Chapter 1: Introduction
1.2 Crystal Field Effect
The local environment within a crystal of a solid greatly influences the energy levels of an atom. The net electric field produced from the neighboring atoms in the crystal is known as the crystal field [25]. The symmetry of the local environment plays a major role in determining the nature of the crystal field effects. In ABO3 type structure, the hybridization and electrostatic interaction of the outermost 3d orbital of B cation with that of the oxygen ion gives rise to the crystal field effect. In the absence of crystal field, the d orbital has fivefold degenerate energy levels namely dxy, dyz, dzx, ()*+)and ,-)*). The first three are known as t2g orbitals whereas the last two are called eg orbitals as shown in Fig 1.2.
Figure 1.2: The electronic distribution of five d orbitals. In presence of cubic crystal field, the fivefold degeneracy of d orbital is lifted, and it splits into two eg
(()*+)and ,-)*)) and three t2g (dxy, dyz and dzx) orbitals. Adapted from [26].
The t2g orbitals are oriented in between x, y and z axes, but the eg orbitals point along the direction of x, y and z axes. However, in an octahedral environment, there exists a Coloumb interaction between 3d electrons of the transition metal ions and 2p electrons of O ions. Since the px, py, pz orbitals of the oxygen point long the x, y and z direction respectively, there will be an overlapping with eg orbitals of the transition metal ions. So, the energy of eg
orbitals is raised compared to the t2g orbitals. On the other hand, no such overlapping occurs in case of t2g orbital. In view of the above crystal field effect, the degeneracy of d orbitals is lifted by raising the energy of eg orbitals with respect to the t2g orbitals. The splitting in an octahedral environment is shown in Fig. 1.3. In case of tetrahedral environment, the t2g
orbitals are lifted up and eg orbitals are pushed down [25]. The ground state spin configuration (high spin or low spin state) of the transition metal ions is determined from the competition between the crystal field energy and the Hund’s pairing energy. A high spin state is favorable if the crystal field energy is lower than that of the pairing energy, where electrons occupy the orbitals as per Hund’s rule. However, electrons will doubly occupy the lower energy orbitals before entering into the higher energy orbitals favoring a low spin state when the crystal field energy is stronger than the pairing energy.
Another important aspect of the crystal field effect is the orbital quenching, commonly observed in the 3
transition metal ions can be calculated relation . / 012(2 3
the above values for most of the
presence of a stronger crystal field effect compared to that of elements which results in
effective magnetic moment of orbitally quenched elements is calculated considering only the spin angular momentum (
rare-earth elements with 4f are deep inside from the electronic configuration of the
Figure 1.3: The crystal field in an (a) octahedral environment and (b) tetrahedral environment of d orbital in transition elements.
In certain electronic orbitals can be further lifted energy is reduced. This effect
Mn3+ (3d4) ions in an octahedral environment exhibits this kind of behavior
Another important aspect of the crystal field effect is the orbital quenching, commonly observed in the 3d transition metal ions. The effective magnetic moment (
transition metal ions can be calculated from the total angular momentum (
1 31) .# but the experimental effective moment doesn’t match with the above values for most of the 3d transition metal ions. This discrepancy
presence of a stronger crystal field effect compared to that of the spin orbit interaction in 3 in quenching of the orbital angular momentum
effective magnetic moment of orbitally quenched elements is calculated considering only the spin angular momentum (S) using the relation . / 014(4 3 1) .#
elements with 4f electrons, no crystal field effect is observed because the 4 the outermost orbital and have negligible
electronic configuration of the neighboring ions.
The crystal field in an (a) octahedral environment and (b) tetrahedral orbital in transition elements.
In certain electronic configurations the degeneracy associated with the orbitals can be further lifted by the spontaneous distortion of the lattice
energy is reduced. This effect is known as the Jahn-Teller (JT) effect
in an octahedral environment exhibits this kind of behavior
Another important aspect of the crystal field effect is the orbital quenching, transition metal ions. The effective magnetic moment (µeff) of from the total angular momentum (J) using the effective moment doesn’t match with discrepancy arises due to the the spin orbit interaction in 3d quenching of the orbital angular momentum i.e. L = 0. Thus, the effective magnetic moment of orbitally quenched elements is calculated considering only the
#. However, in case of no crystal field effect is observed because the 4f levels overlapping with the
The crystal field in an (a) octahedral environment and (b) tetrahedral
he degeneracy associated with the eg and t2g
lattice such that the overall Teller (JT) effect [25,27]. For example, in an octahedral environment exhibits this kind of behavior as shown in
Fig.1.4. The spontaneous distortions can occur in two ways, one by elongation and other by compression. In case of elongation in an octahedron, the overlapping of one of the eg orbitals, ,-)*)with the neigbouring p orbital of oxygen is reduced, whereas for other eg orbital, ()*+) it is enhanced. Therefore, the ()*+) level is lifted up compared to ,-)*)level.
Similarly, in t2g orbital, dxy level is lifted up compared to dyz and dzx levels. On the other hand, the compression in the octahedron lifts up the ,-)*)level compared to ()*+) level in the eg orbital and similarly dyz and dzx levels are lifted up with respect to dxy level in t2g orbital.
Cr3+ is Jahn-Teller inactive ion while Mn3+ is a Jahn-Teller active ion.
Figure 1.4: The Jahn-Teller effect in Mn3+ (3d4) ion that leads to splitting of both t2g and eg
levels.