Incommensurate magnetic structure

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 ... 

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 conclusion, field dependent single-crystal magnetization, specific-heat and neutron diffraction results are presented. They are compared with theoretical calculations based on the use of symmetry analysis and a phenomenological thermodynamic potential. For the description of the incommensurate magnetic structure of copper metaborate we introduced the modified Lifshits invariant for the case of two two-component order parameters. This invariant is the antisymmetric product of the different order parameters and their spatial derivatives. Our theory describes satisfactorily the main features of the behavior of the copper metaborate spin system under applied external magnetic field for the temperature range 2+20 K. The definition of the nature of the low-temperature magnetic state anomalies observed at temperatures near 1.8 K and 1 K requires further consideration. 

We may have defined Equation (44) in a slightly different manner as is usual in the literature. Instead of writing R in the argument of the exponential function, one can write R/ = R/ + [similarly to f,- = x vectors in Equation (29) for atom displacements]. In such a case the Fourier coefficients, Tiy-, of the new expression are related to those of Equation (44) by a phase factor, Sk/ = Tiyexp(—27rikxy), that depends on the atom positions inside the unit cell. We shall see that the convention we have adopted is more convenient for a unified description of commensurate and incommensurate magnetic structures. 

The incommensurate magnetic structure of YbPtAl was determined by neutron diffiac-tion experiments. The wave vector is = [0.3000]. The presence of (000) satellites shows that the directions of the magnetic moments are not parallel to the propagation direction a (Bonville et al. 2000a,b). 

Because of their structural similarities, Gd alloys easily with all the other heavy lanthanide elements, R. These alloys transform from ferromagnets to incommensurate magnetically structured materials once the concentration of R exceeds a certain critical concentration x. We can use the phase diagram to predict these critical alloy concentrations. These are listed in Table 11 and are in good agreement with experimental values where known. 

Fig. 51. Left Tetragonal crystal structure (I4/mmm) of RN12B2C. Low temperature AF2 magnetic structure with [110] easy axis is indicated by arrows. a = b = 3.52 A and c = 10.53 A for R = Ho. Reciprocal lattice vectors are given by 2a, 2b and 2c where a =, etc. Right Magnetic (Tic incommensurate magnetic structure, Tjv simple AF structure) and superconducting (Tc) transition temperatures in Kelvin for the RNi2B2C series.

Fig. 14.40. A schematic representation of the high temperature incommensurate magnetic structure of TbAUj. The gold atoms are not shown. (Atoji, 1968a).

---