Ferromagnetism in polynuclear systems based on non-linear [MnII2MnIII] building blocks

The design of new polynuclear transition metal complexes showing large total spin values through parallel alignment of the spins is an important challenge due to the scarcity of bridging ligands that provide with ferromagnetic coupling. Herein, we report two new complexes, a [Mn4IIMn2III]system containing two non-linear [MnII2MnIII] units, and a 1D chain system with [MnII2MnIII] units that are assembled through dicyanamide bridging ligands coordinated to one of the terminal MnII centers. In both cases, the main exchange interaction is that corresponding to the MnII···MnIII, showing a relatively strong ferromagnetic coupling. Density functional theory calculations corroborate such ferromagnetic interactions and also provide one magnetostructural correlation, showing that larger MnII-O-MnIII angles enhance the strength of the ferromagnetic coupling. Thus, the non-linear [MnII2MnIII] units present in these two complexes are specially suited because of their larger MnIIO-MnIII angles compared to similar previously reported systems containing linear [MnII2MnIII] unit.


Introduction
During the last decades the field of Molecular Magnetism had an important challenge since the discovery in 1993 of single-molecule magnet (SMM) behaviour by Gatteschi and co-workers1 in an Mn12 compound. At very low temperature, individual molecules of such systems behave like magnets, and many research groups have intensively searched for new molecules displaying such an appealing property.2 However, the possible application of such systems has been always circumvented for the requirement of very low temperatures. In such systems, the splitting of Ms states is due to the zero-field splitting phenomenon (ZFS) caused by spin-orbit contributions and the energy difference between the highest and the lowest Ms states is an energy barrier (Ueff), whose height is directly related with the square of the total spin (S) of the molecule and its magnetic axial anisotropy (D). Thus, such energy barrier must be overcome in order to change the spin direction (from +Ms to -Ms states). Also, spin flip processes can occur through quantum tunnelling mechanisms. In order to achieve barriers that difficult the change in the spin direction, large negative D values are required, although for systems with half-integer S values this term can be positive. Slow relaxation of the magnetization at low temperature is responsible for the presence of a hysteresis loop in magnetization curves, which also display some irregular shapes due to the presence of thermally assisted quantum tunnelling to cross the energy barrier.3, 4 These tunnelling effects are also directly related to the magnitude of the magnetic rhombic anisotropy (E). In order to improve the magnetic properties, it is also mandatory to look for systems with large total spin S value. Logically, in polynuclear complexes the best option is the presence of ferromagnetic coupling between the paramagnetic centres, which would lead to a parallel alignment of the spins, resulting in a large total S value. However, there is a lack of systems showing ferromagnetic coupling, and most commonly exchange interaction pathways in this kind of transition metal complexes are found to be antiferromagnetic. Herein, we report an experimental and theoretical study in a family of polynuclear complexes containing [MnII2MnIII] units, showing ferromagnetic coupling between the MnII-MnIII centres. The combination of the MnII and MnIII centres is extremely useful because both cations have relatively large S values, 5/2 and 2 respectively, and they often present ferromagnetic coupling, as has been reported in the Mn19 complex, with a total S = 83/2.5, 6 Furthermore, The d4 configuration of the pseudo-octahedral MnIII cations is a source of magnetic anisotropy.2 Recently, some of us have reported ferromagnetic properties in two linear systems: a discrete Mn3 complex, [Mn 3 (HL) 2 (CH 3 OH) 6 (Br) 4 ]·Br·(CH 3 OH) 2 (1, H2L=2-[(9Hfluoren-9-yl)amino]propane-1,3-diol) and [Mn 3 (HL) 2 (CH 3 OH) 2 (Br) 4 adopting a 1D chain structure.7 Hence, one of the goals in this work is to provide with a comparison of the magnetic properties between such systems a those showing a distortion that causes a bend in the [MnII2MnIII] unit, explaining why such distortion produce an strengthening of the ferromagnetic coupling.

Materials and Methods
Elemental analysis (C, H, and N) was carried out on a Perkin-Elmer 2400 Elemental Analysis.
Single-crystal X-ray diffraction measurements of both compounds were carried out on a Rigaku-RAPID diffractometer equipped with graphite-monchromatic MoKα radiation (λ = 0.71073 Å). Absorption corrections were applied by using SADABS. The structures of 3 and 4 were solved by direct methods and refined by full-matrix least-squares techniques based on F2 using the SHELXS-97 program. All the non-hydrogen atoms were refined with anisotropic parameters.
Crystallographic data have been deposited with the Cambridge Crystallographic Data Centre: CCDC 1482230 for 3 and 1482219 for 4. The magnetic measurements were carried out with a Quantum Design MPMS-XL7 SQUID magnetometer using polycrystalline sample. Magnetic susceptibility data were conducted from 300 to 2 K at various DC field and field-dependant magnetization plots were also performed for applied fields ranging from 0 to 7 T at indicated temperatures. The AC susceptibility measurements were conducted with an oscillating AC field of 3 Oe at various AC frequencies at 0 Oe and 1000 Oe DC fields. Diamagnetic correction has been calculated from Pascal constants and the background of sample holder was also subtracted.   Table S1). These energy values allow us to build up a system of n equations in which the J values are the unknowns. Gaussian0311 calculations were performed with the hybrid B3LYP functional12 using a guess function generated with the help of the fragments option which employs a procedure that allows us to determine individually the local charges and multiplicities of the atoms. A triple-ξ all-electron Gaussian basis set13 was used for all the atoms. The same approach is valid for large polynuclear complexes, for instance a Fe42 system14 or dinuclear complexes with very large bridging ligands.15

Magnetic Properties
Temperature-dependent magnetic susceptibility data of 3 was measured between 2 and 300K under 1000 Oe DC field on polycrystalline samples (Fig. 4). At room temperature, the χT product is 27.61 cm 3 K mol −1 , which is higher than the theoretical spin-only values for where Ja is the Mn II ···Mn III  where it can be seen that the magnetic susceptibility is dependent with the external field.
With field increases, the peak around 5 K reduces firstly and then keeps rough constant till to 5000 Oe, suggesting a possible spin-flop behaviour in the system. This indicates a transition from antiferromagnetic state to spin-flop state. 16 The tail at very low temperature may originate from the trace paramagnetic impurities. In order to confirm the spin-flop behaviour, field-dependent magnetization plots were also displayed from 2 to 5 K. The magnetizations show a little S-shaped behaviour and the magnetization tends to saturate at higher field, especially at 2 K. This phenomenon agrees well with the spin-flop behaviour when the field is higher the critical field that a ferromagnetic state would emerge (Fig. 5a).
Magnetic hysteresis was also observed at 2 K with coercive field about 50 Oe (Fig. 5b). AC susceptibility measurements at 0 Oe DC field was also performed. The real and imaginary plots show peaks at around 5 K with no frequency dependence of signals, implying the existence of antiferromagnetic ordering at about 5 K (Fig. 6). In order to confirm this magnetic ordering, the temperature dependencies of field-cooled (FC) and zero-field-cooled (ZFC) magnetizations were also displayed under a 100 Oe field upon warming from 2 K.
The FC and ZFC plots present a disagreement below ~5 K, suggesting again the onset of the long range antiferromagnetic ordering (Fig. 7).     For complex 4, temperature-dependent magnetic susceptibility data was measured between 2 and 300K under 1000 Oe DC field (Fig. 8a). At room temperature, the χT product is 15.08 cm 3 K mol −1 , which is obviously higher than the theoretical spin-only values for the [Mn II where Ja defines the Mn II ···Mn III magnetic interaction within the [Mn II 2Mn III ] unit. In order to fit the lower temperature data, the interaction between the [Mn II 2Mn III ] units was neglected and regarded it as a molecular field around the trinuclear unit which is described with zJ'. Temperature-independent paramagnetism (TIP) has also been added in the frame of the mean field approximation. [17][18][19] The best fitting affords J/kB = 13.0(1) K, g = 2.02(7), zJ'/kB = -0.34(5) K, TIP = 0.0068(4). The larger positive J indicates the dominant intramolecular ferromagnetic interactions. Field-dependent magnetization plots were also performed from 2 to 10 K (Fig. 8b). The magnetizations increase slowly up to 7 T with a value of 8.20 μB at 7 T at 2 K, which is far from the expected value of 14 μB for a ferromagnetic coupled [Mn II 2Mn III ] unit. This behaviour is a characteristic of a canted antiferromagnetic ground state possessing a small remnant or spontaneous magnetization resulting from the non-compensation of the two antiferromagnetically coupled magnetic sublattices. AC susceptibility measurements at 0 Oe DC field was also performed. However, no any slow magnetic relaxation behaviour was observed (Fig. S1). = 1.98.

Electronic Structure Calculations
The intramolecular magnetic interactions in the 1,3 and 4 complexes were studied with a  Figure 9 for the description of the exchange interactions).   Table 2).
For the two non-linear systems reported in this work (3 and 4), the same type of exchange  For the complex 3, the ground state S = 14 corresponds with the calculated high-spin configuration, thus, we can represent the spin population density corresponding to such state (see Fig. 11). Clearly it is possible to identify the almost spherical spin density shapes of the isotropic d5 MnII centres while those of the MnIII cations are slightly distorted. The presence of one unpaired electron on each d orbital makes predominant the spin delocalization mechanism on the MnII centres predominant, due to the large mixing of the antibonding eg orbitals of the MnII cations with those of the coordinated atoms.25-26 However, the dx2-y2 orbitals of the MnIII centers are empty, and spin polarization should be the predominant mechanism for the four equatorial atoms coordinated with these cations, giving a total negative spin density in these ligand atoms in the region closer to the MnIII cations (see blue lobes in Fig. 11). Comparison with previously reported results for double-bridged alkoxo or phenoxo MnII···MnIII complexes20-24 are collected in Fig. 12 (see also Table S2). There is not a clear correlation with the angle due to the different nature of the ligands and there are more structural parameters that should play a subtle interplay to determine the magnetic properties. However, clearly the family of complexes reported in this work is that showing the strongest ferromagnetic coupling.