Magnetic Properties from Molecules to Solids Materials may be classified by their response to externally applied magnetic fields as diamagnetic paramagnetic ferromagnetic antiferromagnetic ferrimagnetic

Magnetic Properties Diamagnetic: unaffected by a magnetic field no unpaired electrons Paramagnetic: influenced by a magnetic field unpaired electrons Transition metals and their compounds are often paramagnetic Have unpaired d-electrons Eg. Ti2+ Mn2+

diamagnetism : systems contain no unpaired electrons

Magnetic properties Magnetic susceptibility (μ) and the spin-only formula. Materials that are diamagnetic are repelled by a magnetic field, whereas paramagnetic substances are attracted into a magnetic field, i.e. show magnetic susceptibility. The spinning of unpaired electrons in paramagnetic complexes of d-block metal ions creates a magnetic field, and these spinning electrons are in effect small magnets. The magnetic susceptibility, μ, due to the spinning of the electrons is given by the spin-only formula: μ(spin-only) = n(n + 2) Where n = number of unpaired electrons.

Magnetization and Magnetic Susceptibility χ = ∂ M / ∂ H where M : the molar magnetization, a vector, H : the magnetic field strength , an axial vector, χ: molar magnetic susceptibility, a second rank tensor. When H is weak enough, χis independent of H, one can write M = χ H

χ

The measurerement of magnetic susceptibility A Gouy balance, which is used to measure the magnetic susceptibi lities of substances

Electronic configurations of dn complexes from paramagnetism and diamagnetism Magnet on: Paramagnetic Magnet off Magnet on: diamagnetic

Sample problem The magnetic moment of an octahedral Co(II) complex is 4.0 µB. What is its electron configuration? Answer µ = [N(N+2)]1/2 µB 4.0 = [N(N+2)]1/2 N 3 A Co(II) complex is d7. The two possible configu Rations are t52ge2g (high spin) with three unpaired electron Or t62ge1g (low-spin) with one unpaired electron.The spin Only magnetic moment are 3.87 µB and 1.73 µB,repectively (see Tab.).Therefore the only consistent assigment is the High-spin configuration t52ge2g.

Magnetic Measurement Experimental distinctiom between high-spin and low-spin complexes is based on the dertermination of their megnetic properties.Complexes are classified as diamagnetic if they tend to move out magnetic field and paramagnetic if they tend to move into magnetic field.The extent od paramagnetism of a complexes is commonly reported in terms of the magnetic dipol moment.the higher magnetic moment the greater the paramagnetism of the sample. The spin-only paramagnetism which is characteristic of many d-metal complexes. µ = 2[S(S+1)]1/2 µB S: Total spin quantum number; each unpair electron has a spin quantum number of ½, it allows that S= 1/2N, where N is the number of unpaired electrons;therefore µ = [N(N+1)]1/2 µB ; µB is known as Bohr magneton its value is 9.274x10-24 JT-1

t42ge2g ( N= 4, µ= 4.90) configuration and a low-spin t62g (N=0, µ=0) A measurement of the magnetic moment of a d-block complex can be usually be interpreted in terms of the number of unpaired electrons it contains, and hence the measurement can be used to distinguish bet- ween high-spin and low-spin complex. For example, Magnetic measu Rements on d6 complex permit us to distinguish between a high-spin t42ge2g ( N= 4, µ= 4.90) configuration and a low-spin t62g (N=0, µ=0) configuration. ------------------------------------------------------------------ İon N S µ / µB ------------------------- Calc. Exp. ------------------------------------------------------------------- Ti3+ 1 ½ 1.73 1.7-1.8 V3+ 2 1 2.83 2.7-2.9 Cr3+ 3 3/2 3.87 3.8 Mn3+ 4 2 4.90 4.8-4.9 Fe3+ 5 5/2 5.92 5.9  

Magnetic properties The spin-only formula applies reasonably well to metal ions from the first row of transition metals: (units = μB,, Bohr-magnetons) Metal ion dn configuration μeff(spin only) μeff (observed) Ca2+, Sc3+ d0 0 0 Ti3+ d1 1.73 1.7-1.8 V3+ d2 2.83 2.8-3.1 V2+, Cr3+ d3 3.87 3.7-3.9 Cr2+, Mn3+ d4 4.90 4.8-4.9 Mn2+, Fe3+ d5 5.92 5.7-6.0 Fe2+, Co3+ d6 4.90 5.0-5.6 Co2+ d7 3.87 4.3-5.2 Ni2+ d8 2.83 2.9-3.9 Cu2+ d9 1.73 1.9-2.1 Zn2+, Ga3+ d10 0 0

Example: What is the magnetic susceptibility of [CoF6]3-, assuming that the spin-only formula will apply: [CoF6]3- is high spin Co(III). (you should know this). High-spin Co(III) is d6 with four unpaired electrons, so n = 4. We have μeff = n(n + 2) = 4.90 μB energy eg t2g high spin d6 Co(III)

Spin and Orbital contributions to Magnetic susceptibility For the first-row d-block metal ions the main contribution to magnetic susceptibility is from electron spin. However, there is also an orbital contribution from the motion of unpaired electrons from one d-orbital to another. This motion constitutes an electric current, and so creates a magnetic field (see next slide). The extent to which the orbital contribution adds to the overall magnetic moment is controlled by the spin-orbit coupling constant, λ. The overall value of μeff is related to μ(spin-only) by: μeff = μ(spin-only)(1 - αλ/Δoct)

Diagrammatic representation of spin and orbital contributions to μeff d-orbitals spinning electrons spin contribution – electrons are orbital contribution - electrons spinning creating an electric move from one orbital to current and hence a magnetic another creating a current and field hence a magnetic field

Ferromagnetism: In a normal paramagnetic material, the atoms containing the unpaired electrons are magnetically dilute, and so the unpaired electrons in one atom are not aligned with those in other atoms. However, in ferromagnetic materials, such as metallic iron, or iron oxides such as magnetite (Fe3O4), where the paramagnetic iron atoms are very close together, they can create an internal magnetic field strong enough that all the centers remain aligned: unpaired electrons aligned in their own common magnetic field unpaired electrons oriented randomly unpaired electrons paramagnetic, magnetically dilute in e.g. [Fe(H2O)6]Cl2. b) ferromagnetic, as in metallic Fe or some Fe oxides. separated by diamagnetic atoms Fe atoms a) b)

electron spins in opposite directions in alternate metal atoms Antiferromagnetism: Here the spins on the unpaired electrons become aligned in opposite directions so that the μeff approaches zero, in contrast to ferromagnetism, where μeff becomes very large. An example of anti- ferromagnetism is found in MnO. electron spins in opposite directions in alternate metal atoms antiferromagnetism

Ferromagnetism and Antiferromagnetism Curie-Weiss Law χ = C / (T-θ) θ : Weiss constant, have the units of temperature θ > 0, parallel (ferromagnetic) interactions θ < 0, antiparallel (antiferromagnetic) interactions

Ferromagnet

Distribution of high- and low-spin complexes of the d-block metal ions: Co(III) is big exception – all low-spin except for [CoF6]3- 1st row tend to be high-spin except for CN- complexes 2nd and 3rd row are all low-spin except for PdF2 and [PdF6]4-