Edinburgh Research Explorer Magneto-thermal properties and slow magnetic relaxation in Mn(II)Ln(III) complexes: Influence of magnetic coupling on the magneto-caloric effect

A family of Mn(II)Ln(III) dinuclear and tetranuclear complexes (Ln = Gd and Dy) has been prepared from the compartmental ligands N,N’-dimethyl-N,N’-bis(2-hydroxy-3-formyl-5-bromobenzyl)ethylenediamine (H 2 L 1 ) and N,N’,N”-trimethyl-N,N”-bis(2-hydroxy-3-methoxy-5-methylbenzyl)diethylenetriamine (H 2 L 2 ). The Mn(II)Gd(III) complexes exhibit antiferromagnetic interactions between Mn(II) and Gd(III) ions in most cases, which are supported by Density Functional Theory (DFT) calculations. Experimental magneto-structural correlations carried out for the reported complexes and other related complexes found in bibliography show that the highest ferromagnetic coupling constants are observed in di-(cid:3) -phenoxido bridged complexes, which is due to the planarity of the Mn-( (cid:3) -O) 2 -Gd bridging fragment and to the high Mn-O-Gd angles. The effect of these angles has been studied by DFT calculations performed on a di-(cid:3) -phenoxido doubly bridged model. The magneto-thermal properties of the Mn(II)Gd(III) based complexes have also been measured, concluding that the magnitude of the Magneto-Caloric Effect (MCE) is due to the strength rather than to the nature of the magnetic coupling. Moreover, when two Mn(II)Gd(III) dinuclear units are connected by two carbonato-bridging ligands the MCE is enhanced, obtaining a maximum magnetic entropy change of 36.4 Jkg -1 K -1 at E B = 7 T and T = 2.2 K. On the other hand, one of the dinuclear Mn(II)Dy(III) complexes displays Single-Molecule Magnet (SMM) behaviour with an energy barrier of 14.8 K under an applied external field of 1000 Oe.


Introduction
Molecular Magnetism based on coordination compounds directs currently its research attention to materials exhibiting amazing magnetic properties such as Single-Molecule Magnets (SMMs) 1 and low-temperature magnetic coolers, 2 among others.SMMs are nanomagnets that overlap the quantum/classical borderline as they display classical properties, such as slow relaxation of magnetization and magnetic hysteresis below the so-called blocking temperature (T B ), as well as quantum properties such as quantum tunnelling of the magnetization (QTM) and quantum phase interference. 1his exceptional combination of physical properties makes them good candidates for potential future applications, among other areas, in ultra-high density magnetic information storage, 3 molecular spintronics, 4 and as qubits for quantum computing at molecular level. 5he SMM behaviour comes from the existence of an energy barrier (U eff ) for the magnetization reversal, which essentially depends on the magnetic anisotropy of the system. 1 As lanthanide ions exhibit strong magnetic anisotropy, they have been widely employed in the preparation of SMMs, obtaining a large number of 3d/4f clusters and 4f metal complexes that exhibit this behaviour, most of them containing Dy ions. 6In this regard, the highest T B values (close to the boiling point of liquid nitrogen) and coercive fields have been observed in monometallic metallocene Dy derivatives and mixed-valence dilanthanide (Ln = Dy or Tb) complexes with metal-metal bonding. 7It is interesting to note that 3d/4f systems usually possess lower energy barriers and blocking temperatures than the monometallic and low-nuclearity 4f metal complexes.The behaviour observed for 3d-4f systems is due to the effective shielding of the fully occupied 5s and 5p orbitals to the 4f orbitals of the Ln(III) ions, which leads to very weak 3d-4f magnetic exchange interactions and therefore, to multiple lowlying excited states. 8In addition, the random transversal field created by the paramagnetic metal ions on the Ln(III) ions can also contribute to the worsening of the SMM behaviour, as it favours the QTM process. 9In spite of the above considerations,  4 (mdea) 2 (NO 3 ) 2 ] (H 2 mdea = Nmethyldiethanolamine) 10 is an example of how the incorporation of isotropic paramagnetic ions can improve the SMM properties when compared to the diamagnetic Co(III) based analogue, which is due to the fact that the exchange interaction between the Dy(III) and Cr(III) ions is unusually strong, leading to a multilevel exchange type barrier 11 and to the suppression of the QTM.However, in the Co(III) based compound the barrier originates only from one excited state on the individual Dy(III) ions.On the other hand, heteropolynuclear 3d-Gd(III) complexes have been the focus of several magneto-thermal studies as they can display potential applications as low temperature magnetic coolers. 2 This is so because the change of magnetic entropy observed in these and other coordination complexes upon application of a magnetic field, which is called magneto-caloric effect (MCE), can be exploited for molecular refrigeration 2 and, therefore, coordination complexes have emerged as good candidates to replace the rare and expensive He-3 as cryogenic coolers.In contrast to SMMs, the MCE is enhanced in molecules containing isotropic magnetic ions that exhibit weak magnetic interactions between the metal ions, as this generates multiple low-lying excited and field-accessible states that can contribute to the magnetic entropy of the system.Taking this into account, complexes containing the isotropic Gd(III) ion, which has the maximum entropy value calculated as Rln(2S Gd + 1)/M Gd = 110 Jkg -1 K -1 and 3d transition metals complexes such as Mn(II), Fe(III), Cr(III) and Cu(II) would be good candidates for molecular refrigeration.Among them, Mn(II) should be, in principle, the best choice as it has the maximum entropy value of 271 Jkg -1 K -1 and lower oxidation state than Fe(III) ion, which has also d 5 electronic configuration (a lower oxidation state generally implies that a less number of non-magnetic ligands are required to balance the charge).The primary target in this field is to obtain metal complexes with MCE as high as possible.In this regard, it is very helpful to investigate experimentally in a systematic way and with simple compounds the effects of the sign and magnitude of the magnetic coupling between the metal ions on the MCE.In this article we present the synthesis, structural characterization and magnetic properties of a series of closely related Mn(II)Ln(III) dinuclear and tetranuclear complexes (Ln = Gd and Dy) with the compartmental ligands N,N'-dimethyl-N,N'bis(2-hydroxy-3-formyl-5-bromobenzyl)ethylenediamine (H 2 L 1 ) and N,N',N"-trimethyl-N,N"-bis(2-hydroxy-3-methoxy-5methylbenzyl)diethylenetriamine (H 2 L 2 ).It is worth mentioning that Mn-Ln complexes containing only Mn(II) ions are quite uncommon compared to Mn(III)-Ln(III) and Mn(III)/Mn(II)-Ln(III) counterparts. 12The aim of this work is threefold: (i) To establish magneto-structural correlations for the simple Mn(II)Gd(III) dinuclear complexes; (ii) To analyze how magnetothermal properties of this family of closely related Mn(II)Gd(III) based compounds are influenced by the magnitude and sign of the magnetic exchange coupling and (iii) To know if the large anisotropy of the Dy(III) ions, together with the coupling to paramagnetic isotropic Mn(II) ions, could lead to the presence of SMM behaviour in the Dy(III) derivatives.

Experimental Materials and methods
All reactions were performed under ambient laboratory atmosphere, with the reagents purchased from commercial sources and used without further purification.Ligands H 2 L 1 and H 2 L 2 were prepared according to previously described procedures. 13

Physical measurements
Elemental analyses were carried out on a Leco CHNS-932 microanalyzer.Thermogravimetric analysis (TGA) were performed on a TG-Q500 TA Instruments thermal analyser under a synthetic air atmosphere (79 % N 2 / 21 % O 2 ) at a heating rate of 10 °C min -1 .Variable-temperature magnetic susceptibility, magnetization and alternating-current (ac) susceptibility measurements were carried out with Quantum Design SQUID MPMS XL5, Quantum Design SQUID MPMS-7 T, CFMS-VSM-14 T (CryoFree Magnet System -Vibrating Sample Magnetometer) and PPMS (Physical Property Measurement System) -Quantum Design Model 6000 magnetometers.Diamagnetic corrections were estimated from the Pascal's constants.Heat capacity measurements were carried out for 8, using a Quantum Design PPMS, equipped with a 3 He cryostat, on a thin pressed pellet (ca. 1 mg) of polycrystalline sample, thermalized by ca.0.2 mg of Apiezon N grease, whose contribution was subtracted by using a phenomenological expression.

Crystallography
Single crystals of suitable dimensions were used for data collection.The intensity data for compounds 1, 4 and 7 were collected on a Bruker D8 Venture, while for compounds 3, 5, 6 and 9 diffraction intensities were collected on a Bruker AXS APEX diffractometer, both equipped with graphite monochromated Mo 5Y radiation (F = 0.7107 Å).For compound 2 diffraction intensities were collected at 100(2) K on an Agilent Technologies Super-Nova diffractometer, which was equipped with monochromated Mo 5Y radiation and an Eos CCD detector.For 8, data were also collected by using an Agilent Technologies Super-Nova diffractometer, but with monochromated Cu 5Y radiation (F = 1.5418Å) and an Atlas detector.
For 2 and 8, data frames were processed (unit cell determinations, intensity data integrations, routine corrections for Lorentz and polarization effects and analytical absorption corrections) using the CrysAlis Pro software package. 14For the rest of the compounds the data reduction was performed with the APEX2 software 15 and corrected for absorption using SADABS. 16he structures were solved by direct methods and refined by fullmatrix least-squares with SHELXL-2018. 17Final R(F), wR(F 2 ) and goodness of fit agreement factors, details of the data collection and analysis can be found in Table S1.Selected bond lengths and angles are given in Table S2.CCDC reference numbers for the structures are 1561137-1561144 and 2169104.The powder X-ray diffraction patterns were collected on a Philips X'PERT diffractometer using Cu 5Y radiation (F = 1.5418Å) over the range 5 < \ < 50° with a step size of 0.026° and an acquisition time of 2.5 s per step at 25 °C.

DFT calculations
DFT calculations on 1, 4, 6 and 8 were performed by using the SIESTA (Spanish Initiative for Electronic Simulations with Thousands of Atoms) code 18 together with the PBE functional. 19Only valence electrons were included in the calculations, with the core being replaced by norm-conserving scalar relativistic pseudopotentials factorized in the Kleinman-Bylander form. 20The pseudopotentials were generated according to the procedure of Trouiller and Martins. 21For gadolinium atoms, the pseudopotential and !.]basis set proposed by Pollet et al. were used. 22In complex 1, bromine atoms were substituted by chlorine atoms.The J values were determined by calculating the energy difference between the high spin state (E HS ) and broken symmetry state (E BS ), according to the following equation: (Eq. 1) using the Heisenberg Hamiltonian ^ = _J`1`2.`1 and `2 account for the local spin operators for each metal center.

Crystal structures
Complexes 1 and 2 crystallize in the P2 1 /n space group and consist on di-µ-phenoxido/acetate triply bridged Mn(II)Ln(III) complexes based on the ligand H 2 L 1 (Fig. 1 and S5).The fully deprotonated (L 1 ) 2- ligand adopts a d.# 1A , %d.# 2A $ d.# 2A , %d 2 -N,N', %d.# 3A $ d.# 3A , d. O 4A hexadentate coordination mode in these complexes (O 2A and O 3A : phenoxido oxygen atoms, O 1A and O 4A aldehyde oxygen atoms), where the Mn(II) ions are in the inner site coordinated to four of the heteroatoms of the ligand.The MnN 2 O 3 coordination spheres are formed by further coordination to an oxygen atom of a syn-syn acetate group and can be considered as square pyramids according to the continuous shape measure theory and SHAPE software (Table S3). 23The Mn-O and Mn-N distances are found in the 2.053(2)-2.148(2)and 2.220(2)-2.230(2)Å ranges, respectively; the shortest Mn-O distance corresponds to the Mn-O acetate bond.The Ln(III) ions lie in the outer coordination site of the ligand and, in addition to the four oxygen atoms of the ligand (two phenoxido and two aldehyde), they are coordinated by two bidentate nitrate anions and by an oxygen atom belonging to the syn-syn acetate group.The calculation of the degree of distortion of the Ln(III) coordination polyhedron with respect to the ideal nine-vertex polyhedral, by using the SHAPE software (Table S5), indicates that the LnO 9 coordination sphere can be considered intermediate between several reference ideal polyhedra, but close to an spherical capped square antiprism.The Ln-O bond distances are in the 2.295(2)-2.525(2)Å range, the shortest ones corresponding to the Ln-O acetate bond, while the largest ones are those involving the Ln-O nitrate bonds.The average Mn-O-Ln angles are of 97.53 and 97.72° respectively for 1 and 2, while the average hinge angles of the Mn-( -O) 2 -Ln bridging fragment is of 34.85 and 34.86°, respectively.These complexes exhibit hydrogen bond interactions between the crystallization acetonitrile and water molecules, with donor-acceptor distances of 2.986(9) and 3.022(9) Å for 1 and 2, respectively (Fig. S6).Bond lengths and angles for 1 and 2 and the rest of the complexes can be found in Supporting Information (Table S2), together with SHAPE measurement results (Tables S3-S6).Complex 3 also crystallizes in the P2 1 /n space group and is isostructural to the Mn(II)Gd(III) complex previously reported by some of us in 2013. 24Its molecular structure consists of dinuclear molecules in which the Mn(II) and Dy(III) ions are bridged by two phenoxido groups of the (L 2 ) 2-ligand (Fig. 1 and S7).Besides the two phenoxido bridging oxygen atoms, the MnN 3 O 3 coordination polyhedron is formed by three nitrogen atoms from the amine groups of the ligand and one oxygen atom belonging to a methanol molecule.Therefore, the ligand H 2 L 2 acts in a d.# 1A , %d.# 2A $ d.# 2A , %d 3 -N,N',N", %d.# 3A $ d.# 3A , d.# 4A bridging mode (O 2A and O 3A : phenoxido oxygen atoms, O 1A and O 4A methoxo oxygen atoms).The three oxygen atoms and, consequently, the three nitrogen atoms occupy fac positions in the trigonally distorted coordination polyhedron, which shows continuous shapes measures (CshM) values of 5.541 and 6.579 respectively for trigonal prism and octahedron ideal geometries (Table S4).The Mn-O and Mn-N  S8).The structures of complexes 4 and 5 are given in Fig. 1 and S9, where the most significant change compared to 3 is the substitution of the coordinated methanol and one of the bidentate nitrate molecules for a bridging acetate group.As expected, the incorporation of a third bridging fragment forces the structures to be folded with higher hinge angles (23.27° for 4 and 23.72° for 5), which leads to a decrease in the average Mn-O-Ln angles (101.94° for 4 and 102.07° for 5).The acetate bridge also affects the MnN 3 O 3 coordination spheres, leading to octahedral coordination environments according to SHAPE measurement results (Supporting Information, Table S4) and reduces to 9 the number of oxygen atoms coordinated to the lanthanide atoms.These complexes are entirely devoid of hydrogen bonds.The structures of complexes 6 and 7 are shown in Fig. 1 and S10 and are very similar to those of complexes 4 and 5 but with a 9anthracenecarboxylate bridging ligand instead of an acetate ligand connecting the Mn(II) and Ln(III) ions, and with two crystallization acetonitrile molecules.Compared to the acetate bridged analogues, complexes 6 and 7 exhibit similar bond lengths, accompanied with slightly smaller hinge angles (20.74° for 6 and 20.72° for 7).Finally, complexes 8 and 9 consist in centrosymmetric tetranuclear compounds, which are made by two cationic Mn( -L 2 )Ln(NO 3 ) 2+ units connected by two tetradentate carbonate bridging ligands acting in a 3 .d 2 .##=$d.#$d.#@coordination mode (Fig. 1 and S11).The Mn(II) ions show similar coordination environments to those of complexes 4-7, but they are coordinated to a carbonate bridging ligand instead of to an acetate or anthracenate bridging ligands.The lanthanide ions exhibit rather unsymmetric LnO 9 coordination spheres, which are made by the two phenoxido bridging oxygen atoms, the two methoxo oxygen atoms, three oxygen atoms from the carbonate bridging groups and two oxygen atoms belonging to a bidentate nitrate anion.The Ln-O distances are in the 2.300(4)-2.571(5)and 2.266(4)-2.567(4)Å range for 8 and 9, respectively.In these complexes, the LnO 9 coordination spheres can be considered as intermediate between several reference ideal polyhedron, the closest ideal geometry according to SHAPE measurements being muffin (MFF-9) (Supporting Information, Table S5).To end up, the Mn-( -O) 2 -Ln bridging fragments show smaller hinge angles than in complexes 4-7, being of 14.42° for 8 and of 13.34° for 9, whereas the Ln-( -O) 2 -Ln bridging fragments are planar.

Magnetic properties
The temperature dependence of the M T products ( M being the molar paramagnetic susceptibility of the compound) for the reported complexes were measured on polycrystalline samples under an applied magnetic field of 0.1 T and are represented in Fig. 2, 3, S12 and S13.
Please do not adjust margins Please do not adjust margins Please do not adjust margins Please do not adjust margins  5 = N,N',N"-tris(2-hydroxy-3-methoxybenzilidene)-2-(aminomethyl)-2-methyl-1,3-propanedi-amine (18.55 cm 3 •K•mol -1 ).On cooling, the M T product for 2 decreases slowly until 100 K and then in a more abrupt way, reaching a value of 7.82 cm 3 •K•mol -1 at 4.5 K.This behaviour is essentially due to the depopulation of the M J sublevels of the Dy(III), which arises from the splitting of the ground term by the crystal field.In order to determine the nature of the magnetic interaction between Mn(II) and Dy(III) ions, the contribution of the crystal-field effects of the Dy(III) ion was removed by subtracting from the experimental M T data of 2 those of the isostructural complex Zn(II)Dy(III). 30The difference M T = ( M T) MnDy -( M T) ZnDy indicates the nature of the overall exchange interaction between the Mn(II) and Dy(III) ions.Thus, positive and negative values indicate F and AF couplings, respectively.The M T value is almost constant over the whole temperature range (Fig. S14), except for a decrease in the lowest-temperature region to reach negative values below 11 K, thus indicating AF interaction between Mn(II) and Dy(III) ions.On the other hand, the M T products for 5 and 7 stop decreasing in the lowest temperatures region, remaining almost constant below 8 K in the case of 5 and showing a slight increase below 16 K in the case of 7, which could be due in both cases to the presence of very weak F interactions between the metal ions.The F interaction is more pronounced in complex 3, where the M T product increases below 35 K to reach a maximum at 5 K (24.23 cm 3 •K•mol -1 ) and then drops to 23.65 cm 3 •K•mol -1 at 2.5 K probably due to intermolecular interactions.The obtained results are not surprising, as the isostructural Gd(III) based complex reported by some of us 24 exhibits, as far as we know, the strongest F interaction ever observed for a Mn(II)Gd(III) dinuclear complex (J = + 0.99 cm -1 ).The magnetization plots of complexes 3, 5 and 7 (Fig. S12 and S13, insets) show a relatively rapid increase in the magnetization at low fields and a rapid saturation of the magnetization, reaching values of 9.77, 9.79 and 9.87 N B at 5 T, respectively.In the case of complex 2, the magnetization curves exhibit a slower increase, which is probably due to the AF interactions that are expected for this complex.The obtained value of 9.25 N B at 5 T is lower than the expected value of 17 N B (M J = g J JN B ) for a Mn(II)Dy(III) pair, which, as in the case of complexes 3, 5 and 7, is due to crystal field effects of the Dy(III) ion, leading to magnetic anisotropy, and also to possible AF interactions in the case of 2. Finally, the room-temperature M T value for the tetranuclear complex 9 is 37.31 cm3 Kmol -1 (solvent molecules are not considered in the molecular weight), which is consistent with the theoretical value expected for the sum of two Mn(II) and two Dy(III) ions (37.60 cm 3 •K•mol -1 ).On lowering the temperature, the M T starts decreasing at around 150 K to reach a minimum value of 34.06 cm 3 •K•mol -1 at 14 K, whereupon increases until 36.73 cm 3 •K•mol -1 at 2 K.The increase at low temperatures suggests the presence of overall F interactions, while the observed decrease at high temperatures is due to the crystal field splitting effects of the Dy(III) ions.As in the previous Dy(III) based complexes, the magnetization saturation value at 2 K (25.3 N B ) is lower than the expected value (34 N B ), which is also due to the anisotropy of the Dy(III) ions.In order to analyze the magnetic data of the Mn(II)Dy(III) dinuclear complexes (the analysis of the tetranuclear compound 9 could not be carried out because of the large dimension of the matrices), we have followed two approaches recently proposed by Herchel and coworkers. 31The first one uses the following Hamiltonian: Please do not adjust margins Please do not adjust margins and J represent the total angular momentum operator, its z 2 component and the quantum number, respectively.The exchange coupling is defined between the pseudo-spin J Dy = 15/2 and S Mn = 5/2.The simultaneous fitting of the susceptibility and magnetization afforded the parameters given on Table S7.
The second approach uses the |LS> basis for the Dy(III), so that the exchange interaction is defined between true spins.The corresponding Hamiltonian is as follows: 3 ( + 1)) + ) (Eq. 5) $ ( 2 2 ) + ( + + $ where the g Dy spin-orbit coupling parameter and the g L,Dy and g S,Dy were set by default in the PHI software. 25h is the orbital reduction factor that takes into account the covalency and D Ln and E Ln are parameters that act on the angular momentum ( and = 3 0 2 ' 2 = ).The best fit of the magnetic data led to the parameters  S7.It should be noted that the low sensitivity of the magnetic measurements for determining D and E parameters, together with the limitations of these approaches, lead to unconfident values of these parameters, particularly the sign and magnitude of E and the sign of D. Therefore, the D values extracted from the dc magnetic measurements for these complexes, should be taken with some prudence.However, for the magnetic exchange coupling J parameters, rather confident values are extracted.It is worth to mention that the J value extracted from both methods are very similar.Moreover, the magnitude of the interactions follow the same order as for the isostructural Mn(II)Gd(III) complexes, because compound 5 and 7, with J values in the ranges 0.46-0.48cm -1 and 0.16-0.18cm -1 , respectively, exhibit weaker interactions than 2 and 3, with J values in the ranges -0.84-(-0.90)cm -1 and 1.46-1.52cm -1 , respectively.Magneto structural correlations DFT calculations and experimental results 32 have clearly shown that the AF J MGd coupling in di--phenoxido bridged M(II)-Gd(III) complexes (M = Mn, Ni, Cu) decreases when the planarity of the M-( -O) 2 -Gd bridging fragment 9i: and the M-O-Gd bridging angle ( ) increase.Both structural factors are correlated, so that the latter increases as the bridging fragment becomes more planar.As far as we know, Table 1 collects the magneto-structual data reported so far for the dinuclear Mn(II)Gd(III) and trinuclear Mn(II)Gd(III)Mn(II) complexes.In general, it can be said that the highest F coupling constants are shown by double di--phenoxido bridged complexes, which show the lowest hinge angles accompanied with high angles, in agreement with the above considerations.The incorporation of a third bridge to di--phenoxido bridged species leads to more folded structures, which consequently exhibit smaller Mn-O-Gd angles than the planar fragments.If the third bridge is a phenoxido bridge, the magnetic exchange decreases but continues being F as in the case of complexes [L 3 Mn(H 2 O) 2 ] 2 [Gd(NO 3 ) 5 (MeOH)] 27 and [L 5 MnGdMnL 5 ]NO 3 . 29On the other hand, the incorporation of carboxylate and nitrate bridges leads to complexes with very weak AF interactions, as seen in the four complexes reported in this work and in complex [(NO 3 )Mn 2 (L 4 ) 2 ( -NO 3 )Gd](NO 3 ). 28In connection with this, DFT calculations were carried out on a model compound of 6, where the anthracenate bridge was replaced by two non-bridging water molecules, without modifying the remainder of the structure.The calculated coupling constant value increased from -0.32 to + 0.052 cm -1 , underlining that in addition to the hinge angle, the nature of the carboxylate bridge has a significant role in decreasing the magnetic exchange coupling.In fact, syn-syn carboxylate bridges are known for transmitting AF interactions.To end up, the triply alkoxo bridged compound [MnGd{pyCO(OEt)pyC(OH)(OEt)py} 3 ](ClO 4 ) 2 shows the strongest AF coupling, which is consistent with the fact that this complex has the highest i and lowest angles. 26owever, the complexes reported in Table 1 show a rich structural diversity and more specific magneto-structural correlations should be done.With this in mind, DFT calculations were performed on the model compound [Mn(PMTA)(H 2 O)( -OPh) 2 Gd(OCH 3 ) 2 (H 2 O)(NO 3 ) 2 )] (where PMTA = 1,1,4,7,7-pentamethyldiethylenetriamine and OPh _ = 4-methylphenolato anion), in which the part of ligand containing the amino nitrogen atoms were replaced by PMTA, the phenoxidobridging parts of the ligand by 4-methylphenolato bridging groups and the methoxo groups coordinated to the Gd(III) ion by methanol molecules.In addition, the acetate or anthracenate bridging groups were replaced by two non-bridging water molecules, leading to a di--phenoxido bridged simplified model compound (Fig. S15).In the calculations, the hinge angle was first fixed to zero (planar Mn-( -O) 2 -Gd bridging fragment) and the angle was varied in the 100 -115° range.Fig. 4 shows that for planar bridging fragments the crossover point (point in which the magnetic interaction changes from AF to F) is located at around 105°, being the exchange coupling F at higher angles.On the other hand, to know how the folding of the structure affects J MnGd , the angle was fixed to 105° and was varied between 0 and 30°.The results show F interactions for all the angles considered, with an increase in J MnGd with increasing until around 20° and a decrease in J MnGd from that point on (Fig. 4).The Please do not adjust margins Please do not adjust margins variation in J MnGd with in alkoxo triply bridged Mn(II)Gd(III) compounds was already studied by E. Ruiz et al. in 2012, 32 using the model compound [MnGd{pyCO(OEt)pyC(OH)(OEt)py} 3 ](ClO 4 ) 2 (collected in Table 1). 26They showed that, in the ~35 -75° range, the AF contribution increased with the increase of the angle, which is consistent with our calculations.The experimental J MnGd value of + 0.99 cm -1 obtained for the di-phenoxido doubly bridged complex [Mn(CH 3 OH)( -L 2 )Gd(NO 3 ) 3 ], 24 which possesses a hinge angle of 4.06° and a of 110.48°, is consistent with the above calculations.In addition, there exists a linear relationship (with r 2 = 0.96) between the angles and experimental J values obtained for this complex and the four di-phenoxido/carboxylate triply bridged MnGd complexes prepared from ligands H 2 L 1 and H 2 L 2 reported in this work (Fig. S16), which exhibit similar structures.These results demonstrate, in good agreement with the DFT calculations (Fig. S16), that the main structural factor governing the nature and sign of the magnetic coupling in di--phenoxido bridged Mn(II)Gd(III) dinuclear complexes is the Mn-O-Gd bridging angle ( ).The difference between experimental and calculated J MnGd is more likely due to the crude model used in the DFT calculations and to limitations inherent to the method.Noteworthy, it seems that the magneto-structural correlations established for the Mn(II)Gd(III) complexes also apply for the Mn(II)Dy(III) counterparts.Thus, compound 2 exhibits, comparatively, the smallest and the biggest i angles among the Mn(II)Dy(III) complexes, and presents the strongest antiferromagnetic interaction, whereas complex 3 having the biggest and the smallest i angles shows the strongest ferromagnetic interaction.For 5 and 7, which show intermediate and i angles, weaker magnetic couplings are expected, which, depending on small variation on these angles in the bridging region, can lead either to ferro or antiferromagnetic interactions.In the case of these Mn(II)Dy(III) complexes the interaction is very weakly ferromagnetic, whereas in the isotructural Mn(II)Gd(III) complexes very weakly antiferromagnetic.

Magneto-caloric effect
The magneto-thermal properties of the Mn(II)/Gd(III) complexes 1, 4, 6 and 8 have been studied because: (i) the Gd(III) and Mn(II) ions show negligible anisotropy due to the absence of orbital contribution; (ii) the Gd(III) and Mn(II) ions exhibit large single-ion spin (S = 7/2 and 5/2, respectively); (iii) the AF interaction between the Gd(III) and Mn(II) ions is very weak, which generates multiple low-lying excited and field-accessible states, each of which can contribute to the magnetic entropy of the system and (iv) the molecules are relatively small with a large metal/ligand mass ratio, thus limiting the amount of passive, non-magnetic elements.All the above factors should favour a large MCE.The magnetic entropy changes 9.ES m ) that characterize the magnetocaloric properties of complexes 1, 4, 6 and 8 can be calculated from the experimental isothermal field dependent magnetization data (Fig. S17-S19 for 1, 4 and 6 and Fig. 5 for 8) by making use of the Maxwell relation: J 1 = -0.17cm -1 , J 2 = + 0.05 cm -1 and g = 2.00 between 2 and 7 K (solid lines) and extracted from the experimental magnetization data with the Maxwell equation between 1 to 7 T and temperatures from 3 to 6 K (points).where B i and B f are the initial and final applied magnetic fields.The integration results show that the values of .ES m for complexes 1, 6 and 8 under all fields (Fig. S17, S19 and Fig. 5, bottom) increase as the temperature decreases from 7 to 3 K, while for 4 the maximum value is reached at 4 K at 7 T (Fig. S18).The maximum magnetic entropy change values 9.ES m ) for complexes 1, 4, 6 and 8 are given in Table 2.It should be noted that the .ES m values simulated for complexes 1, 4,

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Please do not adjust margins and susceptibility data (Fig. 5 and S17-S19) and the .ES m values extracted from the integration of the field dependence of the magnetization at different temperatures agree rather well, which is a good supporting evidence of the consistency of the MCE values.In the case of the larger tetranuclear complex 8 the .ES m values were further corroborated by temperature-dependent heat capacity (c p ) measurements carried out at applied magnetic fields of up to 7 T (Fig. 6).At high temperatures, the constant increase of experimental c p is related to vibrational phonon modes of the lattice, which can be fitted with the Debye function (dashed line) affording a Debye temperature \ D = 26.2K, which is typical for this class of compounds. 24At lower temperatures, c p is dominated by an appliedfield sensitive magnetic contribution.The temperature and field dependencies of c p can be satisfactorily modelled by the sum (solid lines) of the lattice contribution and the Schottky-like heat capacity calculated from the Hamiltonian in Eq. 3 for J 1 = -0.17cm -1 , J 2 = + 0.05 cm -1 and J 3 = J 4 = 0. Fig. 6 bottom displays the temperature dependence of the entropy, which is obtained by the numerical integration of the experimental heat capacity by using Eq.7: (Eq. 7) The zero-field entropy exhibits a fast increase at the lowest temperatures, reaching a value of ~7.9 R at 3 K (in agreement with the expected saturation value of magnetic entropy, S/R = 2ln(2S Mn +1) + 2ln(2S Gd +1) = 7.74).Above ~8 K, the entropy data increase steadily due to the dominant lattice contribution.The magnetic entropy change, -ES m , is straightforwardly obtained, from Fig. 6, as the difference between the entropy data collected for different applied fields.Fig. 7 shows that the resulting temperature and applied field dependencies of -ES m agree well with the values estimated from the  S8). 33n the case of the Mn(II)Gd(III) dinuclear complexes, the full magnetic entropy content per mole is (Rln(2S Gd + 1) + Rln(2S Mn + 1))/M = 3.87 R/M, which corresponds to 33.3 Jkg -1 K -1 for 1, 38.3 Jkg -1 K -1 for 4 and 29.7 Jkg -1 K -1 for 6.The simulated MCE values at 2 K and 7 T (12.6 Jkg - 1 K -1 , 31.5 Jkg -1 K -1 and 26.5 Jkg -1 K -1 , respectively) are rather smaller than their respective full magnetic entropy content, which is mainly due to the AF magnetic coupling between Mn(II) and Gd(III) ions.
From the magnetothermal study of compounds 1, 4, 6 and 8 the following conclusions can be drawn: 1.-Regardless of the sign of the magnetic coupling (AF or F interactions), the magnetic entropy changes 9.ES m ) decrease with increasing the magnetic interaction between Mn(II) and Gd(III) ions (J).
2.-For J values of similar magnitude but opposite sign, as it occurs in compound 1 and Mn(CH 3 #?:9R. 2 )Gd(NO 3 ) 3 , 24 F interactions between Mn(II) and Gd(III) lead to high values of -ES m .It is worth noting that the magnitude of J has a superior influence on -ES m than F interactions.
3.-Compared to the dinuclear Mn(II)Gd(III) complexes, the tetranuclear Mn 2 Gd 2 complex 8 exhibits enhanced MCE.It is worth noting that even though complexes 4 and 8 exhibit almost the same ligand/metal mass ratio ( 0.34 and 0.37, respectively), however, the MCE is larger for 8, which could be due to the weak F interaction between the Gd(III) ions through the carbonate bridging groups.Therefore, carbonate ions not only play an important role in connecting dinuclear Mn(II)Gd(III) units, but also induce an enhancement of the MCE.The same explanation has been invoked to justify the increase of MCE on going from a dinuclear Gd 2 complex Please do not adjust margins Please do not adjust margins to the Gd 4 complex which is formed by the linking of two Gd 2 by carbonato bridging groups. 34he results for compounds 4 and 8 clearly show that small clusters based on Mn(II)/Gd(III) coordination compounds can be good aspirant for molecular refrigerants.

Ac magnetic measurements
Alternating-current (ac) magnetic susceptibility measurements show that in the absence of an external field, complex 3 shows slightly frequency dependent in-phase ( M ') and out-of-phase ( M ") susceptibility signals (Fig. S20), while the rest of the Dy(III) based compounds do not show any dependency.The ac signals of complex 3 can be improved upon an application of an optimal external field of 1000 Oe, which reduces the quantum tunnelling of the magnetization (QTM) (Fig. 8).
The relaxation times for each temperature were extracted from the M " vs. frequency plots and their fit to the Arrhenius equation afforded an effective energy barrier for the reversal of the magnetization of 14.8 K with a H 0 value of 6.35•10 -7 s.Although the To end up, it is worth mentioning that complexes 2, 5, 7 and 9 showed a very modest frequency dependency of the in-phase and out-of-phase susceptibility in the presence of an external dc field of 1000 Oe (Fig. S21).However, complex 3, with the strongest F interactions between Mn(II) and Dy(III) ions, is the one that displays the most significant SMM behaviour.This fact seems to support that the increase of the magnetic coupling between an isotropic metal ion and Dy(III) favours the SMMs behaviour.
Dc magnetic measurements reveal antiferromagnetic exchange interactions between Mn(II) and Gd(III) ions, while ferromagnetic interactions prevail in most of the Mn(II)Dy(III) counterparts.Experimental magneto-structural correlations have been carried out from the Gd(III) based complexes and other complexes found in bibliography, concluding that the highest ferromagnetic coupling constants are observed in di--phenoxido bridged complexes.The observed behaviour has been ascribed to the planarity of the Mn-( -O) 2 -Gd bridging fragment and to the high Mn-O-Gd angles of di--phenoxido bridged complexes, while the incorporation of a third bridge leads to folded structures, reducing the magnetic coupling constant.In addition, DFT calculations carried out in a di--phenoxido doubly bridged model compound show that for planar bridging fragments, the crossover point in Mn-O-Gd angle is located at 105°, being the interactions F above this angle and AF below it.The influence of the Mn-( -O) 2 -Gd hinge angle has also been studied by fixing the Mn-O-Gd angle to 105° and changing the hinge angle, concluding that J MnGd increases when increasing until around 20° and decreases from that point on.We have estimated the J MnDy coupling constants, and it seems that the magneto-structural correlation established for the Mn(II)Gd(III) complexes also apply for the Mn(II)Dy(III) conterparts.For the Mn(II)Ln(III) dinuclear complexes, the MCE extracted from the field dependence of the magnetization at different temperatures show that the magnetic entropy changes 9.ES m ) decrease with increasing the magnetic coupling (either F or AF) between the metal Please do not adjust margins Please do not adjust margins ions.Nevertheless, ferromagnetic interactions between Mn(II) and Gd(III) lead to higher -ES m values than the AF ones of similar magnitude.Anyway, the magnitude of J seems to have a superior influence on -ES m than the ferromagnetic interactions.For the tetranuclear Mn(II) 2 Gd(III) 2 complex, the relatively low ligand/metal mass ratio and the weak ferromagnetic interaction between the Gd(III) ions through the carbonate bridging groups lead to an enhanced MCE (36.4 Jkg -1 K -1 at EB = 7 T and T = 2.2 K), one of the highest ever observed for Mn(II)/Gd(III) systems.Therefore the connection of Mn(II)Gd(III) dinuclear units with small bridging ligand transmitting ferromagnetic coupling can be a good strategy to enhance MCE.Finally, complex 3, with the strongest ferromagnetic interactions between Mn(II) and Dy(III) ions, is the only one that shows significant SMM behaviour, with an energy barrier of 14.8 K under an applied external field of 1000 Oe.

3 ) 2 •
2CH 3 CN (7) by reacting an acetonitrile solution containing H 2 L 2 , Mn(NO 3 ) 2 •4H 2 O and the corresponding Ln(NO 3 ) 3 •nH 2 O (1:1:1 molar ratio) with another acetonitrile solution containing 9-anthracene Please do not adjust margins Please do not adjust margins Please do not adjust margins Please do not adjust margins

Fig. 2 .
Fig. 2.-Temperature dependence of the M T product for 1 (top), 4 (middle) and 6 (bottom).Insets: field dependence of the magnetization.The solid lines are generated from the best fit to the magnetic parameters.

Fig. 6 .
Fig. 6.-Top: Temperature-dependence of the heat capacity c p , normalized to the gas constant R and measured in the presence of several applied magnetic fields, as labelled.Solid lines correspond to the fits discussed in the text; dashed line is the estimated lattice contribution to the measured heat capacity.Bottom: Experimental entropies as obtained from the corresponding c p data.

Fig. 7 .
Fig. 7.-Temperature-dependencies of the magnetic entropy change .ES m for compound 8, for the indicated applied-field changes EB, as obtained from heat capacity (full markers) and magnetization (empty markers) measurements.

Table 1 .
-Magneto-structural data for polynuclear Mn(II) x Gd(III) (x = 1, 2) complexes and complexes reported in this work.MnGd .b Average Mn-O-Ln angles.c Average hinge angles of the Mn-( -O) 2 -Ln bridging fragments.d Calculated after article publication.
a J e Overall ferromagnetic exchange coupling observed, exchange constants are not obtained.T.w.= this work.

Table 2 .
24aximum magnetic entropy change values 9.ES m ) at 7 T for complexes 1, 4, 6 and 8, as obtained from magnetization data, and for the Mn(II)Gd(III) complex previously reported by us.24