Integer-spin systems

FIGURE 5.9 Effective g-values for half-integer spin systems in axial symmetry. The scheme gives the values for all transitions within the Kramer s doublets of S = nl2 systems assuming gmal = 2.00 and S S S B. 

Equation 12.3 is readily rewritten for any other half-integer spin. For integer spins we have one singulet (the ms = 0 level) and S doublets, but we do not bother writing down the modified equation, because spin counting for integer-spin systems in the weak-field limit is near-to-impossible (Hagen 2006). 

The problem of the electron spin relaxation in the early work from Sharp and co-workers (109 114) (and in some of its more recent continuation (115,116)) was treated only approximately. They basically assume that, for integer spin systems, there is a single decay time constant for the electron spin components, while two such time constants are required for the S = 3/2 with two Kramers doublets (116). We shall return to some new ideas presented in the more recent work from Sharp s group below. 

Kramers theorem requires that all half-integer spin systems be at least doubly degenerate in the absence of a magnetic held. Next, note that the splitting of these levels by a magnetic held depends on its orientation relative to the axes of the ZFS tensor of the metal ion. The VTVH MCD saturation magnetization curve behavior reflects the difference in the population of these levels and their spin expectation values in a specific molecular direchon. This direction must be perpendicular to the polarizations of the transition (Mih where i / j are the two perpendicular polarizations... 

Answer Spin expectation values (and therefore the magnetic hyperfine field) of half-integer spin systems can be saturated in low fields see Section 3.5.2). This is not the case here. In order to drive the magnetic splitting to its saturation, fields of up to 8 T have been applied. In addition, J is EPR silent, which points to an integer-spin species. 

Figure 16 shows plots of the energy levels for both axial (E = 0) and rhombic (D > 3E >0) systems with D hv. In the axial system, it is obvious that a transition cannot be induced between =0 and m = 1 because of the large energy separation (D). A transition also cannot be induced between m = 1 and m = —1, since this is forbidden by selection rules (i.e., this is a Am = 2 transition while only Arris = 1 transitions are allowed). Therefore, transitions are almost never observed in purely axial integer-spin systems. 

EPR transitions have been observed from some integer-spin systems. From the above discussion it is obvious... 

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