The first chapter is followed by a companion overview of nanoscale multilayers involving rare earths and transition metals. One of the important series of rare earth intermetallic compounds are those possessing the ThMn12 type structure.
Introduction
The intermediate phases (except Gd) are oscillatory and are truly characteristic of the lanthanide metals. The robust nature and interesting variety of magnetic phases of lanthanide follow from the specific character of the lanthanide atoms.
Basic properties of lanthanide metals 1. Exchange mechanisms
Magnetic structures
For this case, the yaw angle measures the phase advance of the oscillation in this c-axis modulated phase (CAM). This suggests that the mechanism favoring a low-temperature ferromagnetic phase plays a role in the temperature dependence of the modulation wavelength.
Epitaxial growth of rare earth systems
In the ferromagnetic state, there is a uniform magnetoelastic distortion that results in a net energy gain called the "drive energy". The growth opportunities that can follow by adapting procedures pioneered by other hexagonal systems are summarized in this review.
OTTO]
Magnetism of epitaxial rare-earth crystals
- Strain relaxation
7 make it possible for the first time to separate the effects of strain and strain on the magnetic properties of the epitaxial crystal. Careful investigations of the epitaxial phase diagram have not been completed at this time.
Superlattices
As in the case of the lanthanide elements and their alloys, neutron scattering has played a key role in determining the magnetic structures of rare earth superlattices. In this simplified view, the superlattice consists of two N layers, each consisting of NR atomic planes of the lanthanide element with lattice spacing CR and neutron scattering length bR, and NA planes of a nonmagnetic element with lattice spacing and scattering length CA bA.
Scattering Wavevector, ~
In this case, the z-component of the magnetization alternates in sign with a periodicity described by Qz. Because of the polarization factors in the magnetic neutron scattering cross section, it is necessary to observe these peaks in the vicinity of the (10i0) reflection.
S~ttedng Wavevector, ~
Supedattice ordering
Oscillation of the remanent magnetization and saturation magnetic field for Gd/Y superlattices (from Kwo et al. This is reflected in a reduction in the number of bilayers contributing coherently and, consequently, in a broadening of the magnetic peaks observed in neutron scattering.
Y layers
-CRYSTAL NANOSTRUCTURES 59 of the saturation value and approximately the correct positions for the neutron scattering intensity. Values of the exchange energy, elastic constants and magnetoelastic constants are those of bulk Er (Rosen et al. 1973). 38, along with the coherence of the aligned and unaligned ferromagnetic phases as measured at low temperature.
For Dy, the single-ion magnetoelastic energy is minimized in the ferromagnetic state, resulting in an orthorhombic distortion of the hexagonal structure.
Field (kOe)
We conclude that this arises because the slot features in the Fermi surfaces of the studied nonmagnetic elements (Y and Lu) result in a wave of magnetization surrounding the substituted lanthanide atoms that slowly decays along the c axis. For a superlattice grown along b, the superlattice harmonics are located at a distance of 2x/A from the principal Bragg reflections in the a* direction (Flynn et al. Ferromagnetic (open circles) and antiferromagnetic (circles) neutron scattering intensities solid) peaks for b-[Gd]91Ys]s5.
Much interest, in the case of superlattices, attaches to the way these rare earths develop nanostructures and maintain long-range interlayer order.
![Fig. 43. Neutron scattering near the (002) peak for [DyglSCl4]~: (a) 160K;](https://thumb-ap.123doks.com/thumbv2/123dok/10275040.0/75.702.90.508.508.883/fig-neutron-scattering-near-peak-dyglscl-k.webp)
Conclusions
A caveat of critical importance in this regard is the central role of the deformation state in the description of magnetic behavior. The result is only the energy of the added charge 6q in the existing potential v(0) because this relaxed state is the energy minimum. A j0 average atomic concentration f j t h J0 component (j = 1 and 2 refer to T and R AJij components respectively) Jz A: modulation amplitude jth.
In the second section, we give a brief overview of the magnetic interactions and structures important for understanding amorphous R and R - T alloys.
Magnetic structure
On the other hand, in the 6 = 0 case, a speromagnetic (spin scattered) structure (SM) exists for large values. This can be attributed to the fact that the pure amorphous Fe is disordered magnetically; since the thickness of the Fe layer is between 10 ]k and 20 ]~, the Fe atomic fraction in the central region of the Fe layer is close to unity and its structure is amorphous, making no contribution to the moments. 9a and 10, exhibit the following features. i) Figure 9a shows that the hysteresis loops of Crll change their shape very little as the Fe layer thickness varies from 5 to 20.~, whereas the hysteresis loops of or± change their characteristics noticeably in the same range.
This implies that the magnetic properties in the direction perpendicular to the plane of the film strongly depend on the "interface" which is characterized by the anisotropic distribution of the constituent atoms, but the magnetic properties in the parallel direction are mainly determined by the "inner part" of the Fe layer.
3ooK
H(kOe)
Based on this systematic investigation, a three-dimensional diagram is shown in Fig. 14, which shows the main behavior of the magnetization. The smaller hill of [ ~r± [ on the left side of the valley is the region where the Dy magnetization dominates. iii). The shape of the hysteresis loops changed regularly as the nominal layer thicknesses of Dy and Co increased, as shown in Figure 2.
An example of the Fe layer thickness dependence of hysteresis loops for (4.5 A Tb)/(X ,~ Fe) with fixed Tb layer thickness of 4.5 ]~ is shown in Fig.
6/nwe)
Interface anisotropy
In this subsection we discuss the experimental determination of interfacial anisotropy and show some typical results. This is understandable because this region corresponds to thicknesses less than a few monolayers, where it makes no sense to consider a well-defined volume and interface anisotropy. The reason that ~,K~u maximum exists in the small X region (X'~ 6.~ in this case) is that the microstructure of such a CMF is similar to the interfaces in the large X CMF, which is a positive interface anisotropy. as indicated in (iii).
It is the single-ion anisotropy of R atoms and the anisotropic distribution of R and T atoms in the interfacial region that creates PMA.
MULTILAYERS
Fe moment orientation determinations in Tb/Fe multilayers have been reported by Cherifi et al. As is known, the orientation of the Fe moment can be determined from the intensities of the peaks 2 and 5 of the Fe component in the 3:X :l:l:X:3 ratio with X = 4 s i n 2 6}/(1 +cos26}) where 6} is the angle between the direction of the y-ray, which is perpendicular to the film plane, and the direction of the magnetic Fe moments. It shows that the temperature varies from 4.2 K. Thermal evolution of the angle between the average direction of magnetic moments and the film normal:.
Fe moments compared to the Fe moments in the interfacial region and exhibit in-plane anisotropy, forcing the Fe moments in the interface to lie in the film plane due to the exchange interaction. 1991) have reported MSssbauer studies of Tb/Fe. i) the thickness of the interface inferred from the distribution of hyperfine fields is approx. 2 monolayer Fe (ie ~5A), and this would mean that for sample 2 6 A T b / 1 0 A F e. a) Residual contribution to spectra in fig.
Bhf(T)
Theoretical model for magnetization and anisotropy
Figures 39a,b show an example of the distributions of (a) Co concentration and (b) magnetization for 6 ]~ Dy/6 ]~ Co. The work of Harris et al. can be considered as direct evidence that structural anisotropy is one of the necessary conditions to create PMA. Single-ion anisotropy arises from the interaction between the 4f electrons of R atoms and the local electric field created by neighboring ions.
For the ith slice of the CMF, the local single-ion anisotropy is given by a) Crystal field created by the neighboring ions, (b) local anisotropy K(i) at Z v The resulting anisotropy K u is the average of K(i) over the entire volume of the CME (c) Concentration distribution Cj (j= 1 refers to Co ,j=2 refers to Dy) along the film normal (after Shan et al. 1990).
Magnetization reversal and microscopic effects
The most common experimental approach to study the magnetization reversal is to measure the time dependence of the magnetization (or Kerr rotation angle) near the coercivity field. A model first presented by Street and Woolley (1949) has been widely used to interpret magnetization time decay measurements. The main idea of this approach is that there are two fields HN and HDW representing the nucleation and domain wall critical fields, respectively. the hysteresis loop will be square, as an inverted domain will expand immediately after nucleation.
The differential of the IRM curve, Zirr(H), is the energy barrier distribution of the pinning sites, while the DCD differentials, X~r(H), is the energy barrier distribution associated with nucleation.
Time (s)
Demagnetization anisotropy in CMF
The authors pointed out that the main difference between the techniques stems from the fact that different techniques measure different combinations of the R and T subnetwork magnetizations, for example, the measured torque is associated with the net magnetization of the R and T subnetworks; By measuring r as a function of H and then plotting an (r/H)2 vs r plot, one can find M and Ku simultaneously from the intersection and slope of the straight line passing through the experimental data. The figure also shows the experimental data and the calculated Ku curve in terms of the extraordinary Hall effect.
A can be determined experimentally in terms of the so-called "free powder magnetization" approach that was analyzed in detail by Verhoef et al.
Ivl.-M t (emu/cc)
The relative orientation of the atomic magnetic moment/z i and the local easy axis i at the ith site. H is along the film normal direction Z and H' is the in-plane field (after Wang and Kleemann 1991). . and the energy induced by an in-plane field H I. H ~ is the field in the x - y plane which must be calculated due to the existence of the in-plane magnetic vector in pure Fe layers. Classically the equilibrium position 6) of the momentum is given by. where d = D'/NAIz 2 is the ratio of the single-ion anisotropy energy to the exchange energy Eex = N A / t 2 .
We let h I = 0.1 in the fitting procedure because the in-plane field is much smaller than the exchange coupling and seems reasonable from the fitting procedure.
ThMn12-type structure
See text for distribution of different types of atoms in different locations. Valence of compounds (Ce, Yb)T4A18 a. but for the Cu compound the valence is 3 and in fig. there is no anomaly. Lattice parameters of the respective uranium compounds are included for comparison (Suski et al. 1989, Gueramian et al. 1991).
Lattice parameters a (upper curve) and c (lower curve) for RFeloRe2 compounds; diamonds show parameters for UFe]oRe2 (Gueramian et al. 1991).
Magnetic properties
In a discussion of the influence of the magnetic lanthanide atom on the structure of ThMn]2-type electronics, Amako et al. Compounds of the type (R, An)Fe4A18 have been the most frequently studied of all compounds of the type (R, An)M4Als. The T 2 dependence of the electrical resistance in the temperature range 4.2-100 K and the AF transition at 185 K were found.
These two singular points were confirmed by anomalies in the temperature dependence of the electrical resistance (Chetkowski et al. 1991).
In Table 12a (Feiner et al. 1981b) we present the results of magnetic and ME studies on compounds of Gd, Dy, Er and Lu. The value of the hyperfine field for DyMn6A16 is high, and probably also for DyCr6AI6 (Feiner et al. 1981b). CEF effects are most likely the cause of these slow spin relaxation rates (Feiner et al. 1981b).
Magnetic lanthanide compounds are ferrimagnetic (Feiner et al. 198 la), while Y compounds (Felner et al.
