipole fields (blue vectors) generated by the adjacent molecule.The red number and blue number represent the value of angles θ and φ.TA B L E 1 Magnetic dipole interactions in 1-Dy and 2

F
I G U R E 4 (A) The DC relaxation decays with H = 0 Oe for 2-Dy, 2-Dy@Lu, and 1-Dy@Lu in the range of 0−2000 s, where some data points are skipped for clarity.The absolute value of slope in the plot of ln(M(t)/M 0 ) versus t represents the relaxation rate τ Bloch −1 , according to Bloch equation.(B) The relaxation times of 2−4 K for 1-Dy, 2-Dy, 2-Dy@Lu, and 1-Dy@Lu, where the relaxation times of 1-Dy are obtained by AC susceptibilities, while others are obtained by DC magnetization decays.(C) The hysteresis loop for 1-Dy (green) and 2-Dy (blue) at 2 K, where the dashed lines are related to the QTM resonance field.(D) The scheme of relaxation rates on magnetic dipoles in different environments.
CCDC Deposition numbers 2258275 (H t Bu-DDTP), 2258276 (1-Dy), 2258278 (1-Lu), 2258279 (2-Dy), and 2258230 (2-Lu) contain the supplementary crystallographic data for this paper.These data can be obtained free of charge from The Cambridge Crystallographic Data Centre via www.ccdc.cam.ac.uk/data_request/cif.] A C K N O W L E D G M E N T S This work was supported by the National Key Research and Development Program of China (2018YFA0306001), the NSFC (grant nos 22073115, 22131011 and 21821003), the Pearl River Talent Plan of Guangdong (2017BT01C161), and the Science and Technology Projects in Guangzhou (202201011095).We are grateful for the support of the Guangdong Basic Research Center of Excellence for Functional Molecular Engineering.