Density magnetisability

Go Binary and Ternary Alloyed Thin Films. Most of the thin-film media for longitudinal and perpendicular recording consist of Co—X—Y binary or ternary alloys. In most cases Co—Cr is used for perpendicular recording while for the high density longitudinal media Co—Cr—X is used X = Pt, Ta, Ni). For the latter it is essential to deposit this alloy on a Cr underlayer in order to obtain the necessary in-plane orientation. A second element combined with Co has important consequences for the Curie temperature (T ) of the alloy, at which the spontaneous magnetisation disappears. The for... 

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. 

Magnetisation densities and polarised neutron diffraction optimised flipping ratio measurements... 

Before going further, it may be noted that the flipping ratio does not depend either on the Lorentz factor or on absorption in the sample. Certain instrumental parameters such as the polarisation of the neutron beam for the two spin states, the half wavelength contamination of the neutron beam and the dead-time detector can readily be taken into account when analysing the data. On the other hand, the extinction which may occur in the scattering process is not so easy to assess, but must also be included [14]. Sometimes, it is even possible to determine the magnetisation density of twinned crystals [15]. 

Moze, O., Caciuffo, R., Gillon, B. et al. (1994) Polarised-neutron diffraction study of the magnetisation density in hexagonal Y2Fe17, Phys. Rev. B, 50(13), 9293-9299. 

Concerning the magnetisation density in magnetic neutron scattering experiments... 

In these equations, J is the physical current density. Clearly, the magnetisation density is a derived quantity. 

Why, then, is the magnetisation density used The answer is that the magnetisation density is important for certain approximations which are usually made in analysing neutron scattering experiments. In the standard polarised neutron diffraction (PND) experiment [5], only one parameter is measured - the so-called flipping ratio . It is impossible to determine a vector quantity like the magnetisation density from a single number, unless some assumptions are made. The assumptions usually made are ... 

The magnetic field seen by the probe neutron is solely due to the magnetic dipole moment density of the unpaired electrons. In other words, the magnetisation density is simply related to the electron spin density by a multiplicative factor, and there is no ambiguity in its definition. 

This is the desired result which may be substituted into the scattering amplitude formula (6). The resulting scattering formula is the same as found by other authors [5], except that in this work SI units are used. The contributions to the Fourier component of magnetic field density are seen to be the physically distinct (i) linear current JL and (ii) the magnetisation density Ms associated with the spin density. A concrete picture of the physical system has been established, in contrast to other derivations which are heavily biased toward operator representations [5]. We note in passing that the treatment here could be easily extended to inelastic scattering if transition one particle density matrices (x x ) were used in Equations (12)—(14). 

In view of the central role that a magnetisation density plays for magnetic neutron scattering, it is useful to define a parameter for each reflection, called a canting angle, which gives a quantitative estimate of the deviation from the collinear approximation. The idea is as follows. 

The field of the sample in the applied field is known as its magnetisation, M. The magnetic flux density is now given by Equation (9.2). 

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