Ferromagnetic Lattice Research Articles

Effective Magnetic Fields on Samarium-150 in Ferromagnetic Lattices

The ion-implanation perturbed-angular-correlation technique has been used to determine the hyperfine magnetic fields on samarium-150 nuclei in ferromagnetic iron, cobalt, nickel, and gadolinium lattices. Assuming the published value of 1400 kG for the field on samarium in iron, it follows that the hyperfine fields on samarium in cobalt and nickel, at 300\ifmmode^\circ\else\textdegree\fi{}K, are 1119\ifmmode\pm\else\textpm\fi{}64 and 352\ifmmode\pm\else\textpm\fi{}13 kG, respectively; and in gadolinium at 110\ifmmode^\circ\else\textdegree\fi{}K, -295\ifmmode\pm\else\textpm\fi{}30 kG. The hyperfine fields in iron, cobalt, and nickel are proportional to the atomic monents of the respective hosts. The major contribution to the field on samarium in gadolinium can be accounted for by polarized conduction-electron exchange. The gyromagnetic ratio for the 334-keV ${2}^{+}$ level in ${\mathrm{Sm}}^{150}$ is determined to be 0.47\ifmmode\pm\else\textpm\fi{}0.06.

Coupling of Magnons and Phonons at High Frequencies

AbstractA calculation is given describing the coupling of magnons and phonons, for a general wave vector, in a simple cubic ferromagnetic lattice. The source of magnetoelastic coupling is taken as the strain (or displacement) dependence of the magnetic dipole‐dipole energy, or Van Vleck's pseudodipolar energy. Particular solutions of the secular equation, describing the dispersion relation, are given for k ‖ z, z being the direction along which the spins are aligned.

Surface spin waves

A theoretical investigation has been made of surface spin waves localized at a (001) surface of a ferromagnetic simple cubic lattice with nearest and next-nearest neighbor exchange interactions. The excitations spectrum for the surface spin waves has been obtained and compared with that for bulk spin waves. A discussion is presented of the manner in which the decay of the spin waves from the surface depends on the values of the exchange integrals. The effect of a surface anisotropy field on the surface spin wave excitation spectrum and on the decay from the surface are considered.

Spread of Excitation in a Ferromagnetic Lattice

The spread of excitation in a ferromagnetic system is investigated in the limit of zero temperature. A situation is considered where there is a spin deviation in an otherwise aligned lattice. The second moment of the distribution of the excited spin is calculated and found to be equal to the product of the square of the elapsed time and the square of the group velocity of the magnons averaged over the Brillouin zone. A general expression is obtained for this average. The case of a simple cubic lattice with nearest-neighbor interactions is discussed in detail.

Monomer Pair Correlations

In this paper we evaluate the monomer pair correlation along the diagonals (p, p + 1) and (p + 1, p) of a square lattice otherwise packed with dimers. Using the perturbed Pfaffian technique the correlation can be expressed as a Toeplitz determinant ip |bi−j+1|/2x generated by the function B(θ)= ∑ −∞∞ bkeikθ=iτeiθ[sgn (sin θ)+iτeiθ1+iθeiθ]+ ∑ k=0∞(iτ)ke−ikθ,where τ = x/y and x and y are the activities of x and y dimers. We will calculate the determinant exactly and prove that the correlation decays with increasing monomer separation as B/4r½; where B is simply related to the decay constant of the diagonal spin correlation at the critical point of a square ferromagnetic Ising lattice. The exact value is found to be B = 0.989487291.

Spin-dependent scattering and resistivity of magnetic metals and alloys

Synopsis The purpose of this paper is to review and extend the explanation of the resistivity anomalies observed in certain magnetic metals and alloys in terms of spin-dependent scattering of the conduction electrons, For this purpose, the usual theory of electrical conductivity has been extended to include inelastic collisions with and without spin flip. Assuming the existence of an exchange interaction between the conduction electrons and unpaired electrons localized on particular atoms, the resistivity has been calculated for scattering by (i) isolated magnetic ions, (ii) pairs of exchange-coupled magnetic ions and (iii) 'spin-disorder in a ferromagnetic lattice. For models (i) and (ii) the magnetoresistance has also been investigated.

Diffusion in Cobalt-Nickel Alloys

The self-diffusivities of Co60 and Ni63 in cobalt-nickel solid solutions exhibit a greater activation energy below the Curie temperature (Tc) than above. Values of ΔQ=Q (ferromagnetic) —Q (paramagnetic) are approximately equal to RTc. This is interpreted to indicate that the increment in activation energy arises from an increase in the formation energy of a vacancy in the ferromagnetic lattice, with the additional binding energy arising from the interaction of a spin with the Weiss field.

Theory of random dilute magnets with application to MnZnF 2

The variation of the critical temperature T c of a magnetic crystal randomly diluted with non-magnetic atom s is evaluated as a function of dilution by a method which expands the susceptibility in a pow er series in the concentration p and extrapolates to find the radius of convergence. The method is applied to simple ferromagnetic Bravais lattices using the Ising and the Heisenberg models with spin and com pared with other methods. Values of the critical concentration when T c (p)-> 0 are derived and discussed in relation to those obtained from lattice statistics. The method is extended to antiferromagnetic crystals by considering the divergence of the ‘staggered 5 susceptibility. In particular, results are obtained for the MnF 2 lattice for comparison with experiment.

Low-Temperature Ferromagnetic Relaxation in Yttrium Iron Garnet

The ferromagnetic spin lattice relaxation time, ${\ensuremath{\tau}}_{0}$, has been obtained from 4.2\ifmmode^\circ\else\textdegree\fi{} to 300\ifmmode^\circ\else\textdegree\fi{} K in single-crystal yttrium iron garnet in which considerable care was taken to reduce both the extraneous rare earth and ferrous impurity ions. The measurements are shown to be indicative of the purely ferric ion lattice at temperatures considerably lower than we previously had been able to attain. A new feature brought out in these data is the observation that below approximately 150\ifmmode^\circ\else\textdegree\fi{}K, ${{\ensuremath{\tau}}_{0}}^{\ensuremath{-}1}$ vs $T$ is steeper than proportional to $T$, which implies an extremely low value at 4.2\ifmmode^\circ\else\textdegree\fi{}K. As a result of this, the nature of the ferric ion relaxation is more clearly defined over the low-temperature region.

Spin Wave Spectra for Canted Antiferromagnets and Ferromagnets

The magnetic resonance conditions and the spin wave spectra are found for canted antiferromagnetic and ferromagnetic lattices, where the cant is produced by magnetocrystalline anisotropy fields which are non-collinear. The sublattices are thereby caused to cant towards each other in antiferromagnets and away from each other in ferromagnets. The cant of the antiferromagnetic sublattices may produce a net moment (weak ferromagnetism) but does not alter appreciably the usual antiferromagnetic spin wave spectrum in the presence of anisotropy. The static susceptibility parallel (${\ensuremath{\chi}}_{\mathrm{II}}$) and at right angles (${\ensuremath{\chi}}_{\ensuremath{\perp}}$) to the vector difference of the anisotropy fields is calculated, and is shown to be altered from the noncanted result. It is shown that in antiferromagnets with no apparent weak ferromagnetism, canted sublattices may still be present, and can be detected by a nonzero ratio of ${\ensuremath{\chi}}_{\mathrm{II}}$ to ${\ensuremath{\chi}}_{\ensuremath{\perp}}$ at 0\ifmmode^\circ\else\textdegree\fi{}K. The ferromagnetic spin wave spectrum shows a sudden change from the normal spectrum as soon as one introduces the noncollinear anisotropy fields. An optical branch is formed and a high-frequency k=0 magnetic resonance is expected. This resonance is a consequence of the two-sublattice character of the canted ferromagnet and may be termed an exchange resonance.

A summation method for crystal statistics

A method is given for summing the high- and low-temperature expansions which come out of calculations on crystal statistics. If the series represents an algebraic function of sufficiently transparent structure, it may be summed exactly, otherwise various degrees of approximation result. It is always possible to establish whether the function is algebraic even if it cannot be summed exactly, provided that enough terms of the series are available. The procedure is applied to evaluate the spontaneous magnetization of square and cubical Ising lattices, and also to find approximate expressions for the initial susceptibility of the ferromagnetic and antiferromagnetic square lattices.

Ferromagnetic and Antiferromagnetic Curie Temperatures

The methods of calculating Curie temperatures used by Opechowski and Weiss are extended to higher spin values. Using the former, Curie temperatures are found for the face-centered, body-centered, and simple cubic and the hexagonal and quadratic layer lattices for spin \textonehalf{} to 3. Weiss' method is applied to the body-centered and simple cubics for spin \textonehalf{} to 2 and to the quadratic layer lattice for spin \textonehalf{} and 1. Numerical results show good agreement between the two methods for three-dimensional ferromagnetic lattices. However, the Opechowski method fails to locate the antiferromagnetic transition and predicts a transition for the two-dimensional lattices while the Weiss method does not. A classical-spin approximation is investigated and is found to give Curie temperatures within a few percent of the quantum-mechanical results for spin 1 or greater.

On the Theory of Cooperative Phenomena

§ 1. Introdnction Statistical treatment of the Ising model is important because it is a bommon problem through ferromagnetic lattice, alloy, imperfect gas and liquid (lattice gas), etc., though it is simple for the model of the ferromagnetism. Onsager1), Kaufman2), Nambu: j ) obtained a rigorous form of the partition function of the two-dimensional square lattice without

Some Properties of Homogeneously Distorted Cubic Ferromagnetic Lattices

The work of Becker and Kersten is amplified in that, starting with a convenient expression for the energy of a magnetically saturated and homogeneously distorted cubic ferromagnetic lattice, the problem is treated with especial reference to the crystallographic symmetry, rather than with the assumption of an isotropic medium, as was done by the above named authors. Application is made of the foregoing to the magnetostriction and magnetization of samples of iron, nickel, and their alloys under tension and compression. The agreement with experiment is qualitatively satisfactory. Further experimental data are needed for a quantitative check. Finally, there is a brief discussion of the effect of magnetization on elastic properties and of hysteresis, and a few important problems are listed.