Axial magnetic anisotropy

By contrast, in the strong-field limit Ty saturates and becomes field independent due to Zeeman quenching of magnetic anisotropy. For axial anisotropy along z and no g-anisotropy, the molecular torque follows the simple law... 

Udachin, Yu.M. and M.E. Dyatkina Zh. Strukt. Calculation of magnetic anisotropies in axially... 

Cj is the second-order magnetic axial anisotropy value for the free ion... 

A detailed treatment of the temperature dependence and anisotropy of the magnetic moments of all the dx configurations in pseudo-axial (CooV) symmetry has though now been given by Warren (101), in which variation of the orbital reduction factor, k, and distortions from effective Cv symmetry were also considered. This has lately been followed by a similar treatment due to Cerny (102) of the d d2, d8, and d9 configurations but, although some sophistications were included the results are essentially equivalent to those of the author, and furthermore only the undistorted situation, with k = 1, was considered. Consequently the author s own treatment (101) is here briefly summarised, the theoretical approach being that most appropriate for the sandwich complexes of the 3 d series, to which the bulk of the available experimental material relates. 

FIGURE 5.3 Axial anisotropy in an S = 1/2 system. A simplified representation is drawn of the porphyrin prosthetic group in low-spin ferricytochrome c in a magnet (Hagen 2006). (Reproduced by permission of The Royal Society of Chemistry.)... 

Of two strongly axial doublets on the two sites (the case of extreme magnetic anisotropy)... 

Fig. 2. Magnetic energy of a spm crystal as a function of the tilt angle between the magnetization and the easy axis of uni-axial anisotropy.

Assuming an axially symmetric potential, the anisotropy energy of n) will be an even function of the longitudinal component of the magnetic moment s n. The averages we need to calculate are aU products of the form = (n =i (cn ))a> where the c are arbitrary constant vectors. Introducing the polar and azimuthal angles of the spin d, tp), we can write as... 

An equation for the effect of an axial magnetic anisotropy of a paramagnetic center on the pseudocontact shift is [3,109] ... 

Abbreviations CF - crystal field SH - spin Hamiltonian ZFS - zero-field splitting MA - magnetic anisotropy TIP - temperature-independent paramagnetism MP - magnetic parameter averaged (gav, /tip), axial (gz> g > D /up) CSC - complete space calculation. 

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