The properties of spin-1/2 antiferromagnetic chains with various types of random exchange coupling are studied via an asymptotically exact decimation renormalization-group transformation, which is a generalization of that introduced by Dasgupta and Ma. Random-singlet phases occur in which each spin is paired with one other spin that may be very far away; more exotic phases also occur. The behavior of typical and mean correlation functions is analyzed and found to be very different, with very small sets of spins dominating the latter at long distances as well as the low-temperature thermodynamics. Some of the phase transitions that occur between antiferromagnetically ordered phases and random singlet or other antiferromagnetic phases are also analyzed. For example, if a small uniaxial anisotropy perturbation is added to a random Heisenberg antiferromagnetic chain, a transition occurs from a random-singlet phase to an Ising antiferromagnetic phase, as the anisotropy changes sign from easy plane to easy axis. The staggered magnetization vanishes at the transition with critical exponent β=8/(1+ √7 ). Possible implications for the properties of random quantum magnetic systems in higher dimensions are briefly discussed.

A polycrystalline sample of the solid solution U(${\mathrm{Ni}}_{0.25}$${\mathrm{Cu}}_{0.75}$${)}_2$${\mathrm{Si}}_2$ was prepared and found to have the tetragonal ${\mathrm{ThCr}}_2$${\mathrm{Si}}_2$-type crystallographic structure. The observation of a ferrimagnetic transition at 112±5 K by ac-susceptibility measurements, is confirmed by neutron diffraction, which also indicated three commensurate magnetic structures (below ≊110 K). Two structures are antiferromagnetic (AF), 40% each, and one is ferrimagnetic, 20% in volume. The structures are AF-I (+-+-), ferrimagnetic (++-), and AF-IA (++--), with wave vectors k=(0,0,1), (0,0,2/3), and (0,0,1/2), and ${\mathit{T}}_{\mathit{N}}$=120±3, 115±4, and 110±3 K, respectively. The uranium ordered magnetic moments (2.2±0.1${\mathrm{\mu }}_{\mathit{B}}$ at 1.5 K) are along the tetragonal axis in all three structures. These phases fit well into the proposed magnetic phase diagram of the U(${\mathrm{Ni}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Cu}}_{\mathit{x}}$${)}_2$${\mathrm{Si}}_2$ system, and are compared with corresponding solid solutions in the parallel U(${\mathrm{Ni}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Cu}}_{\mathit{x}}$${)}_2$${\mathrm{Ge}}_2$ system.

Monte Carlo calculations for the classical ferromagnetic Ising-like Heisenberg model suggest that solitons may play an important role in driving the phase transition in that model.

I have extended the one-dimensional spin-diffusion theory of Valet and Fert [Phys. Rev. B 48, 7099 (1993)] [which treats perpendicular giant magnetoresistance (GMR) in magnetic multilayers] to three dimensions in order to deal with the problem of GMR in granular magnetic metals. These materials are composed of tiny precipitates of magnetic granules suspended within an immiscible nonmagnetic metallic matrix. It is assumed that the granules are spherical in shape, and have identical radii. The differential equations are solved separately for three different physical situations: (1) Bulk spin-dependent scattering in the nonmagnetic matrix; (2) Bulk spin-dependent scattering within the magnetic spheres; and (3) surface spin-dependent scattering at the ferromagnetic-normal interface. The magnetically induced electrical interaction between spheres, which gives rise to observed GMR, is treated in lowest order only. It is found to act via an induced electric-dipole field for cases (1) and (3), and an induced spin-diffusion field for case (2). Using these solutions, and macroscopic parameters from experiment, I have attempted to explain the observed singular dependence of the GMR on annealing temperature.

We study the behavior of the random-bond Ising model at zero temperature by numerical simulations for a variable amount of disorder. The model is an example of systems exhibiting a fluctuationless first-order phase transition similar to some field-induced phase transitions in ferromagnetic systems and the martensitic phase transition appearing in a number of metallic alloys. We focus on the study of the hysteresis cycles appearing when the external field is swept from positive to negative values. By using a finite-size scaling hypothesis, we analyze the disorder-induced phase transition between the phase exhibiting a discontinuity in the hysteresis cycle and the phase with the continuous hysteresis cycle. Critical exponents characterizing the transition are obtained. We also analyze the size and duration distributions of the magnetization jumps (avalanches).

Two coercivity models, a phenomenological model developed by Givord et al. and a micromagnetic model developed by Kronmüller et al., have been used to analyze the temperature dependence of the coercive field of sintered ${\mathrm{Pr}}_{17}$${\mathrm{Fe}}_{75}$${\mathrm{B}}_8$ and ${\mathrm{Pr}}_{17}$${\mathrm{Fe}}_{53}$${\mathrm{B}}_{30}$ permanent magnets. A general comparison of these two models is made. The micromagnetic model takes into account the misalignment of grains and the anisotropy imperfections at the grain surface. From the analysis based on this model it follows that the coercivity in sintered ${\mathrm{Pr}}_{17}$${\mathrm{Fe}}_{75}$${\mathrm{B}}_8$ and ${\mathrm{Pr}}_{17}$${\mathrm{Fe}}_{53}$${\mathrm{B}}_{30}$ permanent magnets is controlled by a nucleation mechanism occurring preferentially in the grain surface where the magnetic anisotropy is reduced and the local demagnetizing field is the highest. A simple proportional relationship between the micromagnetic parameters and ${\mathit{N}}_{\mathrm{eff}}$ is found. In addition, the effect of magnetic coupling among grains can be estimated with this model. The phenomenological model takes into account the geometrical effect of nucleated domains, the effect of the disturbance of domain-wall energy, and the thermal activation. From the analysis based on this model, it follows that the expansion of reversed domains takes place preferentially in regions where the domain-wall energy is reduced and where a spikelike reversed domain is energetically favorable. It is demonstrated in the present investigation that the phenomenological model corresponds approximately to the micromagnetic model when the nucleation process dominates the magnetization reversal process and the magnetic coupling between grains is weak.

A relativistic, spin-polarized band theory of magnetic x-ray dichroism (MXD) in solids is briefly described. Calculated circular and linear dichroic x-ray absorptions at the ${\mathit{L}}_{2,3}$ edges from bulk Fe and Co as well as from their multilayers [${\mathrm{Fe}}_2$${\mathrm{Cu}}_6$ (001), ${\mathrm{FeAg}}_5$ (001), ${\mathrm{Co}}_2$Pd(Pt${)}_4$ (111), and ${\mathrm{Co}}_2$${\mathrm{Cu}}_6$ (001)] are presented. Large circular MXD is predicted in both the bulks and the multilayers while linear MXD due to magnetocrystalline anisotropy is found to be small (within 1%). Nevertheless, linear MXD due to a photon polarization change is about 3–8 %. The orbital magnetization sum rule of B. T. Thole et al., [Phys. Rev. Lett. 68, 1943 (1992)] is found to give orbital magnetic moments too small by about 20–35 %. We note that for each ion species, there is a simple linear relationship between the integrated circular MXD signal and the orbital magnetic moment, and we propose that one uses this linear relationship to measure the orbital magnetic moment of an ion in magnetic solids. The recently proposed spin magnetization sum rule [P. Carra et al., Phys. Rev. Lett. 70, 694 (1993)] is found to give rather accurate spin magnetic moments for the Co systems (errors within 15%). However, it does not hold qualitatively for highly anisotropic systems such as Fe multilayers.

The perturbative expansion of a spatially nonuniform ${\mathrm{\phi }}^4$-field theory is rearranged leading to an entropy functional of the magnetization and energy densities. Similarly to the planar Ising model considered earlier, a form local in the two leading orders is achieved in the case of parameters of the theory depending on only one of the d spatial coordinates. The functional then depends on all transverse Fourier components of the energy density. The result forms a basis for future work on the perturbative renormalization-group approach to nonuniform Ising-like systems.

The spin-1/2 and spin-1 Heisenberg antiferromagnet and XY model are studied at zero temperature on the simple-cubic, body-centered-cubic, and (for the XY case only) face-centered-cubic lattices. Series expansions around the Ising limit are calculated, for the ground-state energy, staggered magnetization, transverse susceptibility, staggered parallel susceptibility, energy gap, and dispersion relation, using a linked-cluster technique. The results are compared with spin-wave perturbation theory, which has been extended to third order for the Heisenberg antiferromagnet, and the agreement is excellent. The finite-size scaling corrections which are calculated from the spin-wave theory are also entirely consistent with the predictions of effective-Lagrangian theory.

With simple, exact arguments we show that the surface magnetization $m_1$ at the extraordinary and normal transitions and the surface energy density ${\epsilon }_1$ at the ordinary, extraordinary, and normal transitions of semi-infinite $d$-dimensional Ising systems have leading thermal singularities $B\pm {\mathrm{}\left|t\right|\mathrm{}}^{2-\alpha }$, with the same critical exponent and amplitude ratio as the bulk free energy $f_b\mathrm{}(t,0\mathrm{})\mathrm{}$. The derivation is carried out in three steps: (i) By tracing out the surface spins, the semi-infinite Ising model with supercritical surface enhancement $g$ and vanishing surface magnetic field $h_1$ is mapped exactly onto a semi-infinite Ising model with subcritical surface enhancement, a nonzero surface field, and irrelevant additional surface interactions. This establishes the equivalence of the extraordinary ($h_1=0, g>\mathrm{}0\mathrm{}$) and normal ($h_1\ne 0, g<\mathrm{}0\mathrm{}$) transitions. (ii) The magnetization $m_1$ at the interface of an infinite system with uniform temperature $t$ and a nonzero magnetic field $h$ in the half-space $z>\mathrm{}0\mathrm{}$ only is shown to be proportional to $f_b\mathrm{}(t,0\mathrm{})-f_b\mathrm{}(t,h)\mathrm{}$. (iii) The energy density ${\epsilon }_1$ at the interface of an infinite system with temperatures $t_{+}$ and $t$ in the half-spaces $z>\mathrm{}0\mathrm{}$ and $z<\mathrm{}0\mathrm{}$ and no magnetic field is shown to be proportional to $f_b\mathrm{}(t,0\mathrm{})-f_b(t_{+},0)$.

We present a study of the magnetic and electronic properties of ${\mathrm{Fe}}_{\mathit{N}}$ clusters embedded in antiferromagnetic bcc Cr. The spin-polarized charge distribution is determined self-consistently by solving a realistic spd-band model Hamiltonian including intra-atomic Coulomb interactions in the unrestricted Hartree-Fock approximation. For all the studied clusters (N≤51), the local magnetc moments at Fe atoms close to the Fe-Cr interface, as well as the average magnetic moment of the ${\mathrm{Fe}}_{\mathit{N}}$ impurity, are reduced with respect to the Fe bulk magnetization. The magnetic order within ${\mathrm{Fe}}_{\mathit{N}}$ changes from antiferromagneticlike to ferromagneticlike with increasing cluster size. The calculated critical size for this transition is ${\mathit{N}}_{\mathit{c}}$≃6. Results for the spatial distribution of the magnetic moments and for the local electronic densities of states are given for different N. The role of the structural and chemical local environment of the atoms on the electronic and magnetic properties is discussed, and our results are compared with those found for Fe/Cr multilayers. Some of the implications of the present study for magnetic alloys and ferromagnetic clusters on surfaces are pointed out.

We calculate energies and wave functions of S=1 antiferromagnetic Heisenberg chains with single-ion anisotropy in a symmetry-breaking external magnetic field. From results for the string correlation function for low-lying excited states we identify these states as solitons with respect to the hidden string order. For finite anisotropic chains we investigate the transition to the fully magnetized state at high magnetic fields and conclude that Bose condensation in an external magnetic field occurs also for the anisotropic chain.

Results of ab initio calculations of the structural, electronic, and magnetic properties of crystalline and amorphous Fe-Y alloys are presented. The structure of the amorphous phases is generated via a simulated molecular-dynamics quench, based on effective interatomic forces derived from tight-binding-bond theory. The results show that a pronounced chemical short-range order (preferred heterocoordination) exists at all compositions and that at short distances the local topology is similar in the crystalline and glassy phases. In the Y-rich alloys, medium-range concentration fluctuations are superposed to the local order. The investigation of the electronic structure using self-consistent spin-polarized linear muffin-tin orbital calculations confirms that the bonding properties are similar in the crystalline and amorphous phases. The crystalline compounds are ferrimagnetic, the negative Y moment is induced by a strong covalent interaction of the Y d band with the minority-spin Fe d band. Ferrimagnetism is also found in the amorphous alloys. In the Fe-rich range (more than 80 at. % Fe) competing ferro- and antiferromagnetic Fe-Fe exchange interactions lead to coexisting positive and negative Fe moments. The decrease of the magnetic moments of the Fe atoms with increasing Y content is strongly influenced by the strong coupling of the Fe spins to the Y moments—as a consequence a spontaneous Fe moment exists even at very small Fe-Fe coordination numbers. In addition the structural inhomogeneity of the Y-rich amorphous alloys leads to cluster magnetism.

We use the numerical self-consistent mean-field method to examine the ground-state configurations of finite-size multilayers constructed from ferromagnetic films which are antiferromagetically coupled. At intermediate fields, a surface spin-flop state, as suggested by Keffer and Chow, has been found for even numbered multilayers, but not for odd numbered ones. These are confirmed by experimental observations on systems such as Fe/Cr. A simple macroscopic approach has been devised in calculating the spin-wave excitations for the various field-induced ground states. Special emphasis is placed on the influence of interfilm dipolar couplings on the spin-wave spectrum. We note, for example, that there are substantial differences for the two cases ${\mathit{k}}_{\mathrm{\parallel }}$D≪1 and ${\mathit{k}}_{\mathrm{\parallel }}$D≳1, with D the thickness of the finite superlattice, and ${\mathit{k}}_{\mathrm{\parallel }}$ the wave vector of the spin waves parallel to its surface.

We have investigated Josephson effects in stacks of both artificial and natural Josephson junctions. The measurements have been performed on Nb/Al-${\mathrm{AlO}}_{\mathit{x}}$/Nb multilayers and on small single crystals of ${\mathrm{Bi}}_2$${\mathrm{Sr}}_2$${\mathrm{CaCu}}_2$${\mathrm{O}}_8$. Both systems exhibit multiple branched I-V characteristics in zero magnetic field. In finite magnetic fields coupling via currents flowing along the superconducting layers is essential, since the layers are thinner than the London penetration depth. All observations are in good agreement with numerical simulations of stacks of coupled Josephson junctions. These simulations predict that a large number of junctions can be phase locked in large magnetic fields via Fiske resonances excited in all junctions.

A relation is presented which relates the flux noise spectrum and vortex dissipation for two-dimensional superconductors. The explicit forms of the noise spectrum and vortex dissipation are obtained from simulations of a two-dimensional XY-type model with time-dependent Ginzburg-Landau dynamics. The results are discussed in terms of a phenomenological description and good agreement is found. Consequences for, and comparisons with, experimental data are discussed.

We have measured the current-voltage (IV) characteristics of several two-dimensional arrays of small Josephson junctions as a function of temperature, T and magnetic field B. The junctions have relatively large charging energies ${\mathit{E}}_{\mathit{C}}$≊1 K, and normal-state resistances ${\mathit{R}}_{\mathit{N}}$ in the range of 4–150 kΩ. From the IV characteristics we can deduce the zero-bias resistance ${\mathit{R}}_0$ and the threshold voltage ${\mathit{V}}_{\mathit{t}}$ which reveal important information about the dynamics and statics of charge solitons in the array. ${\mathit{R}}_0$(T) increases with decreasing temperature and may be described by thermal activation of charge solitons, characterized by an activation energy ${\mathit{E}}_{\mathit{a}}$. When the electrodes are in the normal state, ${\mathit{E}}_{\mathit{a}}$ is close to 1/4${\mathit{E}}_{\mathit{C}}$. At low T, the thermal activation behavior breaks down, and ${\mathit{R}}_0$(T) levels off to a value that can be attributed to the quantum fluctuations in the array. This interpretation places limitations on the observability of the charge unbinding, Kosterlitz-Thouless-Berezinskii transition for single electrons. When the electrodes are superconducting, ${\mathit{E}}_{\mathit{a}}$ is much larger and dependent on B. In several samples, both ${\mathit{E}}_{\mathit{a}}$ and ${\mathit{V}}_{\mathit{t}}$ oscillate with B, having a period corresponding to one flux quantum per unit cell. For increasing magnetic fields, ${\mathit{V}}_{\mathit{t}}$ increases until B≊250–450 G where it starts to decrease rapidly. We interpret the B dependence of ${\mathit{E}}_{\mathit{a}}$ and ${\mathit{V}}_{\mathit{t}}$ as a result of competition between Cooper-pair solitons and single-electron solitons.

We highlight a ‘‘transverse’’ interference effect, arising from the coupling between electrons and holes, induced by a superconducting island in contact with a normal metal. As an example we compute the electrical conductance G of a T-shaped mesoscopic sample, formed by joining a horizontal bar of normal metal to a vertical leg of the same material. With a superconducting island located on the vertical leg and the current flowing horizontally, we examine the dependence of G on the distance L of the island from the horizontal bar. Of particular interest is the differential conductance G(E) at an applied voltage E=eV, which due to quantum interference between electrons and Andreev reflected holes, is predicted to oscillate with both L and E. For a system with a spherical Fermi surface, the period of oscillation with E is π${\mathit{E}}_{\mathit{F}}$/${\mathit{k}}_{\mathit{F}}$L and with L is π${\mathit{E}}_{\mathit{F}}$/${\mathit{k}}_{\mathit{F}}$E, where ${\mathit{E}}_{\mathit{F}}$ is the Fermi energy and ${\mathit{k}}_{\mathit{F}}$ the Fermi wave vector.

We consider SNS junctions with a strong-coupling normal layer N, and calculate the Josephson critical current density ${\mathit{J}}_{\mathit{c}}$ as a function of the electron-phonon coupling properties of the N layer. It is shown quantitatively that ${\mathit{J}}_{\mathit{c}}$ drops quickly as the coupling strength increases and that in thick junctions with the thickness 2b≳2π(${\mathrm{\Delta }}_{\mathit{S}}$/ħ${\mathrm{\omega }}_{\mathrm{ph}}$)${\xi }_{\mathit{S}}$, the falling rate depends only on the coupling constant λ regardless of the spectrum of ${\mathrm{\alpha }}^2$F(ω).

The distribution function for the current noise in a normal-metal–superconductor quantum point contact is calculated. It is shown that this distribution describes independent processes when a charge ±${\mathit{e}}_0$ or ±2${\mathit{e}}_0$ passes through the contact. At low temperature and voltage only processes with double-charge transfer are relevant. At zero temperature and low voltage the distribution has a binomial form.