Antiferromagnetic structure

Fig. 12-3. The One-Dimensional Brillouin Zone for the Paramagnetic and Antiferromagnetic Structures. The point T is at the zone center, the point B is at the edge of the antiferromagnetic zone and the point O is at the edge of the paramagnetic zone. This latter point also corresponds to Hie edge of the second Brillouin zone of the antiferromagnetic lattice.

In the preceding section, the magnetic field was mainly used to determine the saturation magnetization of ferromagnets. However, it is now well established that many actinide compounds have complex magnetic behaviour and the application of an external field may change or suppress antiferromagnetic structures. 

In simple cubic compounds like NiO, MnO and CoO the metal ions lie on a face-centred cubic. As pointed out by Ziman (1952), for this structure and for spherical orbitals, antiferromagnetism with a finite Neel temperature must be due to interaction between next-nearest neighbours, because in any antiferromagnetic structure each moment will have as many parallel as antiparallel neighbours. In NiO and CoO the orbitals are not spherical, but in MnO the 3d5 ion is spherical In this compound the Neel temperature is therefore anomalously low, and there remains abnormally strong short-range order above the Neel temperature (Battles 1971). 

The assumption that BX=B2 is of course incorrect, particularly for one-electron centres such as donors in semiconductors. Equally serious is the assumption that the bandwidth B can be calculated neglecting the antiferromagnetic structure, so that electrons can jump to next-nearest... 

Fig. 26. Different types of magnetic structures in the ground stale of ftNijI C compounds, (a) For R = Pr, Dy or Ho commensurate antiferromagnelic structure, (b, c and d) for R = Er, Tb and Tm incommensurate antiferromagnetic structures (spin density waves) with a propagation vector q in the (a, 6)-plane, (b) Moments in the (a, b) plane and X to q. (c) Moments in the (a, b) plane and q. (d) Moments c and X to q (after Lynn et al.

It is obvious that the commensurate antiferromagnetic structure of fig. 39a coexists with superconductivity in HoNi2B2C, similar as in DyNi2B2C. On the other hand, as can be seen in fig. 43(a and c) the superconductivity is suppressed in the small temperature range where the two incommensurate magnetic structures of fig. 39(b and c) occur. Now the question is which of these two structures is more relevant for the near-reentrant behaviour. In Y().i5Hoo.85Ni2B2C the situation is totally different (fig. 43(b and d)). Here the a ... 

As reported by Talik and Neumann (1994) and Talik and lebarski (1995) the two compounds Gd3Ni and GdjRh show some complicated antiferromagnetic structure with ordering temperatures of 7n 100 K and 7n 112 K, respectively. 

Amici and Thalmeier (1998) used the quasi one-dimensional model mentioned in Section 4.9.1. In their approach the presence of ferromagnetically ordered Flo layers with the magnetic moments oriented perpendicular to the tetragonal c-axis is adopted and the competition of the RKKY interaction along the c-axis with the crystalline electric field is analyzed in order to determine the transition between the commensurate antiferromagnetic structure and the incommensurate c spiral shown in Figure 39. 

The value u> — 1) changes sign at y =, and as follows from Eqs.(42), the correlators show the antiferromagnetic structure of the ground state at antiferromagnetic correlations between the pairs. 

Using neutron diffraction and specific heat measurements, the 3-D transition temperature has been found to be 2.65 K159,169). The magnetic moments lie in the ab plane the 3-D antiferromagnetic structure consists of ferromagnetic planes parallel to the c-axis and coupled antiferromagnetically (Fig. 24). Under a low applied field, the 3-D structure is destroyed and the involved processes correspond to variations (increase or decrease) of the domains (see Sect. 3.5)170). The magnetic moment per unit Ni2+ ion is Mok = 2.25 ... 

Some samples exhibit a long-range modulation along the cube edge superimposed on the simple antiferromagnetic structure with a period of approximately 28 unit cells at room temperature. Modulation has been characterized as a sinusoidal variation in amplitude of resultant spin vector (no order perpendicular to this vector). 

Figure 8.6. In a two-dimensional triangular lattice, the colinear antiferromagnetic structure (a) is higher in energy than the noncolinear antiferromagnetic structure (b). The unit cells are shown by the dashed lines.

Magnetic coupling in all the ( a,-alkoxo)-()a,-carboxylato) dinickel(II) complexes is generally weak (171 < 8 cm but may be ferro- or antiferromagnetic. Structural factors that determine the magnetic ground state are not fully clear yet. Titrations with 2-hydroxyethanethiolate, a known inhibitor for urease (cf. Section IV), in most cases led to degradation of the bimetallic complexes (68). 

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