Large-Magnitude High-Spin Nuclear Parameters in a Ti3+Center from X-band EPR Measurements at 10 K

Interpreting electron–nuclear–magnetic field interactions from a hamiltonian expressed in tensorial notation

“…Another area that needs to be addressed is that in the literature we find cases where a mixed hamiltonian involving terms expressed in the form of (1) with higher-order terms expressed in spherical tensor notation in the form of (2)-see for example [6][7][8].…”

“…It also follows that in this case we cannot determine the C-values from the B-values. To use (7) to obtain the C-values the B-values must be chosen as defined in (8).…”

Higher-order Zeeman and spin terms in the electron paramagnetic resonance spin Hamiltonian; their description in irreducible form using Cartesian, tesseral spherical tensor and Stevens’ operator expressions

“…As in section 2.3, equation ( 19) can be compared to the equivalent expressions in Cartesian notation, namely H 0,2,0 S = j =x,y,z =x,y,z D j J j J H 0,4,0 S = j =x,y,z =x,y,z m=x,y,z n=x,y,z D j mn J j J J m J n (20) D G McGavin and W C Tennant and linear relationships between the D parameters and the B k 2 ,q parameters obtained. These parameters are listed in table 3 and have dimensions of energy.…”

“…A good place to start is a consideration of a recent paper [20] that measured and analysed the complex hyperfine structure of 47 Ti and 49 Ti isotopes in 15 K X-band spectra of a Ti 3+ centre in tetragonal zircon. In this study, in addition to the standard second rank 'tensor' terms of equation ( 5), all terms of the types B I 3 , B I 5 , S I 3 , S I 5 and I 4 were found necessary to describe adequately the hyperfine structure.…”

“…The main features observed that were attributable to the inclusion of the high-spin terms: a 20-fold diminution in the RMSD between observed and calculated line positions; a marked increase in the anisotropy of the g principal values; a fitted cos 4θ angular dependence of g eff = 4.3 lines that is dependent on the inclusion of high-spin Zeeman terms in the SH; a set of four three-fold pseudo-symmetry axes [25,26] that are, within error, common to the tensor sets B 1,3 4,m , B 1,5 4,m and B 1,5 6,m . The second study [20,27] (see section 3.3) involved 10 K X-band measurements on a Ti 3+ d 1 centre in tetragonal zircon; the site symmetry of Ti 3+ is 42m(D 2d ) tetragonal. (It should be noted that the dimensioned high-spin parameters of table 2 of [20] are in units 1/g e μ B Gauss and not mT as stated.…”