Electricity and Magnetism,Volume 1: Third Edition,Electricity and Magnetism,Volume 2: Third Edition,by B.I. Bleaney and B. Bleaney

During the last decade the term ‘spin glass’ has become prominent in the literature on magnetism. It refers to magnetic alloys where the spins on the impurities become locked or frozen into random orientations below a characteristic temperature T ₀. In this article the properties of spin glasses are described with particular reference to the two archetypal examples AuFe and CuMn. Interest in spin glasses was mainly stimulated by some a.c. susceptibility measurements which showed sharp, cusp-like peaks, accurately defining T ₀ and suggesting that some type of phase transition was occurring. The Mossbauer effect and the anomalous Hall effect also showed clear features at T ₀ supporting this viewpoint. But measurements of the electrical resistivity and ‘specific heat’, here usually meaning the molar heat capacity, also the remanence, magnetic hysteresis and time-dependent effects observed in spin glasses were difficult to reconcile with a phase transition approach. This article discusses the results obtained from the very wide variety of experimental techniques which have been used to investigate spin glasses, and also deals with some of the important theoretical concepts which have arisen out of these studies. Then follows a short account of the many systems which have been found to exhibit spin glass behaviour and which suggest that it is a widespread magnetic state of matter. Lastly, an example is given which shows that some of the ideas of spin glasses are applicable to problems outside the sphere of magnetic alloys.     

Characterizing a high spin magnetic impurity via Andreev reflection spectroscopy

The ground state properties of a high spin magnetic impurity and its interaction with an electronic spin are probed via Andreev reflection. We see that through the charge and spin conductance one can effectively estimate the interaction strength, the ground state spin and magnetic moment of any high spin magnetic impurity. We show how a high spin magnetic impurity at the junction between a normal metal and superconductor can contribute to superconducting spintronics applications. Particularly, while spin conductance is absent below the gap for Ferromagnet-Insulator-Superconductor junctions we show that in the case of a Normal metal-High spin magnetic impurity-Normal Metal-Insulator-Superconductor (NMNIS) junction it is present. Further, it is seen that pure spin conduction can exist without any accompanying charge conduction in the NMNIS junction.     

Spin-wave impurity states in metallic ferromagnets

It is shown that spin waves in dilute ferromagnetic transition metal alloys can be described in terms of effective matrix-matrix and impurity-matrix exchange integrals. Such a parametrization is exact within the random phase approximation for long-wavelength spin waves. The effective impurity-matrix exchange integral is determined in the tight-binding approximation in terms of the impurity potential and local density of states. The present theory is applied qualitatively to NiFe alloys.     

Mössbauer effect in iron and dilute iron based alloys

Fifteen years of Mössbauer Effect (ME) studies have significantly widened the insight into the physical properties of iron and iron based alloys. In this review article the various contributions to the hyperfine interactions as measured with the ME technique, namely the isomer shift, the magnetic hyperfine interaction and the quadrupole interaction are summarized. Further the impurity effects as the Friedel type oscillations in the charge and the RKKY type oscillations in the spin density distribution are discussed. Special attention is paid to the peculiar magnetic properties of metallic iron and its alloys. From a comparison of the magnetic hyperfine fields and bulk magnetizations as a function of the impurity concentration and from the temperature dependence of the magnetic hyperfine fields at the various sites in iron alloys, it is concluded that the 3d magnetic moments in iron are largely localized. Further the exchange interaction is provided by the remaining small percentage of itinerant 3d electrons. Finally, from a comparison of magnetic hyperfine field and isomer shift data in alloys an overall picture of the electronic changes involved in alloying has been developed.     

Magnetic behaviour of cobalt,iron and manganese dissolved in palladium

This paper is meant to be a report on the experimental work on dilute Pd-based alloys with Co, Fe and Mn. These alloys exhibit the phenomenon of giant moments. The importance of measurements on paramagnetic alloys is emphasized. From these measurements the conclusion can be drawn that Co and Fe dissolved in Pd does not behave like a normal paramagnet, i.e. according to a Brillouin function. This result makes it possible to explain the existing discrepancy in the interpretations of magnetic measurements on one hand and of specific-heat experiments on the other.

The main conclusions of this paper are:

The giant moment should be accounted for by ‘normal’ values of the magnetic quantum number (3/2 for Co, 2 for Fe and 5/2 for Mn) and a large value of geff.

Paramagnetic alloys of Mn in Pd behave according to Brillouin functions, but alloys of Co or Fe in Pd do not. Hence, a number of interpretations of magnetic measurements should be considered as incorrect.

The localized model for ferromagnetism can well account for the magnetic ordering of dilute Pd-based alloys (certainly if c < 1 at.%). A straightforward generalization of the Weiss molecular-field model may be applied.

The transition temperature of Pd-Mn alloys is not proportional to the concentration, but after scaling the behaviour is similar to what has been found for Pd-Co and Pd-Fe alloys. The concentration dependence can be explained from a calculation of the strength of the interaction between two impurity atoms as a function of the distance.

Comparison between alloys with equal concentrations shows that the magnetic ordering in Pd-Mn is not at all exceptional, but analogous to that in Pd-Co and in Pd-Fe. It should be mentioned, however, that Pd-Mn at c > 3 at.% is a so-called spin glass.

Addition of Ag or Rh to Pd alloys with Co, Fe and Mn has important influences on their properties. Unfortunately these effects are not completely understood.     

The resistivity maximum in the ternary spin glass system Au-Cu-Mn

The temperature of the resistivity maximum, T_m, in the ternary spin glass system Au-Cu-Mn has been analysed in terms of Larsen's theory in order to highlight the contribution from the Kondo effect and the RKKY interaction energy to the resistivity maximum in spin glasses. The competition between these two contributions has been effectively illustrated and a good agreement with theory is obtained for samples with varying magnetic and nonmagnetic atom concentration. A comparison of the dependence of T_m and the RKKY interaction energy on the lattice pressure generated due to addition of Au with reported pressure studies on Mn alloys shows that there is a close relation between the lattice pressure and the externally applied pressure.     

Giant magnetic moments in metals as thermodynamic fluctuations

The nucleation of giant magnetic moments in certain dilute alloys is interpreted in terms of a Landau-Ginsburg type fluctuation theory. Beyond a certain threshold value of the coupling energy of the bare impurity spin to the spin density of the host a characteristic fluctuation localized around the impurity spontaneously acquires a non-zero, autonomous value. As observed, the magnitude of the giant moment decreases with increasing impurity concentration, at least at low concentrations.     

Local moment and ferromagnetic state formation in dilute,degenerate d-electron alloys: Ferromagnetic versus antiferromagnetic interactions

In this note the Kim [1] non-degenerate Anderson model (NDAM) of random dilute alloys treatment of local moment and ferromagnetic state formation is generalized to the ten-fold degenerate Anderson model (TDAM) of Siegel and Kemeny [2], Siegel [3,4] and Moriya [12]. We first determine how an impurity state is modified by neighboring impurities. For a simple binary alloy the local electron state at each impurity site depends upon the local distribution of other impurities. Second we derive a TDAM general relationship for the occurrence of a local moment on one impurity and the ferromagnetic ordering of the total impurity spins. Lastly we derive the impurity-impurity TDAM magnetic interaction; for the direct transfer interaction the impurity-impurity magnetic interaction can be ferromagnetic or antiferromagnetic depending upon the fractional occupation of impurity states. At each stage we compare our results with those of Kim's NDAM treatment.     

Origin of the anomalous magnetic circular dichroism spectral shape in ferromagnetic Ga(1-x)MnxAs: impurity bands inside the band gap

The electronic structure of a prototype dilute magnetic semiconductor (DMS), Ga(1-x)MnxAs, is studied by magnetic circular dichroism (MCD) spectroscopy. We prove that the optical transitions originated from impurity bands cause the strong positive MCD background. The MCD signal due to the E0 transition from the valence band to the conduction band is negative indicating that the p-d exchange interactions between the p carriers and d spin is antiferromagnetic. The negative E0 MCD signal also indicates that the hole doping of the valence band is not so large as previously assumed. The impurity bands seem to play important roles for the ferromagnetism of Ga(1-x)MnxAs.     

Spin glasses: Comments on some experimental results

Some of the experimental results on spin glasses commonly interpreted as showing a sharp magnetic phase transition are re-examined. Recent neutron scattering measurements add significantly to our understanding of the phenomena occuring in spin glasses. These results together with those on other physical properties are discussed in terms of a unified picture of freezing of spins in the binary alloys.     

The spin wave stiffness constant in itinerant electron ferromagnetic transition metal dilute alloys

The spin wave stiffness constant is calculated for itenerant electron ferromagnetic transition metal dilute alloys. Calculations are made in the Random Phase Approximation, using the method of effective magnon Hamiltonian. The term in the magnon energy proportional to impurity concentration is calculated by summing up exactly a perturbational series.     

稀磁合金中“电阻极大”现象的双杂质散射理论

本文基于s-d相互作用,考虑杂质之间存在RKKY相互作用,提出了一种新的双杂质散射模型。按照这个模型,当一个杂质作自旋翻转散射时,由于杂质之间存在着RKKY关联,它的自旋作为内部自由度会受到限制。由于这种关联,抑制了杂质的自旋翻转散射,结合Kondo的logT项,能形成电阻极大。本文计算了所有可能的“DIS”图(双杂质自能图),在Kondo电阻公式中加入了A/(T₀²—T²)这样的项。其中A是一个正常数。T₀是一个临界温度。当T≤T₀时,这个公式不再有意义。这个理论和已有的分子场理论在本质上是不同的.因为它并不依赖于合金中的磁有序.因此当T≥T_c时(T_c是磁有序转变温度),这种机制仍起作用,但分子场理论则不行.这是一种顺磁效应.我们和Cd-Mn(杂质浓度从0.01到0.1at./0)的实验曲线进行了比较,发现符合得很好.最后,我们认为即使在极低浓度下这种机制也是消除Kondo logT发散的主要原因. 关键词：     

The electronic structure of some transition metal alloys

Thermal neutron scattering experiments have provided detailed information on the distributions of magnetic moment in a number of disordered ferromagnet binary alloys. The general features of these distributions together with saturation magnetization data are discussed and compared with various simple theories. Attention is focused on dilute alloy systems. After an introduction the paper is divided into four sections, the first of which deals with alloys which tend to follow the Slater-Pauling curve. Here a simple Thomas-Fermi treatment due to Friedel suggests that magnetic moment changes, largely confined to the minor constituent (solute) sites, should occur with a sign dependent on the nature of the density of states at the Fermi level in the pure major constituent (solvent). Comparison with experiment shows qualitative agreement except in the case of Fe-based alloys containing transition element solutes from the right of Fe in the periodic table. This discrepancy is examined and an explanation put forward. The next section outlines a discussion of the electronic structure of alloys of transition elements with non-transition metal solutes. The view is taken that the electronic configuration of a solute atom is roughly similar to the configuration found in the pure non-transition metal: it follows that no partially filled d orbitals are expected at solute sites. Use of a simple Thomas-Fermi model based on this assumption indicates that some of the electric screening associated with a non-transition metal solute takes place in the surrounding transition metal slovent. Additional electrons introduced in this way into the solvent occupy mainly d states and cause a reduction in magnetic properties. This reduction together with the total loss of d-state effects from the solute sites themselves can account qualitatively for the changes observed in Ni, Pd and Fe-based alloys with non-transition elements. The fourth section deals with the transition metal alloys which show marked departures from Slater-Pauling behaviour, e.g. NiCr. An explanation for these alloys has been provided by Friedel's bound impurity state model and the mechanism suggested by Comly, Holden and Low to account for the similarity in shape of the magnetic disturbances observed in different systems. The final section discusses ferromagnetic alloys of PdFe and PdCo. The giant moments associated with the Fe and Co solutes result from a widespread polarization of the Pd solvent contiguous to the solute atoms. This polarization can be interpreted with the use of a non-local exchange-enhanced susceptibility function for the Pd host. With increasing solute content this function becomes modified to an extent dependent on the shift of d holes from one spin direction to the other, i.e. on the mean polarization of the Pd.     

Local spin configurations of Fe atoms in the Rh1−x Fex (x=0.1, 0.2, and 0.3) system with competing exchange interactions

The local spin configurations of Fe atoms in the magnetically ordered alloys Rh_1?x Fe_x (x=0.1, 0.2, and 0.3) have been investigated by Mössbauer spectroscopy. The Mössbauer absorption spectra are measured in the range from 5 K to temperatures of the transition to the paramagnetic state. The measurements in magnetic fields with a strength up to 5 T are carried out at a temperature of 4.2 K. Analysis of the magnetic-hyperfinefield distribution functions demonstrates that Fe atoms form discrete sets of collinear spin configurations corresponding to different net moments of the nearest coordination sphere. The spin structure of the alloys is governed by a random distribution of Fe atoms over the lattice sites and the competition between the Fe-Rh ferromagnetic exchange interaction and the antiferromagnetic interaction of the neighboring Fe atoms. No spin frustration and spin “melting” effects characteristic of spin glasses are revealed in the Rh-Fe alloys.     

Combined effect of the perpendicular magnetic field and dilute charged impurity on the electronic phase of bilayer AA-stacked hydrogenated graphene

We address the electronic phase engineering in the impurity-infected functionalized bilayer graphene with hydrogen atoms (H-BLG) subjected to a uniform Zeeman magnetic field, employing the tight-binding model, the Green's function technique, and the Born approximation. In particular, the key point of the present work is focused on the electronic density of states (DOS) in the vicinity of the Fermi energy. By exploiting the perturbative picture, we figure out that how the interaction and/or competition between host electrons, guest electrons, and the magnetic field potential can lead to the phase transition in H-BLG. Furthermore, different configurations of hydrogenation, namely reduced table-like and reduced chair-like, are also considered when impurities are the same and/or different. A comprehensive information on the various configurations provides the semimetallic and gapless semiconducting behaviors for unfunctionalized bilayer graphene and H-BLGs, respectively. Further numerical calculations propose a semimetal-to-metal and gapless semiconductor-to-semimetal phase transition, respectively, when only turning on the magnetic field. Interestingly, the results indicate that the impurity doping alone affects the systems as well, leading to semimetal-to-metal and no phase transition in the pristine system and hydrogenated ones, respectively. However, the combined effect of charged impurity and magnetic field shows that the pristine bilayer graphene is not influenced much as the functionalized ones and phase back transitions appear. Tuning of the electronic phase of H-BLG by using both types of electronic and magnetic perturbations play a decisive role in optical responses.     

Screening and interaction of magnetic impurities in Luttinger liquids

The spin and charge correlations induced in the conduction electron sea by the presence of a spin-1=2 magnetic impurity are investigated for one-dimensional electrons. For correlated conduction electrons, the RKKY interaction between magnetic impurities exhibits only a slow algebraic decay with distance. Increasing the exchange coupling between conduction electrons and magnetic impurity leads to a competition between the RKKY interaction and the Kondo effect. For a two-impurity model, we study the influence of the electronic correlations on this competition. Furthermore, the Kondo screening cloud and the local spin susceptibility far away from a magnetic impurity are discussed.     

A study of the temperature and pressure dependence of the electrical resistivity of a dilute Cr-Ge system

The electrical resistivity of a series of dilute Cr-Ge alloys containing up to 1.5 atm % Ge, was measured as a function of temperature and pressure. The measurements clearly demonstrate the existence of resistivity anomalies at the incommensurate-commensurate spin density wave transition temperature (T_IC) in contrast with recently reported results. The complete magnetic phase diagram, determined for the first time from electrical resistivity measurements, contains a triple point in contrast with previous neutron diffraction results but in agreement with thermal expansion measurements. It was found that the incommensurate spin density wave state is absent in alloys with more than 1 atm % Ge. The Néel temperatures and incommensurate-commensurate transition temperatures are affected differently by pressure. Pressure decreases T_N in all the alloys while it increases T_IC for those alloys in which the incommensurate-commensurate transition occurs. The decrease of T_N with pressure is much larger for the commensurate-paramagnetic than for the incommensurate-paramagnetic transition. The electrical resistivity of the alloys at room temperature behaves anomalously with applied pressure. This anomalous behaviour is attributed to an antiferromagnetic-paramagnetic phase transition that is induced in the alloys by applied pressure.     

The use of positive muons in metal physics

The present status of work in metal physics by the new method of “muon spin rotation” is reviewed. This spectroscopy is based on the spin interactions of positive or negative muons and resembles NMR as far as the interpretation of interactions in metals is concerned. The positive muon behaves in several respects as a light isotope of hydrogen in metals. Local properties like site symmetry, local magnetic field, dynamic effects from surrounding spins as well as effects from the diffusion of the particle itself can be measured with high sensitivity.A brief review of the technical aspects is given. The problems of diffusion of light positive particles in metals are discussed, with regard to specific mechanisms at low temperatures, trapping of muons by impurities, etc. The local electronic structure around this kind of impurity in normal metals as well as ferromagnets has been subject to a large nnumber of studies. Other applications include the interaction of muons with other kinds of defects, the study of metal hydrides and measurements on the dynamics of spin glasses.     

Experimental evidence for many-body effects in dilute alloys

The macroscopic and local properties of 3d transition metal impurities in normal metals are reviewed and compared with the theoretical situation in this field.

The parameters of the Anderson and s-d exchange models are derived from direct and indirect experimental data using as a guide the Hartree-Fock approximation of the non-degenerate Anderson model. The basic observations about the magnetic-non-magnetic transition, and the behaviour of the magnetic, thermal and transport properties when going through the transition region are demonstrated for specific examples. A detailed comparison between the present status of theory and experiment is performed by inspecting the large body of experimental data of two typical alloys, which served as testing materials for the development of the existing theories. CuFe is often regarded as a typical ‘yes moment’ system, and the experiments are therefore compared with the predictions based on the s-d exchange model; in the case of AlMn, the spin-fluctuation concept was chosen as a theoretical basis. It is shown that various approaches of the models fail to describe the fine experimental details. Evidence is presented which calls for a unified theory with no distinction between magnetic (Kondo-type) and non-magnetic (spin-fluctuation) alloys. It is suggested that the range of applicability of a model depends not only on the basic parameters of the dilute alloy but on the temperature, too, and the question of the relevance of the models to the actual state of affairs is to be answered by inspecting the temperature regions where the various approximations of the models are expected to work; the T≥T_K properties are compared with the Kondo approach, the Tˇ-T_K properties with the spin fluctuation model, although in the latter case the analysis is based on the concept of a narrow resonance level, which is not a feature of the spin-fluctuation concept only.

Finally, the basic experimental facts and indications are absorbed into a phenomenological model, which describes both the single-particle resonances and the many-body effects involved in resonance formation in classical dilute alloys.     

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.