Self-consistent Renormalization Research Articles

Spin Fluctuations of Itinerant Electrons in MnSi Studied by Muon Spin Rotation and Relaxation

The static and the dynamic character of the hyperfine field in weak itinerant helimagnet MnSi has been probed by using positive muon spins. The Knight shift has been measured by the transverse-field muon spin rotation method, which revealed a large negative hyperfine field at interstitial sites, even larger compared with other ferromagnetic metals. The hyperfine coupling constant A hf has been determined to be -4.8 kOe/µ B . The divergence of the muon spin-lattice relaxation rate near magnetic ordering has been observed for the first time by using the longitudinal-field muon spin relaxation method. The observed temperature dependence was found to be in agreement with the prediction of the self-consistent renormalization theory of itinerant electron spin fluctuations developed by Moriya and his collaborators.

NMR Investigations on the Spin Fluctuations in Itinerant Antiferromagnets. I. V3Se4 and V5Se8

The properties of the spin density fluctuations in the itinerant antiferromagnetic compounds V 3 S 4 and V 5 S 8 have been investigated in both the paramagnetic and the antiferromagnetic states by using the pulsed NMR technique. Although it has been proposed that V 3 S 4 is one of weak itinerant antiferromagnets because of the low ordering temperature, small staggered moment M Q and the temperature dependence of M Q , the temperature dependence of the nuclear spin-lattice relaxation rate 1/ T 1 are not in accord with the prediction based on the self-consistent renormalization theory of spin fluctuations for weak itinerant antiferromagnets. In V 5 S 8 , the observed temperature independent process of 1/ T 1 in the paramagnetic state and the temperature dependences of the bulk susceptibility and M Q are not explained from either weakly magnetic limit or localized moment limit, suggesting this material is in the intermediate magnetic regime.

Recent progress in the theory of itinerant electron magnetism

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.

Longitudinal Ultrasonic Attenuation in Anisotropic Itinerant Electron Ferromagnets

The longitudinal ultrasonic attenuation due to spin fluctuations in anisotropic itinerant electron ferromagnets is investigated by using the self-consistent renormalization theory of spin fluctuations by Moriya and Kawabata. The anomalous attenuation at the phase boundary and the broad peak above the Curie temperature are derived, and the temperature and magnetic field dependences of the attenuation coefficient are discussed. The numerical calculations were performed using an electron gas model.

Observation of the Antiferromagnetic Order in Metallic Compounds V3S4and V3Se4

The 51 V NMR in the metallic V 3 S 4 and V 3 Se 4 have been investigated in the temperature range between 1.4 K and 300 K by the phase-coherent pulsed NMR technique. The spin-echo spectra for V 3 S 4 and V 3 Se 4 are broadened rapidly below 9 K and 16 K, respectively, showing the antiferromagnetic long range order below these temperatures. The temperature dependences of the 51 V Knight shift, the uniform susceptibility and the hyperfine field which corresponds to the sublattice magnetization are in general accord for both cases with the prediction of the self-consistent renormalization theory for weak itinerant antiferromagnets.

Observation of theT(T−Tc)Divergence of theμ+Spin-Lattice Relaxation Rate in MnSi nearTc

The spin-lattice relaxation time (${T}_{1}$) of the interstitial ${\ensuremath{\mu}}^{+}$ spin in the paramagnetic phase of a weak itinerant-electron helimagnet MnSi has been measured near the magnetic-ordering temperature in a 700-Oe longitudinal magnetic field. The observed temperature dependence of $\frac{1}{{T}_{1}}$ is represented very well by $\frac{T}{(T\ensuremath{-}{T}_{c})}$ which was predicted on the basis of the self-consistent renormalization theory of spin fluctuations in itinerant-electron ferromagnets.

Magnetoresistance in Antiferromagnetic Metals

The magnetoresistance of itinerant electron antiferromagnets is studied on the basis of the two band model where the electrons in one conduction or s-band are the current carriers and are scattered by the spin fluctuations due to the d electrons. The self-consistent renormalization theory of spin fluctuations is applied to the d electrons. The resistivity shows a cusp at the Neel temperature and becomes linear in T at high temperatures. The resistivity under a perpendicular field shows a negative magnetoresistance for small fields and a narrow peak at the antiferromagnetic to paramagnetic transition point H c . In the case of a parallel applied field with the uniaxial anisotropy, we expect a large increase in the magnetoresistance on both sides of the spin flopping transition point. Numerical calculations are made with the use of the free electron gas model with Umklapp processes.

Spin Fluctuations in Concentrated Ferromagnetic Alloys

We investigate the effect of spin fluctuations in isoelectronic alloys, A x B 1- x , by using the self-consistent renormalization (SCR) theory combined with the coherent potential approximation (CPA). The static susceptibility, the Knight shift, K i (i=A, B), and the nuclear spin-lattice relaxation time, T 1i , relevant to each constituent atom of the alloy are calculated as functions of concentration, x , and of the temperature, T . The relation that (γ n A K A ) 2 T 1A =(γ n B K B ) 2 T 1B is shown to hold irrespective of x and T , where γ n i is the nuclear-gyromagnetic ratio of the nucleus of the i-atom. Since the CPA breaks down near the critical point, at which the susceptibility diverges, we adopt the virtual-crystal approximation in place of the CPA for the study of the Curie temperature, which is given by T c ∝( x c - x ) 6/7 very near the critical concentration, x c . Numerical calculations are made for the electron-gas model.

Effect of Spin Fluctuations on the Electric Field Gradient in Itinerant Electron Magnets

The effect of spin fluctuations on the electric field gradients at nuclear sites in itinerant electron magnets is studied by using the self-consistent renormalization theory. The coupling between the quadrupole charge density and the spin density fluctuation modes is shown to lead to a significant temperature dependence of the nuclear quadrupole coupling constant as was observed recently in MnSi.

Theory of Helical Spin Structure in Itinerant Electron Systems. II

The self-consistent renormalization theory of spin fluctuations as developed previously for ferro- and antiferromagnetic metals is extended to the case of a helical spin structure with the use of a model for the dynamical susceptibility χ 0 ( q ,ω) of the noninteracting system. The magnetic properties of MnSi having a helical spin structure of a long period below T C =29 K are discussed on the basis of this theory.

Effect of Magnetic Field on Itinerant Electron Antiferromagnetism

The effects of magnetic field on itinerant electron antiferromagnetism are studied by using the self-consistent renormalization theory of spin fluctuations. The effects are shown to be particularly significant when the wave vector-dependent susceptibility χ q 0 without the electron-electron interaction, having a maximum at q = Q , has an additional competing peak at q = 0 . The magnetic field dependences of the Neel temperature, the staggered susceptibility and the nuclear magnetic relaxation rate, etc., are calculated. As a numerical example some results of calculations based on an electron gas model with Umklapp processes are shown.

Electrical Resistivity of Antiferromagnetic Metals

The electrical resistivity of antiferromagnetic metals is discussed on the basis of the two band model. The general expression in terms of the dynamical susceptibility is obtained. The resistivity is studied by using the self-consistent renormalization theory of spin fluctuations. The resistivity at low temperatures is proportional to T 2 and its coefficient diverges as |α-1| -1/2 as one approaches the critical boundary of antiferromagnetism. It is pointed out that in the ordered phase the effect of the gap in the conduction band is important. Especially, this effect plays a crucial role in the temperature dependence of the contribution of the spin waves. It is proportional to T 5 and T 2 at the temperatures lower and higher, respectively, than the gap energy. At high temperatures the resistivity is significantly suppressed from that calculated by using RPA results for the spin fluctuations and can have a tendency towards saturation.

Nuclear Magnetic Resonance and Relaxation in Itinerant Electron Ferromagnet Sc3In

Nuclear magnetic resonance and nuclear spin-lattice relaxation of 45 Sc in an itinerant-electron ferromagnet Sc 3 In have been studied in both ferro- and paramagnetic states. The temperature dependences of the Knight shifts and susceptibilities give the hyperfine field due to d-spin of +58.4 kOe per Bohr magneton per Sc atom suggesting strong s-d admixture in the wave function at the Fermi surface and the d-spin contribution to the susceptibility. The external field dependence of the internal field at 45 Sc has been measured and analyzed in terms of the hyperfine fields proportional to d-spin moment and the external field. The observed magnetic field dependence of ( T 1 T ) -1 in both states is explained very well by the self-consistent renormalization theory of spin fluctuations in which the effect of magnetic field was taken into account, in conjunction with the negative magnetoresistance measured by us.

Recent developments in the theory of spin fluctuations in itinerant electron magnets

The static and dynamical Hartree-Fock approximations (HFA) as a conventional approach to the itinerant electron magnetism are insufficient in describing either the equilibrium state or the spin density fluctuations and related physical properties at finite temperatures. Recent theoretical developments have been focussed on improving over HFA by taking account of the mode-mode coupling or the renormalization effect. The self-consistent renormalization theory, as an approach from the weakly ferro- and antiferromagnetic limits, seems to work well in resolving classical difficulties associated with HFA as well as in predicting qualitatively new results on various physical properties of weakly ferro- and antiferromagnetic metals.

Theory of helical spin structure in itinerant electron systems

Helical spin structure of a long period shown by an itinerant electron system and the effect of an external magnetic field on it are discussed from a general point of view by extending the recent self-consistent renormalization theory of spin fluctuations for weakly ferro- and antiferromagnetic metals. The magnetic properties of MnSi are discussed in the light of the present theory.

Kondo effect in superconductors: Depression of the transition temperature

The influence of magnetic impurities on the transition temperature of superconducting alloys is investigated by means of the higher order parquet theory, which is essentially a self-consistent renormalization of the s-d interaction vertex and the quasi-fermion self-energy. The effective electron-electron interaction is evaluated beyond the logarithmic approximation, in terms of the renormalized spin-flip amplitude, which is responsible for the pair-breaking effect of the magnetic impurities. An expression for the maximal pair breaking, which is dependent on the spin and the superconducting coupling constant, is derived.

Effect of pressure on the dielectric properties of a paraelectric material

Employing a self-consistent renormalization procedure for the treatment of the frequency spectrum of a model paraelectric, the essential features of the pressure dependence of the static dielectric constant of the incipient ferroelectric KTaO 3 are reproduced.