Magnetic analyses of isosceles tricobalt(II) complexes containing two types of octahedral high-spin cobalt(II) ions

The observed magnetic data for two isosceles tricobalt(II) complexes have been successfully analyzed, considering the axial distortion around each cobalt(II) ion, the local spin-orbit coupling, the anisotropic exchange interactions, and the intermolecular exchange interactions. The complexes each contains two types of octahedral high-spin cobalt(II) ions (CoA and CoB) in the shape of an isosceles triangle (CoA1-CoB-CoA2), and the contribution of the orbital angular momentum is significant. The exchange interaction between the CoA and CoB ions is practically negligible (J = ~ 0), whereas the interaction between the CoA1 and CoA2 ions is ferromagnetic (J’ > 0) for both complexes.


INTRODUCTION
Magnetic analysis of multinuclear octahedral high-spin cobalt(II) complexes is a challenging subject because the orbital angular momentum makes the theoretical treatment difficult [1].One of the most difficult points is that the local spin-orbit coupling is much larger than the exchange interactions [2].Another difficult point is that the effect of local distortion is generally too large to be ignored, and that the anisotropic treatment is necessary [2,3].

EXPERIMENT Magnetic Analysis
The entire calculation was performed on a Power Macintosh 7300/180 computer using the MagSaki(T) program developed by Sakiyama.Nine independent parameters κ A ,λ A , Δ A , κ B , λ B , Δ B , J, J', and θ were determined as described below.First, the susceptibility data above 50 K (or 100 K) were fitted using six local parameters κ A , λ A , Δ A , κ B , λ B , and Δ B , excluding the effect of exchange interactions between cobalt(II) ions.Secondly, fixing the six local parameters, the susceptibility data in the entire temperature range (2 -300 K) were fitted to determine the remaining parameters J, J', and θ, and finally all the parameters were optimized.

Magnetic Susceptibility Equation for Isosceles Tricobalt(II) Complexes
In a trinuclear octahedral high-spin cobalt(II) complex, each cobalt(II) ion (O symmetry) has a local 4 T 1 ( 4 F) ground term, which is split into six Kramers doublets due to a spin-orbit coupling.When the cobalt(II) ion is axially distorted, the order of the six Kramers doublets changes; however, the second-lowest doublet is always more than 100 cm -1 higher than the lowest doublet [2].Since the local spin-orbit coupling is much larger than the exchange interactions, the exchange interaction is effective only between the lowest doublets of cobalt(II) ions.Therefore, it is appropriate to assume that the exchange interaction causes no effect to the higher doublets [2,5].
Here we want to obtain a magnetic susceptibility equation for an isosceles tricobalt(II) core, as shown in If we assume isotropic exchange interactions between local true spins (S A1 = S A2 = S B = 3/2), the exchange part of the Hamiltonian can be written as Since the local 4 T 1 ground term is split by spin-orbit coupling larger than the exchange interactions, the local effective spins (s A1 = s A2 = s B = 1/2) for the local lowest Kramers doublets are introduced [2,8].
(U = A1, A2, and B) (5) Assuming axial symmetry for local effective spins (β U = α U and s U,y = s U,x ), the exchange Hamiltonian can be rewritten as where and The coefficients α U and γ U (U = A1, A2, and B) can be expressed by the local parameters κ U , λ U , and Δ U [2,8], where κ U is the orbital reduction factor, λ U is the spin-orbit coupling parameter, and Δ U is the axial splitting parameter.The zero-field splitting parameter (D quin ) within an effective quintet state, generated from the three local effective spins (1/2), can be expressed as D quin = D eff /3 + D' eff /6 [16].
At this stage, the susceptibility equation can be expressed as follows: where θ is the Weiss constant to describe the intermolecular exchange interactions.This interaction is actually temperature-dependent, but it is approximated as a constant in this study.The zero-field energies and first-and second-order Zeeman coefficients for each cobalt(II) ion A z x n , and , ( ) x n (n = ±1 -±6) can be expressed using equations reported previously [5,6].
e e e g g g

Structural Features of 1 and 2
The crystal structures of 1 and 2 have been reported previously [15]; thus, only the structural features are briefly mentioned here.Both 1 and 2 have tricobalt(II) structures as shown in Figure 3, and the structures are very similar.Both ligands L1 -and L2 -have an N 2 O coordination site and an NO site (see Figure 1).The N 2 O site of a ligand incorporates a cobalt(II) ion (Co A ), and another cobalt(II) ion (Co B ) is incorporated by two NO sites of the two ligands, forming a trinuclear structure in the shape of an isosceles triangle.Co A and Co B are bridged by a phenolic oxygen atom of the ligand and an oxygen atom from an external acetate ion.Two Co A ions (Co A1 and Co A2 ) are bridged by two pairs of syn-anti bidentate oxygen atoms of two acetate ions.The coordination geometry for each cobalt(II) ion is distorted octahedral.

Magnetic Data Analysis
Magnetic data for complexes 1 and 2, as well as the preparations and crystal structures, were reported earlier [15], but no theoretical analysis of the data was made.The temperature dependencies of χ M and µ eff for the Co 3 unit for 1 and 2 are shown in Figures 4 and 5, respectively.The µ eff values for the Co 3 unit for 1 and 2 at room temperature are 8.36 and 8.45 µ B , respectively.These values are larger than the spin-only value of the high-spin cobalt(II) ion (6.71 µ B ; µ SO = [3{4S(S+1)}] 1/2 ; S = 3/2) but close to the value expected when the spin momentum and orbital momentum exist independently [9.00 µ B ; µ LS = [3{L(L+1)+ 4S(S+1)}] 1/2 ; L = 3, S = 3/2].This indicates a contribution of the orbital angular momentum typical of the local 4 T 1 ground term.Moreover, the characteristic slopes of µ eff curves are typical for the result of spin-orbit coupling.Therefore, the data were analyzed using the equation in Section 3.1, considering the local axial distortions, the local spin-orbit couplings, the anisotropic exchange in-teractions, and the intermolecular exchange interactions.The obtained parameters are summarized in Table 1.
The orbital reduction factor κ corresponds to the delocalization of unpaired electrons from metal ions to ligand, but it also contains the admixture of the upper 4 T 1 ( 4 P) state into the 4 T 1 ( 4 F) ground state.The κ value is known to be ~0.93 for the free cobalt(II) ion [4,17], and the obtained κ A and κ B values for both complexes are close to the free ion value.Comparing the axial splitting parameters Δ A and Δ B , Δ B is larger than Δ A for both complexes.All the Δ values for both complexes are normal for octahedral high-spin cobalt(II) complexes (~ 200 -~ 800 cm -1 ) [3].The spin-orbit coupling parameter λ for the free cobalt(II) ion is theoretically expected to be ~ -172 cm -1 [18], but is generally smaller in the complexes.For complex 1, the λ A value is normal (~70% of the free ion value), whereas the λ B value is slightly smaller than the normal value.This occurs presumably because the assumed symmetry is less suitable for Co B .That is, the local distortion axes are assumed to be parallel in this study, and this assumption may not be adequate.A similar tendency is also seen for complex 2.
Figures 4 and 5.This indicates the existence of ferromagnetic interaction in both complexes.Considering both the intramolecular and intermolecular interactions, the data were successfully analyzed.The result indicated that the exchange interaction between Co A (Co A1 and Co A2 ) and Co B is practically negligible (J = ~ 0), but the interaction between Co A1 and Co A2 is ferromagnetic (J' > 0).As mentioned above, Co A and Co B are bridged by a phenolic oxygen atom and an oxygen atom of an acetate  ion, whereas Co A1 and Co A2 are bridged by two pairs of syn-anti bidentate oxygen atoms of two acetate ions.Since an exchange interaction parameter is described as the sum of the ferromagnetic and antiferromagnetoic components and a phenolate bridge generally contributes to an antiferromagnetic interaction, the result (J' > J) is consistent with this idea.Judging from the obtained parameters, we can explain the temperature dependencies as follows.The magnetic moments decrease with decreasing the temperature, and the decrease above 50 K is mainly due to the thermal population on the Kramers doublets generated from the local 4 T 1 ground term by the spin-orbit coupling.Below 50 K, the ferromagnetic interaction between Co A1 and Co A2 appears, and the drop below 10 K is due to the intermolecular antiferromagnetic interaction.

CONCLUSIONS
In this study, a new magnetic susceptibility equation was developed for trinuclear octahedral high-spin cobalt(II) complexes in the shape of an isosceles triangle considering the local axial distortion, the spin-orbit coupling, the exchange interactions, and the intermolecular exchange interactions.Using the equation, the magnetic data for two tricobalt(II) complexes 1 and 2 were successfully analyzed.For both complexes, ferromagnetic interaction between Co A1 and Co A2 ions and practically negligible interaction between Co A and Co B ions were observed.

ACKNOWLEDGMENTS
This work was supported by the Saneyoshi Scholarship Foundation.

Figure 2 .
Full Hamiltonian is written as H = H LF + H LS + H ZE + H ex , where H LF , H LS , H ZE , and H ex are the ligand field term, LS coupling term, Zeeman term, and the exchange term of the Hamiltonian, respectively.The Hamiltonians H LF , H LS , and H ZE are as follows: (see Equations (1

Table 1 .
Magnetic parameters and discrepancy factors for complexes 1 and 2.