Magnetic modulated structure

Neutron diffraction data indicate magnetic modulated structures for the compounds. The magnetic structure of TbCoSn in the temperature range 1.4-5 K is described by the wave vector = (0,5,-j ). With an increase of the temperature, the wave vector changes at f k = 5 K to 2 = (0, 5,0). The R moments of other compounds form a square modulated magnetic structure along the V axis. The wave vector is k = (0,ky,0) with ky = j in DyCoSn, in HoCoSn and in ErCoSn. 

Figure 6.5. ED in (001) of (a) O2-annealed 2212 and (c) the HRTEM modulated image—the atom columns are shown with an incommensurate (modulated) structure, (c) N2-annealed with 2212. (Temperature of anneal 400 °C.) (d) its HRTEM image (/ , d) show the commensurate structure, (e) Changes in magnetic flux inclusion annealed in (a) N2 (b) in oxygen. The resulting changes in the electronic structure due, e.g., to oxygen interstitials, influence the catalytic process, (f) (001) CBED of sample annealed in oxygen. HOLZ is arrowed. (After Gai J. Solid State Chem. 104 119.)...

Fig. 11. Orthorhombic distortion of tetragonal HoNi2B2C (a) upon cooling from 15 K to 1.5 K the neutron diffraction reflection (332) splits into two peaks, (b) Schematic presentation of the distortion a,b — original tetragonal axes dashed line tetragonal basal plane —f shift of the Ho atoms leading to the orthorhombic cell with the axes onh- Thick arrows Ho magnetic moments in the commensurate c-axis modulated structure...

Dertinger (2001) also found that the a-axis modulated structure a of Figure 39 is much more sensitive to pressure, compared to the other two magnetic structures of Figure 39, and it even disappears at relatively low values of P. Interestingly he observed near-reentrant behavior also at temperatures and pressures where the a structure had disappeared. Therefore he concluded that the near-reentrant behavior in H0M2B2C cannot mainly be caused by the presence of the a incommensurate magnetic structure. This problem will be further discussed in the next Section 4.9.4. 

In addition to one-dimensional modulations considered above, both two-and three-dimensional modulations are possible. Furthermore, atomic parameters affected by modulations may be one or several of the following positional (as shown in Figure 1.52 and Figure 1.53), occupancy, thermal displacement, and orientation of magnetic moments. The latter, i.e. commensurately or incommensurately modulated orientations of magnetic moments are quite common in various magnetically ordered structures (e.g. pure lanthanide metals such as Er and Ho), and both the value of the modulation vector and the amplitude of the modulation function often vary with temperature. 

Measurements of the temperature dependence of x indicate the onset of antiferromagnetic ordering in UPd2Ge2 below 139 K (Ptasiewicz-Bak et al. 1981). Results of neutron diffraction measurements point to a longitudinally modulated structure with an amplitude of 2.80jub and a propagation vector [0, 0, ]. Magnetic moments were found only on the U atoms. 

Fig. 7.17. Arrangement of magnetic moments in more complex ordered materials (a) a helimagnetic structure (b) a sine wave modulated structure.

The antiferromagnetic spin structure of YbNiAl was determined by neutron dif action experiments. Below Tn = 2.9K a sinusoidal modulated structure with an amplitude of /4=1.9(2))1b is observed (Ehlers et al. 1997). The magnetic propagation vector is m = [0.779(1)00], and the ytterbium magnetic moments lie perpendicular to the hexagonal c-axis. These investigations are paralleled by a detailed study of Al nuclear spin-lattice relaxation measurements (Fay et al. 1997). 

Fig. 56. Magnetic phase diagram of CeAlj as derived from thermal expansion (solid lines, Schefzyk et al. 1985a) and neutron diffraction ( , O, dashed lines Barbara et al. 1980). Dotted line is an interpolation (schematic) II, type-II antiferromagnetic structure M, modulated structure PM, paramagnetic phase.

In this section we give a brief review of the experimental results including the layered or compositionally modulated structure for R/T multilayers, the layer thickness and temperature dependencies of magnetic properties for Dy/Fe, Dy/Co and Tb/Fe multilayers. We will not provide a comprehensive review of all recent work in this field. Rather, our aim is to focus on discussing die above fimdamental properties, and only limited references which are closely related to this discussion are dted. The role that the interfacial magnetism plays in determining magnetic properties will be emphasized. 

Kini [29] considered the electric field-induced static modulated structures of nematic liquid crystals. The electric field E was applied parallel to the sample, and the initial uniform director orientation was tilted with respect to the sample boundaries in the plane normal to E. The formation of modulated structures was shown to be favored when a stabilizing magnetic field H of sufficient strength was applied along the initial director orientation. This type of modulated instability was observed in experiment [30]. 

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