Takeo Nagamiya

Helical Spin Ordering—1 Theory of Helical Spin Configurations

Publisher Summary This chapter discusses the theory of helical and modified-helical spin ordering, confining to molecular field treatments and spin-wave calculations. Modifications of a helical spin order arise from anisotropy energies and an external magnetic field. Also, a description of the theory of complex helical spin configurations in complex crystalline lattices is given. A basic assumption made is that there exist isotropic exchange interactions between atomic spin moments of further neighbors as well as between neighboring moments. The coefficients of these exchange interactions are assumed as given constants. In this sense, the spin system dealt with may be called the Heisenberg magnet. Experimental observations relevant to the theory are referred to and are useful to elucidate the theory. This chapter deals with the role of conduction electrons in the exchange interaction; it reviews and discusses the observed magnetic and other properties of heavy and light rare-earth metals, and finally discusses the spin density wave in chromium.

Theory of the Ortho-Para Conversion in Solid Hydrogen

The rate of ortho-para conversion in solid hydrogen (H 2 ) is calculated taking two kinds of interactions between ortho-molecules into consideration: interaction between the nuclear spins of one molecule and those of the other molecule and interaction between the rotational magnetic moment of one molecule and the nuclear spins of other molecule. When an ortho-molecule converts into a para molecule, the rotational energy of the former is emitted as lattice phonons; we take the Debye model for the lattice vibrations and find that the dominant process is the emission of two phonons. The result for the rate of conversion (including a small effect arising from the emission of three phonons) is 1.94 percent per hour, which is comparable with the observed value of 1.75 percent per hour due to Cremer and of 0.9 percent per hour obtained recently by Hill. Further, the effect of a small amount of oxygen dissolved in solid hydrogen is treated and curves for the increase in average concentration as functions of time ...

Methods of Calculating the Crystalline Electric Field

Two convenient methods are developed for calculating the coefficients of expansion of the crystalline potential in spherical harmonics. One consists in extending Evjens elementary method of obtaining Madelungs constant, dividing the lattice into multipoles, and summing their contributions in an elementary way, and the other is an extension of Bertauts Fourier method of obtaining the electrostatic lattice energy of a point-charge lattice and that of a point-dipole lattice. For the latter, two slightly different methods are proposed. Applications to NaCl-type and CsCl-type lattices and to FeF 2 and CoF 2 lattices are given, and the merits and dismerits of the methods are discussed.

Modification of Spin Screw Structure due to Anisotropy Energy and Applied Magnetic Field

Recent development in the theory of screw structure of spins and its modification due to anisotropy energy and applied magnetic field is reviewed, with reference to neutron diffraction work on rare-earth metals and MnAu2.

Spin Arrangements in Magnetic Compounds of the Rocksalt Crystal Structure

The ground state spin arrangements in magnetic compounds of the NaCl type structure are studied by consideration of exchange interactions between nearest neighbors ( J 1 ) and between next-nearest neighbors ( J 2 ). Ferromagnetic arrangement as well as antiferromagnetic arrangements of the first kind, second kind, and improved first kind are obtained in different intervals of the parameter γ= J 2 / J 1 . Each of the three antiferromagnetic arrangements is degenerate due to the cubic symmetry of the crystal and the spin arrangement indefinite. Since the monoxides of the iron group elements are slightly distorted below the Neel point, the relevant small changes in J 1 and J 2 are taken into account to see if the degeneracy is removed. It turns out that the degeneracy is removed partially or completely. Helical spin arrangements appear in certain intervals of γ. Finally, anisotropy energy of the form D S z 2 is taken into account, but the degeneracy still remains unlifted in some cases.

Origin of the Magnetic Anisotropy Energy of Antiferromagnetic Cr2O3

The magnetic anisotropy constant Cr 2 O 3 arising from the dipolar interactions among the chromic ions was calculated to be -0.059 cm -1 per ion at absolute zero, and the magnetic anisotropy constant due to the crystalline field combined with the spin-orbit coupling was estimated from the fine-structure coupling constant of ruby and compared with that deduced from the antiferromagnetic resonance experiment by Dayhoff. The value from ruby is too large. The temperature dependence of the anisotorpy constant and that of the antiferromagnetic resonance frequency at zero field are discussed.

Magnetic Anisotropy Measurement of MnO Single Crystal

The magnetic anisotropy of MnO single crystal, grown by the Verneuil method, was measured using a torque balance. The results of the torque measurements at liquid air temperature could be summarized within experimental errors by a formula \begin{aligned} T{=}\text{C}_{1}\text{H}^{2}\sin\ (2\theta+\varepsilon_{1})+\text{C}_{2}\text{H}^{4}\sin\ (4\theta+\varepsilon_{2})+\text{C}_{3}\text{H}^{6}, \end{aligned} where H is the applied field intensity, θ the angle of rotation of H relative to the crystal, and e s and Cs are constants which depend in a certain way on the kind of crystallographic axis of suspension. In the case where [111] is the direction of suspension, C 2 =0. The C 3 H 6 term changed its sigh when the rotation was made in the revere sense; thus it represents a rotational hysteresis term. Alternative theoretical interpretations of the new 4θ-term are presented: it arises either from a possible small anisotropy energy within the easy plane of magnetization, or from reversible movements of the ...

Triangular Spin Ordering in Mn3Sn and Mn3Ge

The Fourier-transformed exchange matrix for the crystalline structure of Mn 3 Sn and Mn 3 Ge is analyzed in the case of a propagation vector parallel to the hexagonal principal axis and two modes of spin ordering are predicted, a helix of ferromagnetic basal net planes and a helix of triangular basal net planes. The effect of anisotropy energies is studied for the triangular spin ordering with zero propagation vector to uniquely determine the spin configuration and to account for the observation. Triangular helix, observed in Mn 3 Sn at low temperatures, is also discussed.

Spin‐Density Wave in Chromium and its Alloys

Sinusoidal, helical, and antiferromagnetic spin‐density waves are derived by the self‐consistent Hartree‐Fock method on the assumption of a simplified band structure consisting of octahedral electron‐ and hole‐Fermi surfaces, and it is found that the sinusoidal spin‐density wave has the lowest energy. To consider alloys, the sizes of the electron‐ and hole‐Fermi surfaces are varied. A possible flow of electrons from other bands into these electron and hole bands in the process of the formation of the sinusoidal and antiferro‐magnetic spin‐density wave is considered. Then, it is found that the wave number of the spin‐density wave jumps and approaches 1, i.e., comes closer to the antiferromagnetic wave, at a certain alloy concentration on the Cr–Mn side. The exact antiferromagnetism appears only when the electron‐ and hole‐Fermi surfaces have the same size.

Theory of the α-γ Phase Transition in the Ce Metal

The phase transition between the high density fcc phase, α, and the low density fcc phase, γ, of the Ce metal is discussed by introducing an explicit volume dependence of the Helmholz free energy in the Ramirez-Falicov model. It is shown that the phase boundary curve in the p , T -plane and the critical pressure and temperature, p c and T c are quantitatively in agreement with those observed for an appropriate choice of the parameters involved. Discussion is given for these parameters.