Comparison with experiment

The satellite lines for which interactions were measured are due to some of the twenty closest ions around the dopant Lu3+ ion. For these sites, Equation (7.1) pre-

dicts dipole-dipole interaction strengths of the order of 0.1 MHz, with the strongest interaction (between, for instance, sites 1 and 5 (lines J and V)) −2.9 MHz. These

interactions are two orders of magnitude smaller than the observed interactions. The dipole-dipole model also does not agree qualitatively with the expected interac- tions. This can most clearly be seen by considering the two sets of satellite lines for which both expected interactions were observed: J and D, and B and H. Lines J and D, due to sites 1 and 4, are predicted to have interaction frequencies of 0.45 MHz

and 0.82 MHz: both in the same direction, and of a similar size. In contrast, the

observed shifts are −46.1 MHz and 3.5 MHz, in opposite directions and with an

order of magnitude difference in size. Likewise, lines B and H are predicted to have two almost identical frequencies, while actually their shifts of −16.729 MHz and

1.734 MHz differ in sign and in magnitude.

The dipole-dipole interaction can be ruled out as the source of the observed frequency shifts on the basis of its qualitative and quantitative disagreement with the data. The dipole-quadrupole interaction can also be ruled out. From Equation (7.2), the dipole-quadrupole interaction is dependent on cosθ whereθ is the angle between

the C2 axis and the position vector joining the two interacting ions. This means

that the interaction is zero when the interacting sites are in a plane perpendicular to the C2 axis. The satellite lines D and J are due to ions in such a plane, so the

dipole-quadrupole interaction predicts zero frequency shift for these lines, contrary to the observed shifts.

There is not enough information to determine whether the interaction is quadrupole-quadrupole. This interaction has three unknowns– the three compo- nents of the quadrupole tensor– which it is not possible to measure because the large field gradients required are not experimentally accessible. There are no qual- itative arguments similar to that given above for the dipole-quadrupole interaction that can rule this interaction out. If all the interactions between the seven satellite lines investigated were known, it would be feasible to try to fit the quadrupole tensor to the data. However, this would be difficult with the current data as nearly half of the interaction frequencies are unknown.

In addition to the missing interactions, there is some uncertainty in the sepa- rations of almost all pairs of satellite lines for which interactions were measured, because lines A, B and C could only be assigned to one of two sites in Chapter 5. This makes it difficult to determine the contribution of superexchange, as this inter-

action is normally characterised by a strong dependence on separation with a sharp cutoff at some separation. The two pairs of lines J and D, and B and H, give some information on the distance dependence. The ions in lines J and D are separated by 7.94 and 9.66 Å, and have interactions at −46.081 and 3.52 MHz , while the ions in

lines B and H are separated by 13.75 and 14.44 Å, and have interactions at−16.729

and 1.734 MHz. The interaction frequencies of D and J are larger than those of B

and H, but only by a factor of≈2.5, so the distance dependence of the interaction is

not very strong, and there is no sharp cutoff in the range 7.94 – 14.44 Å. The largest distance, 14.44Å, is much larger than the maximum distance superexchange has been reported over previously, 10 Å [113]. The large distances and lack of a strong distance dependence or a distance cut-off suggest that superexchange does not make a large contribution to the interaction of the satellite line pairs measured, but this argument does ignore the strong angular dependence of superexchange interactions. While the argument above shows that a superexchange interaction cannot ex- plain the interaction shifts of most satellite line pairs, it is still possible that it contributes to the interaction between closely separated ions. Chapter 5 showed that superexchange made a small contribution to the magnetic interaction between Eu3+ _{and a Kramers dopant over distances of less than 7 Å. Separations of less that}

7 Å are expected for some of the satellite line pairs for which electronic interactions were measured: in lines D and H, lines J and I, and lines J and H one of the two possible separations between ions in the different lines is less than 7 Å. Because only one of the two separations for a pair of lines was less than 7 Å and, for these three pairs of lines, only one of the two interaction frequencies was measured, it cannot be confirmed that any of the observed interaction shifts were due to closely separated ions. If the observed shifts were due to the closely separated ions in two satellite lines, then the size of the shifts would suggest that superexchange does not make a significant contribution to the interaction mechanism. However, it is equally likely that the observed shifts were due to the ion pairs with large separations, and the ion pairs with small separations have interaction frequencies so large that they are outside the detection range.

In summary, the short range electronic ion-ion interactions between Eu3+_satellite

lines measured in this section cannot be electric dipole-dipole or dipole-quadrupole. Superexchange is unlikely, but electric quadrupole-quadrupole and higher order elec- tric multipole interactions are possible. These sources of interactions are very differ- ent from those identified in the energy transfer measurements between satellite lines of Nd3+ _{and Pr}3+ _{described in Section 2.9, where dipole-dipole and superexchange}

were commonly found. However, those interactions were between ions ≈ 4−5 Å

resonant, and much stronger than the interactions measured here: the direct ion-ion interaction frequencies were only an order of magnitude smaller than the shifts of the satellite lines, which result from the static perturbation to the crystal field by the dopant ions. Here, the interactions are three orders of magnitude smaller than the satellite line shifts. It is likely that the interactions measured here represent a completely different regime from the earlier measurements in Nd3+ and Pr3+.