Criticism of the use of the Ising model to describe linear chains of antiferromagnetically coupled copper(II) ions

Abstract

Major disadvantages of the use of the anisotropic Ising model to describe strong antiferromagnetic coupling in infinite linear chains of copper(I1) ions are discussed with particular reference to cupric oxalate. EXAMINATION of the several recent reviews on antiferromagnetically coupled CuII ions reveals that the Ising model has been fairly generally accepted as the most convenient basis for the interpretation of infinite linearchain systems.1 This model involves the simplification of the effective spin-exchange Hamiltonian [equation (l)] by setting y = 0.2This practice considerably simplifies the sums-indeed it is the only way that analytical equations for the magnetic susceptibility have been obtained3-but it contrasts dramatically with the methods used for finite polynuclear systems (the Heisenberg model) in which y is set equal to unity. Few workers appear to have appreciated what a Machine calculations on chains with up to 11 members have been carried out by Bonner and Fisher4 using different values of in equation (1). This is a much neglected paper, for it shows that the predictions of the king and Heisenberg models do not converge significantly as chain-length increases and, secondly, i t provides empirical data for the approximate description of infinite linear chains with the preferred model of Heisenberg. We have fitted these data [modified to be consistent with equation ( l ) ] to the polynomial expression given in equation (2). The agreement is better than 1% over the whole range studied by these workers and the equation therefore provides a convenient basis for the interpretation of appropriate experimental data. (N.b. this expression cannot be used for ferromagnetic coupling.)where P = RT/ I J I TABLE. Magnetic data for copper(I1) dicarboxylatesa [Equations Ising [Equation Dimer model Heisenberg model (3) and (4) ] model (3)] CompoundRef.-J (cm-1) 10% -J (cm-l) 10%-J (cm-l)106u -J (cm-l) lO6o Cupric oxalate,0.3H20

Is Solid Copper Oxalate a Spin Chain or a Mixture of Entangled Spin Pairs?

“…The thermodynamic properties of this model are well known and have been used to explain experimental observables of real materials, containing, for instance, copper, , vanadium, and magnesium magnetic centers. We note that earlier studies often employed the Ising model, which can be described as an approximation to the Heisenberg model in which only the S z components of the spin operators S are retained; however, such a treatment yields an incorrect state degeneracy pattern in the dimers and noticeably different results for magnetic susceptibility of extended systems …”

“…These contradictory explanations prompted a question of which model should be used to interpret magnetic susceptibility . Jotham compared the results of fitting magnetic susceptibilities of several copper salts (including copper oxalate) to the Ising, Heisenberg, and dimer models and explained the limitations of the Ising model, arguing in favor of the dimer model for some salts while emphasizing that for copper oxalates the infinite Heisenberg spin-chain model provides the best description. Later, EPR and EXAFS experiments , also proposed the infinite quantum Heisenberg model.…”

“…We note that earlier studies often employed the Ising model, which can be described as an approximation to the Heisenberg model in which only the S z components of the spin operators S are retained; however, such a treatment yields an incorrect state degeneracy pattern in the dimers and noticeably different results for magnetic susceptibility of extended systems. 16 An oxalate ligand is a common building block in transitionmetal compounds. Despite its simplicity, the magnetic structure of copper oxalate has not been settled.…”

Anisotropic exchange and temperature-dependent electron paramagnetic resonance line width in one-dimensional copper(II) complexes. 2. Magnetic properties of copper(II) oxalate-1/3-water

“…On the other hand, the exchange parameters Jo/k obtained are very nearly the same for all of the data and are in the range 180-195 K. This amounts to a relatively minor dependence of Jo on the particular data set. A representative73 set of susceptibility data is shown in Figure 1, along with the best fit to (23). The calculated curve in Figure 1 was generated with \Jo/k\ = 195 K and g = 2.13.…”

Combining Three Different Functional Groups in One Linker: A Variety of Features of Copper(II) Aminocarboxyphosphonate

“…Above 10 K these results practically fit in with the calculated values for the Ising model, but for obvious reasons the HTSE model is inadequate at lower temperatures. Individual character of each interaction is the same as in the Ising model, but the values of the exchange integrals are smaller, which is normally seen when comparing the two types of magnetic interactions. , The Heisenberg exchange model can also be used, assuming the opposite signs of the exchange integrals ( J 1 , J 3 < 0, J 2 > 0), but it is unlikely in light of the magneto­structural considerations (see below).…”