Paramagnetism

In diamagnetism substances are repelled through a magnetic field: this property is related with all closed electron shells. Paramagnetic substances are involved into a magnetic field, the force being associated to the magnetic susceptibility. Paramagnetism generally occurs from the spin of unpaired electrons. The Curie law for the susceptibility per mole (χ_m) is

In which N_A is Avogadro's number, μ₀ of free space the magnetic permeability, μ_eff the efficient magnetic moment of the paramagnetic species, k is Boltzmann's remain unchanged and T the temperature in kelvin. The opposite temperature dependence arises since thermal agitation works against the alignment of moments in an applied field. For several d-block compounds the spin-only formula is a comparatively good approximation to the effective magnetic moment:

In which S is the spin quantum number, equivalent to half the number of unpaired electrons n, and μ_B the Bohr magneton, equivalent to about 9.274×10^-24 J T^-1. The simplest application of magnetic measurements is thus to establish the number of unpaired electrons, and thus to differentiate between high- and low-spin states. For instance, most Co³⁺ complexes contain μ_eff=0 as supposed for low-spin d⁶; though, [CoF₆]^3- has μeff approximately 5μ_B, subsequent to four unpaired electrons and a high-spin state.

Magnetic measurements are occasionally used to provide information about metal-metal bonding. For instance, dimeric Cr²⁺ complexes like [Cr₂(CH₃CO₂)₄] contain μ_eff=0, suggesting that all four d electrons of Cr²⁺ are paired to create a quadruple bond. Though, there are several other issues that can complicate magnetic properties. The oxygen-bridged complex [(RuCl₅)₂O]^4- also has μ_eff=0. There is no metal-metal bond and the electrons are paired like a consequence of the Ru-O bonding in this case.