Lanthanide-Based Single-Molecule Magnets Derived from Schiff Base Ligands of Salicylaldehyde Derivatives

The breakthrough in Ln(III)-based SMMs with Schiff base ligands have been occurred for the last decade on account of their magnetic behavior, anisotropy and relaxation pathways. Herein, we review the synthetic strategy, from a structural point of view and magnetic properties of mono, di, tri and polynuclear Ln(III)-based single-molecule magnets mainly with Schiff bases of Salicylaldehyde origin. Special attention has been given to some important breakthroughs that are changing the perspective of this field with a special emphasis on slow magnetic relaxation. An overview of 50 Ln(III)-Schiff base complexes with SMM behavior, covering the period 2008–2020, which have been critical in understanding the magnetic interactions between the Ln(III)-centers, are presented and discussed in detail.


General Introduction to Single-Molecule Magnets (SMMs)
SMMs are subunits of metal-organic compounds that show superparamagnetic behavior below a certain blocking temperature (T B ), purely of molecular origin [1]. Since the discovery of the manganese coordination cluster, [Mn 12 O 12 (O 2 CMe) 16 (H 2 O) 4 ] [2], behaving as a single-domain magnet, numerous discoveries have been devoted to the "hot" area of molecular magnetism [3][4][5]. Because of the large magnetic moment and single-ion anisotropy, lanthanides(III) (Ln(III)) have entered into this area. Among them, some of the mononuclear complexes of Ln(III) have drawn maximum attention compared to the polynuclear ones, owing to their small size and bistable nature and so could be ideal candidates for high-density storage and quantum computing [6][7][8][9].
After the report of the first SMM, [Mn 12 O 12 (O 2 CMe) 16 (H 2 O) 4 , a tremendous amount of SMMs were investigated with 3d transition metals on account of their strong coupling while less interest was with Ln(III) systems due to their week exchange interaction when they are in their most stable trivalent oxidation state. Furthermore, much work has been done on a single-ion magnet (SIM)/SMMs with 4d and 5d transition metal, owing to their magnetic anisotropy, which received much attention in the area

The Anisotropy of Lanthanide Ions-Oblate/Prolate Model
In Ln(III) systems, the magnetic anisotropy typically arises from the extensive splitting of M J ground state caused by the ligand field [14] and is quantified by a g-factor, which characterizes the shape of the ions and the amplitude of anisotropy. In most of the SMM's, there is an anisotropic axis in a "hard plane" (Figure 2d). When the magnetic axis of the metal ion is in line with the anisotropic axis, and the value of gz will be maximized [15]. This anisotropy is also can be called an Ising type anisotropy, which is an ideal condition for an SMM. The higher the "pure" excited state, the bigger the effective energy barrier will be obtained [16]. In some cases, the easy axis can be a plane, where it is possible to find magnetization, which can be called "easy plane", where g z < g x ≈ g y .
In other words, there is a way to maximize the single-ion anisotropy by modifying the coordination environment of the Ln(III)-ion. Rinehart and Long suggested simple rules in order to optimize 4f-SMMs, simply by exploiting their single-ion anisotropy [13]. For increasing the anisotropy of the oblate ions which are equatorially expanded (Figure 2a), we should place it in a ligand field for which the ligand electron density is located above and below the xy plane ("sandwich" type ligand geometry), which means donor atoms should be on the axial position ( Figure 2b). It is not a coincidence that most of the geometries of mononuclear Tb(III) and/or Dy(III) SMMs with the highest energy barriers are square-antiprismatic (SARP-8) [15]. However, for prolate ions, which are axially expanded (Figure 2a), equatorial coordination geometry is preferred (Figure 2c), and here, the donor atoms should be on the equatorial plane. . Europium is not shown as it has a J = 0 ground state; low and high energy configurations of the f-orbital electron coupled to the orbital moment (J): density with respect to the crystal field environment for an oblate (left) (b) and a prolate (right) (c) electron density of Ln(III) ions. The green arrow represents the orientation of the spin angular momentum (L), (d) the representation of the easy axis and hard plane in three-dimensional space. Reproduced with permission from [13,15]; Published by Royal Society of Chemistry, 2011 and Elsevier, 2014.
For Dy(III) single-ion magnet (SIM) with ground state J = 15/2 under extremely axial crystal field, the energy landscape of the magnetic microstates could resemble the time-reversal symmetric double-well potential as depicted in Figure 3a. It is important mentioning the difference between the height of the double-well potential and the effective energy barrier (U eff ) for magnetization reversal. Provided all, but Orbach mechanisms of relaxation (vide infra, Figure 3a) are prohibited, the molecules in principle can revert their magnetization moment (i.e., jumping from one potential well to other in the double-well potential) via climbing through all the possible M J states as shown by dashed green arrows in Figure 3a. The energy required for such a magnetization reversal equals the height of the double-well potential (U = U eff ). However, in practice, spin-lattice relaxations (direct/Raman) and quantum tunneling of magnetization accompany the Orbach process. The former processes are more prone in the excited states. Therefore, it is not needed for the system to climb all the possible M J states for magnetization reversal. In most of the Ln(III) based SIMs/SMMs, magnetization reversal takes place through first (e.  [13,[17][18][19][20]. Therefore, the effective energy (U eff ) required for the magnetization reversal is the energy between the ground state and first excited state where M J = +15/2 and +13/2, respectively or the ground state (M J = +15/2) and the second excited state (M J = +11/2), respectively in the above cases.
It is worthwhile to note that the eigenstates are not necessarily organized following the decreasing/increasing order of the M J values. As shown in Figure 3b, the ground, the first-and second excited states for Tb analog are associated with M J = ±6, ±5 and 0, respectively. On the other hand, those states for Dy analog correspond to M J = ±13/2, ±11/2 and ±9/2, respectively. However, the best performing SMMs are indeed those for which magnetization relaxes via the third [21], fourth [22] and even fifth [23] excited states since this provides a larger anisotropy barrier.  [26]. The radical analog [TbPc 2 ] has shown a strong frequency dependence of out-of-phase signal, with a peak maximum observed at 50 K. The resulting Arrhenius analysis revealed a remarkable U eff = 410 cm −1 , which is considerably higher than any analogous value extracted for [Pc 2 L n ] − from ac susceptibility data [27].  (2) in Figure 4c using o-vanillin as a ligand (Figure 4d). Ever since, pure Dy(III) based SMMs have drawn the attention of many investigators, as evident by the plethora of contributions with Dy(III) to this interesting field of molecular magnetism. In the Dy 3 triangle, despite an almost nonmagnetic ground state, all the characteristics of SMM have been observed with an effective energy barrier of 61.7 K, possibly derived from the thermally populated excited state. Antiferromagnetic linking of two Dy 3 triangles to form Dy 6 gave an increase in the temperature at which the magnetization is observed from 8 to 25 K, suggesting a promising strategy to increase the blocking temperature of lanthanide-based SMMs [28]. The above pioneering investigations shed light on the further development of lanthanide-based mononuclear and cluster-based SIMs and SMMs.

The Current Progresses in Ln(III)-Based SMMs
After the published work of Ishikawa [26], a number of Ln(III)-SMMs have been reported. Two main features are continuously optimized, namely, the energy barrier value (U eff ) and T B . Before 2016, the largest record of energy barrier was 938 K [30], and the highest T B was 14 K [31]. In 2016, a striking development of the value of the energy barrier was pushed forward. Here the complex [Dy(bbpen)Br] (H 2 bbpen = N,N -bis(2-hydroxybenzyl)-N,N -bis(2 methylpyridyl)ethylenediamine) synthesized by Liu et al. [32], breaks the record of the energy barrier, surpassing 1000 K. The Dy(III) ions is in a pseudo-D 5 h symmetry, surrounded by four neutral atoms and one bromide ion in the equatorial plane, and two oxygens occupying the capping positions. The spin flips from the ground state to the third excited doublet, which increases the effective energy barrier dramatically to 1025 K, accompanied by a magnetic hysteresis of up to 14 K.
In 2018 Guo et al. also reported a dysprosium metallocene cation [(Cp i Pr 5 )Dy(Cp*)] + (Cp i Pr 5 , penta-iso-propylcyclopentadienyl; Cp*, pentamethylcyclopentadienyl), which displays magnetic hysteresis above liquid-nitrogen temperatures with an effective energy barrier to a reversal of the magnetization of U eff = 1541 cm −1 and having magnetic blocking temperature of T B = 80 K. In the same year, McClain and coworkers have synthesized and reported dysprosium metallocenium SMMS, [Dy(Cp i Pr 4 R) 2 ] [B(C 6 F 5 ) 4 ], where R = H (3), Me (4), Et (5), i Pr(6) [33]. A slight variation of the cyclopentadienyl ring substituents resulted in large changes of the molecular structures and in an increase of 45 K in the operating temperature for 3-6 and also led to the manifestation of the highest 100 s blocking temperatures reported for an SMM till now. Complex 3 has the highest operating temperature along the series, having a 100 s T B at 62 K. It is interesting to note that 4 displays an energy barrier of 1468 cm −1 with hysteresis at 72 K [33].
By comparing the success of different SMMs, the bigger the magnitude of the anisotropic barrier, the more prominent the SMM properties at higher temperatures. A breakthrough in SMM based technology can only be achieved when these two major problems get addressed. One of the imposing challenges in this field is to design and synthesis well-organized SMMs, that operating at ambient temperature for practical uses [6,34].

Schiff Base Ligands
Schiff bases are prepared from amines and aldehyde precursors by condensation reaction [35] (Scheme 1). The ligand designs can be tailored by incorporating new functionalities to either the aldehyde or the amine precursor component. This makes them ideal candidates for the development of a library of ligands for metal aggregate synthesis. The number of amino and keto precursors that can be selected for condensation reactions, leading to azomethine compounds, are numerous and practically limitless [35]. The careful selection of both aldehydic and amino precursors enables us to perfectly switch the donating ability of the resulting ligands, the nature of the donor atoms and the

Designing Schiff Bases in Ln(III)-Based SMM Systems
Schiff base ligands have been widely used for the purpose of synthesizing Ln(III)-based SMMs [36][37][38][39]. The growing interest in Ln(III)-SMMs leads to a great demand for ligand architecture since the coordination environment is the main factor in the properties of metal aggregates. Usually, Schiff base ligands are derived from aldehydes and primary amines, reactions commonly taking place in alcohol through condensation [40]. The straightforward synthesis could be one of the reasons that Schiff base ligands are so popular, and also the basic imine nitrogen, which exhibits pi-acceptor property, shows affinity to Ln(III) ions, making it the preferred choice.
Additionally, Schiff base ligands can be easily modified by controlling the amines and aldehydes of different sizes, flexibilities and basicities [41,42], which provides different "pockets" for Ln(III) ions to occupy the resulting dinuclear, trinuclear, tetranuclear and even more polynuclear structures [43][44][45][46]. Additionally, the flexibility of the diamines or the linkers potentially introduces chirality to the complex by increasing the chances of forming helicate or mesocate structures [47]. Schiff base ligands derived from o-vanillin have proven to be particularly suitable for the synthesis of Ln-SMMs [37][38][39]45,46,48]. In his recent review, Andruh has discussed several relevant structural types of heterobinuclear 3d-3d' and 3d-4f complexes obtained from o-vanillin-based Schiff ligands, which show interesting magnetic, luminescence, catalytic, cytotoxic, and ferroelectric properties [49].
The ligands can be designed to provide a coordination environment favored by a 3d metal such as Mn(III) or Cu(II) (relatively N rich) as well as a site (relatively O rich) more favored by a "hard" metal ion such as Fe(III) or any Ln(III). For example, combining o-vanillin and tris (hydroxymethyl) aminomethane to give the ligand (H 4 L, Chart 1) provides a system that captures two Ln(III) and transition metal ions [50]. While this ligand had been previously employed to prepare homometallic clusters [51], it seemed reasonable to expect that the oxygen donor rich tripodaltris(hydroxymethyl) aminoethane derived group would capture the oxophilic Ln(III), while the transition metal in +2 oxidation state like ions would be coordinated by both the imine nitrogen and oxygen donors [51]. Schiff base ligands can also be designed with the aim of getting spin-crossover (SCO) materials [52]. Some important theoretical and experimental studies on Ln(III)-based Schiff base complexes, namely Dy-(trenovan), have been done by Lucaccini et al. The studies reached the conclusion that the crucial parameter in determining the slow relaxation of the magnetization is the number of unpaired electrons (only Kramers ions showing in-field slow relaxation) than the shape of the charge distribution for different Ln(III) ions when the complex exhibits trigonal symmetry and the Ln(III) ion is heptacoordinated [53].
With respect to the scope of the review, we have attempted an overview on the synthesis, structural and magnetic properties of Ln(III)-based complexes with the following list of Schiff base ligands (HL1-H 2 L20), mainly of salicylaldehyde origin (Chart 2).

Ln(III)-Based Schiff Base SMMs of Different Nuclearities
In the following sections, we are discussing the lanthanide complexes of Schiff base ligands listed in Chart 2 of different nulcearity varying from mononuclear to hexanuclear, with a special reference to their synthetic strategy, structure and magnetic behavior. .77 and 11.38 cm 3 K mol −1, respectively. For 7, χ M T gradually decreases on decreasing T till 2 K, reaching the value of 11.60 cm 3 K mol −1 for 7 [54]. The τ vs. T −1 plots the presence of more than one relaxation pathway with a crossover from a linear increase of thermally activated to a temperature-independent regime of QTM (Figure 5d) [54].
Both in-phase (χ ) and out-of-phase (χ ) ac susceptibilities for complex 7 show frequency and temperature dependence (Figure 6a). However, no maximum peaks of the temperature dependence of the out-of-phase (χ ) signal are observed in the range of 1-1488 Hz, which may be caused by the quantum tunneling of the magnetization (QTM), as indicated by strong temperature-independent peaks below 9 K (Figure 6a) [54]. For 8, there are no out-of-phase (χ ) signals observed above 1.9 K at 997 Hz, attributed to the quick quantum tunneling of the magnetization at zero dc field. The rather different magnetic properties of 7 and 8 are correlated with the axial ligand field of trigonal-prismatic coordination geometry, as Dy(III) is oblate and Er(III) is prolate [13].
Both 7 and 8 show frequency and temperature-dependent and temperature-dependent χ and χ signals (Figure 6a) at low-temperature [54], proving its field-induced SMM behavior. The Cole-Cole plots (Figure 6b) of both 7 and 8 are asymmetrical semicircular in shape and can be well fitted by the generalized Debye model, with a series of α parameters below 0.11 from 1.9 to 13 K and 0.13 from 1.9 to 3.7 K, respectively, which shows a narrow distribution of the relaxation time for both complexes [54].  Complex 9 (Figure 7a) is a nine coordinated species having a spherical tricapped trigonal prism geometry with one H 2 L2, two nitrates and two DMF molecules in the coordination sphere. The Schiff base ligand H 2 L2 coordinates through both oxygen atoms (O1 and O2) and one N atom (N3) to the central metal ion. Upon comparing with the earlier report, [Dy(hmb)(NO 3 ) 2 (DMF) 2 ] (Hhmb: (N -(2-hydroxy-3-methoxybenzylidene)benzohydrazide) [56], it is interesting to note that the electron-withdrawing nature of the nitro group para to the phenoxide group in H 2 L2 has a pronounced effect on the coordination nature of the ligand. Complex 10 is 8 coordinated species with a spherical triangular dodecahedron geometry with two ligands as well as two water molecules. The ligands are coordinated in keto form and NO 3 − are also present in the crystal lattice as a counter anion ( Figure 7b) [55].  The RT value of χT for complexes 9 and 10 are 13.96 and 14.69, cm 3 K mol −1 , respectively (Figure 7c), and a gradual decrease with temperature for both complexes may be due to inherent magnetic anisotropy from the Dy(III) ion, the stark level depopulation and/or occurring of SMM behavior [55]. The AC measurements show out of phase signal χ below 11 K for 9 indicate low-temperature SMM behavior (Figure 8a,b). Compound 9 exhibits an anisotropic energy barrier of U eff = 34 K [55]. For 10, the dynamics of magnetization shows a frequency χ in the absence of DC field (Figure 8c). The effective energy barrier and relaxation time are U eff = 19 K and τ 0 = 3.8 × 10 −7 s, respectively, which is larger than that of complex 9. The AC measurements of various DC fields show that the broad peaks under 200 and 400 Oe, is an indication of multiple exchange interactions with tunneling electrons [55]. For further investigation of QTM, the AC measurements were done under the magnetic field of 800 Oe. However, the relaxation got slower with a higher energy barrier of U eff = 41 k [55].

Dinuclear and Trinuclear Schiff Base Ln(III) SMM Complexes
The investigations on multinuclear Ln(II) systems were very crucial with respect to the advancement of T B, and these types of compounds generated showed significant progress to quench QT effects. Hence, designing ligands with appropriate symmetry, and incorporating Ln(III) centers, may enhance exchange coupling and quench the QT effects. Controlling intermolecular interactions using bulky counter anions/ligands and then utilizing enriched lanthanides to avoid hyperfine couplings is a hot research area in molecular magnetism in general and Ln(III) based Schiff base SMMs in particular. Here we are attempting to show how these different multinuclear Schiff base Ln(III) compounds derived from salicylaldehyde derivatives will have an effect on quenching QT and thereby generating SMMs with improved T B .
The Ln(III)-coordination sphere of 11-13 are slightly longitudinally compressed with comparable parameters of skew angles (ϕ) 56.03, 56.12 and 55.64 • , respectively. As shown in Figure 9a, the ligand binds to the central metal ion through the N 4 O 4 coordination environment generating a square-antiprismatic geometry (SAP). The α angles shown in Figure 9c corresponds to the magic angle, 54.74 • for 13 using H 3 L3 [57]. Here the obtuse and acute angles are in accordance with the compression and elongation along the tetragonal axis [12]. However, the ϕ values, 42.9, 36.9 and 42.9 • of 11-13 show that in 12, the coordination sphere deviates from the ideal square-antiprismatic than 11 and 13 ( Figure 9b). The shortest intermolecular distance between Dy(III)-ions (from different dinuclear units) is 9.142 Å, and this shows that there are no significant intermolecular interactions [57].
For 11, the χ M T remains constant till 50 K, then shows a sharp decrease to a minimum value of 10.64 cm 3 K mol −1 at 2 K, suggesting dominant intramolecular antiferromagnetic interaction between Gd(III) ions ( Figure 10b). The RT DC magnetic susceptibilities of 11-13 in a magnetic field of 1000 Oe are 14.98, 21.82 and 26.99 cm 3 K mol −1 , respectively ( Figure 10a). The variation in these values from the expected theoretical values is due to the weak magnetic exchange interaction between the metal centers through the bridging phenoxy group. The magnetization (M) data for 11-13 in 0-70 kOe field below 5 K shows the occurrence of weak antiferromagnetic coupling for 11 ( Figure 10b). The AC measurement of 13 exhibits a frequency-dependent out-of-phase signal under 800 Oe DC filed, showing slow relaxation of magnetization having an energy barrier of 18.9 K (Figure 10c) [57]. For 13, above 3.5 k, the magnetic relaxation follows a thermally activated Orbach mechanism having an energy gap of 18.9 k (Figure 10d).     (Figure 12a,b). Phenoxide-bridged Dy-dimers resulted from this reaction, where the positioning of the pyridyl groups helps the formation of an extended network that can control the arrangement of the SMM units in a three-dimensional way. However, with regard to complex 16, the pyridyl N atoms further coordinate to the Dy atoms of the adjacent complexes forming a two-dimensional network of the dimetallic Dy complexes. Dy(III) is eight coordinated in 15 and 16, and a square-antiprismatic geometry may be assigned in both cases [38].
The magnetic properties of 15 and 16 are somewhat similar as they possess the same coordination environment (Figure 12d). At RT, the χ M T values of 30.4 and 30.0 cm 3 K mol −1 for 15 and 16, respectively and they are in accordance with the expected value of 28.34 cm 3 K mol −1 for two Dy(III) ions [61,62]. For both complexes, the χ M T product remains roughly constant before reaching a minimum value of 29.3 cm 3 K mol −1 at 23 K. The χ M T then sharply increases to a maximum value of 38.4 cm 3 K mol −1 for 15 and 36.6 cm 3 K mol −1 for 16 at 1.8 K, which confirms the presence of intramolecular ferromagnetic interactions between metal centers [38].
Repeated magnetic measurements on 16 showed that this compound possessed one of the largest energy barriers, at 71 K, reported for an Ln(III)-complex at that time with Schiff base ligands. The magnetization curve below 10 K exhibits a rapid increase at low field, which is expected for ferromagnetically coupled spins. Magnetization increases linearly up to 11.9 µB (15) and 11.6 µB (16) at 1.8 K and 7 T without clear saturation. From the M vs. H/T data inset (Figure 12d), we can reach a conclusion that there is a significant magnetic anisotropy and/or low-lying excited states in these compounds. It is interesting to note that the M vs. H data does not exhibit a hysteresis effect above 1.8 K, but below 12 K (at about 1500 Hz), the indication of out-of-phase AC signal reveals a slow relaxation of the magnetization (Figure 12e) [38].
From the frequency dependence measurement, the relaxation time (t) is derived and is plotted as a function of 1/T (in the range 1.8-10 K) (Figure 12e). The dynamics of 15 and 16 below 2 K are temperature-independent as expected in a pure quantum regime with a τ value of 0.3 × 10 −2 s and 1.2 × 10 −2 s for 15 and 16, respectively and above 2 K, the relaxation becomes thermally activated. Above 8 K, remarkably big energy barriers are observed at 56 K and 71 K, and the pre-exponential factors of the Arrhenius laws (τ o ) are 3 × 10 −7 s and 7 × 10 −8 s for 15 and 16, respectively.   [37]. The Ligand H 3 L7 (Figure 14a), with a large inner compartment having N 3 O 2 coordination sites, is particularly appropriate to accommodate a sizable 4f-ion. While in a previous study of 2007, Dou et al. structurally characterized two mononuclear complexes with the same ligand H 3 L7 with large La(III) and Nd(III) ions where the outer donor O 4 set of H 3 L7 was involved in the coordination [64], but in Murugesu's report, the synthetic methods they promptly employed the functionality to promote coordination in both compartments of H 3 L7. For a matter of discussion, the structure of the Dy-analog, compound 22, was described as in-depth as a representative of the other families (Figure 14b).
For all compounds 19-23 ( Figure 14c) at RT, the χT values are in good agreement with the expected theoretical values for two non-interacting Ln(III)-ions. For the europium analog 19, the nonmagnetic ground state ( 7 F 0 ) is observed at low-temperatures as indicated by the χT value of 0.04 cm 3 K mol −1 at 1.8 K [2]. While in the gadolinium analog 20, the decrease of the χT when lowering the temperature reveals the presence of antiferromagnetic interaction between the Gd(III) ions. For complexes, 21-23, the χT vs. T curves for complexes 21-23 reach a value of 10.2, 5.2, and 7.1 cm 3 K mol −1 at 1.8 K, respectively (Figure 14c). The frequency dependence of the maximum of 22 related only with a single relaxation process and which appears clearly on a tridimensional plot of the variation of χ vs. the temperature and the frequency of the oscillating field between 1 and 1500 Hz (Figure 14e), confirming the slow magnetic relaxation. Here, the existence of a single relaxation process agrees with the presence of a unique crystallographic Dy(III) ion in the dinuclear structure. The relaxation process in the tridimensional plot gives two regimes of relaxation, as indicated in Figure 14e. The χ vs. χ in the temperature range 2-12 K additionally confirms the single relaxation process (Figure 14d). The effective energy barrier obtained from fitting, for 22 (Figure 14f), is U e f f = 76 K [37].  (Figure 15a), and Hdbm = 1,3-diphenyl-1,3-propanedione) (Chart 3). As a representative, complex 24 is discussed, and its crystal structure is depicted in Figure 15b. The asymmetric unit consists of two Gd(III)-ions, one HL8 2− , four dbm − ligands and two free methanol molecules. The two Gd(III) ions in the Gd2 dimeric unit are bridged by three µ2-O atoms from two HL8 2− (O2 and O4) and one dbm − (O8), respectively (Figure 15c) [65]. The Gd1 located in an N2O6 pocket (N1, N2, O2, O4, O6, O7, O8 and O9), is eight coordinated with a distorted dodecahedron coordination geometry, and Gd2 has a nine coordination environment with O9 set (O1, O2, O4, O5, O8, O10, O11, O12 and O13), exhibiting a three-capped trigonal prism [65].
Variable temperature DC magnetic susceptibility for 24 and 25 was done under an applied magnetic field of 1 kOe and in between 2-300 K (Figure 15d). The RT, χMT values for 24 and 25 are 15.70 (3) and 28.28(4) cm 3 Kmol −1 , respectively. For 24, on decreasing the temperature, the χMT values almost keep constant up to 25 K, then decrease to a minimum of 6.78 cm 3 K mol −1 at 2 K, proving the existence of weak antiferromagnetic exchange between the gadolinium ions. While in 25, the χMT values drop gradually over the temperature range from 300 to about 50 K, then drop abruptly to the minimum value 8.63(0) cm 3 K mol −1 at 2 K, which may be due to either the depopulation of excited Stark sublevels and/or a weak antiferromagnetic interaction of Dy(III) ions [66]. The magnetization data of 24 is collected in the temperature range from 2.0 to 10.0 K under the external magnetic field of 0-80 kOe. The M vs. H plots in Figure 15e show a continuous increase with the increasing of the magnetic field and reach the saturation value of 14.05(1) Nβ at 80 kOe and 2.0 K, which is in good agreement with the expected value of 14.0 Nβ for two isolated Gd(III) (g = 2, 8 S7/2) ions [65]. Further to investigate the dynamics of the magnetization, the AC-susceptibility measurements for 25 were performed as a function of temperature and frequency under zero DC field with an oscillation of 3.0 Oe. On increasing the frequency (111-2311 Hz), the frequency dependence below 20 K cannot be clearly observed from the (χ′) vs. T plots (Figure 15f (top)). The frequency dependence of out-of-phase AC signal below 12 K suggests slow magnetization relaxation, indicating the presence of QTM (Figure 15f (Figure 15a), and Hdbm = 1,3-diphenyl-1,3-propanedione) (Chart 3). As a representative, complex 24 is discussed, and its crystal structure is depicted in Figure 15b. The asymmetric unit consists of two Gd(III)-ions, one HL8 2− , four dbm − ligands and two free methanol molecules. The two Gd(III) ions in the Gd 2 dimeric unit are bridged by three µ 2 -O atoms from two HL8 2− (O2 and O4) and one dbm − (O8), respectively (Figure 15c) [65]. The Gd1 located in an N 2 O 6 pocket (N1, N2, O2, O4, O6, O7, O8 and O9), is eight coordinated with a distorted dodecahedron coordination geometry, and Gd2 has a nine coordination environment with O9 set (O1, O2, O4, O5, O8, O10, O11, O12 and O13), exhibiting a three-capped trigonal prism [65].
Variable temperature DC magnetic susceptibility for 24 and 25 was done under an applied magnetic field of 1 kOe and in between 2-300 K (Figure 15d). The RT, χ M T values for 24 and 25 are 15.70(3) and 28.28(4) cm 3 Kmol −1 , respectively. For 24, on decreasing the temperature, the χ M T values almost keep constant up to 25 K, then decrease to a minimum of 6.78 cm 3 K mol −1 at 2 K, proving the existence of weak antiferromagnetic exchange between the gadolinium ions. While in 25, the χ M T values drop gradually over the temperature range from 300 to about 50 K, then drop abruptly to the minimum value 8.63(0) cm 3 K mol −1 at 2 K, which may be due to either the depopulation of excited Stark sublevels and/or a weak antiferromagnetic interaction of Dy(III) ions [66]. The magnetization data of 24 is collected in the temperature range from 2.0 to 10.0 K under the external magnetic field of 0-80 kOe. The M vs. H plots in Figure 15e show a continuous increase with the increasing of the magnetic field and reach the saturation value of 14.05(1) Nβ at 80 kOe and 2.0 K, which is in good agreement with the expected value of 14.0 Nβ for two isolated Gd(III) (g = 2, 8 S 7/2 ) ions [65]. Further to investigate the dynamics of the magnetization, the AC-susceptibility measurements for 25 were performed as a function of temperature and frequency under zero DC field with an oscillation of 3.0 Oe. On increasing the frequency (111-2311 Hz), the frequency dependence below 20 K cannot be clearly observed from the (χ ) vs. T plots (Figure 15f (top)). The frequency dependence of out-of-phase AC signal below 12 K suggests slow magnetization relaxation, indicating the presence of QTM (Figure 15f (bottom)). minimum achievable volume for injection, without compromising the quality of the mAb in formulation. Viscosity remains a key limiting factor for formulating as a SC administration-certain mAb therapies are suitable and others not based on their solubility, self-association, and aggregation profiles. Alternative non-invasive administration strategies such as pulmonary delivery causes additional mechanical stress that further contribute to mAb instability and loss. Furthermore, oral delivery is unsuitable due to chemical and enzymatic degradation, as well as poor absorption in the gastric and intestinal environments.  (Figure 16d), and HDBM = 1,3-diphenyl-1,3-propanedione) (Chart 3). The compound 26 is centro-symmetric, with two Dy(III), two doubly deprotonated HL9 2− , two singly deprotonated co-ligands dbm − , two water molecule and one free acetonitrile molecule (Figure 16a) [67]. Each independent Dy(III) ion is eight-coordinated with an N 2 O 6 coordination environment displaying a distorted bicapped trigonal-prismatic geometry. Compound 27 (Figure 16b) has a structure different from that of 26 and 28. The asymmetric unit is composed of two Dy(III) ions, with singly deprotonated Schiff base ligand H 2 L9 − , doubly deprotonated Schiff base ligand HL9 2− , three singly deprotonated DBM − , one coordinated MeOH molecule and one free methanol molecule [67].
The coordination sphere of N 2 O 6 for Dy1 ion is constructed by two oxygen atoms O5 and O6 from dbm − , two phenoxide oxygen atoms from O7 and O12, two carbonyl oxygen atoms O8 and O11 also two imidogen nitrogen atoms N1 and N4 from H 2 L9 − and HL9 2− . Dy2 has a different coordination environment compared with Dy1. It is located in O 7 N set completed by four oxygen atoms O1, O2, O3 and O4 of two dbm − , one oximido nitrogen atom N6, one carbonyl oxygen atom O11 of HL9 2− , phenoxide oxygen atom O7 of H 2 L9 − ligand as well as the oxygen atom O13 of methanol molecule. The coordination geometries of Dy1 and Dy2 show a distorted bicapped trigonal-prismatic geometry [67].
The variable temperature DC magnetic susceptibility for 26-28 was collected between 2-300 K under 1000 Oe (Figure 16c The lnτ vs. T −1 plot for 28 is shown in Figure 16e, with spin-reversal energy barrier (∆E/k B ) of (45.6 ± 3.24) K having pre-exponential factor τ 0 = (5.14 ± 1.61) × 10 −8 . However, the values of ∆E/k B for 26 and 27 cannot be extracted by the Arrhenius law due to the lack of χ maxima. It is assumed that only one relaxation exists in 26 and 27, thus their susceptibilities could be fitted to the Debye function ln(χ /χ ) = ln(ωτ 0 ) + Ea/k B T (Figure 16g,h) [38], resulting in the energy barrier ∆E/k B of (2.29 ± 1.17) K for 26 and 1.31 ± 1.05 K for 27, and the pre-exponential factor τ 0 of (0.31 ± 0.21) × 10 −5 s for 26 and (0.20 ± 0.09) × 10 −5 s for 27 [67]. The Cole-Cole plots of 28 having a semicircular shape (Figure 16f [70] having interesting magnetic optical, and catalytic properties [70]. Complex 29·MeOH contains two crystallographically independent, centrosymmetric molecules ( Figure 17b). The two Gd(III) atoms are bridged by the syn, syn-carboxylate groups of two η 1 :η 1 η 1 µ 2 of HL10 − ligands. Two bidentate chelating nitrato groups, two-terminal MeOH molecules, and one terminal phenolate O atom complete 9-coordination at each metal ion. The H atom of the phenol −OH group of HL10 − has "emigrated" to the imine N atom, and the latter is thus protonated without coordination.
The two Dy(III) atoms in the representative centrosymmetric molecule 30 (Figure 17c) are bridged by the syn, syn-carboxylate groups of the four η 1 :η 1 η 1 µ 2 HL10 − ligands. In addition to this, there is a bidentate chelating nitrato group and two terminal phenolate O atoms, which complete 8-coordination, resulting in a square-antiprismatic geometry for the metal ion [70]. The DC molar magnetic susceptibility (χ M ) data on 29 and 30 were collected at 0.03 T in the temperature range 300−2.0 K and plotted as χ M T vs. T in Figure 17d Figure 18a. Dy(III) in 31 was bonded to two H 4 L11 and two DMF terminal solvents, leading to an eight coordinated triangular dodecahedron [55]. The coordination modes of the three ligands between any two Dy(III) ions are similar, where the two Dy(III) ions are held together by µ-κ 3 :κ 3 -HL11 3− .
In contrast to the report of similar ligands [71], the trans-trans conformations were switched to cis-trans conformation in 31, leading to the N-N pathway (Figure 18b) (N2-N3, N2a-N3a and N2b-N3b between Dy1-Dy1a, Dy1a-Dy1b and Dy1b-Dy1, respectively) [55]. On account of this, the three intramolecular Dy-Dy distances are 5.862 Å (Figure 18c), which are longer than other literature triangular complexes with Schiff base ligands [72] with Dy-Dy-Dy angles close to 60.0 • , giving a nearly perfect equilateral triangle. In addition to this, N3, N3a and N3b are also settled on the triangular plane, where the three O, N, N coordination environments of the 3 ligands are all above the plane, as shown in Figure 18d [55].
The RT χT of 31 and 32 are 40.23 and 21.89 cm 3 K mol −1 , respectively (Figure 18e). The χT product shows weak antiferromagnetic interactions between the Dy(III) ions. The gradual decrease with temperature for 31 till 100 K, then a rapid decrease to a value of 27.73 cm 3 K mol −1 at 1.8 K can be due to weak antiferromagnetic interactions between the Dy(III) ions. In Gd(III) analog 32, the χT value reach of a minimum of 18.99 cm 3 K mol −1 at 1.8 K shows the presence of weak antiferromagnetic coupling between the metal centers [55]. The dynamics of magnetization for 31 between 30 and 1.8 K show frequency-dependent χ above 6 K, indicating SMM properties (Figure 19a) [55]. The ac susceptibility at 10 K in an applied field of 5000 Oe was done to investigate the feasibility of lowering the relaxation probability via the quantum pathway. At 1.8 K, the relaxation dynamics of 31 was affected by a static field with a shift of the peaks towards the left and having the tail of the peak in the 100-10,000 Hz range. Above 7 K out-of-phase signal was observed having a shift of the peak maxima with an energy barrier of 81 K (Figure 19a). The χ vs. χ plot of 31 6-13 K and 5-15 K also supports the relaxation process (Figure 19b) [55]. The longer Dy(III)-Dy(III) distances and Dy 3 plane of 31 are shown in Figure 19c,d [55].

Tetranuclear Schiff Base Ln(III)-Complexes of SMMs
In the construction of tetranuclear complexes, Tang and coworkers have successfully isolated two discrete linear Ln 4 isostructural complexes [Dy 4 (L12) 2 (C 6 H 5 COO) 12 (Figure 20a) may provide effective hindrances to prevent the formation of extended structures and result in tetranuclear complexes. The structural description of Dy analog is taken as a phototype [73].
Magnetization dynamics also reveal mainly one thermally-activated discrete linear Ln 4 complexes, instead of 1D Ln(III) chains (Figure 20b). The temperature-dependent magnetic susceptibility measurements ( Figure 20d) were performed on the polycrystalline samples in the range of 300-2 K under 1000 Oe of the external field. For compound 34, χ M T of 32.58 cm 3 K mol −1 at 300 K is consistent with the spin-only value based on Gd(III) [73] ions ( 8 S 7/2 , S = 7/2; L = 0, g = 2) and almost remains constant till 14 K. Upon cooling, the χ M T value shows small decrease below 10 K, reaching a minimum value of 30.63 cm 3 K mol −1 at 2 K, showing the existence of antiferromagnetic coupling between Gd(III) ions (Figure 20c) for 34. The χ M T product of 33 at RT is 57.5 cm 3 K mol −1 , and it decreases gradually over the operating temperature range to reach a minimum of 47.8 cm 3 K mol −1 at 2 K (Figure 20c). This behavior can be related to the thermal depopulation of the Dy(III) excited states because the Dy-Dy exchange interactions are insignificant by comparison [73]. The χ vs. χ plots of 33 (Figure 20e) show multiple relaxations associated with distinct anisotropic centers indicating the Dy(III) complex exhibits SMM characteristics.
The relaxation times of 33 at different temperatures were obtained from frequency-dependent out-of-phase AC susceptibility measurements and plotted as a function of lnτ vs. 1/T between 1.9 and 5.0 K (Figure 20f). Above 4 K, the relaxation follows a thermally activated mechanism and can be determined by the Arrhenius law (lnτ = lnτ 0 + ∆/k B T) with an energy barrier of 17.2 K and a pre-exponential factor of τ 0 = 6.7 × 10 −6 s, which is consistent with the expected τ 0 of 10 −6 -10 −11 for an SMM [74]. At lower temperatures, a gradual crossover to a temperature-independent regime is observed, while below 2.5 K, a dominant temperature-independent quantum regime is observed with a characteristic time of 0.005 s. This behavior is predictable for an SMM when the quantum tunneling of the magnetization becomes dominant [38].
Other  (Figure 21d) have also been reported by Tang et al. [75].
As shown in Figure 21c, the χ M T value at 300 K is 53.6 cm 3 K mol −1 for 35 and 50.2 cm 3 K mol −1 for 36. χ M T slowly decreases until 50 K and then additionally decreases, reaching a minimum of 23.1 cm 3 K mol −1 for 35 and 23.8 cm 3 K mol −1 for 36 at 2 K, indicating a progressive depopulation of excited Stark sublevels [75]. The non-superimposition of the M vs. H/T data on a single master curve (Figure 21e,f) suggests the presence of a significant magnetic anisotropy and/or low-lying excited states. The magnetization eventually reaches the value of 24.4 µ β for 35 and 22.2 µ β for 36 at 2 K and 70 kOe without clear saturation. This value is much smaller than the expected saturation value of 40 µ β for four non-interacting Dy(III) ions, which may be due to the crystal-field effect of Dy(III), which cancels the 16-fold degeneracy of the 6 H 15/2 ground state. The AC susceptibility measurements were performed for 35 and 36 under a zero-DC field to investigate the dynamics of the magnetization. Checking the bond distances and angles of the respective [Dy 4 (µ 3 -OH) 4 ] cores reveal small but apparently important disparities in the M-O-M angles. These angle differences (induced by the presence of additional µ-OHbridges in 35) clearly affect the orbital overlaps between the metal centers and the µ 3 -hydroxido ligands, as well as the local tensor of anisotropy on each Dy(III) site and their relative orientations, generating dissimilar dynamic magnetic behavior [75].
More recently in 2018, Hong-Ling and coworkers have reported five tetranuclear Ln(III)-complexes represented by the following chemical formulae [76], [Ln 4 (dbm) 4 (L14) 6  The dynamics of the magnetization of 39 were investigated in both temperature and frequencydependent AC fields under a zero DC field. Here the relaxation parameters from lnτ vs. 1/T plots came out with an energy barrier of 89.38 K (Figure 22f) [77]. From (Figure 22e), complex 39 shows the presence of strong frequency-dependent in-phase (χ′) and out-of-phase (χ″) signals, with slow magnetic relaxation at a lower temperature, proving its SMM nature [76]. The dynamics of the magnetization of 39 were investigated in both temperature and frequency-dependent AC fields under a zero DC field. Here the relaxation parameters from lnτ vs. 1/T plots came out with an energy barrier of 89.38 K (Figure 22f) [77]. From (Figure 22e), complex 39 shows the presence of strong frequency-dependent in-phase (χ ) and out-of-phase (χ ) signals, with slow magnetic relaxation at a lower temperature, proving its SMM nature [76].  [78], where H 4 L15 = (3,6-bis(vanillidenehydrazinyl)-1,2,4,5-tetrazine) ( Figure 23c) and a = 8.07 and b = 0.65 for 42 and a = 8.19 and b = 0.91 for 43. The ligand H 4 L15 has a tetrazine ring at the center and two identical hydrazone moieties [78]. The ligand has four coordination pockets comprising of N1, N4a and O1 tridentate coordination sites, and a bidentate pocket consists of O1 and O2 coordination sites. A distorted spherical capped square antiprism geometry is assigned for Dy1 and a spherical tricapped trigonal prism for Dy2 in 42 (Figure 23a).
The χT vs. T product exhibits the presence of non-negligible ferromagnetic coupling between spin carriers (Figure 23b). On lowering from RT, the χT values of 42 and 43 remain unchanged till 12 K and abruptly increased to a value of 69.86 cm 3 K mol −1 for 42 and 33.73 cm 3 K mol −1 for 43 at 1.9 K, showing an indication of intramolecular ferromagnetic exchange [78]. The AC susceptibility of 42 under zero applied DC field (Figure 23d) shows both the in-phase (χ ) and out-of-phase (χ ) signals, and the shifting of peak maxima shows slow relaxation of the magnetization with an energy barrier of 158 K. The micro-SQUID measurement of 42 at below 0.5 K with a sweep rate of 14 T s −1 shows hysteretic behavior (Figure 23e). The width of the magnetic hysteresis loop of complex 42 indicates a strong dependence on temperature and moderate dependence on sweep rate [78]. A tetranuclear Dy-cluster having the structural formula, [Dy 4 (HL16) 4 (MeOH) 6 ]·2MeOH (44) was reported by Tang et al., whose molecular structure is depicted in Figure 24a, where H 3 L16 = 2-hydroxy-3-methoxybenzioc acid [2-hydroxy-3-methoxyphenyl) methylene] hydrazide (Figure 24d) [44]. The central Dy(III) ions of the Dy 4 core are connected by two µ-O units. Strong inter-and intramolecular hydrogen bonding interactions give a two-dimensional supramolecular array with a zigzag arrangement of the molecules. The Dy 4 compound derived from a rigid hydrazone ligand shows a nearly linear Dy 4 core, one being in a distorted bicapped trigonal-prismatic geometry and the other in a nearly perfect mono-capped square-antiprismatic environment [44].
Direct-current magnetic susceptibility studies of 44 were carried out in an applied magnetic field of 1 kOe in the temperature range 300-2 K Figure 24e. The χ M T value of 54.9 cm 3 K mol −1 at 300 K observed is slightly lower than the value of 56.7 cm 3 K mol −1 . The value of χ M T gradually decreases until ∼30 K, where it drops abruptly to a minimum of 31.3 cm 3 K mol −1 at 2 K, indicating a progressive depopulation of excited Stark sublevels. Magnetization data are shown in the inset of (Figure 24e,f).
The non-super position of the χ M T vs. H/T data on a single master curve suggests the existence of significant magnetic anisotropy or/and low-lying excited states [44].
It is interesting to note that more than one peak is seen in the temperature-dependent ac magnetic susceptibility curves (Figure 24b), showing an unusual multiple relaxation mechanism operating in 44. Additionally, in terms of the χ vs. frequency plots characterized by two clear maxima, two effective energy barriers identified are 19.7 and 173 K corresponding to fast and slow relaxation phases, respectively [44], which was confirmed by the Cole-Cole plots, that clearly indicate the evolution from fast relaxation to slow relaxation phases with the changing of temperature observed at 7 and 8 K (Figure 24b). The two different relaxation processes might be associated with distinct anisotropic centers, that is, two Dy(III) ions with different geometries [44]. The (χ ) vs. frequency plot of 44 at 7 K (Figure 24c) exhibiting two peaks centered at 1.2 and 1200 Hz, respectively, could be because of the spin noncollinearity of two types of Dy(III) ions in the weakly coupled molecular system. It is interesting to note that the peaks in the frequency-dependent AC susceptibility are quite distorted, exhibiting a unique double-ridge structure (Figure 24c) as opposed to the shoulder structure in the Dy 3 system [29].  (Figure 25d), whose molecular structure is in Figure 25a [79]. Here H 2 L10 has three different binding modes (Chart 4). Two full deprotonated tetradentate L10 2− wrap Dy atoms in η 1 :η 1 :η 2 :η 2 :µ 3 -fashion and two peripheral fully deprotonated L10 2− ligands bind in a η 1 :η 1 :η 2 :η 1 :µ 2 -way. Furthermore, two peripheral zwitterionic ligands coordinate in η 1 :η 1 :η 1 :µ 2 way generating a linear metal array. Lastly, two peripheral zwitterionic-tridentate ligands bind in a η 1 :η 1 :η 1 :µ 2 -condition, and a linear metal array is generated. The peripheral zwitterionic ionic HL10 − ligands block the N-coordination to the metal ions.
A molecule of methanol is also coordinated to Dy1, generating an 8-coordinated species with a square-antiprismatic geometry, while for Dy2, a molecule of methanol and an anthranilato ligand is also coordinated for an 8-coordination around Dy2 in between a bi-capped trigonal prism and a square antiprism. The χ M T vs. T curve of 45 shows a value of 56.3 cm 3 K mol −1 at 300 K, and it decreases gradually to reach a minimum of 31.7 cm 3 K mol −1 at 2 K (Figure 25b) [80]. The magnetization data collected in the 0-70 kOe shows significant magnetic anisotropy, which rapidly increases and reaches 27.0 µB at 1.9 K and 70 kOe without clear saturation (Figure 25b), which is lower than the expected saturation value for four non-interacting Dy(III) ions [81]. The relaxation time was extracted from the frequency-dependent data between 1.9 and 9 K (Figure 25c). Below 3 K, a temperature-independent relaxation regime is observed with a characteristic time of 0.00068 s. Such behavior is expected for an SMM when the quantum tunneling of the magnetization becomes dominant [38,82].  (Figure 26a), was synthesized by the condensation of pyridazine-3,6-dicarbohydrazide and o-vanillin [83,84] and it exhibits flexible coordination modes (Chart 5), owing to structural tautomerism. It is interesting to note that the coordination centers always reside on the same side of H 4 L17, which favors the formation of polynuclear clusters [85]. With respect to the scope of this review, the pure Ln(III) compound, [Dy 4 (HL17) 2 L17(DMF) 8 ]·2ClO 4 ·CH 2 Cl 2 ·4DMF·(CH 3 CH 2 ) 2 O·H 2 O (46) is discussed.
The compound 46 is a linear array of Dy 4 core (Figure 26b). In 46, among the three ligands, one is completely deprotonated and connects with four Dy(III) ions with the binding mode indicated in Chart 5 (left) by utilizing NO-bidentate and ONO-tridentate coordination nature. The other two are tri-deprotonated and coordinate to four Dy(III) ions, as shown in Chart 5 (right) using three kinds of coordination pockets [86]. For compound 46, the smallest intermolecular Dy-Dy distance is 9.495, indicating relatively weak intermolecular magnetic interactions [86]. Chart 5. Coordination nature of the H 4 L17 with different deprotonated conditions in 46 (Harris notation). Reproduced with permission from [86]; Published by Royal Society of Chemistry, 2020.
The DC susceptibility measurement was carried out for compound 46 from 2 to 300 K in an applied field of 1 kOe (Figure 26c). The χ M T products at 300 K, for compound 46 is 57.31 cm 3 K mol −1 . When the temperature is lowered, the χ M T product of 46 progressively decreases and reaches a value of 48.37 cm 3 K mol −1 at 12 K, and then sharply increases to a value of 63.36 cm 3 K mol −1 at 2 K, suggesting dominant ferromagnetic interactions [39,87,88].
The field-dependent magnetization measurements were done for compound 46 between 0-70 kOe at 1.9, 3 and 5 K, respectively (Figure 26e). For compound 46, the magnetizations quickly rise to 10 kOe and reach the value of 20.96 µB, at 70 kOe at 1.9 K, which is much lower than the expected saturation value of 40 µB for four independent Dy(III) ions [86], which may be due to the significant crystal-field effect [29,89]. The non-superposition of magnetization plots over a single master curve proves the presence of considerable magnetic anisotropy and/or low-lying excited states [31,90]. In order to investigate the dynamics of magnetization of 46, the AC measurements were conducted under a zero DC field (Figure 26d). The χ signals of 46 show frequency dependence below 20 K, indicating the slow relaxation of magnetization. On cooling, a remarkable increase without well-defined peaks indicates a fast QTM effect at low-temperatures, as observed in most of the early reports [89][90][91][92][93][94]. The U eff of 46 is reported as~4 k [86]. The coordination modes of H 2 L18 and TTA in cluster 47 are shown in Figure 27c. As shown in Figure 27b, the molecular structure of 47 mainly consists of four Dy(III) ions, four TTA − , four L18 2− and two coordinated waters. Six oxygen atoms (O1, O2, O4, O7, O8 and O11) and two nitrogen atoms (N1and N2) are coordinated to the central Dy(III) ion with the N 2 O 6 coordination environment. The four Dy(III) ions are bridged by two carboxyl oxygen atoms and four µ 2 -O atoms from four L18 2− , resulting in a Dy 4 parallelogram core. The coordination polyhedrons for both 8-coordinate Dy1 and Dy2 central ions are described as a distorted square-antiprismatic geometry with a quasi-D 4 d symmetry, which was calculated using Shape 2.0 software [96].
As shown in Figure 27d, for 47, at RT χ M T value is 56.64 cm 3 K mol −1 [95], which is in conformity with the expected value of four non-interacting Dy(III) ions. On decreasing the temperature, the χ M T values decrease slowly between 300-50 K, and then rapidly falls to a minimum of 38.15 cm 3 K mol −1 at 2.0 K [95]. This behavior generally can be attributed to the weak antiferromagnetic exchange between the adjacent Dy(III) ions in the system and/or the thermal depopulation of the Dy(III) Stark sub-levels [92]. In the 0-80 kOe magnetic field range and at T = 2.0 K, the M vs. H curve for 47 was investigated [95]. M value increases quickly at low field and then increases slowly without complete saturation till H = 80 kOe. The M value of 47 is 23.05 Nβ at 80 kOe, which is much lower than the theoretical saturated value of 40 Nβ for four free Dy(III) ions. Furthermore, like shown in Figure 27e, the M vs. HT −1 curves at 2.0-8.0 K show non-superimposed magnetization curves for cluster 47, which also suggests the existence of significant anisotropy and/or low-lying excited states of Dy(III) ions [97].
In order to understand the magnetic relaxation dynamics of 47, AC susceptibility measurement was done at zero DC magnetic field in the temperature range 2.0-15.0 K and frequency 111-3111 Hz. As shown in Figure 27f [95], there is no obvious frequency dependence below 15.0 K in the in-of-phase (χ ) component susceptibility for 47, however, the out-of-phase susceptibility (χ ) clearly displays frequency-dependent signals below 10 K, but no well-defined peaks are seen till the temperature drops to 2.0 K, which may be due to quantum tunneling of the magnetization(QTM) [98].  (Figure 28a). This unique Dy(III) 6 cluster, formed by the exclusive combination of two vertex-sharing and one edge-sharing high-anisotropy Dy 3 triangles (Figure 28b), gives rise to an unprecedentedly asymmetric Dy(III) 6 homometallic core. The crystal packing reveals that the molecules of 48 are in contact through π-π interactions, generating an infinite supramolecular array, where there is a strong π-π interaction (d = 3.268 Å) between two ligands of the two closely situated molecules, generating intermolecular π-π interactions. The hexanuclear Dy(III) complex is represented in Figure 28b. Each Dy(III) in the hexanuclear aggregate is 8-coordinated, and a square-antiprismatic geometry may be assigned around the metal ion [99].
The dynamics of the magnetization measurements operating in a 3.0 Oe AC field oscillating at frequencies of 3-1200 Hz and with a zero DC field for Dy 6 is shown in Figure 28d, as the plots of χ vs. T and χ" vs. T. The DC magnetic susceptibility studies of a polycrystalline sample ( Figure 28c) gives a room-temperature χ M T value equal to 82.39 cm 3 K mol −1 . The χ M T values decrease gradually with decreasing the temperature. The M vs. H data at different temperatures show a swift rise in the magnetization at low fields, reaching values of 32.09 µ B at 1.9 K and 7 T for Dy 6 ( Figure 28f). The non-superimposed curves validate the existence of anisotropy and/or low-lying excited states [99]. Linear fitting of the experimental ln(χ /χ ) data to the equation ln(χ /χ ) = ln(ωτ) + U eff /kT generating the parameters U eff ≈ 3.0 K and τ 0 ≈ 8.3 × 10 −6 s can be seen in Figure 28e. The frequency-dependent out-of-phase signals signify the onset of slow magnetization relaxation. The nonexistence of frequency-dependent peaks in the out-of-phase susceptibility signals for this Dy 6 system is most probably attributed to the fast quantum tunneling of the magnetization [99].
Continuing the search for hexanuclear aggregates, a distinctive hexanuclear Dy(III) compound having the formula [Dy 6 (µ 3 -OH) 3 (µ 3 -CO 3 )(µ-OMe)(L20) 6 (Figure 29d). The hexanuclear core of complex 49 contains six Dy(III) ions, which can be considered as the amalgamation of three capped triangular Dy 3 units [100]. The structure of 49 consists of two crystallographically unique but structurally same, Dy 6 units in the unit cell, as shown in Figure 29a. A total of six polydentate Schiff-base ligands surround the Dy 6 cluster core and exhibit three different binding modes in its di-deprotonated forms. Four methanol molecules, two water molecules, and one CO 3 2− anion occupy the remaining coordination sites of Dy(III) ions. Importantly, the CO 3 2− anion coordinated to the three Dy(III) ions in a η 2 :η 2 -µ 3 bidentate fashion. Each metal center in 49 is 8-coordinated, and a square-antiprismatic geometry may be assigned around the Dy(III) ions in the aggregate [100]. The DC magnetic susceptibility studies for complex 49 was performed in a magnetic field of 1000 Oe in the temperature range 300-2 K (Figure 29b). The room temperature χ M T value of 49 is 84.8 cm 3 K mol −1 , which corresponds to the anticipated value of 85.02 cm 3 K mol −1 for six uncoupled Dy(III)-ions. The χ M T values decrease up to 50 K with an additional drop at 2 K and reach a minimum of 68.6 cm 3 K mol −1 probably due to the progressive depopulation of excited stark sub-levels and the additional drop at 2 K may be due to the competition between the ligand field effect and the ferromagnetic interaction between the Dy (III) ions. The M vs. H/T (Figure 29b), inset data at different temperatures disclose a prompt surge of the magnetization at low magnetic fields, which finally reaches a value of 30.9 µ B at 1.9 K and 7 T without the saturation value of 60 µB (six no-interacting Dy(III) ions). This could be due to the anisotropy and the crystal field effects of Dy(III) ions.
The non-superposition of the M vs. H/T data on a single master curve refers to the existence of noteworthy magnetic anisotropy and/or low-lying excited states in compound 49 [100]. The dynamics of the magnetization by AC susceptibility measurements at zero static fields and a 3.0 Oe AC field oscillating from 1 to 1500 Hz are shown in Figure 29c. At temperatures below~30 K, a frequency-dependent out-of-phase (χ ) AC signal reveals the onset of slow relaxation of the magnetization. The relaxation time was calculated from the frequency-dependent data between 1.9 and 17 K, with the Arrhenius plot (Figure 29c). It is important to note that the two relaxation processes, which are clearly observed, may be due to the single-ion interaction of individual Dy(III) ions and the weak coupling at high and low-temperatures, respectively [100]. It is interesting to note the energy gap (∆) between the two relaxation regimes are 5.6 and 37.9 K with pre-exponential factors (τ 0 ) of 4.2 × 10 −5 and 3.8 × 10 −6 s for the low-and high-temperature domain, respectively [100]. In compound 50, three H 4 L17 wrap around six-Dy(III), generating a linear hexanuclear triple helical structure (Figure 30b) [86]. The asymmetric unit of 50 consists of three fully deprotonated H 4 L17, six-coordinated benzoate and methanol molecules also having solvent molecules in the lattice. H 4 L17 coordinated with six Dy(III), as shown in Chart 7 [86]. Chart 7. Coordination nature of the H 4 L17 with various deprotonated forms in compound 50 (Harris notation). Reproduced with permission from [86]; Published by Royal Society of Chemistry, 2020.
The DC susceptibility was done on 50, between 2 and 300 K in an applied field of 1 kOe (Figure 30c). The χ M T products at 300 K, for 50 is 84.77 cm 3 K mol −1 , which slightly decreases on decreasing temperature to a value of 78.44 cm 3 K mol −1 at 50 K, and then decreases rapidly to a value of 68.61 cm 3 K mol −1 at 2 K. The lowering of χ M T products can be attributed to the thermal depopulation of excited Stark sub-levels, with the possibility of weak antiferromagnetic interactions between the Dy(III) ions at low-temperatures [86].
The AC measurements were done on 50 under a zero DC field (Figure 30d). It has been observed that the out-of-phase (χ ) signals for 50 at 11 K indicate the slow magnetic relaxation behavior. χ component shows a significant increase in cooling without well-defined peaks, probably induced by the fast QTM effect at low-temperatures. The field-dependent magnetization measurements were done in the range of 0-70 kOe and at 1.9, 3 and 5 K, respectively, for 50 ( Figure 30e). It has been observed that up to 10 KOe, the magnetization rises quickly and reaches a maximum value of 33.14 µB with 70 kOe at 1.9 K, which is less than the expected saturation value of six non-interacting DY(III) ions is 60 µB [86]. Further, the non-superposition of the M vs. H/T plots over a single master curve shows the presence of magnetic anisotropy and 50 exhibits an effective energy barrier around 2 K [86]. The above discussed Ln(III)-based Schiff base complexes are categorized in Table 1 according to their nuclearities, coordination environment and polyhedra, as well as their indicative SMMs characteristics like energy barrier (U eff ). [Dy 6 (µ 3 -OH) 3 (µ 3 -CO 3 )(µ-OMe)(L20) 6

Conclusions
To summarize, we have done a brief up to date review of important, notable work on pure Ln(III) based SMMs, mainly with Schiff bases of salicylaldehyde. There is a remarkable interest in Ln(III)-based SMMs in the quest to synthesize SMMs with higher effective energy barriers and blocking temperatures, whereby the synthetic strategies can play an important role. However, custom tuning of the SMM properties still remains a big challenge. Emphasis has been given for Dy(III) SMMs in the present discussions as it shows superiority in magnetism, resulting from high anisotropy of the Dy(III)-ions so as to reach the limit of the effective energy barrier.
The great potential of Schiff base ligands was used to achieve this goal by incorporating new functionalities in both amines as well as aldehydic precursors in the ligand synthesis. It was inferred from the structures discussed that by varying precursors of Schiff base condensation, we could create coordination pockets or compartments that can be used for a particular lanthanide ion to occupy, facilitating suitable magnetic exchange interactions in the clusters so generated with SMM behavior. In spite of the numerous complexes synthesized to date, the Schiff base chemistry is far from being exhausted. Among the various Schiff bases and the lanthanide (III) SMMs discussed, the Dy 4 cluster reported by Tang et al. from 2-hydroxy-3-methoxybenzioc acid (2-hydroxy-3-methoxyphenyl) methylene) hydrazide H 3 L16 exhibits the highest energy barrier (U eff = 173 K). While not having exhaustively reviewed the results of the past twelve years from various research groups, what we have discussed will give an insight into the very promising field of SMMs based on Ln(III)-ions with Schiff base ligands, mainly from salicylaldehyde derivatives.