DFT-Based Studies on the Jahn−Teller Effect in 3d Hexacyanometalates with Orbitally Degenerate Ground States

Interplay between transition-metal K-edge XMCD, slight structural distortions and magnetism in a series of trimetallic (CoxNi(1-x))4[Fe(CN)6]3/8 Prussian blue analogues

The magnetic properties of a series of trimetallic (Co,Ni)Fe Prussian blue analogues (PBAs) were investigated by SQUID magnetometry and X-ray magnetic circular dichroism (XMCD) at the three transition metal (TM) K-edges. In turn, the PBA trimetallic series was used as a tool in order to better understand the information contained in TM K-edge XMCD and particularly the chemical nature of the probed species (extended sub-lattice or localized entities). The results show that the magnetic behavior of the compounds is dictated by competing exchange interactions between the Co-Fe and Ni-Fe pairs, without spin frustration. They also show that XMCD at the TM K-edge is a local atomic probe of the element at the N side of the cyanide bridge and a local probe of the absorbing atom and its first magnetic neighbors on the C side of the bridge. At last, XMCD at the TM K-edge turns out to be highly sensitive to very small structural distortions.

Exploring Jahn-Teller distortions: a local vibrational mode perspective

The characterization of normal mode (CNM) procedure coupled with an adiabatic connection scheme (ACS) between local and normal vibrational modes, both being a part of the Local Vibrational Mode theory developed in our group, can identify spectral changes as structural fingerprints that monitor symmetry alterations, such as those caused by Jahn-Teller (JT) distortions. Employing the PBE0/Def2-TZVP level of theory, we investigated in this proof-of-concept study the hexaaquachromium cation case,[ Cr ( OH 2 ) 6 ] 3 + /[ Cr ( OH 2 ) 6 ] 2 + , as a commonly known example for a JT distortion, followed by the more difficult ferrous and ferric hexacyanide anion case,[ Fe ( CN ) 6 ] 4 - /[ Fe ( CN ) 6 ] 3 - . We found that in both cases CNM of the characteristic normal vibrational modes reflects delocalization consistent with high symmetry and ACS confirms symmetry breaking, as evidenced by the separation of axial and equatorial group frequencies. As underlined by the Cremer-Kraka criterion for covalent bonding, from[ Cr ( OH 2 ) 6 ] 3 + to[ Cr ( OH 2 ) 6 ] 2 + there is an increase in axial covalency whereas the equatorial bonds shift toward electrostatic character. From[ Fe ( CN ) 6 ] 4 - to[ Fe ( CN ) 6 ] 3 - we observed an increase in covalency without altering the bond nature. Distinct π back-donation disparity could be confirmed by comparison with the isolated CN- system. In summary, our study positions the CNM/ACS protocol as a robust tool for investigating less-explored JT distortions, paving the way for future applications.

Interplay between Transition-Metal K-edge XMCD and Magnetism in Prussian Blue Analogs

To disentangle the information contained in transition-metal K-edge X-ray magnetic circular dichroism (XMCD), two series of Prussian blue analogs (PBAs) were investigated as model compounds. The number of 3d electrons and the magnetic orbitals have been varied on both sites of the bimetallic cyanide polymer by combining with the hexacyanoferrate or the hexacyanochromate entities' various divalent metal ions A²⁺ (Mn²⁺, Fe²⁺, Co²⁺, Ni²⁺, and Cu²⁺). These PBA were studied by Fe and Cr X-ray absorption spectroscopy and XMCD. The results, compared to those obtained at the A K-edges in a previous work, show that transition-metal K-edge XMCD is very sensitive to orbital symmetry and can therefore give valuable information on the local structure of the magnetic centers. Expressions of the intensity of the main 1s → 4p contribution to the signal are proposed for all K-edges and all compounds. The results pave the way toward a new tool for molecular materials able to give access to valuable information on the local orientation of the magnetic moments or to better understand the role of 4p orbitals involved in their magnetic properties.

Macrocycle-Induced Modulation of Internuclear Interactions in Homobimetallic Complexes

A synthetic route has been developed for a series of 3d homobimetallic complexes of Mn, Fe, Co, Ni, and Cu using three different pyridyldiimine and pyridyldialdimine macrocyclic ligands with ring sizes of 18, 20, and 22 atoms. Crystallographic analyses indicate that while the distances between the metals can be modulated by the size of the macrocycle pocket, the flexibility in the alkyl linkers used to construct the macrocycles enables the ligand to adjust the orientation of the PD(A)I fragments in response to the geometry of the [M₂(μ-Cl)₂]²⁺ core, particularly with respect to Jahn-Teller distortions. Analyses by UV-vis spectroscopy and SQUID magnetometry revealed deviations in the properties [M₂(μ-Cl)₂]²⁺-containing complexes bound by standard mononucleating ligands, highlighting the ability of macrocycles to use ring size to control the magnetic interactions of pseudo-octahedral, high-spin metal centers.

Effect of Spin-Orbit Coupling on Phonon-Mediated Magnetic Relaxation in a Series of Zero-Valent Vanadium, Niobium, and Tantalum Isocyanide Complexes

Spin-vibronic coupling leads to spin relaxation in paramagnetic molecules, and an understanding of factors that contribute to this phenomenon is essential for designing next-generation spintronics technology, including single-molecule magnets and spin-based qubits, wherein long-lifetime magnetic ground states are desired. We report spectroscopic and magnetic characterization of the isoelectronic and isostructural series of homoleptic zerovalent transition metal triad M(CNDipp)₆ (M = V, Nb, Ta; CNDipp = 2,6-diisopropylphenyl isocyanide) and show experimentally the significant increase in spin relaxation rate upon going from V to Nb to Ta. Correlated electronic calculations and first principle spin-phonon computations support the role of spin-orbit coupling in modulating spin-phonon relaxation. Our results provide experimental evidence that increasing magnetic anisotropy through spin-orbit coupling interactions leads to increased spin-vibronic relaxation, which is detrimental to long spin lifetime in paramagnetic molecules.

Slow Magnetic Relaxation, Antiferromagnetic Ordering, and Metamagnetism in MnII (H2 dapsc)-FeIII (CN)6 Chain Complex with Highly Anisotropic Fe-CN-Mn Spin Coupling

Reactions of [Mn(H₂ dapsc)Cl₂ ]⋅H₂ O (dapsc=2,6- diacetylpyridine bis(semicarbazone)) with K₃ [Fe(CN)₆ ] and (PPh₄ )₃ [Fe(CN)₆ ] lead to the formation of the chain polymeric complex {[Mn(H₂ dapsc)][Fe(CN)₆ ][K(H₂ O)_3.5 ]}_n ⋅1.5n H₂ O (1) and the discrete pentanuclear complex {[Mn(H₂ dapsc)]₃ [Fe(CN)₆ ]₂ (H₂ O)₂ }⋅4 CH₃ OH⋅3.4 H₂ O (2), respectively. In the crystal structure of 1 the high-spin [Mn^II (H₂ dapsc)]²⁺ cations and low-spin hexacyanoferrate(III) anions are assembled into alternating heterometallic cyano-bridged chains. The K⁺ ions are located between the chains and are coordinated by oxygen atoms of the H₂ dapsc ligand and water molecules. The magnetic structure of 1 is built from ferrimagnetic chains, which are antiferromagnetically coupled. The complex exhibits metamagnetism and frequency-dependent ac magnetic susceptibility, indicating single-chain magnetic behavior with a Mydosh-parameter φ=0.12 and an effective energy barrier (U_eff /k_B ) of 36.0 K with τ₀ =2.34×10^-11  s for the spin relaxation. Detailed theoretical analysis showed highly anisotropic intra-chain spin coupling between [Fe^III (CN)₆ ]^3- and [Mn^II (H₂ dapsc)]²⁺ units resulting from orbital degeneracy and unquenched orbital momentum of [Fe^III (CN)₆ ]^3- complexes. The origin of the metamagnetic transition is discussed in terms of strong magnetic anisotropy and weak AF interchain spin coupling.

Synthesis, Structure, and Magnetic Properties of 1D {[MnIII(CN)6][MnII(dapsc)]}n Coordination Polymers: Origin of Unconventional Single-Chain Magnet Behavior

Two one-dimensional cyano-bridged coordination polymers, namely, {[Mn^II(dapsc)][Mn^III(CN)₆][K(H₂O)_2.75(MeOH)_0.5]}_n·0.5n(H₂O) (I) and {[Mn^II(dapsc)][Mn^III(CN)₆][K(H₂O)₂(MeOH)₂]}_n (II), based on alternating high-spin Mn^II(dapsc) (dapsc = 2,6-diacetylpyridine bis(semicarbazone)) complexes and low-spin orbitally degenerate hexacyanomanganate(III) complexes were synthesized and characterized structurally and magnetically. Static and dynamic magnetic measurements reveal a single-chain magnet (SCM) behavior of I with an energy barrier of U_eff ≈ 40 K. Magnetic properties of I are analyzed in detail in terms of a microscopic theory. It is shown that compound I refers to a peculiar case of SCM that does not fall into the usual Ising and Heisenberg limits due to unconventional character of the Mn^III-CN-Mn^II spin coupling resulting from a nonmagnetic singlet ground state of orbitally degenerate complexes [Mn^III(CN)₆]^3-. The prospects of [Mn^III(CN)₆]^3- complex as magnetically anisotropic molecular building block for engineering molecular magnets are critically analyzed.

Light-induced relaxation dynamics of the ferricyanide ion revisited by ultrafast XUV photoelectron spectroscopy

The photoexcited ferricyanide undergoes an ultrafast spin crossover followed by Jahn–Teller distortion.

Single-ion anisotropy and exchange interactions in the cyano-bridged trimers MnIII2MIII(CN)6 (MIII = Co, Cr, Fe) species incorporating [Mn(5-Brsalen)]+ units: an inelastic neutron scattering and magnetic susceptibility study

The electronic structures of the compounds K[(5-Brsalen)(2)(H(2)O)(2)-Mn(2)M(III)(CN)(6)].2H(2)O (M(III) = Co(III), Cr(III), Fe(III)) have been determined by inelastic neutron scattering (INS) and magnetic susceptibility studies, revealing the manganese(III) single-ion anisotropy and exchange interactions that define the low-lying states of the Mn-M(III)-Mn trimeric units. Despite the presence of an antiferromagnetic intertrimer interaction, the experimental evidence supports the classification of both the Cr(III) and Fe(III) compounds as single-molecule magnets. The value of 17(2) cm(-1) established from AC susceptibility measurements for a spin-reversal barrier of K[(5-Brsalen)(2)(H(2)O)(2)-Mn(2)Cr(CN)(6)].2H(2)O may be readily rationalized in terms of the energy level diagram determined directly by INS. AC susceptibility measurements on samples of K[(5-Brsalen)(2)(H(2)O)(2)-Mn(2)Fe(CN)(6)].2H(2)O are contrary to those previously reported, exhibiting but the onset of peaks below temperatures of 1.8 K at oscillating frequencies in the range of 100-800 Hz. INS measurements reveal an anisotropic ferromagnetic manganese(III)-iron(III) exchange interaction, in accordance with theoretical expectations based on the unquenched orbital angular momentum of the [Fe(CN)(6)](3-) anion, giving rise to an M(s) approximately +/-9/2 ground state, isolated by approximately 11.5 cm(-1) from the higher-lying levels. The reported INS and magnetic data should now serve as a benchmark against which theoretical models that aim to inter-relate the electronic and molecular structure of molecular magnets should be tested.