Incommensurate spin structure

If the canting is not the same for each magnetic cation but varies in a regular way, then a number of commensurate or incommensurate spin structures can arise, including helical, helicoidal, cycloidal and sinusoidal. The helicoidal and sinusoidal ordering patterns are illustrated by the magnetic structure of TbMnOj (Section 7.10). 

The Bessel-fimction-type oscillations (Jo(o)t)) are in keeping with an incommensurate spin structure. Using dipolar sum modeling, the best agreement to the measured (iSR... 

The Mossbauer spectra of NpSe below at 38 K exhibit a fairly broad distribution of hyperfine fields pointing towards an incommensurate spin structure. The field distribution clearly changes shape with temperature meaning that details of the spin modulation are also temperature dependent. The spectral shape near indicates a first-order phase transition. A positive determination of spin structure by neutron diffraction is still outstanding (Blaise et al. 1992). At low temperatures type-II multi-fe order seems to be indicated, but this does not explain the distribution in hyperfine fields which still prevails at 4.2 K in the Mossbauer spectrum. 

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.

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. 

ZF-pSR spectra for T < 7n on polycrystalline material (Kalvius et al. 1994, 1995b) revealed a rather well defined (i.e., comparatively weakly damped) spontaneous muon spin precession pattern containing two distinct frequencies (fig. Ill, left). The variation of the precession frequencies with temperature is in agreement with a second-order phase transition at Tn (fig. Ill, right). But why two well-defined frequencies are observed, when the spin structure is allegedly incommensurate, is a serious problem. We return to this issue below within the discussion of CePtSn. 

The rather well-defined spin precession frequencies in CePdSn and CePtSn (especially the single frequency in the upper AFM state of CePtSn) are inconsistent with an incommensurately modulated spin structure. Dipolar sum calculations were carried out for the muon stopping site mentioned earlier and the spin structure of the upper AFM state of CePtSn as derived by Kadowaki et al. (1993), in order to elucidate the problem somewhat further (Kalvius et al. 1995b). The calculations generated four fi eld distributions of file type discussed in sect. 3.7 (see eq. 51) ... 

Fig. 2. Schematic description of the spin structures in the heavy rare earth metals. The initial high-T ordering, in all except the ferromagnet Gd, is to an incommensurate periodic spin order with propagation direction along the c-axis. CAM (c-axis modulation) is a structure in which the c-axis components of the moment are sinusoidally modulated which evolves into the APD (quasi anti-phase domain) in Er in which a gradual squaring-up of the c-axis moment occurs with additional order appearing in the basal plane. The temperatures of the transitions are from magnetization and neutron diffraction data. (After Legvold 1980.)...

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