**13. Electron spin resonance**

Electron Spin Resonance (ESR) is a branch of spectroscopy in which radiation of microwave frequency is absorbed by molecules possessing electrons with unpaired spins. It is known by different names such as Electron Paramagnetic Resonance (EPR), Electron Spin Resonance (ESR) and Electron Magnetic Resonance (EMR). This method is an essential tool for the analysis of the structure of molecular systems or ions containing unpaired electrons, which have spin-degenerate ground states in the absence of magnetic field. In the study of solid state materials, EPR method is employed to understand the symmetry of surroundings of the paramagnetic ion and the nature of its bonding to the nearest neighbouring ligands.

When a paramagnetic substance is placed in a steady magnetic field (H), the unpaired electron in the outer shell tends to align with the field. So the two fold spin degeneracy is

removed. Thus the two energy levels, E1/2 and E-1/2 are separated by gH, where g is spectroscopic splitting factor and is called gyro magnetic ratio and is the Bohr magneton. Since there is a finite probability for a transition between these two energy levels, a change in the energy state can be stimulated by an external radio frequency. When microwave frequency () is applied perpendicular to the direction of the field, resonance absorption will occur between the two split spin levels. The resonance condition is given by, h = gH, where h is Planck's constant.

The resonance condition can be satisfied by varying or H. However, EPR studies are carried out at a constant frequency (), by varying magnetic field (H). For a free electron, the g value is 2.0023. Since h and are constants, one can calculate the g factor. This factor determines the divergence of the Zeeman levels of the unpaired electron in a magnetic field and is characteristic of the spin system.

In the crystal systems, the electron spins couple with the orbital motions and the g value is a measure of the spin and orbital contributions to the total magnetic moment of the unpaired electron and any deviation of magnetic moment from the free spin value is due to the spinorbit interaction. It is known that the crystal field removes only the orbital degeneracy of the ground terms of the central metal ion either partially or completely. The strong electrical fields of the surrounding ligands results in "Stark Splitting" of the energy levels of the paramagnetic ion. The nature and amount of splitting strongly depends on the symmetry of the crystalline electric field. The Stark splitting of the free ion levels in the crystal field determines the magnetic behaviour of the paramagnetic ion in a crystal. Whenever there is a contribution from the unquenched orbital angular momentum, the measured g values are isotropic as a result of the asymmetric crystal field since the contribution from the orbital motion is anisotropic. To decide the ultimate ground state of a paramagnetic ion in the crystal, the two important theorems, Kramers and Jahn-Teller, are useful. Using group theory, one can know the nature of the splitting of the free ion levels in the crystal fields of various symmetries.

Jahn-Teller theorem states that any nonlinear molecule in an electronically degenerate ground state is unstable and tends to distort in order to remove this degeneracy. The direction of distortion which results in greatest stabilization can often be deduced from EPR and other spectroscopic data.

Kramers' theorem deals with restrictions to the amount of spin degeneracy which can be removed by a purely electrostatic field. If the system contains an odd number of electrons, such an electrostatic field cannot reduce the degeneracy of any level below two. Each pair forms what is known as a Kramers' doublet, which can be separated only by a magnetic field. For example, Fe(III) and Mn(II) belonging to d5 configuration, exhibit three Kramers' doublets labeled as 5/2, 3/2 and 1/2.

If the central metal ion also possesses a non-zero nuclear spin, I, then hyperfine splitting occurs as a result of the interaction between the nuclear magnetic moment and the electronic magnetic moment. The measurement of g value and hyperfine splitting factor provides information about the electronic states of the unpaired electrons and also about the nature of the bonding between the paramagnetic ion and its surrounded ligands. If the ligands also contain non-zero nuclear spin, then the electron spin interacts with the magnetic moment of the ligands. Then one could expect super hyperfine EPR spectrum.

The g value also depends on the orientation of the molecules having the unpaired electron with respect to the applied magnetic field. In the case of perfect cubic symmetry, the g value does not depend on the orientation of the crystal. But in the case of low symmetry crystal fields, g varies with orientation. Therefore we get three values gxx, gyy, and gzz corresponding to a, b and c directions of the crystal. In the case of tetragonal site gxx = gyy which is referred to as g and corresponds to the external magnetic field perpendicular to the Z-axis. When it is parallel, the value is denoted as g. Hence one can deduce the symmetry of a complex by EPR spectrum i.e., cubic, tetragonal, trigonal or orthorhombic. Anyhow, it is not possible to distinguish between orthorhombic and other lower symmetries by EPR.

## **13.1. EPR signals of first group transition metal ions**

14 Advanced Aspects of Spectroscopy

where h is Planck's constant.

various symmetries.

and other spectroscopic data.

doublets labeled as 5/2, 3/2 and 1/2.

and is characteristic of the spin system.

removed. Thus the two energy levels, E1/2 and E-1/2 are separated by gH, where g is spectroscopic splitting factor and is called gyro magnetic ratio and is the Bohr magneton. Since there is a finite probability for a transition between these two energy levels, a change in the energy state can be stimulated by an external radio frequency. When microwave frequency () is applied perpendicular to the direction of the field, resonance absorption will occur between the two split spin levels. The resonance condition is given by, h = gH,

The resonance condition can be satisfied by varying or H. However, EPR studies are carried out at a constant frequency (), by varying magnetic field (H). For a free electron, the g value is 2.0023. Since h and are constants, one can calculate the g factor. This factor determines the divergence of the Zeeman levels of the unpaired electron in a magnetic field

In the crystal systems, the electron spins couple with the orbital motions and the g value is a measure of the spin and orbital contributions to the total magnetic moment of the unpaired electron and any deviation of magnetic moment from the free spin value is due to the spinorbit interaction. It is known that the crystal field removes only the orbital degeneracy of the ground terms of the central metal ion either partially or completely. The strong electrical fields of the surrounding ligands results in "Stark Splitting" of the energy levels of the paramagnetic ion. The nature and amount of splitting strongly depends on the symmetry of the crystalline electric field. The Stark splitting of the free ion levels in the crystal field determines the magnetic behaviour of the paramagnetic ion in a crystal. Whenever there is a contribution from the unquenched orbital angular momentum, the measured g values are isotropic as a result of the asymmetric crystal field since the contribution from the orbital motion is anisotropic. To decide the ultimate ground state of a paramagnetic ion in the crystal, the two important theorems, Kramers and Jahn-Teller, are useful. Using group theory, one can know the nature of the splitting of the free ion levels in the crystal fields of

Jahn-Teller theorem states that any nonlinear molecule in an electronically degenerate ground state is unstable and tends to distort in order to remove this degeneracy. The direction of distortion which results in greatest stabilization can often be deduced from EPR

Kramers' theorem deals with restrictions to the amount of spin degeneracy which can be removed by a purely electrostatic field. If the system contains an odd number of electrons, such an electrostatic field cannot reduce the degeneracy of any level below two. Each pair forms what is known as a Kramers' doublet, which can be separated only by a magnetic field. For example, Fe(III) and Mn(II) belonging to d5 configuration, exhibit three Kramers'

If the central metal ion also possesses a non-zero nuclear spin, I, then hyperfine splitting occurs as a result of the interaction between the nuclear magnetic moment and the electronic magnetic moment. The measurement of g value and hyperfine splitting factor provides Transition metal ions of 3d group exhibit different patterns of EPR signals depending on their electron spin and the crystalline environment. For example, 3d1 ions, VO2+ and Ti3+ have s = 1/2 and hence are expected to exhibit a single line whose g value is slightly below 2.0. In the case of most abundant 51V, s = 1/2 and I = 7/2, an eight line pattern with hyperfine structure of almost equal intensity can be expected as shown in Fig-1. In the case of most abundant Ti, (s = 1/2 and I = 0), no hyperfine structure exists. However, the presence of less abundant isotopes (47Ti with I = 5/2 and 49Ti with I = 7/2) give rise to weak hyperfine structure with six and eight components respectively. This weak structure is also shown in Fig-1.

Cr(III), a d3 ion, with s = 3/2 exhibits three fine line structure. The most abundant 52Cr has I = 0 and does not exhibit hyperfine structure. However, 53Cr with I = 3/2 gives rise to hyperfine structure with four components. This structure will be weak because of the low abundance of 53Cr. Thus each one of the three fine structure lines of 53Cr is split into four weak hyperfine lines. Of these, two are overlapped by the intense central line due to the most abundant 52Cr and the other two lines are seen in the form of weak satellites.

Mn(II) and Fe(III) with d5 configuration have s = 5/2 and exhibit five lines which correspond to a 5/2 3/2, 3/2 1/2 and +1/2 -1/2 transitions. In the case of 55Mn, which has I = 5/2, each of the five transitions will give rise to a six line hyperfine structure. But in powders, usually one observes the six-hyperfine lines corresponding to +1/2 - 1/2 transition only. The remaining four transition sets will be broadened due to the high anisotropy. Fe3+ yields no hyperfine structure as seen in Fig -1.

Co2+, a d7 configuration, with s value of 3/2 exhibits three fine structure lines. In the case of 59Co (I = 7/2), eight line hyperfine pattern can be observed as shown in the Fig-1.

**Figure 1.** EPR signal of 3d ions
