How Magnetochemistry Can Help Us Understand and Design Magnetic Materials
What is Magnetochemistry?
Magnetochemistry is the branch of chemistry that studies the magnetic properties of matter and the interactions between magnetic fields and chemical substances. It is a multidisciplinary field that combines aspects of physics, chemistry, materials science, and biology. Magnetochemistry has many applications in various fields, such as catalysis, energy storage, medicine, nanotechnology, and information technology.
Magnetochemistry (Oxford Chemistry Primers)
In this article, we will introduce the basic concepts and principles of magnetochemistry, such as magnetic moments, susceptibility, exchange interactions, and anisotropy. We will also review some of the experimental techniques used to measure and characterize the magnetic properties of matter, such as magnetometry, EPR spectroscopy, and MCD spectroscopy. Finally, we will explore some of the most interesting and important classes of magnetic materials in chemistry, such as transition metal complexes, lanthanide and actinide complexes, and molecular materials.
Magnetic Properties of Matter
Matter can be classified into different types according to its response to an external magnetic field. The most common types are paramagnetic, diamagnetic, ferromagnetic, and antiferromagnetic.
Magnetic moments and susceptibility
A magnetic moment is a vector quantity that measures the strength and direction of a magnet or a magnetic dipole. It can be induced by an electric current or by the orbital or spin motion of electrons in atoms or molecules. The SI unit of magnetic moment is the ampere-meter squared (Am).
A susceptibility is a scalar quantity that measures how easily a material can be magnetized by an external magnetic field. It is proportional to the ratio of the induced magnetization to the applied field. The SI unit of susceptibility is the meter per ampere (m/A).
Paramagnetic materials have positive susceptibility and weak magnetic moments that align with the external field. They are attracted by magnets. Examples of paramagnetic materials are oxygen gas, iron(III) oxide, and copper(II) sulfate.
Diamagnetic materials have negative susceptibility and no permanent magnetic moments. They are slightly repelled by magnets. Examples of diamagnetic materials are water, carbon dioxide, and bismuth.
Paramagnetism and diamagnetism
Paramagnetism and diamagnetism are intrinsic properties of matter that depend on the electronic configuration of atoms or molecules. Paramagnetism arises from unpaired electrons that have nonzero spin angular momentum. Diamagnetism arises from paired electrons that have zero net spin angular momentum.
The magnitude of the paramagnetic moment depends on the number and type of unpaired electrons, as well as the temperature. The magnitude of the diamagnetic moment depends on the orbital angular momentum and the shape of the electron cloud. The direction of both moments depends on the external field.
Paramagnetic and diamagnetic effects are usually small and can be masked by other types of magnetism, such as ferromagnetism and antiferromagnetism.
Ferromagnetism and antiferromagnetism
Ferromagnetism and antiferromagnetism are collective properties of matter that depend on the interactions between neighboring magnetic moments. Ferromagnetism arises from parallel alignment of moments that results in a net magnetization. Antiferromagnetism arises from antiparallel alignment of moments that results in zero net magnetization.
The origin of ferromagnetic and antiferromagnetic interactions is the exchange energy, which is related to the Pauli exclusion principle and the Coulomb repulsion between electrons. The exchange energy can be positive or negative, depending on the overlap and symmetry of the electron orbitals.
Ferromagnetic and antiferromagnetic materials exhibit spontaneous magnetization below a critical temperature called the Curie temperature or the Néel temperature, respectively. Above this temperature, thermal fluctuations destroy the long-range order and the materials become paramagnetic.
Examples of ferromagnetic materials are iron, nickel, cobalt, and their alloys. Examples of antiferromagnetic materials are manganese oxide, iron(II) oxide, and chromium.
Magnetic Interactions and Exchange
Magnetic interactions and exchange are the key concepts that explain the origin and behavior of magnetic materials. They describe how magnetic moments interact with each other and with external fields, and how they affect the electronic structure and properties of matter.
Heisenberg and Ising models
The Heisenberg model and the Ising model are two simple but powerful models that describe the magnetic interactions between spins in a lattice. They are based on the Hamiltonian formalism of quantum mechanics, which relates the energy of a system to its observable quantities.
The Heisenberg model considers spins as vectors that can point in any direction in space. The energy of the system depends on the dot product of neighboring spins, as well as an external field. The Heisenberg model can describe both ferromagnetic and antiferromagnetic interactions, depending on the sign of the coupling constant.
The Ising model considers spins as scalars that can only point up or down along a fixed axis. The energy of the system depends on the product of neighboring spins, as well as an external field. The Ising model can also describe both ferromagnetic and antiferromagnetic interactions, depending on the sign of the coupling constant.
The Heisenberg model and the Ising model are useful for studying phase transitions, critical phenomena, and statistical mechanics of magnetic systems.
Superexchange and double exchange
Superexchange and double exchange are two mechanisms that explain how magnetic interactions can occur between ions that are separated by nonmagnetic atoms or molecules. They involve virtual electron transfer processes that mediate the exchange energy between distant spins.
Superexchange occurs when two ions with opposite spins share a common ligand or bridge atom that has a filled or partially filled orbital. The electron transfer is unfavorable due to Coulomb repulsion, but it lowers the energy by increasing the overlap between orbitals. Superexchange usually leads to antiferromagnetic coupling, but it can also lead to ferromagnetic coupling in some cases.
Double exchange occurs when two ions with parallel spins share a common ligand or bridge atom that has an empty or partially empty orbital. The electron transfer is favorable due to Coulomb attraction, but it raises the energy by decreasing the overlap between orbitals. Double exchange usually leads to ferromagnetic coupling, but it can also lead to antiferromagnetic coupling in some cases.
Superexchange and double exchange are important for understanding the magnetic properties of transition metal oxides, such as perovskites and manganites.
Spin-orbit coupling and anisotropy
Spin-orbit coupling and anisotropy are two effects that result from the interaction between the spin angular momentum and the orbital angular momentum of electrons in atoms or molecules. They cause deviations from the ideal behavior predicted by simple models, such as Heisenberg or Ising.
Spin-orbit coupling is a relativistic effect that arises from the motion of electrons in an electric field generated by the nucleus or other electrons. It causes a mixing of different spin states and orbital states, resulting in a splitting of energy levels and a modification of magnetic moments.
of the magnetic moments and susceptibility on the direction of the external field or the crystal axis. Anisotropy arises from the symmetry breaking of the electron orbitals due to the crystal field or the spin-orbit coupling.
Spin-orbit coupling and anisotropy are important for understanding the magnetic properties of lanthanide and actinide complexes, as well as single-molecule magnets and molecular spintronics.
Experimental Techniques in Magnetochemistry
Experimental techniques in magnetochemistry are methods that allow measuring and characterizing the magnetic properties of matter. They involve applying a magnetic field to a sample and detecting its response in terms of magnetization, absorption, emission, or polarization.
Magnetometry and susceptibility measurements
Magnetometry and susceptibility measurements are techniques that measure the magnetization or the susceptibility of a sample as a function of the applied field, temperature, or frequency. They can provide information about the type, strength, and temperature dependence of the magnetic interactions and phases in a material.
There are different types of magnetometers and susceptometers, such as vibrating sample magnetometer (VSM), superconducting quantum interference device (SQUID), Faraday balance, Gouy balance, Evans balance, and AC susceptometer. They differ in their sensitivity, resolution, range, and operation mode.
Electron paramagnetic resonance (EPR) spectroscopy
Electron paramagnetic resonance (EPR) spectroscopy is a technique that measures the absorption of electromagnetic radiation by paramagnetic samples in a magnetic field. It can provide information about the electronic structure, spin state, environment, and dynamics of paramagnetic centers in a material.
EPR spectroscopy is based on the resonance condition that occurs when the energy difference between two spin levels matches the energy of the applied radiation. The frequency of the radiation is usually in the microwave range. The intensity, shape, and position of the EPR signal depend on various factors, such as g-factor, hyperfine coupling, exchange coupling, spin-orbit coupling, and anisotropy.
Magnetic circular dichroism (MCD) spectroscopy
Magnetic circular dichroism (MCD) spectroscopy is a technique that measures the difference in absorption of left-handed and right-handed circularly polarized light by a sample in a magnetic field. It can provide information about the electronic transitions, orbital angular momentum, spin-orbit coupling, and magnetic anisotropy of a material.
MCD spectroscopy is based on the Zeeman effect that occurs when a magnetic field splits an energy level into two sublevels with opposite magnetic quantum numbers. The frequency of the light is usually in the visible or ultraviolet range. The intensity and sign of the MCD signal depend on various factors, such as transition moment, selection rules, symmetry, and temperature.
Magnetochemistry of Transition Metal Complexes
Magnetochemistry of transition metal complexes is one of the most active and important areas of magnetochemistry. It deals with the magnetic properties of coordination compounds that contain transition metal ions as central atoms. Transition metal complexes exhibit a rich variety of magnetic phenomena due to their diverse electronic configurations and geometries.
Crystal field theory and ligand field theory
Crystal field theory and ligand field theory are two theories that explain how the electronic structure and properties of transition metal complexes are affected by the presence of ligands or other metal ions around them. They are based on the electrostatic interactions between point charges or dipoles.
Crystal field theory considers only the repulsion between the metal d-orbitals and the ligand lone pairs or charges. It predicts how the degeneracy of the d-orbitals is lifted by different coordination geometries, such as octahedral, tetrahedral, square planar, etc. It also predicts how the splitting energy affects the color, magnetism, and stability of complexes.
the ligand orbitals. It predicts how the symmetry and nature of the ligands affect the orbital mixing and splitting. It also predicts how the ligand field affects the spectroscopic, magnetic, and redox properties of complexes.
High-spin and low-spin complexes
High-spin and low-spin complexes are two types of transition metal complexes that differ in their electronic configuration and magnetic behavior. They are determined by the relative magnitude of the crystal field splitting energy and the electron pairing energy.
High-spin complexes have a large number of unpaired electrons and a small crystal field splitting energy. They are usually formed by metals with low oxidation states and weak-field ligands. They exhibit strong paramagnetism and high spin-orbit coupling.
Low-spin complexes have a small number of unpaired electrons and a large crystal field splitting energy. They are usually formed by metals with high oxidation states and strong-field ligands. They exhibit weak paramagnetism or diamagnetism and low spin-orbit coupling.
Magnetic anisotropy and single-molecule magnets
Magnetic anisotropy and single-molecule magnets are two concepts that describe the directional dependence and memory effect of the magnetization in some transition metal complexes. They are related to the spin-orbit coupling and the crystal field effects.
Magnetic anisotropy is a property that makes the magnetic moment of a complex prefer a certain direction or orientation in space. It can be caused by different factors, such as orbital angular momentum, zero-field splitting, exchange coupling, or external field. Magnetic anisotropy can result in different types of magnetism, such as axial, planar, or rhombic.
Single-molecule magnets are complexes that behave like tiny magnets with a large magnetic moment and a high magnetic anisotropy. They can retain their magnetization even in the absence of an external field, due to a large energy barrier that prevents spontaneous reversal of the spin orientation. Single-molecule magnets have potential applications in data storage, quantum computing, and nanotechnology.
Magnetochemistry of Lanthanide and Actinide Complexes
Magnetochemistry of lanthanide and actinide complexes is another important area of magnetochemistry. It deals with the magnetic properties of coordination compounds that contain lanthanide or actinide ions as central atoms. Lanthanide and actinide complexes exhibit unique and complex magnetic phenomena due to their f-electron configuration and relativistic effects.
Atomic and ionic properties of f-elements
The f-elements are the elements that have partially filled f-orbitals in their electronic configuration. They include the lanthanides (elements 57-71) and the actinides (elements 89-103). The f-elements have some common atomic and ionic properties that distinguish them from other elements.
The f-orbitals are inner orbitals that are shielded by the outer s- and p-orbitals. They have a low energy and a high radial extension. They also have a complex shape and symmetry that give rise to seven possible magnetic quantum numbers. These properties make the f-electrons weakly interact with the environment and strongly interact with each other.
The f-elements have variable oxidation states, ranging from +2 to +7. The most common oxidation states are +3 for lanthanides and +4 for actinides. The f-elements have similar ionic radii, especially for the same oxidation state. The ionic radii decrease with increasing atomic number, due to the effective nuclear charge. This is known as the lanthanide contraction or the actinide expansion.
Crystal field splitting and magnetic anisotropy
Crystal field splitting and magnetic anisotropy are two effects that influence the electronic structure and properties of lanthanide and actinide complexes. They are related to the interaction between the f-orbitals and the ligand field or the spin-orbit coupling.
the weak interaction between the f-electrons and the ligands. Crystal field splitting is usually large for actinide complexes, due to the strong interaction between the f-electrons and the ligands.
Magnetic anisotropy is a property that makes the magnetic moment of a complex prefer a certain direction or orientation in space. It can be caused by different factors, such as orbital angular momentum, zero-field splitting, exchange coupling, or external field. Magnetic anisotropy is usually large for lanthanide complexes, due to the strong spin-orbit coupling of the f-electrons. Magnetic anisotropy is usually small for actinide complexes, due to the weak spin-orbit coupling of the f-electrons.
Lanthanide contraction and actinide expansion
Lanthanide contraction and actinide expansion are two phenomena that describe the variation of the ionic radii of lanthanide and actinide ions along the series. They are related to the effective nuclear charge and the screening effect of the f-electrons.
Lanthanide contraction is a phenomenon that occurs when the ionic radii of lanthanide ions decrease with increasing atomic number, for a given oxidation state. This is due to the increase in the effective nuclear charge that attracts the outer electrons more strongly. The f-electrons do not contribute much to the screening effect, due to their low energy and high radial extension.
Actinide expansion is a phenomenon that occurs when the ionic radii of actinide ions increase with increasing atomic number, for a given oxidation state. This is due to the decrease in the effective nuclear charge that attracts the outer electrons less strongly. The f-electrons contribute more to the screening effect, due to their relativistic effects and orbital mixing.
Lanthanide contraction and actinide expansion have important consequences for the chemical and physical properties of lanthanide and actinide complexes, such as coordination number, bond length, bond angle, bond strength, color, magnetism, and reactivity.
Magnetochemistry of Molecular Materials
Magnetochemistry of molecular materials is a new and emerging area of magnetochemistry. It deals with the magnetic properties of materials that are composed of discrete molecules or molecular assemblies. Molecular materials exhibit novel and tunable magnetic phenomena due to their low dimensionality, high diversity, and strong intermolecular interactions.
Molecular magnets and spin crossover compounds
Molecular magnets and spin crossover compounds are two types of molecular materials that show reversible changes in their magnetization or spin state in response to external stimuli, such as temperature, pressure, light, or electric field. They have potential applications in sensors, switches, displays, and memory devices.
Molecular magnets are materials that consist of molecules that have a large magnetic moment and a high magnetic anisotropy. They can retain their magnetization even in the absence of an external field, due to a large energy barrier that prevents spontaneous reversal of the spin orientation. Examples of molecular magnets are single-molecule magnets (SMMs) and single-chain magnets (SCMs).
Spin crossover compounds are materials that consist of molecules that have two possible spin states with different electronic configurations and magnetic moments. They can switch between these states by crossing an energy barrier that depends on various factors, such as ligand field, crystal field, intermolecular interactions, and entropy. Examples of spin crossover compounds are iron(II) complexes with N4S2 or N6 ligands.
Magnetic nanoparticles and nanowires
Magnetic nanoparticles and nanowires are two types of molecular materials that have nanoscale dimensions and enhanced magnetic properties. They have potential applications in biomedicine, cata