Norikiyo Uryû

A new effective field theory for the anisotropic Heisenberg ferromagnet

A new type of effective field theory (NEFT) is developed for the quantum spin system with anisotropic exchange interaction. The calculation is based on a two-atom cluster approximation, and effects from the rest spins are treated by the operator expansion technique assuming Ising character for surrounding spins. The Curie temperature Tc and spontaneous magnetization m are calculated for all Ising-, Heisenberg- and XY-like spin systems, and discussed comparing with results by other traditional pair spin theories. It is practically confirmed that Tc of the NEFT correctly reflects details of the geomtry of the lattice more than coordination number, and that it gives no anti-Curie point even for the XY-like spin system.

Ising Model with General Spin and Planar Rotator Model on the Bethe Lattice

In the Bethe lattice in which the Bethe approximation is exact, the Curie temperatures of the Ising model with spin \(S=\frac{1}{2}\), 1,…, \(\frac{5}{2}\) are obtained exactly by generalizing the method of Katsura and Takizawa for the system with \(S=\frac{1}{2}\). This method is applied to the planar rotator model on the infinite Cayley tree, and the critical temperature and the susceptibility are rigorously calculated. It is pointed out that the susceptibility diverges below the critical temperature, on the other hand the spontaneous magnetization vanishes as the ground state is degenerated infinitely.

Renormalized Spin Wave Theory of Nearly Two-Dimensional Ferromagnet K2CuF4

The temperature and the magnetic field dependences of the magnetization of the ferromagnetic layer-type compound K 2 CuF 4 have been analyzed by the spin wave theory which takes into account the spin wave interaction. It is shown that the spin wave interaction plays rather important role in the nearly two-dimensional magnetic system and gives rise to a logarithmic term in the expansion of the magnetization with respect to the temperature. The apparent T 3/2 temperature dependence of the magnetization can be shown to be realized in a certain temperature region. With the use of the exchange interaction constants estimated in the previous investigations, the present calculation shows excellent agreements with the experiments.

Higher Order Spin Coupling in Complex Compounds

From the analyses of the magnetic susceptibility and/or the magnetic heat capacity of the polynuclear complex compounds of iron group ions, it has been suggested that there exists an additional higher order spin coupling besides the usual Heisenberg exchange interaction. It is shown that the higher order spin coupling can be derived from the minimum condition of the free energy of the cluster system. For that purpose, a magnetoelastic term is introduced in the free energy and a dependence of the exchange coupling on the distance between interacting ions is assumed. In an alternative way, it is also shown that the higher order spin coupling can be derived from the perturbation procedure in which the spin-orbit interaction and the usual exchange interaction are taken as the perturbation. A quantitative comparison of the present theory with the values obtained from data analyses makes it clear that the magneto-striction is an important origin for the appearance of the higher order spin coupling.

The effect of the biquadratic exchange interaction on the Curie temperature of the mixed Ising ferromagnet

Abstract For the mixed Ising ferromagnet with S = 1 and S = 1 2 , the effect of the biquadratic exchange interaction J′ on the Curie temperature has been calculated by the use of the Bethe-Peierls approximation and its effect is shown to be large for J′ > 0.

The Curie Temperatures of Magnetically Dilute Ferromagnetics

By the method of concentration expansion, the initial gradient I g for a curve of the Curie temperature θ c ( p ) vs the concentration p of magnetic ions in randomly dilute Ising ferromagnet is calculated. The calculation is performed for the eight kinds of crystal lattices and the results are discussed with particular emphasis as to its dependence on the crystal structure and the second neighbor interactions. Various experimental data are compared with the present results of I g together with the other critical properties p c , θ c ( p ) obtained in the previous paper. As a whole, the behaviors of θ c ( p ) determined experimentally are well explained by the theory, and an importance of the second neighbor interactions is indicated for some compounds.

Effects of the Biquadratic Exchange Interaction in Linear Chain Antiferromagnet

The effects of the biquabratic exchange interaction on the temperature dependence of the magnetic specific heat and sublattice magnetization have been calculated with the use of the spin wave theory for linear chain antiferromagnet. The antiferromagnetic spin structure changes abruptly and begins to make a cant at a certain ratio P c of the biquadratic exchange interaction to the Heisenberg one, which is reasonably small enough to appear in the real antiferromagnet with large spin. This change of the spin structure is shown to give significant effects on the magnetic properties.

On the Magnetically Dilute Ferromagnetic System

The problems on the magnetic dilution in the ferromagnetic system are discussed by the use of the Ising model of spin 1/2. In addition to the exchange interaction between nearest neighbors, the next nearest neighbor (n.n.n.) interaction has been taken into consideration, and the magnetic properties are calculated by the method of concentration expansion. Particularly the critical concentration and the concentration dependence of the Curie temperature have been calculated for several lattice structures. In some crystal lattices, the n.n.n. interaction concerns to the change of the dimensionality of the magnetic lattice and then the effects of the n.n.n. interaction are quite remarkable in the concentration dependence. The numerical values of the critical concentration and the Curie temperature calculated in the present method are compared with the results previously calculated by various methods and good agreement is obtained.

Effects of the uniaxial anisotropy on the Curie temperature of the anisotropic Heisenberg ferromagnet with mixed spins S = 12 and S = 1

With the use of the pair model approximation, the effects of the D-term on the Curie temperature of the anisotropic Heisenberg ferromagnet with mixed spins S = 12 have been investigated and shown to be significant for D > 0.

Concentration Expansion Study of the Randomly Dilute Ising Ferromagnet with Second Neighbor Interaction

The critical properties of the randomly dilute Ising ferromagnet are discussed for the square lattice by the method of concentration expansion. The studies are mostly limited to the investigation of the effects of the second neighbor interaction on the concentration dependence of the Curie temperature T c ( p ) and on the temperature dependence of the critical exponent \barγ(θ) describing the susceptibility divergence. The series obtained is analysed by the root, ratio, and Pade approximant methods, respectively. As for T c ( p ), the previous results are reconfirmed by raising the degree of series expansion. The present calculation gives an apparent temperature dependence of \barγ(θ) and its behavior can be compared with the results previously calculated for some three-dimensional lattices. Furthermore, it is found that the essential feature of \barγ(θ) is not affected by the presence of the second neighbor interaction.