Spin slip

Erbium. The easy direction in Er is the c-axis, and below the second-order Neel transition (Tn = 85 K), the moments order in a longitudinal sine-wave structure. As the temperature is lowered the sine squares up. Aroimd Tb = 52 K, a basal plane component begins to order, leading to a helical AFM structure. Finally, at 7c = 20K a first-order transition into a steep cone (opening angle 30 ) FM spin structure takes place. Several (first-order) spin-slip transitions occur in the helical AFM phase. 

The neutron scattering observation of (long-range) magnetic incommensurability and the p.SR observation of local magnetic commensuration are reconcilable in a spin-slip model, as has been developed for the magnetic ordering of holmium and erbium (see, for... 

While a number of other lanthanide systems have been prepared as multilayers, few have been examined systematically as epitaxial films. The Oxford group, Jehan et al. (1993), report that 5000 A of Ho on Y exhibits clearer spin-slip structures than the bulk. They also report that Tn is depressed by 1 K, and the low-temperature c /6 phase is absent. 

Without question the results summarized here afford just a first glimpse of a rich field in which the magnetism of epitaxial films responds in an interesting and sensitive manner to the epitaxial constraint. The actual state of strain in this limit depends on both the film thickness and the growth conditions. In turn the magnetic state must depend on the state of strain and other factors that may influence, for example, the magnetic domain structure, in addition to the natural variables of field and temperature. An eventual complete description must include the statistical behavior of the spin-slip system. 

Erbium exhibits a complex magnetic behaviour, with at least four obserrable characteristic temperatures below rN = 85K, the moments order in a sinusoidal c-axis modulated (CAM) structure at rH=54K, there appears a component perpendicular to the c-axis resulting in a helicoidal structure this intermediate phase exhibits a sequence of lock-in transitions of commensurate phases (spin-slip structures) with wave vectors fm = f, 4 observed by iX-ray scattering (Gibbs et al. 1986), the... 

Fig. 81. Low-fleld magnetization process along the [100] axis at 1.5 K in hexagonal PrGa the first transition at 2.3 kOe (increasing field) is of spin-flip type, the other ones of spin-slip type the propagation vector is C = (, 0) in...

Fig. 82. Low-field magnetic structures of PiGa at 1.8 K note the successive spin-flip and spin-slip behaviours...

Fig. 83. Phase diagram of hexagonal holmium metal at 2 K with a magnetic field applied along the c axis note the successive values of the propagation vectors illustrating the spin-slip behaviour (after Jehan et al. 1992).

The concept of spin-slips or discommensurations was first introduced to explain the observed lock-in transitions in the magnetic spirals of lanthanide metals such pure Ho and Dy in terms of simple commensurate structures (fig. 127). More generally this term can be used to characterize structures which present periodic faults in a simple sequence of magnetic moments. For instance, let us consider, in an Ising chain, a sequence of 4 moments up followed by 3 moments down (this is found in some compounds). The propagation vector is In certain r ons of H-T space the propagation vector is slightly... 

Fig. 127. Self-consistent mean-field calculations of periodic stmctuies in Ho. Each circle represents the magnitude and direction of the ordered moment in a specific plane, relative to the size of the moment at absolute zero (lO/tg), indicated by the length of the horizontal lines. The orientation of moments in adjacent planes is depicted by the positions of the neighbouring circles, (a) The 12-layer zero-spin-slip structure at 4K. The open circle in the centre indicates the ferromagnetic component in the cone structure (b) the 11-layer one-spin-slip structure at 25 K. The bunched pairs of moments are disposed asymmetrically with respect to the easy axis in the vicinity of the spin slip (after Jensen and Mackintosh 1992).

It may be worth speculating here that the first-generation structural investigations of these materials are now coming to an end. In a second-generation round of experiments, using better instrumental resolution, we can anticipate the discovery of new effects. The situation may well parallel that of the lanthanide metals, for which the higher resolution available with synchrotron X-ray machines allowed the introduction of the spin-slip model (Bohr et al. 1989). 

Fig. 4. A schematic of the magnetic structure of Ho. (a) Its low-temperature cone phase shown projected onto the hexagonal plane. The structure is modulated along the c-axis with a unit cell of twelve atomic planes, and has a small ferromagnetic component along the c-axis. (b) The one spin-slip phase. (From Simpson et al.

Throughout this time is was appreciated that the helical structure of Ho, and indeed the rich diversity of complex structures that were discovered in the same period in many of the other lanthanides, resulted from a competition between the crystal-field and exchange interaction. It was first suggested by Vigren (1976) that this finely balanced competition could give rise to a structure with spin discommensurations or spin slips , but it was not until the first X-ray magnetic scattering experiments were performed that the full importance of this proposal was realized. 

Fig. 7. Temperature dependence of the modulation wave vector for three different Ho samples Ho(l) (crosses), Ho(2) (open circles), and thin film (solid circles). The spin-slip structure for the simply commensurate wave vectors are shown on the right. The data for r = j in Ho(l) were obtained from neutron scattering. Note also the appearance of two new lock-in wave vectors at j and (From Gibbs 1989.)...

Summary of the spin-slip phases and the associated wave vectors of the peaks observed in the non-resonant x-ray scattering experiments in Er (after Gibbs et al. 1986)... 

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