I have been through a great deal of literature but have failed to find a simple explanation for how symmetry of Fe in a lattice will change the spin-lattice coupling. I have seen the papers that calculate the whole thing and understand that this falls out of the math but I am having trouble visualizing how the population of the orbitals for Fe2+, and the symmetry that creates, relates to the probability of relaxation through coupled lattice vibrations.
Fe3+ is high-spin in most cases, e.g. in Fe_3O_4, with a d^5 electron configuration and occupies tetrahedral or octahedral sites. According to the discussion given in the link below, there is no Jahn-Teller distortion. For Fe2+, an octahedral site is strongly preferred. Since there is an (t2g)^4 (eg)^2 electron configuration in the high-spin case, Jahn-Teller effect is nonzero but weak, again referring to the link below. The Jahn-Teller effect will lead to a distortion from octahedral to some lower symmetry where the t2g orbitals split up. The Jahn-Teller effect clearly is related to spin-lattice couplings, since the vibrational degrees of freedom mediate the split-up of the degenerate states.
https://en.wikibooks.org/wiki/Introduction_to_Inorganic_Chemistry/Coordination_Chemistry_and_Crystal_Field_Theory#.C2.A0.C2.A05.7_Jahn-Teller_effect
Hi Eli:
Wish I could help, but that fancy physics stuff is beyond me. Naturally, since you put this bug in my head I'll actually have to go and find out. Thanks a lot!
Ed
Fe3+ is high-spin in most cases, e.g. in Fe_3O_4, with a d^5 electron configuration and occupies tetrahedral or octahedral sites. According to the discussion given in the link below, there is no Jahn-Teller distortion. For Fe2+, an octahedral site is strongly preferred. Since there is an (t2g)^4 (eg)^2 electron configuration in the high-spin case, Jahn-Teller effect is nonzero but weak, again referring to the link below. The Jahn-Teller effect will lead to a distortion from octahedral to some lower symmetry where the t2g orbitals split up. The Jahn-Teller effect clearly is related to spin-lattice couplings, since the vibrational degrees of freedom mediate the split-up of the degenerate states.
https://en.wikibooks.org/wiki/Introduction_to_Inorganic_Chemistry/Coordination_Chemistry_and_Crystal_Field_Theory#.C2.A0.C2.A05.7_Jahn-Teller_effect
The explanation cannot be "simple", because the Zeeman energy of the electron moment is quite smaller than either the coupling energy between the 3d electrons or the electric energy fom the neighbours (ligands). Here are some suggestions for a reflection:
in insulating crystalline solids, Spin-Lattice (SL) relaxation generally takes place through the correlated small motions of the ions around their mean position (phonons). Phonons modulate the Crystal Field (CF) from the neighbours (ligands), which acts on the paramagnetic ion, more precisely upon the magnetic moment associated with the electron spin, this not directly (an electric field does not act on a magnetic moment ) but indirectly, via the Spin-Orbit (SO) coupling.
The formal description of this effect has to use some perturbation scheme. When facing a 3d ion, the CF is greater than the SO (this is not true with a 4f ion), and is comparable with the coupling between the 3d electrons. Using the language from the canonical book by Abragam and Bleaney (AB), and considering a 3d^5 or 3d^6 so-called ground configuration, one may adopt two (equivalent) approaches: either the intermediate ligand field approximation, or the strong ligand field approximation. Hereafter, I use the intermediate ligand field approximation:
- the 3d^5 configuration: the so-called ground "term" is (L=0, S=5/2). L=0 means no orbital moment . Here, the spin-orbit coupling, strictly speaking, does not exist, and as a consequence ESR should observe that g=2.0023 (free electron value). In fact, contributions of excited configurations and/or terms should slightly correct this: weak SO coupling. Instead of g=2.0023, g value near the free electron g-value. for instance, for Mn2+ in ZnS, isotropic g tensor, with g=2.0025 (plus or minus 0.0002). What then will the phonons do? In a first approximation, they will have no effect on SL relaxation. In fact, they have a "weak" effect : long T1, e.g, for Mn2+ in ZnS, rougly 0.3 s at 4.2 K,
- the 3d^6 configuration: the ground term is 5D (L=2, S=2). A CF with cubic symmetric splits this 5D term into an orbital doublet and an orbital triplet (cf. AB). If you know the concept of "quenching of the orbital moment", let us say that quenching does not presently exist (it does exist when the ground orbital state is a singlet). Since there is an orbital ground state with an orbital moment, one should expect that the SO will be efficient here, and therefore also that the phonons should be more efficient in SL relaxation (quite shorter T1 at the same temperature). I take the following case: Fe^2+ in MgO. There g=3.428: the CF effects are important. Rather than giving the T1 value at some temperature, I think more significant to mention some qualitative phenomenon: do you know APR (Acoustic Paramagnetic resonance)? This experimental technique is possible only when there is a strong coupling between spin and phonons. APR is possible with Fe2+ in MgO, which means strong spin-phonon coupling, and therefore short T1. I know of 1978 experimental results (non-resonant ultrasound experiments) giving a T1 roughly equal to 10 nanoseconds around 4 K.
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