Magnetic-field gradient tensor

The components Gu of the magnetic-field gradient tensor G are defined as the spatial derivatives of the magnetic field,... 

Table IX - Charge density pe(0) at the nucleus and Isomer Shift 6, Electric Field Gradient tensor, contact spin density p,(0), Magnetic Dipolar Field tensor, and net magnetic field Hjr at iron site in annite. Results are given for clusters containing only first, and first plus second coordination shells about iron. Principal values and directions of principal axes (in parentheses) are given for EFG and dipolar field. The 57Fe nuclear quadrupole moment is taken as 0.16 barn [91].

If they are independent of space, they are constant and the magnetic field varies linearly with space. Because the magnetic field B is a vector with components Bx, By, and B, the magnetic-field gradient is a second-rank tensor with nine components. It can be written as the dyadic product of the gradient operator V and the magnetic field. 

If the electric field gradient tensor is axially symmetric and its principal axis makes an angle 6 with the magnetic axis, then a relatively simple solution exists providing that e qQ (iH in this case the quadrupole interaction can be treated as a first-order perturbation to the magnetic interaction. The eigenvalues are... 

The angular terms are formulated as the radiation probability in a direction B to the principal axis (z axis) of the magnetic field or the electric field gradient tensor. The appropriate functions (/, m) are listed in Table 3.3. The... 

In the event that the Mdssbauer absorber is unsplit or is a random polycrystal, the observed spectrum shows no new features. However, if both source and absorber are directionally polarised by a magnetic field which can be internal in origin or by an electric field such as is associated with the electric field gradient tensor in a single-crystal absorber the polarisation of each emission line becomes important. 

Fe3(P04)2.4H20, known as ludlamite, also contains two iron sites, Fe(l) and Fe(2), in the ratios 1 2 and is antiferromagnetic below 15 K. The ordered phase gives a Mossbauer spectrum with two hyperfine fields [56]. The relation between the electric field gradient tensors and the spin axes were determined and the symmetry was shown to be lower than in Fe3(P04)2.8H20 however, the magnetic ordering has not yet been studied in detail. 

At 4-2 K the magnetic field is 460 kG and from single-crystal data the spin axis lies in the ac plane. Application of a 30-kG field parallel to the c axis splits the antiparallel sublattices, but has no effect when perpendicular to the c axis, and confirms that the spins are collinear and aligned in the c axis. Data with a single crystal at room temperature and a polarised Co/iron metal source showed that the major axis of the electric field gradient tensor lies in the ac plane at 55° to the c axis, and the sign of e qQ is negative. 

Magnetic ordering occurs in Fc2Si04 below 66 K, and at 9 K there are two magnetic patterns with fields of 120 kG and 323 kG which have different orientations with respect to their electric field gradient tensor [215]. 

The magnetic field in SmCl3.6H20 corresponds closely to that predicted for the free-ion Sm + in the fully magnetised state J — J and, by assuming that this configuration also produces the electric field gradient tensor, a value of +0-40(6) barn was derived for the quantity (1 — [11]. 

Figure 3 Energy level splittings and transitions for half-integer quadrupolar nuclei, as illustrated for the example of a spin-3/2 nucleus, (Oy is the NMR transition frequency in the absence of the quadrupolar interaction, Wy is the quadrupolar frequency, and 0 is the angle between the magnetic field and the principal axis of the electric field gradient tensor.

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