Microscopic spin state

Abstract This review reports on the study of the interplay between magnetic coupling and spin transition in 2,2 -bipyrimidine (bpym)-bridged iron(II) dinuclear compounds. The coexistence of both phenomena has been observed in [Fe(bpym)(NCS)2]2(bpym), [Fe(bpym)(NCSe)2]2(bpym) and [Fe(bt)(NCS)2]2(bpym) (bpym = 2,2 -bipyrimidine, bt = 2,2 -bithiazoline) by the action of external physical perturbations such as heat, pressure or electromagnetic radiation. The competition between magnetic exchange and spin crossover has been studied in [Fe(bpym)(NCS)2]2(bpym) at 0.63 GPa. LIESST experiments carried out on [Fe(bpym)(NCSe)2]2(bpym) and [Fe(bt)(NCS)2]2(bpym) at 4.2 K have shown that it is possible to generate dinuclear molecules with different spin states in this class of compounds. A special feature of the spin crossover process in the dinuclear compounds studied so far is the plateau in the spin transition curve. Up to now, it has not been possible to explore with a microscopic physical method the nature of the species... 

For the ensemble of microscopic magnetic moments /r that correspond to the eigenvalues En of their respective spin states, we thus obtain... 

Given a molecule that possesses C2p symmetry, let us try to figure out how to calculate ( Ai ffsol Bi) from wave functions with Ms = 1. The coupling of an Ai and a B state requires a spatial angular momentum operator of B2 symmetry. From Table 11, we read that this is just the x component of It. A direct computation of (3A2, Ms = 1 t x spin-orbit Hamiltonian with x symmetry and So correspondingly for the zero-component of the spin tensor. This is the only nonzero matrix element for the given wave functions. 

Only spatially degenerate states exhibit a first-order zero-field splitting. This condition restricts the phenomenon to atoms, diatomics, and highly symmetric polyatomic molecules. For a comparison with experiment, computed matrix elements of one or the other microscopic spin-orbit Hamiltonian have to be equated with those of a phenomenological operator. One has to be aware of the fact, however, that experimentally determined parameters are effective ones and may contain second-order contributions. Second-order SOC may be large, particularly in heavy element compounds. As discussed in the next section, it is not always distinguishable from first-order effects. 

The energies of the magnetic interaction of orbital and spin angular momenta are —A and +A/2 in the atomic ion, while they are —A/2, 0, and +A/2 in the molecular ion. Here, A is a spin-orbit coupling constant in the ground state of atomic ion. An additional off-diagonal matrix element arises in the molecular ion from the microscopic spin-orbit operator... 

Several transition metal complexes, especially those with d4 to d1 metal ion configuration, can exist either in the low-spin (LS) or high-spin (HS) states. Exceptionally, they can exist also in an intermediate-spin (IS) state. When the high-spin state is the ground one, this is not altered by temperature variation. However, when the ground state is the low-spin, a spin transition to the high-spin state can occur. Whether the spin transition is observable within the accessible temperature interval depends upon the individual substance and its microscopic properties (electronic structure, vibration spectrum). 

Redfield theory [18-20] is a microscopic semi-classical theory of spin relaxation in which the spin system is treated quantum mechanically whilst the coupling of the spins with the lattice is treated classically. In this classical approximation, the spin states are in equilibrium and a correction factor is needed to ensure the spin ensemble relaxes to the correct limits. This problem can be overcome by treating the lattice quantum mechanically, however, the details and nature of the computational details are beyond the scope of this thesis. In this section a brief introduction to Redfield theory for spin relaxation is provided, a more detailed analysis of the theory can be found elsewhere [21]. 

In the PPF, the first factor Pi describes the statistical average of non-correlated spin fiip events over entire lattice points, and the second factor P2 is the conventional thermal activation factor. Hence, the product of P and P2 corresponds to the Boltzmann factor in the free energy and gives the probability that on<= of the paths specified by a set of path variables occurs. The third factor P3 characterizes the PPM. One may see the similarity with the configurational entropy term of the CVM (see eq.(5)), which gives the multiplicity, i.e. the number of equivalent states. In a similar sense, P can be viewed as the number of equivalent paths, i.e. the degrees of freedom of the microscopic evolution from one state to another. As was pointed out in the Introduction section, mathematical representation of P3 depends on the mechanism of elementary kinetics. It is noted that eqs.(8)-(10) are valid only for a spin kinetics. 

Previous attempts to distinguish between the different kinds of pairs by applying microscopic methods such as conventional Mossbauer spectroscopy were unsatisfactory, since the Mossbauer spectra corresponding to the HS state of the iron(II) atoms in the [HS-LS] and [HS-HS] spin pairs are indistinguishable. Zero-field Mossbauer spectroscopy applied to the bpym-bridged iron(II) dinuclear compounds only gives access to the total fraction... 

Deep state experiments measure carrier capture or emission rates, processes that are not sensitive to the microscopic structure (such as chemical composition, symmetry, or spin) of the defect. Therefore, the various techniques for analysis of deep states can at best only show a correlation with a particular impurity when used in conjunction with doping experiments. A definitive, unambiguous assignment is impossible without the aid of other experiments, such as high-resolution absorption or luminescence spectroscopy, or electron paramagnetic resonance (EPR). Unfortunately, these techniques are usually inapplicable to most deep levels. However, when absorption or luminescence lines are detectable and sharp, the symmetry of a defect can be deduced from Zeeman or stress experiments (see, for example, Ozeki et al. 1979b). In certain cases the energy of a transition is sensitive to the isotopic mass of an impurity, and use of isotopically enriched dopants can yield a positive chemical identification of a level. 

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