Towards the theory of ferrimagnetism

Two-sublattice ferrimagnet, with spin-$s_1$ operators $\bf{S_{1i}}$ at the sublattice $A$ site and spin-$s_2$ operators $\bf{S_{2i}}$ at the sublattice $B$ site, is considered. The magnon of the system, the transversal fluctuation of the total magnetization, is a complicate mixture of the transversal fluctuations of the sublattice $A$ and $B$ spins. As a result, the magnons' fluctuations suppress in a different way the magnetic orders of the $A$ and $B$ sublattices and one obtains two phases. At low temperature $(0,T^*)$ the magnetic orders of the $A$ and $B$ spins contribute to the magnetization of the system, while at the high temperature $(T^*,T_N)$, the magnetic order of the spins with a weaker intra-sublattice exchange is suppressed by magnon fluctuations, and only the spins with stronger intra-sublattice exchange has non-zero spontaneous magnetization. The $T^*$ transition is a transition between two spin-ordered phases in contrast to the transition from spin-ordered state to disordered state ($T_N$-transition). There is no additional symmetry breaking, and the Goldstone boson has a ferromagnetic dispersion in both phases. A modified spin-wave theory is developed to describe the two phases. All known Neel's anomalous $M(T)$ curves are reproduced, in particular that with "compensation point". The theoretical curves are compared with experimental ones for sulpho-spinel $MnCr2S_{4-x}Se_{x}$ and rare earth iron garnets.Comment: 9 pages, 8 figure

On the rotational dynamics of the Rattleback

The Rattleback is a very popular science toy shown to students all over the world to demonstrate the non-triviality of rotational motion. When spun on a horizontal table, this boat-shaped object behaves in a peculiar way. Although the object appears symmetric, the dynamics of its motion seem very asymmetric. When spun in the preferred direction, it spins smoothly, whereas in the other direction it starts to oscillate wildly. The oscillation soon dies out and the rattleback starts to spin in the preferred way. We will construct and go through an analytical model capable of explaining this behaviour in a simple and intelligible way. Although we aim at a semi-pedagogical treatise, we will study the details only when they are necessary to understand the calculation. After presenting the calculations we will discuss the physical validity of our assumptions and take a look at more sophisticated models requiring numerical analysis. We will then improve our model by assuming a simple friction force.Comment: 17 pages and 2 figures, typos corrected, some minor additions and rewording

Theory of ferromagnetic (III,Mn)V semiconductors

The body of research on (III,Mn)V diluted magnetic semiconductors initiated during the 1990's has concentrated on three major fronts: i) the microscopic origins and fundamental physics of the ferromagnetism that occurs in these systems, ii) the materials science of growth and defects and iii) the development of spintronic devices with new functionalities. This article reviews the current status of the field, concentrating on the first two, more mature research directions. From the fundamental point of view, (Ga,Mn)As and several other (III,Mn)V DMSs are now regarded as textbook examples of a rare class of robust ferromagnets with dilute magnetic moments coupled by delocalized charge carriers. Both local moments and itinerant holes are provided by Mn, which makes the systems particularly favorable for realizing this unusual ordered state. Advances in growth and post-growth treatment techniques have played a central role in the field, often pushing the limits of dilute Mn moment densities and the uniformity and purity of materials far beyond those allowed by equilibrium thermodynamics. In (III,Mn)V compounds, material quality and magnetic properties are intimately connected. In the review we focus on the theoretical understanding of the origins of ferromagnetism and basic structural, magnetic, magneto-transport, and magneto-optical characteristics of simple (III,Mn)V epilayers, with the main emphasis on (Ga,Mn)As. The conclusions we arrive at are based on an extensive literature covering results of complementary ab initio and effective Hamiltonian computational techniques, and on comparisons between theory and experiment.Comment: 58 pages, 49 figures Version accepted for publication in Rev. Mod. Phys. Related webpage: http://unix12.fzu.cz/ms

MAGNETIC PROPERTIES OF Cu1/2In1/2Cr2S4 AND SOME RELATED COMPOUNDS

Les propriétés magnétiques des composés spinelles M1/2In1/2Cr2X4 où M = Cu ou Ag et X = S ou Se ont été examinées. Dans le cas des sulfures, les moments de Cr sont ordonnés antiferromagnétiquement avec TN = 40 °K dans le cas M = Cu et TN = 17 °K dans le cas M = Ag. Aucun ordre magnétique à grande distance n'est observé à 4 °K pour Cu1/2In1/2Cr2Se4, tandis que le composé M = Ag est ferromagnétique en dessous de Tc ≈ 60 °K. La structure magnétique de Cu1/2In1/2Cr2S4 a été déterminée par diffraction des neutrons. Elle est bâtie à partir de quatre sous-réseaux d'aimantation parallèles aux grandes diagonales du cube.The magnetic properties of the spinels M1/2In1/2Cr2X4 with M = Cu or Ag and X = S or Se were investigated. In the sulphides the Cr spins order antiferromagnetically at TN = 40 °K for M = Cu and at TN = 17 °K for M = Ag. No spin ordering above 4 °K was observed in Cu1/2In1/2Cr2Se4, while Ag1/2In1/2Cr2Se4 is ferromagnetic below Tc ≈ 60 °K. The antiferromagnetic spin structure of Cu1/2In1/2Cr2S4 as determined by neutron diffraction, consists of four spin sublattices with sublattice magnetizations along the cubic body diagonals

STRONG ANISOTROPY IN THE CUBIC FERRIMAGNET FeCr2 S4

On a mesuré l'aimantation des monocristaux de FeCr2S4 en fonction du champ magnétique dans les directions [100], [110] et [111] entre 4 °K et Tc = 195 °K ; [100] est l'axe d'aimantation facile et la direction [111] est très difficile. A 4 °K la rigidité magnétique dans la direction [100] correspond a K1 = 3 x 106 erg. cm-3. Des spectres Mössbauer du 57Fe dans FeCr2S4 ont été mesurés à 4 et 77 °K. A 4 °K il y a un dédoublement quadrupolaire non axial. Dans Cd0.9857Fe0.02Cr2S4 à 4 °K, au contraire, le dédoublement quadrupolaire est axial. L'anisotropie magnétique et les dédoublements quadrupolaires sont discutés partant d'un schéma de niveaux d'énergie d'un ion Fe2+ isolé situé dans un site tétraédrique.The magnetization of single crystals of FeCr2S4 has been measured between 4 °K and Tc = 195 °K with the field in the [100], [110] and [111] directions. [100] is the easy axis of magnetization, [111] is very hard. At 4 °K the stiffness in the [100] direction corresponds to K1 = 3 x 106 erg.cm-3. 57Fe Mössbauer spectra of FeCr2S4 has been obtained at 77 and 4 °K. A non axial quadrupole splitting is observed at 4 °K. A uniaxial quadrupole splitting is found in Cd1-xFe57xCr2S4 (x = 0.02) at 4 °K. The magnetic anisotropy and the quadrupole splittings are discussed on the basis of a single ion energy level scheme of tetrahedrally coordinated Fe2+

MAGNETIC PROPERTIES OF THE INTERMETALLIC COMPOUNDS RFe2

Nous avons déterminé les aimantations à saturation à 4,2 °K, la température de Curie et les paramètres de la maille pour un certain nombre de composés intermétalliques du type RFe2 (R = Ce, Sm, Gd, Tb, Dy, Ho, Er, Y, Zr). Le comportement magnétique des composés RxY1-xFe2 (R = Gd, Tb, Er, Ce) a été étudié en fonction de x. On discute les moments variables du Fe dans les composés RFe2 et l'absence d'une température de compensation dans la variation thermique de l'aimantation des composés RFe2 (R = Gd, Tb, Dy, Ho).For a number of compounds RFe2 (R = Ce, Sm, Gd, Tb, Dy, Ho, Er, Y, Zr) the lattice constant, the saturation moment at 4.2 °K and the Curie temperature have been determined. The magnetic properties of the compounds RxY1-xFe2 for R = Gd, Tb, Er and Ce have been studied as a function of composition. The variable iron moment in the compounds RFe2 is discussed in terms of a rigid-band model with a non-saturated d-band magnetization. It is shown that the absence of a compensation point in the temperature dependence of the magnetization for R = Gd, Tb, Dy and Ho is a result of a relatively strong negative R-Fe interaction