Takehiko Oguchi

Zero-Point Spin Reduction of an Antiferromagnet

Zero-point spin reduction in the low-dimensional antiferromagnet is discussed by the spin wave theory taking into accOtmt kinematical interaction due to finite magnitude of spin. This method is applied to KCuF, and the result is in good agreement with the obxad served one. Furthermore the values of zero-point spin reduction of several other chain· structure antiferromagnets are predicted. §.1. Introduction A large zero-point spin reduction in the antiferromagnet of the low dimen~ sionality has recently been observed. In the layer-structure antiferromagnet K 2MnF 4, the observed values of zero-point spin reduction agree with those of a simple two-dimensional spin-wave theory.D It has been found that the zero-point spin reduction in the one-dimensional antiferromagnet KCuF 8 is nearly 45%. 2) However, the kinematical interaction d,ue .to the restriction on the number of spin deviations possible at any given site cannot always be neglected i.n the antiferro- · magnet of the low dimensionality even at absolute zero. Especially the zero-point spin reduction of the ideal spin-wave theory diverges in the one0dimensional Heisenxad berg antiferromagnet. As the zero-point spin reduction should not. be over the spin magnitude S, the divergence means that the spin-wave theory which does not take· account of the kinematical interaction cannot be trusted. The effect of the kinematical interaction for zero-point spin reduction was first estimated by Herbert 8J for the Heisenberg antiferromagnet with each spin 8=1/2,, but he did not give any attention to the low-dimensional antiferromagnet. In the present paper his method is extended to the case of general S, and the effect of the ki~ematical interaction is taken into account in the calculation of the zero-point spin reduction, and several antiferromagnetic chain-structure compounds are disxad cussed.

Theory of" Random Mixtures of Ising Spins

Magnetic properties of the annealed and quenched systems each in the bond and site models are investigated by the Kikuchi pair approximation. In the annealed system, phase diagrams and susceptibilities are obtained. Two critical temperatures in some case in the bond system and no critical concentration in the site system are obtained. The physical interpretation of them is given. In the quenched system, two different approximate conditions are considered for the complete randomness. The case of the· first condition is equivalent to the cluster variation method proposed by Sato, Arrott. and Kikuchi, and the results are in agreement with those obtained by Katsura, and Matsubara. The second is essentially equivalent to the average coordination number method by Sato, Arrott and Kikuchi for the dilute ferromagnetism. However, the results for both cases are unreliable at low temperaxad tures, because of the appearance of negative entropy. This is fnevitable under the pair condition.

Phenomenological Theory of the Random Ordered Phase

Very recently Miyako et aJ.ll ,2l have observed nonlinear susceptiblities in some dilute magnetic alloys. They (X 2 and X4) seem to show a divergent behavior at the freezing temperature Tr. The divergence of X2 at Tr was predicted first by Katsura3 l and phenomenologically by SuzukiY Takayama5l also obtained this result on the basis of the ROP.6 l, 7 l Ueno8l showed exactly the divergence of X2 in the spherical model with random infinite-ranged interactions. For the experiments by Miyako et al., 1, 2J Suzuki9 l gave a comment by presenting a phenomenological theory of the ROP. His theory does not seem to be compatible with the original idea of the ROP nor the experiment. We shall show another one and try to interpret the experiments, in particular, that on (Ti 1 -x V x) 2 03. 2) As Toulouse pointed out, 10 l the frustration effect plays an essential role in the competing random bond system. It is necessary for the frustration to occur that the lattice has closed loops. Works based on the ROP took account of the frustration effect by investigating clusters with closed loops.7l ,lu Takayama5l treated this effect by using a phenomenological parameter. On the other hand, in many of the theories in which the Edward-Anderson order parameter was used, it is not clear how the frustration is taken into account. The replica method of spin glass 12l seems to obscure it. It is also difficult to trace the effect in the theory of the GLP.13l, 3l Recently, making use of the gauge invariance and the measure of frustration introduced by Toulouse, several authors studied the ground-state properties14 l and made a reformation in terms of the frustration.5)

Theory of random bond model

Abstract The free energy of random bond model (± J model) is derived by the effective hamiltonian method. The average of the free energy over sites contains a parameter ξ concerned with the frustration effect. The second-order phase transition is shown to occur only when ξ is larger than a critical value.

Two-Magnon Bound States in the Triangular and Honeycomb Heisenberg Ferromagnets

The oound state problems associated with two magnons ir{ the two-dimensional triangular and honeycomb ferromagnet Of spin. l/2 with nearest neighbor exchange integral J(>O) are studied. The Hamiltonians are rewritten in terms of Dyson-MaUiev boson representation and .the 3 X 3 secular equations to determine the bound state energies are obtained for both ferromagnets. At most two bound states exist for a triangJJiar ferromagnet and, on the other hand, for a honeycomb ferromagnet three bound states were found to exist extremely . near the free two-magnon band and at the corner· of the first Brillouin zone for the total wave vector K of the pair. The effect of the number z of nearest neighboring bonds on the appearance of bound states is discussed.

Theory of the three-state ferromagnetic and antiferromagnetic Potts model

Abstract The three-state generalized Potts model is expressed by the spin Hamiltonian and solved by the effective Hamiltonian method. For the three-state antiferromagnetic Potts model, the high temperature series of staggered susceptibility is obtained, which indicates that the second-order transition occurs except the two-dimensional lattice.

Ground-state properties of the Heisenberg antiferromagnet-numerical study

Abstract The ground states of the spin-1/2 antiferromagnetic Heisenberg and XY models are investigated on the fully-frustrated triangular lattice. We extrapolate numerically exact properties of finite size systems (up to 21 spins) to the infinite lattice to estimate the energy and spin state.

An Approximate Method for Incommensurate Phase Transitions and Its Application to NaNO2

The temperature dependence of the wavevector qm of the maximum fluctuating mode and the wavevector qo characterizing the ordered state in incommensurate phase are obtained by taking account of the difference of fluctuation between the short range and long range inter· actions. The former interaction is treated by the Bethe-Peierls approximation and the latter by the molecular field approximation. The application to NaNO, gives a qualitative explana· tion of the temperature dependence of qm and susceptibility X (qm) above the critical temperature except the critical region. It is pointed out that the temperature dependence of qm and qo shows a critical behavior.