Introduction

The magnetism discussed in this article is paramagnetism. Paramagnetism occurs when there are one or more unpaired electrons in a compound. (The opposite, when all electrons are paired, is called diamagnetism). Di- and para-magnetism are often affected by the presence of coordination complexes, which the transition metals (d-block) readily form.

Singular electrons have a spin, denoted by the quantum number m_s as +(1/2) or –(1/2). This spin is negated when the electron is paired with another, but creates a slight magnetic field when the electron is unpaired. The more unpaired electrons, the more likely paramagnetic a material is. The electron configuration of the transition metals (d-block) changes when in a compound. This is due to the repulsive forces between electrons in the ligands and electrons in the compound. Depending on the strength of the ligand, the compound may become paramagnetic or diamagnetic.

Ferromagnetism

Some paramagnetic compounds are capable of becoming ferromagnetic. This means that the compound shows permanent magnetic properties rather than exhibiting them only in the presence of a magnetic field. In a ferromagnetic element, electrons of atoms are grouped into domains, where each domain has the same charge. In the presence of a magnetic field, these domains line up so that charges are parallel throughout the entire compound. Whether a compound can be ferromagnetic or not depends on how many unpaired electrons it has and on its atomic size.

• Small atoms pair up too easily and their charges cancel.
• Large atoms are difficult to keep together, their charge interaction is too weak.

Therefore, only the right sized atoms will work together to group themselves into domains. Elements with the right size include: Fe, Co, Ni. That means that Fe, Co and Ni are paramagnetic with the capability of permanent magnetism; they are also ferromagnetic.

Ligand Field Theory Background

For a full explanation, please see the article on Ligand Field Theory. An element can have up to 10 d electrons in 5 d-orbitals, d_xy, d_xz, d_yz, d_z², and d_x²-y². During the formation of a complex, the degeneracy (equal energy) of these orbitals is broken and the orbitals are at different energy levels.

(Assuming a 6-ligand compound)

In an octahedral complex, the ligands approach along the x, y, and z axes, so the repulsion is strongest in the orbitals along these axes (dz² and dx²-y²). As a result, the dz² and d_x²-y² orbitals are higher in energy than the dxy, dxz, and dyz orbitals. In a tetrahedral complex, the splitting is opposite, with the dxy, dxz, and dyz orbitals higher in energy to avoid the ligands approaching between the axes. The splitting in a square planar complex has four levels (lowest to highest): d_yz and d_xz, d_xy, dz², dx²-y².

Depending on the strength of the ligand, the splitting energy between the different d-orbitals may be large or small. Ligands producing a smaller splitting energy are called ‘weak field’ ligands, and those with a larger splitting energy are called ‘strong field’ ligands.

Filling of d-orbitals in a complex

Hunds' Rule states that electrons will fill all available orbitals with single electrons before pairing up, while maintaining parallel spins (paired electrons have opposing spins). For a set of degenerated d-orbitals (not in a complex), electrons fill all orbitals before pairing to conserve the pairing energy, otherwise needed. With the addition of ligands, the situation becomes more complicated. The splitting energy between the d-orbitals means that additional energy is required to place single electrons into the higher-energy orbitals. Once the lower-energy orbitals have been half-filled (one electron per orbital), an electron can either be placed in a higher-energy orbital (preserving Hund’s rule) or pair up with an electron in a lower-energy orbital (when the splitting energy is greater than the pairing energy). The strength of the ligands determine which option is chosen.

With a strong-field ligand, the splitting energy is very large and low-spin complexes are usually formed. With a weak-field ligand, the electrons can easily enter the higher-energy orbitals before pairing (high-spin).

How does this relate to magnetism?

Low-spin complexes contain more paired electrons since the splitting energy is larger than the pairing energy. These complexes, such as [Fe(CN)₆]^3-, are more often diamagnetic or weakly paramagnetic. High-spin complexes usually contain more unpaired electrons since the pairing energy is larger than the splitting energy. With more unpaired electrons, high-spin complexes  are often paramagnetic.

The unpaired electrons in paramagnetic compounds create tiny magnetic fields, similar to the domains in ferromagnetic materials (see above or the related article). The higher the number of unpaired electrons (often the higher-spin the complex), the stronger the paramagnetism of a coordination complex. We can predict paramagnetiism and its relative strength by determining whether a compound is a weak field ligand or a strong field ligand. Once we have determined whether a compound has a weak or a strong ligand, we can predict its magnetic properties:

How can we measure magnetism in a compound?

The Gouy balance is used to measure paramagnetism by suspending the complex in question against an equivalent weight with access to a magnetic field. We first weigh the complex without a magnetic field in its presence, then, we weigh it again in the presence of a magnetic field. If the compound is paramagnetic, it will be pulled visibly towards the electromagnet, which is the distance proportional to the magnitude of the compound's paramagnetism. If the compound, however, is diamagnetic, it will not be pulled towards the electromagnet, instead, it might even slightly be repelled by it. This will be proven by the decreased weight or the no change in weight. The change in weight directly corresponds to the amount of unpaired electrons in the compound.

How Magnetic Properties relate to the "Real World"

Ferromagnetism, the permanent magnetism associated with nickel, cobalt, and iron, appears throughout everyday life, from Aristotle's discussion in 625 BC, through the use of the compass in 1187, up to the modern-day refrigerator. Einstein declared that electricity and magnetism are inextricably linked in his theory of "special relativity." He also showed examples that a magnet can be disturbed by electricity.

Paramagnetism and diamagnetism explain and describe some of the properties of certain elements and complexes, which we work with on a regular basis. In the early days of complex-compound chemistry, paramagnetism was often used to help identify the shape of complexes. A technique known as electron paramagnetic resonance has been used in systems with certain para- and dia- magnetic properties to distinguish between bond types and identify the probable location of an individual element within a compound.

References

1. Petrucci [ chapter 23. p. 968 and chapter 24 section 24-5].
2. Johnson, Ronald C. and Basolo, Fred, "Coordination Chemistry: The Chemistry of Metal Complexes, W. A. Benjamin, Inc. pp40-44. 1964
3. Jones, Mark M. Elementary Coordination Chemistry Prentice-Hall, Inc. 1964

Contributors

• Neele Holzenkaempfer, Jesse Gipe

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