Tôru Moriya

Anomalous Properties around Magnetic Instability in Heavy Electron Systems

Spin fluctuations in heavy electron systems around their antiferromagnetic instability are discussed from a phenomenological point of view by using a sum rule for the dynamical susceptibility valid in the strong correlation limit. As a result the dynamical susceptibility takes the same form as in the standard spin fluctuation theory of weak itinerant antiferromagnetism, although the values for the parameters are substantially different from those in d-metals. The expression for the Neel temperature given in terms of the staggered magnetization at 0 K and the spin fluctuation parameters are successfully compared with experiment. Anomalous (non-Fermi liquid) behaviors reported for the specific heat and electrical resistivity in some heavy electron systems around their magnetic instabilities are explained in terms of this theory.

Antiferromagnetic Spin Fluctuations and Superconductivity in Two-Dimensional Metals -A Possible Model for High Tc Oxides

Spin fluctuations in antiferromagnetic and nearly antiferromagnetic two dimensional (square lattice) itinerant electron systems, as a possible model for high T c superconductors, are investigated by using the self-consistent renormalization theory. The electrical resistivity and the nuclear spin relaxation rate due to the spin fluctuations in the normal state are calculated. The results in the nearly antiferromagnetic regime as applied to high T c oxides seem to explain the experimental results both in their temperature dependence and in their orders of magnitudes. By using the same spin fluctuations we discuss superconductivity due to the spin fluctuation mechanism within a weak coupling theory. The order parameter is shown to have B 1 g or A 2 g symmetry and the critical temperature is evaluated to be of the right order of magnitude.

Recent progress in the theory of itinerant electron magnetism

Abstract A review is given of recent theoretical investigations toward unified understanding of magnetism in narrow-band electron systems. It is emphasized that the classical controversy between the itinerant and localized models have been resolved into a more general and well-defined problem of spin density fluctuations in a general sense. The local moment picture is a limiting form of general spin fluctuations; and in its opposite limit we have weakly ferro- and antiferromagnetic metals. As an approach from the latter limit, the self-consistent renormalization theory of spin fluctuations is shown to have been quite successful in explaining and predicting a number of qualitatively new physical properties of this class of materials. More recent theoretical studies of spin fluctuations from a general point of view interpolating between the above-mentioned two limits seem to lead to a unified picture of magnetism in narrow-band electron systems including 3d transition metals and magnetic compounds.

The Effect of Electron-Electron Interaction on the Nuclear Spin Relaxation in Metals

The rate of the nuclear spin-lattice relaxation due to the hyperfine interaction is shown to be enhanced by a repulsive electron-electron interaction. The relaxation time is expressed in terms of the wavelength and frequency dependent magnetic susceptibilities of the conduction electrons. The magnetic susceptibilities are calculated taking account of the electron-electron interaction of the δ-function type with a random phase approximation. The Korringa relation between the frequency shift and the relaxation time is shown to be altered by the electron-electron interaction. The theory applies also to the electron spin relaxation of localized magnetic atoms in certain alloys.

Effect of Spin Fluctuations on Itinerant Electron Ferromagnetism. II

The theory of the effect of spin fluctuations on itinerant electron ferromagnetism, which we have developed previously, is extended to include the ferromagnetic phase. The correction to the Hartree-Fock free energy as a function of magnetization is expressed in terms of the transversal dynamical susceptibilities and is actually calculated by using a modified random phase approximation for the dynamical susceptibilities; the random phase approximation is modified so as to give a consistent static limit throughout the whole temperature range covering both below and above the Curie point. As a result, the magnetization at low temperatures shows a T 3/2 dependence due to the spin wave excitations, the Curie temperature is generally lowered from the Stoner (Hartree-Fock) value and the magnetic susceptibility above the Curie temperature shows an approximate Curie-Weiss behavior.

Magneto-volume effect and invar phenomena in ferromagnetic metals

Abstract The magneto-volume effect is discussed in terms of the recent unified theory of ferromagnetic metals based on general spin fluctuations. Explanations are given for the large negative thermal expansion observed in weakly ferromagnetic metals and for the invar effect in some f.c.c. alloys. Large thermal expansion in nearly ferromagnetic metals is also pointed out.

Contribution of Spin Fluctuations to the Electrical and Thermal Resistivities of Weakly and Nearly Ferromagnetic Metals

The electrical and thermal resistivities due to the spin fluctuations in weakly and nearly ferromagnetic metals are studied by using the s-d band model and the self-consistently renormalized spin fluctuation theory for the d-band electrons. The resistivities are calculated in the whole temperature range of interest and their temperature dependences are discussed in detail. The resistivities are shown to be suppressed significantly by the renormalization from those calculated by using the RPA results for the spin fluctuations. Particularly the electrical resistivity can have a tendency towards saturation with increasing temperature.

Spin fluctuations and high temperature superconductivity

Theory of spin fluctuations for itinerant magnetism and its application to high temperature superconductivity are reviewed. After a brief introduction to the whole subject the developments of the self-consistent renormalization theory of spin fluctuations are summarized with particular emphasis on critical properties at the quantum phase transitions. Most of the anomalous properties in the normal state of high-Tc cuprates are understood as due to the critical behaviours for the two dimensional antiferromagnetic metals. By analysing the nuclear magnetic relaxation rate and the T-linear term of resistivity, the set of parameters to specify the spin fluctuations are determined. It is shown that by using the parameters thus obtained one can describe other quantities as well, e.g. optical conductivity. Then we proceed to the theory of superconductivity by the spin fluctuation mechanism. After some discussion on the weak coupling treatments, the strong coupling theory is reviewed. It is shown that the set of parameters determined by the normal state properties of the high-T c cuprates just give a transition temperature of the right order of magnitude. Among the parameters, the most sensitive one for T c is the frequency spread of the spin fluctuations. This fact enables us to present a possible unified picture of the antiferromagnetic spin fluctuation-induced superconductors, including heavy fermion superconductors and organic superconductors. This point of view may be confirmed to a certain extent by microscopic calculations based on the fluctuation exchange approximation for the two-dimensional Hubbard models representing not only the cuprates but also organic and trellis lattice compounds. The review is concluded with some discussions on future problems, e.g. the pseudo spin-gap in the under-doped region.

Spin Fluctuation Theory of Itinerant Electron Ferromagnetism –A Unified Picture

Spin fluctuations and the thermodynamical properties of itinerant electron ferromagnets are discussed from a general point of view by using a simple model with a small number of physical parameters and approximations in the functional integral formalism. We give unified expressions for the Curie temperature and the magnetic susceptibility which interpolate between the weakly and strongly ferromagnetic limits. In general, both the transversal and longitudinal components of the local spin fluctuations contribute to the Curie constant and the former (latter) is predominant in the local moment (weakly ferromagnetic) limit. It is pointed out that the amplitude of the local spin fluctuations can be saturated when there is an upper or lower bound of the energy band not too far from the Fermi level, resulting in a Curie-Weiss susceptibility of a local moment type, even without well-defined local moments. A transition between two different kinds of local spin states can also be expected in some cases.

Nuclear magnetic relaxation in weakly ferro-and antiferromagnetic metals

Abstract Nuclear spin—lattice relaxation rates 1 T 1 in weakly ferro- and antiferromagnetic metals are studied by using the renormalized spin fluctuation theory. The results predict different temperature dependences of T1 for ferro- and antiferromagnets. They are also compared with the consequences of the random phase approximation and the localized moment theory.