Transport properties of dilute magnetic alloys

The electrical resistivity, thermopower, and the electronic part of the thermal resistivity of dilute magnetic alloys are calculated in the framework of the Suhl-Nagoaka theory. Using Bloomfield's and Hamann's solution of the Nagaoka equations, we derive expressions for the transport quantities in the limitT? ¯ T_K andT?¯ T_K to order (In ¯T _K /T)^?4 where ¯T _K is the Kondo temperature which may depend on the spin independent scattering. We find that the thermopower and deviations from the Wiedemann-Franz law in this limit decrease as ¦In ¯T_K/T¦^?3 if one neglects a trivial temperature dependence of the thermopower due to the electron-phonon interaction.     

Magnetic susceptibility of dilute magnetic alloys

The magnetic susceptibility of dilute magnetic alloys is calculated using the Nagoaka approximation to the Kondo problem. We use the exact solutions of the Nagaoka equations, or equivalently Suhl's dispersion relations, as obtained recently. Our result is represented by a universal function of a certain temperature parameter. In the case of ferromagnetic coupling no appreciable change of the free spin susceptibility is found over the whole temperature range. In the case of antiferromagnetic coupling we find that the free spin susceptibility is greatly reduced. In fact, for spin 1/2, the result indicates the breakdown of the expansion in terms of the impurity concentration and suggests the onset of impurity ferromagnetism.     

Magnetoelastic effects in dilute magnetic alloys

Ultrasonic studies of $\text{Cu}$Mn, $\text{Au}$Mn and $\text{Au}$Fe alloys where the concentrations of the transition metal ranges between 1 and 10% show that the longitudinal sound velocity has a marked field dependence at temperatures below the peak in the magnetic susceptibility and a negligible field dependence above it. This suggests that there may be an ordered magnetic state in these alloys.     

Hall effect in dilute magnetic alloys

We review the theory and the experimental results on the Hall effect in noble metals containing magnetic impurities of transition metals. In order to illustrate the various types of observed effects, we focus succesively on selected systems: $\text{Cu}$Mn, with only enhancement of the ordinary Hall effect due to the existance of different spin-up and spin-down currents; $\text{Au}$Fe and $\text{Au}$Cr, with skew scattering by magnetic impurities; $\text{Cu}$MnT ternary alloys (where T is a non-magnetic impurity), with skew scattering effects due to combined spin—orbit scattering by non-magnetic impurities and spin scattering by Mn impurities. The skew scattering in $\text{Au}$Fe and $\text{Au}$Cr can be ascribed to the orbital character of the impurity moments and accounted for in an orbitally degenerate virtual bound state model. However, the anomalous temperature dependence of the skew scattering in Kondo alloys at low temperature is not well understood. We also present some magnetoresistance data in order to describe the links between the Hall effect and the magnetoresistance in magnetic alloys. In particular, we relate the skew scattering and the magnetoresistance anisotropy observed in $\text{Au}$Cr alloys.     

Spin correlation in dilute magnetic alloys

The correlation of a magnetic impurity spin with the spin density of the conduction electrons in a dilute magnetic alloy is calculated non-perturbationally on the basis of the Nagaoka theory. It is shown that there are anomalies due to the Kondo effect in the long range behaviour of this correlation which contradicts the bound state interpretation of the Kondo effect. The most interesting detail is the appearance of a non-oscillating contribution to the correlation.     

Ground state energy of dilute magnetic alloys

The ground state energy of dilute magnetic alloys as described by thes-d-exchange Hamiltonian is calculated within the Nagaoka-Suhl theory. For integral impurity spinS it is shown that for positive coupling constantγ the energy is a holomorphic function ofγ. For negative coupling one obtains an additional singular contribution of the form (?1) ^s?1 e ^1/γ (γ<0). As this changes sign for different integral s-values, the interpretation of the singular part as a binding energy suggested previously does no longer hold. For half integral spin the energy is a singular function for bothγ>0. The singularities are not as elementary as in the case of integral spinS, but are rather related to those of the exponential integral function. In particular, forγ>0 the origin (γ=0) is a branch point. Earlier variational calculations are compared with our new results.     

Nearly magnetic antiparallel pairs in dilute alloys

When a dilute alloy exhibits exchange enhancement of the isolated impurity susceptibility, it is shown that pairs of impurities may exhibit a low lying anti-parallel fluctuation mode such that the pair susceptibility in a uniform field is less enhanced than that of the isolated impurity, while the specific heat may be strongly enhanced. N.M.R. properties of such a pair should exhibit a small shift in frequency and a fast nuclear spin lattice relaxation time, leading to possibly large deviations from the Korringa relation.     

On the magnetoresistance in dilute magnetic alloys

Many-particle contributions to extended Suhl equations are considered to derive a magnetoresistance, which saturates for nonzero magnetic fields below the unitatarity limit in agreement with experiments.     

Inelastic collision term in dilute magnetic alloys

The collision term derived by Kohn and Luttinger [1] to describe elastic scattering to third order in the potential is generalized to include inelastic processes for a system of conduction electrons interacting with localized spins. This result is obtained by using the Kadanoff and Baym [6] derivation of the Boltzmann equation.     

窄禁带稀磁半导体二维电子气的磁阻振荡研究

通过改变温度和磁场方向对调制掺杂的n型Hg_0.82Cd_0.16Mn_0.02Te/Hg_0.3Cd_0.7Te第一类量子阱中磁性二维电子气磁阻拍频振荡进行了深入的研究，发现不仅温度的变化能够引起磁阻拍频节点位置的变化. 而且改变磁场方向，可以分别调整塞曼分裂和朗道分裂. 从对拍频的分析中，可以将依赖于磁场垂直方向的朗道能级分裂和依赖于整个磁场大小的塞曼分裂区分开来. 关键词： 磁性二维电子气 自旋分裂 塞曼分裂 拍频     

Renormalized vertex modification of Hall conductivity for dilute magnetic alloys

By means of the renormalized vertex procedure for the motion of Green's function developed by the authors, the vertex function of magnetic alloys, based on thes-d exchange interaction, is solved exactly and the corresponding Hall conductivity tensors are obtained. It is found that the value of the renormalized Hall conductivity is (1+h ²)^–1 times less than that before the renormalization (hereh is a reduced magnetic field). It is shown that the renormalized modification of the conductivity is very important in the cases with not too weak external magnetic field and slow relaxation time.     

Deviations from the Curie-Weiss law in the magnetic susceptibility of dilute magnetic alloys

The magnetic susceptibility of dilute magnetic alloys of Mn in Rh and Fe in a Nb-Mo solid solution deviates from the Curie-Weiss law. The following temperature dependence is observed: Δ_χ = C/(T + T_K) + log (T_K/T), with ≡ 0 for T > T_K⁰.     

On Suhl's dispersion equations for dilute magnetic alloys in a finite magnetic field

A one dimensional, nonlinear, singular integral equation was recently shown to be equivalent to Suhl's dispersion equations for the Kondo-problem of a half-spin magnetic impurity in a finite magnetic field. We investigate this integral equation further analytically and numerically and obtain numerical solutions which we use for a calculation of transport coefficients. The normal part of the scattering potential of the magnetic impurity is included via ans-wave phase shift. The transport coefficients are universal functions of the ratiosT/T _K andB/B _K of the temperatureT and the zero magnetic field Kondo-temperatureT _K and of the magnetic inductionB and the Kondo magnetic inductionB _K. We find maxima in the electrical and thermal resistivities as functions ofT/T _K forBB _K. These are typical Kondo phenomena, and can be influenced by. Interference of and the phases of Kondo-scattering amplitudes leads to dramatic effects in the thermopower and the Hall coefficient.SFB 125The numerical part of this work was performed at the Institut für Festkörperforschung, Kernforschungsanlage Jülich, F.R. Germany     

On Suhl's dispersion equations for dilute magnetic alloys in a finite magnetic field

The system of six coupled, nonlinear, singular integral equations, devised by Suhl to treat the problem of a spin 1/2 magnetic impurity in a finite magnetic field is shown to be reducible to a single integral equation. Analytic properties and symmetries of the system are discussed, which may serve as a guideline for numerical studies of the final integral equation. The first few steps of an iteration in terms of the magnetic field strength are carried out analytically.On leave from the Institut für Theoretische Physik der Universität Köln.     

Investigation of impurity diffusion in dilute alloys by nuclear magnetic resonance

The diffusion of Al in a Cu: 3.8 at % Al alloy has been investigated by observing the rotating-frame nuclear magnetic relaxation time T_1π of ²⁷Al as a function of temperature. It is shown that relaxation measurements of the solute atoms in a dilute alloy provide the correlation time of the diffusive motion of these atoms, if quadrupolar interactions form the main contribution to the relaxation time. From the correlation times the Al-diffusion coefficient in the alloy has been determined.     

Green's function theory of the Kondo effect in dilute magnetic alloys

The exact solution of thet-matrix integral equation derived from the self-consistent Nagaoka equations in the theory of dilute magnetic alloys is established. It is shown that the unique solution for thet-matrix involving all Kondo type anomalies can be found under quite general assumptions. Using the exact solution we have calculated thermodynamic properties of dilute magnetic alloys. It is found that the excessive specific heat of the system due to the anomalous scattering of conduction electrons from the magnetic impurities is of the order ofBoltzmann's constant per local moment at low temperatures. In the limit of vanishing temperature the specific heat goes to zero asymptotically as (lnT)^?4. Finally the entropy difference of the interacting system as compared to the free system is calculated.     

Pressure as a parameter in the study of dilute magnetic alloys

A large body of data is reviewed, which illustrates how the high pressure technique can be used to gain information about the magnetic and electronic state of dilute magnetic alloys. Values for the pressure dependence of the elementary effective exchange interaction between a magnetic impurity spin and the conduction electron sea are extracted from the data and tabulated for a number of extremely dilute alloys containing both transition metal and rare earth impurities. Results of experiments on host alloy series employing ‘lattice pressure’ are compared to the present ‘external pressure’ results and critically analysed; it is shown how such a comparison can be used to give information about the extent of the electronic screening around an impurity potential. The effect of pressure on impurity-impurity interactions in spin glasses is also examined; a comparison of the pressure studies on extremely dilute alloys to those on spin glasses allows an estimate of the nature of the interaction mechanisms important in the latter case. Evidence for a pressure-induced spin glass to Kondo transition in LaCe is also presented. It is suggested that the present results fit into a larger picture that magnetism, when present, tends to be weakened when high pressure is applied.