Magnetic structure factor

As at room temperature Bragg reflections contain both nuclear and magnetic structure factors, the nuclear structure was refined from a combination of polarized and unpolarized neutron data. Contrary to the ideal structure where only three atomic sites are present, it has been shown [11, 12] that some Y atoms were substituted by pairs of cobalt. These pairs, parallel to the c-axis are responsible for a structure deformation which shrinks the cobalt hexagons surrounding the substitutions. The amount of these substituted Y was refined to be 0.046 0.008. Furthermore, the thermal vibration parameter of Coi site appeared to be very anisotropic. The nuclear structure factors Fn were calculated from this refined structure and were introduced in the polarized neutron data to get the magnetic structure factors Fu. 

Therefore, an atomic model, made of a superposition of independent densities centered at the magnetic atoms, was built. The magnetic structure factor can be written as... 

After a simple Fourier inversion of a set of magnetic structure factors MbU, one can retrieve the magnetisation density. A much better result, e.g. the most probable density map, can be obtained using the Maximum Entropy (MaxEnt) method. It takes into account the lack and the uncertainty of the information not all the Bragg reflections are accessible on the instrument, and all the values contained in the error bars are satisfactory and have to be considered. However, as this method extracts all the information contained in the data, it is important to keep in mind that it may show spurious small details associated to a low accuracy and/or a specific lack of information located in (/-space. 

Table 1. Canting angles 0(hkl) (degree) for various reflections (hkl), with nuclear structure factors and scaled scalar magnetic structure factors (Bohr magneton). 

A detailed study of the spin density and bonding of the [CrFel3- ion in K3[CrF6] has appeared.1067 The results of polarized neutron diffraction experiments1068 were reinterpreted. A chemically based model of the [CrF6]3- ion has been fitted to the 92 observed magnetic structure factors by a least squares procedure. The spin density in the chromium(III) orbitals has t2g symmetry 06spin density centred on the... 

Polarized neutron diffraction makes it possible to measure magnetic structure factors and thus to obtain the distribution of unpaired spins in magnetic materials (see, e.g., Ref. 201). Let us discuss here the use of this technique for the study of low-dimensional organic conductors. 

Such an experiment is not easy to perform and is very time consuming because of the very small magnetic structure factors for the forbidden reflections. The investigation of MnF2 was important however, both in demonstrating the application of polarized neutron techniques to antiferromagnetic materials and in revealing directly the covalent spin density transferred to the fluorines [the existence of this spin density was already known of course, from NMR measure-... 

Magnetic Structure Factor. From Equation (43) we can develop in a compact form the magnetic structure factor of the crystal defined as ... 

For a particular magnetic reflection indexed as in Equation (50) the magnetic structure factor of the unit cell is ... 

In the case when the general decomposition in terms of atomic basis functions [Equation (54)] is used, the magnetic structure factor is written as ... 

P M magnetic structure factor m antiferromagnetic propagation vector... 

Figure 12 World-line Monte Carlo results for the square lattice Heisenberg antiferro-magnet Structure factor S and the long-distance limit C of the correlation function as functions of the linear system size L. The intercept on the vertical axis can be used to find the staggered magnetization. (Taken with permission from Ref. 104.)...

Figure 7.9 Dynamic magnetic structure factor S(q,co) is plotted along the (1,1) and (1, tt[-directions of the Brillouin zone for different ratios t lt.

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