PCCP View Article Online PAPER View Journal | View Issue Magnetic properties of coordination clusters with This article is licensed under a Creative Commons Attribution 3.0 Unported Licence. {Mn4} and {Co4} antiferromagnetic cores† Open Access Article. Published on 18 January 2022. Downloaded on 10/31/2022 11:57:42 AM. Cite this: Phys. Chem. Chem. Phys., 2022, 24, 3780 Simona Achilli, *ab Claire Besson, c Xu He, d Pablo Ordejón, d e bdf Carola Meyer and Zeila Zanolli We present a joint experimental and theoretical characterization of the magnetic properties of coordination clusters with an antiferromagnetic core of four magnetic ions. Two different compounds are analyzed, with Co and Mn ions in the core. While both molecules are antiferromagnetic, they display different sensitivities to external magnetic field, according to the different atomic magnetic moments and strength of the intra-molecular magnetic couplings. In particular, the dependence of the magnetization versus field of the two molecules switches with temperature: at low temperature the magnetization is smaller in {Mn4} than in Co4, while the opposite happens at high temperature. Through Received 25th August 2021, a detailed analysis of the electronic and magnetic properties of the two compounds we identify a Accepted 17th January 2022 stronger magnetic interaction between the magnetic ions in {Mn4} with respect to {Co4}. Moreover {Co4} DOI: 10.1039/d1cp03904k displays not negligible spin–orbit related effects that could affect the spin lifetime in future antiferro- magnetic spintronic applications. We highlight the necessity to account for these spin–orbit effects rsc.li/pccp together with electronic correlation effects for a reliable description of these compounds. 1 Introduction applications can leverage on the technology developed for functionalization with nanoparticles.6,7 Molecular magnets constitute an excellent platform for In recent years, research has concentrated on molecular molecular spintronics and quantum information storage and magnets with large overall spin generated by ferromagnetic processing as their properties can be controlled at the nano/ coupling between magnetic centers.8–10 On the other hand, the micro-scale during fabrication.1–3 Coordination clusters incorporation of molecular antiferromagnets in spintronic formed by an inner magnetic core and a surrounding shell of devices11,12 is still a new area of research. Recent proposals organic ligands can be synthesized to control both the are only theoretical, and concern molecular AFM crystals13 or magnetic interactions between the ions within the molecule systems that can hardly be realized experimentally.14 The and the coupling between magnetic core and environment,4 expected advantages of antiferromagnetic coordination clusters while practically reducing to nothing the influence of inter- are the same as for antiferromagnetic spintronic devices, i.e. molecular interactions on the magnetic properties. Single- robustness against perturbation due to magnetic fields, molecule magnets are particularly attractive for spin-dependent absence of stray fields, and capability to generate ultrafast quantum transport applications5 as the spin retains its dynamics and large magnetotransport effects.15 Antiferro- orientation in the absence of an external magnetic field and magnetic molecules can be used to functionalize other organic systems, as carbon nanotubes, with the advantage that the a Dipartimento di Fisica ‘‘Aldo Pontremoli’’, Universitá degli Studi di Milano, current flowing through the tube does not alter the magnetic Via Celoria 16, Milan, Italy. E-mail: simona.achilli@unimi.it properties of the molecules16,17 and the low spin–orbit coupling b European Theoretical Spectroscopy Facilities allows long spin-flip lengths and spin lifetimes. c Department of Chemistry, The George Washington University, Washington, D‘C The application of molecular magnets in spintronics and 20052, USA d Catalan Institute of Nanoscience and Nanotechnology - ICN2 (CSIC and BIST), quantum technologies would benefit from molecular design Campus UAB, Bellaterra, 08193 Barcelona, Spain aimed at identifying the most suitable combinations of magnetic e Department of Physics, Universität Osnabrück, 49076 Osnabrück, Germany ions and organic ligands to ensure long spin coherence times, f Chemistry Department, Debye Institute for Nanomaterials Science, Condensed efficient spin injections and tunable transitions between spin Matter and Interfaces, Utrecht University, PO Box 80 000, 3508 TA Utrecht, states.18–20 Property-tuning efforts are usually concentrated on The Netherlands † Electronic supplementary information (ESI) available: Full experimental modifications of the ligands surrounding a given metal core. details, Heisenberg fit of the SQUID data. Spin dynamics calculation. Relaxed This approach, however, has some limitations for integrating the structures. See DOI: 10.1039/d1cp03904k molecule in a device: the ligands are also the place where the 3780 | Phys. Chem. Chem. Phys., 2022, 24, 3780–3787 This journal is © the Owner Societies 2022 View Article Online Paper PCCP interaction with the environment takes place. Changing the ligands The structure was relaxed with a tolerance on the forces on can have unwanted and unpredictable effects on the electronic the atoms equal to 0.03 eV Å1. In the LDA+U calculations the properties of the device-molecule interface, in addition to changes finesse of the real-space grid (mesh-cutoff) was set to 400 Ry of the magnetic properties of the core. We propose here a reverse and the smearing of the electronic occupation (electronic approach: the ligand system is kept identical, and the magnetic temperature) to 100 K. In order to increase the accuracy in properties are modified by changing the metal atoms. the convergence, SOC calculations where performed with We selected the architecture of a M4O4 cubane structure 600 Ry mesh cutoff and 1 K electronic temperature. The based on the family of {Mn4} antiferromagnets with the general structural relaxation has been refined with SOC, starting from formula [(RCO2)4Mn4L2] (R = CF3, CH3, Ph, H2L = 2,6-bis(1-(2- the LDA+U equilibrium geometry. The exchange coupling This article is licensed under a Creative Commons Attribution 3.0 Unported Licence. hydroxyphenyl)iminoethyl)pyridine) previously reported by parameters Ji,j were obtained by considering the lowest energy Open Access Article. Published on 18 January 2022. Downloaded on 10/31/2022 11:57:42 AM. Kampert et al.21 The presence of four metal centers offers a spin configurations of the Mn and Co centers and solving a rich landscape of electronic and magnetic levels for spintronic system of equations (Heisenberg model) in the DFT energies applications. Through a joint experimental and theoretical with four Ji,j parameters. The geometry of the various spin characterization we compare the {Mn4} acetate complex with configurations was kept fixed to the ground state one in order its newly prepared cobalt analogue. to exclusively account for the effect of the spin-flip on the total Many M4O4 cubane complexes are reported in the literature, energy of the molecules.33 Further, we exploited the model for M = Co and Mn. However, their magnetic properties have P! ! Heisenberg Hamiltonian H ¼ S^ i  Ji;j  S^ j þ mB gS ~  B, ~ where been investigated only in four cases22–25 showing a switching or i;j an enhancement of the magnetic coupling by changing the ! S^ i is the spin vector of atom i and Ji,j is the matrix of the inner core. In [M4(dpd-H)4(OAc)3(OH2)1]+ and [M4(dpd- exchange parameters, to fit experimental temperature and H)4(OAc)2 {N(CN)2}2] (dpd-H2 = di-2-pyridylketone in gem-diol field-dependent magnetization data, as allowed by the imple- form), the overall magnetic coupling shifts from antiferromag- mentation in the PHI code.34 In the following we label J1 = J1,4 = netic for manganese(II) centers to ferromagnetic for J2,3, J2 = J1,3 = J2,4, J3 = J1,2, J4 = J3,4, with the Mi atoms numbered cobalt(II).22,23 In [M4(cit)4]8 (cit = citrate) and [M4(nic)4(OMe)4] as indicated on Fig. 1. (nic = nicotinate) the coupling is antiferromagnetic for both ions, but the coupling is larger for manganese in the former 2.2 Experiment case24 and for cobalt in the latter.25 Additionally, while MnII centers are adequately described by the spin magnetic moment The complexes [M4L2(OAc)4] (M = Mn, Co, Zn, {M4} for short), (spin-only model), CoII centers in octahedral or pseudo- where H2L = 2,6-bis-(1-(2-hydroxyphenyl)iminoethyl)pyridine, octahedral environments are characterized by significant orbital moments, leading to spin–orbit coupling (SOC) effects that are expected to significantly affect more complex devices. Our theoretical analysis, performed through a first- principles approach and a Heisenberg model Hamiltonian explains the marked experimental differences between the two compounds, opening the door to using in silico work to design complexes with targeted magnetic properties. 2 Methods 2.1 Theory Theoretical calculations were performed in the Density Functional Theory (DFT) framework, using a pseudopotential description of the core electrons and atomic orbital basis set, as implemented in the SIESTA code.26,27 We adopted the local density approximation (LDA)28,29 for the exchange–correlation energy functional. A Hubbard correction for Mn and Co was included to account for the strong Coulomb interaction of localized d electrons. We use U = 6 eV for Mn and U = 4 eV for Co, according to the literature.21,30 To evaluate the role of spin–orbit coupling, which is relevant in Co, we also performed calculations including spin–orbit correction using the formalism of ref. 31, as implemented in Fig. 1 Molecular structure of the {M4} complex. (a) Side view. Blue: Mn, SIESTA.32 The current version of the SIESTA code does Co or Zn atoms; red: O; green: N; gray: C, white: H. (b) Top view of the not allow to simultaneously include Hubbard and spin–orbit lower half of the molecule. (c) Top view of the upper half of the molecule. corrections, thus the two effects are treated separately. Relaxed coordinates are available in ESI.† This journal is © the Owner Societies 2022 Phys. Chem. Chem. Phys., 2022, 24, 3780–3787 | 3781 View Article Online PCCP Paper HOAc = acetic acid, and M = MnII, CoII or ZnII) were synthesized by one pot reaction of 2-aminophenol, diacetylpyridine and manganese, cobalt or zincacetate, as described by Kampert et al. for the manganese complex,21 with some modifications for the cobalt and zinc analogues. Full details of the synthesis methods are given in the ESI.† The two new molecular complexes were characterized via single crystal diffraction conducted on a SuperNova (Agilent Technologies) diffract- ometer using Mo K radiation at 120 K. The crystals were This article is licensed under a Creative Commons Attribution 3.0 Unported Licence. mounted on a Hampton cryoloop with Paratone-N oil to prevent Open Access Article. Published on 18 January 2022. Downloaded on 10/31/2022 11:57:42 AM. solvent loss. Thermogravimetric analysis was performed using a Mettler-Toledo TGA/SDTA 851e instrument with a heating rate of 10 K min1. Cyclic voltammograms were recorded in dry Fig. 2 Cyclic voltammograms of the {M4} complexes (M = Mn, Co, Zn, and deaerated acetonitrile solutions containing tetrabutylam- concentration ca. 3 mM) in acetonitrile. Tetrabutylammonium perchlorate monium perchlorate (0.1 M) as electrolyte and 3 mM of the (0.1 M) is used as electrolyte and the scan rate is 50 mV s1. analyte, using a SP-150 potentiostat (BioLogic Science Instru- ments) controlled by the EC-Lab software and a standard three- previously published manganese complex:21 the complexes electrodes setup including a glassy carbon working electrode consist of a cubic M4O4 core with two sets of two different (diameter 3 mm), a platinum wire counter electrode and an Ag/ ligand groups, for a total of 118 atoms (Fig. 1). The metallic core is AgNO3 (0.1 M) reference electrode. Ferrocene was used as an a quasi-tetrahedron composed of two 7-coordinated ions (M1, M2) internal standard. Magnetometry was performed on a Quantum with pentagonal bipyramidal coordination and two 6-coordinated Design MPMS-5XL SQUID magnetometer. The crystalline ions (M3, M4) with pseudo-octahedral symmetry. samples were crushed and placed under vacuum for 16 h before The metal ions with the same coordination number are the complete removal of solvate molecules was checked by TGA. almost equivalent, as they overall face a quasi-identical chemical The resulting powders were compacted and immobilised into environment. The molecular cluster has an approximately C2 PTFE capsules. All data were corrected for the contribution of symmetry and can be described as two identical structures on the sample holder (PTFE capsule). Measurements on {Zn4} were different planes that are rotated of 901 one respect to the other used to determine the diamagnetic susceptibility of this (Fig. 1), taking the rotation axis along z. Seven-coordinated M1 complex wdia(Zn4) = 5.3  109 m3 mol1. The diamagnetic and M2 lie on different planes, each being connected in-plane to contribution in {Co4} and Mn4 was then calculated from this a pentadentate pyridine–diimine–diphenoxide type ligand (L2), value and Pascal’s constants35 for the Zn2+, Co2+ and Mn2+ ions, completed by the oxygen of a bridging acetate and a k3 yielding wdia(Co4) = 5.1  109 m3 mol1 and wdia(Mn4) = 5.2  phenoxide oxygen from the other L2 ligand. The coordination 109 m3 mol1, and subtracted from the experimental sphere of M3, M4 is a pseudo octahedron of six oxygen atoms susceptibility data. provided by a bidentate acetate ligand, the other oxygen of the two bridging acetate and two phenoxide oxygen from the L2 ligand (relaxed coordinates available in ESI†). 3 Theoretical and The inner cage of the three molecules is composed by four experimental analysis transition metal ions with different atomic valence configurations, 3.1 Synthesis and redox properties 3d5 for Mn(II), 3d7 for Co(II) and 3d10 for zinc(II). The latter complex is therefore diamagnetic; it was used experimentally to determine The {M4} are stable towards oxidation in the solid state as well as the diamagnetic contribution to the susceptibility of the complexes in solution, despite the sensitivity of the {Co4} precursors to and will not be discussed further. Both Mn(II) and Co(II) ions oxidation by O2 during synthesis. This observation is confirmed display high spin configurations, i.e. S = 5/2 for Mn and S = 3/2 by the cyclic voltammetry of the complex (Fig. 2, purple dotted for Co. line), which displays two quasi-reversible (DE = 120 mV) one- Despite the similarity between the structures of the manganese electron oxidation waves at 0.30 and 0.80 V vs. Fc+/Fc which can and cobalt complexes, experimental evidence and DFT calculations be assigned as {CoII4 } - {Co3 Co } - {Co2 Co2 }. As expected, the II III II III show small differences in bond lengths in the inner core. In redox couples in the manganese complexes are shifted to lower agreement with the larger atomic radius of Mn with respect to potentials and show the large peak-to-peak characteristic of Co, the {Mn4} central cage is slightly larger than the {Co4} one, due MnII(HS) - MnIII(LS) processes (Fig. 2, yellow solid line). to larger M–O and M–N bond-lengths. Details of the structure are Finally, the zinc derivative shows irreversible ligand-centered oxida- reported in Table 1. tion processes above 0.5 V vs. Fc+/Fc (Fig. 2, gray dashed line). 3.2 Molecular structure 3.3 Behavior in magnetic field The structure of the cobalt and zinc complexes was determined In order to quantify the strength of the magnetic interaction by single crystal X-ray diffraction to be analogue to that of the within the molecule and the response to an external magnetic 3782 | Phys. Chem. Chem. Phys., 2022, 24, 3780–3787 This journal is © the Owner Societies 2022 View Article Online Paper PCCP Table 1 Theoretical (DFT) and experimental (XRD) bond-lengths (Å) of the calculations. The agreement between theory and experiment is {Mn4} and {Co4} molecular complexes. XRD data was obtained at 208 K for fairly good in the LDA+U approximation (see the discussion in {Mn4}21 and at 100 K for {Co4} Section 3.6). d (Å) M1–M2 M3–M4 M1–M3a M2–OB,1b M4–OA,2b 3.4 Magnetic and electronic properties {Mn4} DFT 3.35 3.45 3.64/3.65 2.20–2.30 2.15–2.22 In order to characterize the magnetic configuration of the inner XRD 3.62 3.47 3.50/3.55 2.27–2.31 2.21–2.22 cage and to ascertain the role of spin–orbit coupling in {Co4} we {Co4} DFT 3.26 3.21 3.42/3.44 2.15–2.21 2.07–2.11 performed DFT calculations which show that the ground state XRD 3.39 3.19 3.15/3.16 2.17–2.29 2.11–2.19 is characterized by an antiferromagnetic coupling between non- This article is licensed under a Creative Commons Attribution 3.0 Unported Licence. equivalent metal ions (M1/M3 and M2/M4), and a ferromagnetic Open Access Article. Published on 18 January 2022. Downloaded on 10/31/2022 11:57:42 AM. a b The two values correspond to the equivalent pairs of atoms. Range given for all equivalent distances in the complex. one between the equivalent pairs (M1/M2 and M3/M4) giving rise to a up-up-down-down (uudd) configuration, referring to the relative alignment of the spins of the four metal ions. field we performed SQUID magnetometry experiments (Fig. 3). The magnetic moments of Co, Mn, N and O in the two molecular A singlet ground state is observed in both complexes, indicating complexes, deduced from the Mulliken charge population, are the presence of antiferromagnetic coupling between the reported in Table 2. Due to the chemical interaction with magnetic ions in the molecule. The molecular moment mmol the ligands the magnetic moment of the metal atoms in the as a function of magnetic field (H = 0–5 T) and temperature molecular complexes is reduced with respect to the isolated ions (T = 20–300 K) was fitted to a mean field model (Curie–Weiss (B4% in {Mn4}, B10% {Co4}). Accordingly, the induced magne- law, eqn (1)), yielding Néel temperatures of TN = 23 K for {Mn4} tization of the ligands is smaller for {Mn4} than for {Co4}, as can and TN = 12 K for {Co4}: be appreciated also through the small differences in the spatial CH distribution of the spin density (rup  rdown on the oxygen mmol ¼ (1) atoms, Fig. 4). In {Mn4} the magnetic moment of OA and OB is T  TN Those values, as well as the larger slope of the molecular negligible. In {Co4} the bridging phenoxy oxygens have opposite moment at low field/low temperature observed for {Co4} in magnetization: OB2 and OB3 are magnetized up while OB1 and comparison to {Mn4}, suggests that the antiferromagnetic cou- OB4 are magnetized down. Out of the eight acetate oxygens OA, pling between the metal atoms in {Co4} is smaller than in {Mn4}. only two (OA+) display a small positive magnetic moment while Notably, the behavior is reversed at high temperature with a the other six (OA) have a larger (in modulus) negative magnetic larger magnetic moment for {Mn4} than for {Co4}, which is in moment (mean value reported in Table 2). The average agreement with the higher spin moment of the Mn centers. magnetization of the N atoms is comparable to the average The Curie constant C obtained for the {Mn4} complex (3.0  contribution of OA but with opposite sign. As a consequence, 103 mB K Oe1) is in good agreement with a spin-only model despite the presence of local magnetic moments, the total spin (3.1  103 mB K Oe1 for g = 2 and S = 5/2). Such a model is not adequate for octahedral cobalt(II) complexes, with their 4T1g Table 2 Magnetic moment (mB) of the {Mn4} and {Co4} molecular complexes. ground term, and effective orbital momentum L = 1.36 Indeed, Average values are reported for N (variance 0.004 mB), and OA atoms with the Curie constant of {Co4} (2.4  103 mB K Oe1) obtained positive (OA+ = OA3,7) and negative (OA = OA1,2,4,5,6,8) magnetic moment (variances in {Mn4}/{Co4} are 0.0/0.001 mB and 0.001/0.002 mB, respectively). from the Curie–Weiss fit deviates significantly from the one Note the (anti)ferromagnetic coupling between (non-) equivalent metal ions: calculated by the spin-only model (1.3  103 mB K Oe1). M1 B M3, M2 B M4, M1 = M2, M3 = M4 The measured magnetic susceptibility is reported in ESI,† together with the theoretical one obtained from spin dynamics (mB) M1,2 M3,4 N OA+ OA OB2,3 OB1,4 {Mn4} 4.82 4.89 0.01 0.01 0.01 0.00 0.00 {Co4} 2.71 2.73 0.05 0.03 0.04 0.02 0.02 Fig. 4 Spin density on {Mn4} and {Co4}. Yellow (blue) isosurfaces corre- Fig. 3 SQUID magnetometry data of {Mn4} (orange) and {Co4} (purple) at spond to positive (negative) values with a fixed value of 0.025. Spin density T = 3.6 K (open symbols) and T = 50 K (filled symbols). on the ligands is more pronounced in the {Co4} case. This journal is © the Owner Societies 2022 Phys. Chem. Chem. Phys., 2022, 24, 3780–3787 | 3783 View Article Online PCCP Paper of both molecules is STOT = 0 confirming their antiferromagnetic Table 3 Net atomic charges of the atomic species in the {Mn4} and {Co4} character. Nevertheless, the major spread of the magnetic molecular complexes (in units of electron charge e). Positive (negative) values indicate donor (acceptor) behavior. Average values are reported for moment observed in {Co4} is an indication of a possible large the equivalent centers magnetic interaction of this molecule with other systems when the complex is used for functionalization. Dq (e) M1,2 M3,4 N OA OB In Fig. 5 the DOS of the two molecules projected on different {Mn4} +1.10 +1.32 +0.29 0.39 0.60 atoms of the complex (PDOS), is reported. The PDOS of Mn ions is {Co4} +1.49 +1.63 +0.21 0.44 0.68 characterized by the prevalence a single spin population, due to the almost complete filling of the spin-up 3d electrons. In Co, This article is licensed under a Creative Commons Attribution 3.0 Unported Licence. The hybridization with states of the ligands is also respon- instead, majority and minority spins are present, according to the Open Access Article. Published on 18 January 2022. Downloaded on 10/31/2022 11:57:42 AM. sible for the charge transfer from the magnetic ions to the more-than-half filling of the 3d orbitals. The oxygen atoms display nearby atoms. In the molecular complexes, Mn and Co atoms a different PDOS depending on the group they are attached to. display a number of electrons smaller than the valence of the In particular the states of the bridging oxygen atoms OB partially isolated atom, as reported in Table 3 in term of the net atomic overlap with the states of the magnetic ions, with larger extent for charge, i.e. they donate electron charge. This reduction of the seven-coordinated ones (M1,2) in the majority-spin component charge is larger for the two metal ions bound to the pyridine– and with the six-coordinated ones (M3,4) in the minority spin diimine group (M1,2) with respect to the 6-coordinated component. This overlap, which appears to be slightly more magnetic atoms in the same molecule (M3,4). Moreover, the intense in {Mn4}, is responsible for the coupling between mag- percentage of lost charge is larger in {Mn4} (B25%) than in netic ions via superexchange interaction mechanism.37 {Co4} (B22%), according to the larger hybridization with the For both complexes, the OA atoms are characterized by surrounding coordination groups. The oxygen atoms act as majority spin states in the [3, 1] eV energy range and electron acceptors in both molecules. The maximum charge minority states centered around 2.5 eV, with a moderate transfer is toward the bridging oxygens that acquire 0.60 and overlap with the metal atoms in both cases. We can therefore 0.68 electrons (mean values) in {Mn4} and {Co4}, respectively. conclude that they contribute to the magnetic coupling For OA atoms the absolute values of the acquired charge between metal centers with a similar strength. (B0.4e) are similar in the two complexes. N atoms participate to charge transfer towards the ligands by donating electrons, with a slightly larger fraction in {Mn4} (B0.29e) than in {Co4} (B0.21e). On the basis of the results reported by Kampert et al.21 the charge withdrawn from the [M4O4] core (by the ligands) is inversely proportional to the strength of the magnetic interaction within the complex. For both complexes, the analysis of Mulliken charges predicts that the [M4O4] core acts as a donor, with 2.45 and 3.43 electrons donated in the Mn and Co case, respectively. Therefore, we expect that a stronger antiferromagnetic coupling in {Mn4} than in {Co4}, supporting the experimental findings. 3.5 Role of spin orbit coupling In the previous paragraphs we have analyzed the results obtained with the LDA+U approximation, necessary to account for the electronic correlation of localized 3d orbitals, but limited in the SIESTA code to a collinear-spin description of magnetism. This approximation is valid for the Mn(II) ions, as the high-spin d5 electronic configuration does not have a net orbital momentum. In Co(II) centers, instead, the d7 configuration leads to an orbital momentum L = 3 for an isolated ion. While the orbital momentum is quenched in low symmetry environments, including pentagonal bipyramidal, it is not in a perfect octahe- dron, where L = 1. As two of the metal centers in {Co4} display a pseudo-octahedral geometry, SOC is expected to have a significant effect on the magnetic properties of this complex. In order to investigate the role of SOC in the complexes, Fig. 5 Density of states projected on the magnetic ions and different we have performed DFT calculations including SOC for both oxygen atoms (OA and OB) in the two molecular complexes. The average molecules at U = 0 using the fully relativistic pseudopotential PDOS per atom type is reported. formalism31 implemented in SIESTA.32 The magnetization 3784 | Phys. Chem. Chem. Phys., 2022, 24, 3780–3787 This journal is © the Owner Societies 2022 View Article Online Paper PCCP direction has been set along the z axis for {Mn4}. Indeed 3.6 Exchange coupling we verified that for this molecule the magnetic anisotropy In order to ascertain the strength of the (anti)ferromagnetic related to spinflip along five independent directions is at coupling in the two complexes we computed the exchange most B100 meV per molecule. For {Co4}, which is expected to coupling parameters (Ji) from first-principles total energies by display strong spin–orbit effects, we have explored 30 different considering the five lowest-energy spin configurations of the direction of the magnetization. The easy axis for {Co4} is molecules (uudd, udud, uddu, uddd, uuuu) as explained in rotated with respect to the z direction with a polar angle 1501 Section 2.1. The calculated exchange parameters, obtained in and azimuthal angle 451. The maximum magnetic anisotropy the LDA+U approximation, are reported in Table 6, where for spinflip amounts to 12 meV per molecule. The results This article is licensed under a Creative Commons Attribution 3.0 Unported Licence. positive and negative values correspond to ferromagnetic reported below are relative to {Co4} with the spin along the Open Access Article. Published on 18 January 2022. Downloaded on 10/31/2022 11:57:42 AM. (FM) or antiferromagnetic (AFM) coupling. easy axis. The calculated Ji are of the same order of magnitude of those In Tables 4 and 5 the computed S, L, and their sum ( J) are extracted from experimental susceptibility (see ESI†), and are in reported for both molecular complexes. In both cases, the fair agreement with those reported in ref. 21 for a three-J atomic spin is slightly reduced with respect to the LDA+U model. Both J1 and J2 are negative, confirming the antiferro- calculation. The four metal ions in {Co4} display an orbital magnetic coupling between not equivalent atoms. One of the moment which is smaller than the value expected for other two parameters describing the coupling between equiva- the isolated ion, but significantly larger than the manganese lent atoms (J3 or J4) is positive (FM), in agreement with the data analogue. The quenching is stronger for the two ions in the extracted from the experiments. The overall exchange inter- pffiffiffiffiffiffiffiffiffi pentagonal bipyramidal coordination, for which hL2 i  0:15. action, estimated as the average of the Js (3.7 meV for {Co4} For the 6-coordinated pseudo-octahedral Co ions L is not and 1.4 for {Mn4}), is AFM for both molecular complexes. negligible (B0.4) and contributes to an overall value of The strongest Ji (J1 in {Co4}, J2 in {Mn4}) corresponds to the pffiffiffiffiffiffiffiffiffi hJ 2 i  3. interaction between the two pairs of not-equivalent ions and it is related to the energy difference between the AFM ground state and the high spin FM state (S = 12 for {Co4} and S = 20 for Table 4 Spin (S), orbital moment (L) and their composition (J) for the four {Mn4}) which is larger for {Co4}. The FM interaction between magnetic atoms of the {Mn4} core. The data are reported in units of mB equivalent ions (intra-pair) is, instead, smaller for {Co4}. The latter governs the transition to low-spin FM states (for example Mn1 Mn2 Mn3 Mn4 uddd) which influences the behavior of the magnetization at pffiffiffiffiffiffiffiffiffi hS2 i 4.33 4.37 4.34 4.34 low fields and low temperatures, hence explaining the observed Sx 1.43 1.35 0.17 0.37 switching with temperature of the magnetization curves M(B) of the Sy 1.097 0.59 0.20 0.058 two molecules (Fig. 3). To further explore this behavior, we have Sz 3.94 4.11 4.33 4.32 exploited a model Heisenberg Hamiltonian with J parameters and pffiffiffiffiffiffiffiffiffi g-factor fitted from the experimental low-field susceptibility (ESI†) hL2 i 0.052 0.057 0.058 0.058 and used them to calculate M(B) at two different temperatures. Lx 0.013 0.015 0.007 0.003 We find that the observed (Fig. 3) switch of M(B) with temperature Ly 0.006 0.008 0.004 0.01 Lz 0.05 0.054 0.057 0.057 is an effect of the more marked AFM character of {Mn4} giving rise to a positive curvature of M(B) at low field/low T. At high field/high pffiffiffiffiffiffiffiffiffi T, instead, the most relevant factor is the larger saturation value of hJ 2 i 4.38 4.40 4.39 4.40 the magnetization in {Mn4} compared to {Co4}. By increasing the range of the magnetic field beyond the experimental one, a crossing of the two theoretical curves is observed due to the combination of these two aspects (ESI†). Table 5 Spin S, orbital moment L and their composition (J) for the four magnetic atoms of the {Co4} core. The data are reported in units of mB The inclusion of SOC in the calculation leads to Js with a sign that reflects the uudd magnetic order of the ground state, Co1 Co2 Co3 Co4 i.e. AFM (FM) coupling between M1/M4 and M2/M3 non- pffiffiffiffiffiffiffiffiffi hS 2 i 2.56 2.56 2.57 2.58 equivalent (M1/M2 and M3/M4 equivalent) ions (see Table S2 Sx 0.19 1.92 1.92 0.975 in ESI†). Nevertheless, the exchange parameters obtained with Sy 1.355 1.6 1.62 0.72 Sz 2.61 0.56 0.52 2.29 pffiffiffiffiffiffiffiffiffi Table 6 Exchange coupling parameters (Ji, meV) of {Mn4} and {Co4} hL2 i 0.15 0.14 0.46 0.35 molecular complexes extracted from DFT calculations with LDA+U. S is Lx 0.004 0.121 0.33 0.057 normalized to 1 Ly 0.051 0.065 0.33 0.06 Lz 0.14 0.033 0.033 0.33 LDA+U (meV) J1 J2 J3 J4 pffiffiffiffiffiffiffiffiffi {Mn4} 0.2 0.9 0.2 0.9 hJ 2 i 2.71 2.71 3.03 2.92 {Co4} 1.8 0.19 0.8 0.6 This journal is © the Owner Societies 2022 Phys. Chem. Chem. Phys., 2022, 24, 3780–3787 | 3785 View Article Online PCCP Paper SOC are too large compared to those extracted from the strength of the magnetic interaction within the molecule. This experiments,21 suggesting that the electronic correlation can result confirms the possibility to tune the magnetic properties not be neglected for a reliable estimate of the strength of the of the molecule through the chemical synthesis by acting on magnetic interactions. A complete description of the magnetic the magnetic inner core. Nevertheless, a general rule explaining properties of the clusters requires treating spin–orbit coupling the relationship between the choice of the magnetic atoms and and Hubbard-U correction on the same footing. However, the the magnetic coupling in the molecule can not be established usual formulation of the Hamiltonian for exchange interaction because the ligands, which are molecule-specific, also play a only depends on the spin quantum number. This is accurate role. We also verified that the different magnetic properties of when the orbital moment are negligible with respect to the spin the two chemical species lead to a different spatial extension of This article is licensed under a Creative Commons Attribution 3.0 Unported Licence. moment. We verified this is the case (Table 4) and use the the magnetic moment and electronic charge density on the Open Access Article. Published on 18 January 2022. Downloaded on 10/31/2022 11:57:42 AM. LDA+U approximation to predict the exchange coupling ligands, which could influences the interaction with foreign parameters. systems and affects the efficiency of the two compounds when For a deeper insight of the exchange interaction, we have employed for magnetic functionalization. computed the exchange parameters also with the Liechten- We find and explain an unusual switch with temperature of stein–Katsnelson–Antropov–Gubanov (LKAG) formula38 the dependence of the magnetic moment from the applied 39 implemented in the TB2J package, which treats the local spin magnetic field M(B) for the two molecules. We relate it to two rotation of the numerical atomic orbitals for the magnetic competing effects: the stronger AFM coupling in {Mn4} and the atoms as a perturbation. large value of magnetization in {Mn4} which dominate at low The Ji, evaluated with this approach present the same overall and high temperature, respectively. trend as those computed from total energies (Table 6), for both The calculations clarify the role of spin–orbit effects: LDA+U and SOC case, and are reported in the ESI† (Table S3). negligible in {Mn4} and relevant in {Co4}, showing that SOC The different predictions of the various approximations has to be considered for a reliable theoretical description of the (LDA+U or SOC) are a consequence of the complexity of the magnetic moments of the latter. In perspective of future magnetic potential energy landscape of these molecular complexes. exploitation of these compounds in spintronics the SOC effects A small perturbation (geometry, electron correlation, spin found in {Co4} should be taken into account as possible source alignment) can drive the results out of equilibrium and towards a of spin decoherence. different local minimum. Despite these difficulties, all the Our study of the exchange coupling parameters and spin computed Ji parameters predict the experimentally observed uudd dynamics demonstrate that it is necessary to explicitly include ground state, regardless of the approach (total energies or pertur- electron correlations (for instance, via a Hubbard U parameter) bative) and inclusion of correlations or SOC. This has been verified to properly recover these properties. The complete description by feeding the computed Ji in the Heisenberg Hamiltonian and of the molecular complexes can only be performed in a frame- computing the various spin configurations (Fig. S3, ESI†). work in which electronic correlation and SOC are treated on the Finally, we used all the computed Ji parameters as input for same footing. spin dynamics simulations40–42 to predict the magnetic susceptibility, finding a good agreement with experiment in the LDA+U case (ESI†). The results obtained without U Conflicts of interest correction are, instead, in striking contradiction with experi- There are no conflicts to declare. ments, confirming the importance of taking into account electron correlation in the transition metal sites. Acknowledgements 4 Conclusions The authors thank Natalya Izarova for acquisition of the crystal- lographic data, Brigitte Jansen for acquisition of the TGA data Through a joint experimental and theoretical analysis we have and Christina Houben for acquisition of some of the SQUID characterized the properties of two coordination complexes, data. The Authors acknowledge EU H2020 project NFFA (Grant {Mn4} and {Co4}, that display the same chemical structure but No. 654360) under Transnational Access Activity ID-753. Com- different inner magnetic core formed by Mn and Co atoms, putational resources in MareNostrum4 at the Barcelona Super- respectively. The theoretical analysis was performed under computing Center were provided by the Red Española de different approximations (LDA+U, SOC) and methods (first- Supercomputacion (Grants FI-2019-2-0038 and FI-2020-1-0022) principles, model Hamiltonians, perturbation theory). and PRACE (grant OptoSpin, project id. 2020225411). ZZ The experimental data and the theoretical calculations show acknowledges financial support by the Ramon y Cajal program that by changing the magnetic core, the robustness of the AFM RYC-2016-19344 (MINECO/AEI/FSE, UE) and the Netherlands configuration in an external magnetic field is changed, being Sector Plan program 2019-2023. PO, HX and ZZ thank stronger in {Mn4} than in {Co4}. The reason for this behavior the support by the EU H2020-NMBP-TO-IND-2018 project can be found in the different interaction of the magnetic atoms ‘‘INTERSECT’’ (Grant No. 814487), the EC H2020-INFRAEDI- with the surrounding ligands, which determines a different 2018-2020 MaX ‘‘Materials Design at the Exascale’’ CoE 3786 | Phys. Chem. Chem. Phys., 2022, 24, 3780–3787 This journal is © the Owner Societies 2022 View Article Online Paper PCCP (Grant No. 824143), Grant PGC2018-096955-B-C43 funded by 21 E. Kampert, F. F. B. J. Janssen, D. W. Boukhvalov, MCIN/AEI/10.13039/501100011033 (Spain) and ‘‘ERDF A way of J. C. Russcher, J. M. M. Smits, R. de Gelder, B. de Bruin, making Europe’’ (European Union), the ‘‘Centro de Excelencia P. C. M. Christianen, U. Zeitler, M. I. Katsnelson, J. C. Maan Severo Ochoa’’ Grant SEV-2017-0706 funded by MCIN/AEI/ and A. E. Rowan, Inorg. Chem., 2009, 48, 11903–11908. 10.13039/501100011033 (Spain) and Generalitat de Catalunya 22 M.-L. Tong, S.-L. Zheng, J.-X. Shi, Y.-X. Tong, H. K. Lee and (CERCA program and Grant 2017SGR1506). CM acknowledges X.-M. Chen, J. Chem. Soc., Dalton Trans., 2002, 1727–1734. funding by Niedersächsisches Vorab, Akz. 11-76251-14-3/ 23 G. S. Papaefstathiou, A. Escuer, F. A. Mautner, 15(ZN3141). C. Raptopoulou, A. Terzis, S. P. Perlepes and R. Vicente, Eur. J. Inorg. Chem., 2005, 879–893. This article is licensed under a Creative Commons Attribution 3.0 Unported Licence. 24 T. A. Hudson, K. J. Berry, B. Moubaraki, K. S. Murray and Notes and references Open Access Article. Published on 18 January 2022. Downloaded on 10/31/2022 11:57:42 AM. R. Robson, Inorg. Chem., 2006, 45, 3549–3556. 1 M. Ganzhorn and W. Wernsdorfer, Molecular Magnets, 25 C.-B. Tian, H.-B. Zhang, Y. Peng, Y.-E. Xie, P. Lin, Z.-H. Li Springer, Berlin, Heidelberg, 2014. and S.-W. Du, Eur. J. Inorg. Chem., 2012, 4029–4035. 2 E. Coronado, Nat. Rev. Mater., 2020, 5, 87–104. 26 J. M. Soler, E. Artacho, J. D. Gale, A. Garca, J. Junquera, 3 M. Gobbi, M. A. Novak and E. Del Barco, J. Appl. Phys., 2019, P. Ordejón and D. Sánchez-Portal, J. Phys.: Condens. Matter, 125, 240401. 2002, 14, 2745. 4 D. Maniaki, E. Pilichos and S. P. Perlepes, Front. Chem., 27 A. Garcı́a, N. Papior, A. Akhtar, E. Artacho, V. Blum, 2018, 6, 461. E. Bosoni, P. Brandimarte, M. Brandbyge, J. I. Cerdá1, 5 L. Bogani and W. Wernsdorfer, Nat. Mater., 2008, 7, F. Corsetti, R. Cuadrado, V. Dikan, J. Ferrer, J. Gale, 179–186. P. Garcı́a-Fernández, V. Garcá-Suárez, S. Garcı́a, G. Huhs, 6 Z. Zanolli, R. Leghrib, A. Felten, J.-J. Pireaux, E. Llobet and S. Illera, R. Korytár, P. Koval, I. Lebedeva, L. Lin, P. López- J.-C. Charlier, ACS Nano, 2011, 5, 4592–4599. Tarifa, S. G. Mayo, S. Mohr, P. Ordejón, A. Postnikov, 7 Z. Zanolli and J.-C. Charlier, ACS Nano, 2012, 6, Y. Pouillon, M. Pruneda, R. Robles, D. Sánchez-Portal, 10786–10791. J. M. Soler, R. Ullah, V. Wen-zhe Yu and J. Junquera, 8 H. Oshio and M. Nakano, Chem. – Eur. J., 2005, 11, J. Chem. Phys., 2020, 152, 204108. 5178–5185. 28 W. Kohn and L. J. Sham, Phys. Rev. B, 1965, 140, A1133. 9 S. Brooker and J. A. Kitchen, Dalton Trans., 2009, 7331–7340. 29 D. M. Ceperley and B. J. Alder, Phys. Rev. Lett., 1980, 45, 566. 10 K. S. Pedersen, J. Bendix and R. Clerac, Chem. Commun., 30 A. M. Ritzmann, M. Pavone, A. B. Muñoz Garcı́a, J. A. Keith 2014, 50, 4396–4415. and E. A. Carter, J. Mater. Chem. A, 2014, 2, 8060–8074. 11 T. Jungwirth, X. Marti and P. Wadley, Nat. Nanotechnol., 31 R. Cuadrado and J. I. Cerdá, J. Phys. Condens. Matter, 2012, 2016, 11, 231–241. 24, 086005. 12 M. Bragato, S. Achilli, F. Cargnoni, D. Ceresoli, 32 R. Cuadrado, R. Robles, A. Garcı́a, M. Pruneda, P. Ordejón, R. Martinazzo, R. Soave and M. I. Trioni, Materials, 2018, J. Ferrer and J. I. Cerdá, Phys. Rev. B, 2021, 104, 195104. 11, 2030. 33 Z. Zanolli, C. Niu, G. Bihlmayer, Y. Mokrousov, 13 N. Makoto, H. Satoru, K. Hiroaki, Y. Yuki, M. Yukitoshi and P. Mavropoulos, M. J. Verstraete and S. Blügel, Phys. Rev. S. Hitoshi, Nat. Commun., 2019, 10, 4305. B, 2018, 98, 155404. 14 X.-X. Fu, F. Wei, Y. Niu and C.-K. Wang, Phys. E, 2021, 34 N. F. Chilton, R. P. Anderson, L. D. Turner, A. Soncini and 131, 114737. K. S. Murray, Phys. Rev. Lett., 2013, 34, 1164. 15 V. Baltz, A. Manchon, M. Tsoi, T. Moriyama, T. Ono and 35 G. A. Bain and J. F. B. Berry, J. Chem. Ed., 2008, 85, 532–536. Y. Tserkovnyak, Rev. Mod. Phys., 2018, 90, 015005. 36 F. Lloret, M. Julve, J. Cano, R. Ruiz-Garcı́a and E. Pardo, 16 R. Frielinghaus, C. Besson, L. Houben, A.-K. Saelhoff, Inorg. Chim. Acta, 2008, 361, 3432–3445. C. M. Schneidera and C. Meyer, RCS Adv., 2015, 5, 84119. 37 J.-P. Launay and M. Verdaguer, Electrons in molecules, 17 C. Besson, P. Stegmann, M. Schnee, Z. Zanolli, S. Achilli, Oxford University Press, 2014. N. Wittemeier, A. Vierck, R. Frielinghaus, P. Kögerler, 38 A. I. Liechtenstein, M. I. Katsnelson, V. P. Antropov and J. Maultzsch, P. Ordejón, C. M. Schneider, A. Hucht, V. A. Gubanov, J. Magn. Magn. Mater., 1987, 67, 65–74. J. König and C. Meyer, 2021, arXiv:2107.07723. 39 X. He, N. Helbig, M. J. Verstraete and E. Bousquet, Comput. 18 A. Ardavan, O. Rival, J. J. L. Morton, S. J. Blundell, Phys. Commun., 2021, 264, 107938. A. M. Tyryshkin, G. A. Timco and R. E. P. Winpenny, Phys. 40 L. Landau and E. Lifshitz, Perspectives in Theoretical Physics, Rev. Lett., 2007, 98, 057201. Elsevier, 1992, pp. 51–65. 19 Y. Yu, C. Li, B. Yin, J.-L. Li, Y.-H. Huang, Z.-Y. Wen and 41 T. L. Gilbert, IEEE Trans. Magn., 2004, 40, 3443–3449. Z.-Y. Jiang, J. Chem. Phys., 2013, 139, 054305. 42 X. Gonze, B. Amadon, G. Antonius, F. Arnardi, L. Baguet, 20 B. Yin, J. Li, H. Bai, Z. Wen, Z. Jiang and Y. Huang, Phys. J.-M. Beuken, J. Bieder, F. Bottin, J. Bouchet and E. Bousquet, Chem. Chem. Phys., 2012, 14, 1121–1130. et al., Comput. Phys. Commun., 2020, 248, 107042. This journal is © the Owner Societies 2022 Phys. Chem. Chem. Phys., 2022, 24, 3780–3787 | 3787