Showing papers on "Exchange interaction published in 1972"

Magnetic Properties of K 2 CuF 4 —A Transparent Two-Dimensional Ferromagnet—

Abstract: It has been found that K 2 CuF 4 is ferromagnetic below 6.25 K. The two-dimensionality of this compound as expected from its K 2 NiF 4 type structure is strongly supported by magnetic and specific heat measurements. The torque as well as zero field NMR measurements suggest that the c -plane is an easy plane, in which the spins are very weakly bounded to the direction of a -axis. On the assumption that this magnetic system to be purely two-dimensional, the exchange interaction J between the spins within the c -plane is found to be the Heisenberg type with about one percent XY-like anisotropy and j / k =10.0 K is obtained from the series expansion analysis of the high temperature susceptibility as well as linear dependence of the low temperature specific heat. The transition at 6.25 K may be caused by inter-layer exchange interaction. The exchange field between the adjacent layers is expected at least larger than 400 Oe.

Theory of Spin Resonance in Dilute Magnetic Alloys

Abstract: The scheme of Kadanoff and Baym is shown to be useful for the rigorous derivation of Bloch or Boltzmann equations for spin systems. The scheme is applied to a system of conduction electrons in a metal interacting via an exchange interaction $J$ with a low density of local spins. The coupled Bloch equations appropriate to conduction-electron spin resonance are derived rigorously to second order in $J$. The prominent features of the derived equations are that (i) the disturbed magnetizations are shown to relax to the instantaneous local equilibrium magnetization with the result that correct static susceptibilities are obtained, (ii) the instantaneous magnetizations are not proportional to the effective magnetic fields causing the magnetizations to precess, and (iii) the equations are consistent with conservation of the total magnetization.

Singlet‐Triplet Splitting in Diffusing Radical Pairs and the Magnitude of Chemically Induced Electron Spin Polarization

Abstract: A previous theory of anomalous electron spin resonance spectra of free radicals in solution attributes the electron spin polarizations to the combined effects of singlet‐triplet mixing by magnetic interactions in a diffusing radical pair and singlet‐triplet splitting by the exchange interaction when, and if, the diffusing radicals reencounter each other. This theory is studied in more detail by considering the exchange interaction at all times during the diffusive trajectory of the radical pair, in contrast to the original treatment of approximating it as a rectangular pulse which is nonzero only briefly during the second encounter of the radicals. Time dependent perturbation theory is used to calculate the radical pair wavefunction and the corresponding electron spin polarization to first order in the exchange interaction. The polarization is averaged over all possible diffusion paths of the radicals by averaging the exchange interaction over the distribution of radical pair separations obtained by solution of the diffusion equation with appropriate boundary conditions. These boundary conditions take into account the facts that polarization begins when the radicals separate to a point where the magnetic and exchange interactions are roughly equal, and that the developing polarization is destroyed by spin exchange if the radicals subsequently come too close together. The calculated polarizations are of the right order of magnitude to account for the experimental results, and the dependence of the polarization on the magnetic interactions and the diffusion parameters is essentially the same as predicted by the earlier simpler theory.

EPR of Mn2+ pairs in MgO and CaO

Abstract: Nearest neighbour Mn2+ pairs in MgO and CaO have been studied using EPR. The isotropic exchange interaction measured in MgO cannot be written in the simple form Jsi.sj and it is shown that although a small contribution due to intrinsic biquadratic exchange is possible, the anomalous effect arises mainly as a result of exchange striction. This exchange striction is found to be consistent with a variation of J with ionic separation r given approximately by J=J0 exp(-19r/r0), and this variation gives good agreement with exchange interactions deduced for MnO. Exchange striction effects also appear in the crystal field interactions and in the magnetic dipole-dipole interactions for both pair systems.

The Elastic Constants of Dysprosium and Holmium

Abstract: The five single-crystal elastic constants of dysprosium and holmium have been measured within the temperature range 4.2 to 300 K. The large contributions to the elastic constants due to domain and spin rotation effects were eliminated by applying a magnetic field of 2.5 T along the magnetic easy directions. Extrapolation of the temperature dependence in the paramagnetic region to 0 K indicates large magnetic contributions to the elastic constants which have been interpreted as arising from the strain dependence of the exchange energy. Analysis of these contributions permits the evaluation of the first and second derivatives of the nearest and next-nearest exchange interaction parameters. The results are consistent with more limited information obtainable from the anomalous thermal expansion and are consistent with an oscillatory J ( r ).

Coherent-Potential Approximation for Disordered Ferromagnetic Binary Alloys

Abstract: The magnetic properties of spin-\textonehalf{} Heisenberg ferromagnetic alloys are calculated. We calculate the spin-wave Green's function in the random-phase approximation and treat the disordered composition-dependent exchange interaction in a coherent-potential approximation (CPA). In the weak-scattering limit, the CPA reproduces the result of the mean-field theory as expected, and in the strong-scattering limit, the CPA predicts such properties as critical concentration, which is beyond the scope of the mean-field theory.

The influence of exciton motion on spin-resonance absorption

Abstract: We use a stochastic model for the exciton motion which comprises both the coherent and the incoherent motion. The incoherent part is taken care of by a stochastic process which allows the local excitation energy and the transition matrix element to fluctuate by means of a Markovian process. The interaction between the spins and their surroundings is described by the usual spin-Hamiltonian which is, however, simplified to a spin 1/2 particle (instead of the triplet state). In the present paper we solve exactly the two limiting cases of completely coherent and incoherent motion (for two molecules). In the incoherent case the influence of the exchange interaction integral is taken into account by perturbation theory. We find expressions which are immediately comparable with ESR-experimental data. This comparison and additional information derived from optical absorption measurements allow us to determine all free parameters of our model uniquely. In particular, the fluctuations of the exchange interaction integral (with strength γ1) play an important role. From these parameters we may furthermore calculate the correlation time of the proton spin resonance in agreement with experimental data. The results show clearly that at room temperature in anthracene crystals the exciton undergoes a hopping process.

Electron Spin Resonance in One Dimensional Antiferromagnet Cu(C6H5COO)23H2O

Abstract: Precise temperature and angular dependences of ESR line in a typical linear chain antiferromagnet Cu(C 6 H 5 COO) 2 3H 2 O were measured in a temperature region from 1.4 to 300 K over a microwave frequency range from 10 to 48 GHz. The angular dependence of line width at room temperature can be quantitatively explained by taking account of the spin diffusion effect in addition to the dipolar and anisotropic exchange interactions under a strong one-dimensional antiferromagnetic exchange interaction. At low temperatures, the line width along the a ''-axis becomes narrow at temperature decreases whereas it becomes unmeasurably broad and shows a strong frequency dependence along the c ''-axis. The g -shift due to the one-dimensional antiferromagnetic spin correlations was also found at low temperatures.

Exchange Splitting of Electron Spins in Copper-Based Kondo Alloys

Abstract: Modification of the Zeeman splitting of conduction-electron spins by an s–d exchange interaction has been studied in the de Haas – van Alphen effect at fields up to 50 kG and temperatures of order 1 K in very dilute copper-based alloys of Cr, Mn, Fe, and Co. In Cu(Cr) there is a linear relationship between an effective exchange energy and solute concentration, and the results indicate an antiferromagnetic interaction between conduction electrons and polarized impurity spins with very little Kondo screening. The effects of increasing field or decreasing temperature are consistent with a simple polarization of the impurity spins. The variation of the exchange energy from orbit to orbit is explained by the variation over the copper Fermi surface of the d-like part of the wave function. The occurrence of clean spin-splitting zeros in the Cu(Cr) system is believed to be a fortuitous result of a symmetrical positioning of the Friedel virtual bound states relative to the Fermi energy. In Cu(Mn) the exchange ener...

Dielectric Constant of an Exchange-Polarized Electron Gas and the Metal-Semiconductor Transition in Doped EuO

Abstract: This paper reports calculations of the linear responses (the dielectric constant and the magnetic susceptibility) of an electron gas interacting through an exchange interaction with a set of localized magnetic moments. This allows one to account for the metal-semiconductor transition which has been observed in moderately doped EuO, in agreement with experimental data.

Elastic and Quasi-Elastic Neutron Scattering from K2MnF4 near the Critical Point

Abstract: Elastic and quasi-elastic neutron scattering experiments on K 2 MnF 4 single crystal which is a typical two-dimensional antiferromagnet with Heisenberg exchange interaction, have been carried out. From the measurements of the temperature variation of magnetic Bragg intensities, existence of two types of the magnetic structure (K 2 NiF 4 -type and Ca 2 MnO 4 -type) with different Neel temperatures T N (42.37±0.02 K and 58.0±0.5 K, respectively) has been confirmed. The temperature variation of sublattice magnetization has been determined from the (1, 0, 0) magnetic Bragg inten-sity. The results can be expressed by a simple power law for 4.2 K< T < T N with β=0.188±0.01. After the quasi-elastic scattering measurements, two-dimensional spin correlation is found to be long-range over all the critical region. The diverging nature of the correlation length among intra-planar spins κ -1 at T N strongly suggests the two-dimensionality in this substance.

Magnetic Properties of Some Iminoxyl Polyradicals. III. Exchange Interaction in Iminoxyl Biradicals

Abstract: The EPR spectra of TEMPAD and Sulfite biradicals in a dilute solution have been reasonably interpreted in terms of the variation in the ratio of the intra-molecular exchange interaction to the 14N hyperfine interaction. Comparing these spectra with the theoretical ones, the authors have estimated the intra-molecular exchange interactions as 10.0·A=2×10−2k and 3.0·A=5×10−3k respectively. The magnetic susceptibility of the TEMPAD biradical exhibits a broad maximum at a temperature of 16.5°K, while 50 and 75% TEMPAD diluted in corresponding diamine have no maximum in the temperature range measured. The magnetic susceptibility of the sulfite biradical also shows a broad maximum at 15.0°K, in spite of the weak intra-molecular exchange interaction. These results indicate that the origin of the short-range ordering is the inter-molecular exchange interaction between unpaired electrons in different molecules.

Exchange interaction between ionic and covalent states of two atoms at large distances

Abstract: The exchange interaction between the ionic and the covalent states in the system of two atoms is considered at large internuclear distances. This interaction determines the nonadiabatic transition probabilities in the systems such as A*+B or A++B-. An asymptotically exact expression for this interaction is obtained accounting for the long range (polarization) interaction in the system.

A Theory for a Self-Trapped Antiferromagnetic Polaron at T=0 K

Abstract: Self-trapped antiferromagnetic polaron at T =0 K is studied for the localized moments of the classical spin limit. Nonlinear effect, which is most important for the magnetic polaron, is taken into account completely. It is found that when the band width is larger than the s – f exchange energy, the direction of the electron spin is nearly constant and then, for the exchange energy between the localized spins smaller than a critical value, a large magnetic polaron can exist in which the localized spin within the polaron is nearly completely saturated. When the former becomes smaller than the latter, however, the electron spin follows after the localized spins and then the magnetic polaron becomes unstable for the limit of the narrow band, contrary to the case of the usual lattice phonon polaron. The situation is, however, sensitive to the type of the magnetic ordering and the transfer matrix.

Exchange-Energy Constants in Some S = 1 2 Two-Dimensional Heisenberg Ferromagnets

Abstract: Several of the ferromagnetic two-dimensional magnetic structures similar to ${(\mathrm{C}{\mathrm{H}}_{3}\mathrm{N}{\mathrm{H}}_{3})}_{2}$Cu${\mathrm{Cl}}_{4}$ have been studied by electron-paramagnetic resonance (EPR) methods and also by measuring magnetic susceptibility as a function of temperature, in order to determine the exchange-energy constants. A linear temperature dependence of the EPR linewidths shows (after Castner and Seehra) that the Dzialoshinsky-Moriya antisymmetric exchange interaction ${\stackrel{\ensuremath{\rightarrow}}{\mathcal{D}}}_{\mathrm{ij}}\ifmmode\cdot\else\textperiodcentered\fi{}{\stackrel{\ensuremath{\rightarrow}}{\mathrm{S}}}_{i}\ifmmode\times\else\texttimes\fi{}{\stackrel{\ensuremath{\rightarrow}}{\mathrm{S}}}_{j}$ must be included with the usual symmetric terms in the calculation of the moments. These compounds indicate an "intermediate" case where the antisymmetric exchange term is comparable in magnitude to the dipole-dipole energy. The values of the isotropic exchange energy $J$ are derived by fitting the susceptibility data to a high-temperature expansion of the susceptibility with the leading contribution of $\stackrel{\ensuremath{\rightarrow}}{\mathcal{D}}$ included in the expansion. Values of $J\ensuremath{\approx}10$ ${\mathrm{cm}}^{\ensuremath{-}1}$ are found with $\stackrel{\ensuremath{\rightarrow}}{\mathcal{D}}$ more than twenty-times smaller. Additional comments are made about the thermochroic transition exhibited by these substances.

Exchange Interaction Model of Ferromagnetism

Abstract: The Schrodinger exchange operator for arbitrary spin has been used to form an interaction Hamiltonian for a nearest‐neighbor model of ferromagnetism. Through use of the cluster expansion method and new group theoretic results in conjunction with the diagrammatic method, eight terms in the high temperature series for the zero‐field partition function and the low‐field susceptibility are obtained for arbitrary spin and general crystal lattice. Critical parameters are estimated from these series by means of various ratio tests and Pade approximants. For the cubic lattices the Curie temperature Tc and the critical index γ are given by kBTC/J=0.547(q−1.6)(Y−1+0.21) and γ=0.48+2.16Y−1 for S>12;=1.41±0.02 for S=12, respectively, where Y = 2S + 1. Comparison of these results with those appropriate to the Heisenberg model as well as to experimental values is made. The concept of multipolar ordering is also discussed. It is shown that for the present model all of the 2S ``independent'' multipolar phase transitions ...

Exchange interactions in rare earth chalcogenides

Abstract: The author obtains explicit formulae for the admixtures of the J=1 level of Sm2+ (4f)6 7F into the J=0 level by exchange coupling to an adjacent Eu2+ (4f)7 8S ion. The problem is formulated using states which are antisymmetric with respect to interchanges of electrons. An unperturbed Hamiltonian is defined which is symmetric with respect to interchanges, and the difference between it and the full Hamiltonian is treated by perturbation theory, taken to second order. It is found that the dominant processes are those in which, in the intermediate states, either two electrons, one from each 4f shell, have been excited into unoccupied orbitals, or two electrons from closed shells have been excited into the 4f shells, one electron to each rare earth ion. By the use of equivalent operator techniques, it is shown that the admixtures can be derived from an equivalent anisotropic exchange interaction, with the important feature that the spin operators which appear are defined in second quantized forms and are not identical with the commonly used spin operators. It is suggested that in phenomenological exchange spin Hamiltonians these new definitions should be used.

The Intermolecular Potential of Hydrocarbon Dimers as Examined by the Perturbation Theory Including Exchange Energy in the PPP Approximation

Abstract: By using the perturbation method, including the exchange energy, the interaction potential curves for the intermolecular distances from 2.0 A to 6.0 A of the ethylene dimer, the butadiene dimer, the hexatriene dimer, and the benzene dimer were obtained. The matrix elements were evaluated in the Pariser-Parr-Pople approximation. Reasonable intermolecular potential curves were obtained for all the dimers studied. The analysis of the perturbation energy leads to the conclusion that the induction and dispersion energies and the exchange repulsion energy of the second order in the overlap integral give the potential minimum for the interaction of small molecules, such as ethylene or butadiene dimers, but for large molecules, such as benzene or hexatriene dimers, the exchange repulsion energy of the fourth order in the overlap integral should also be included in order to obtain the potential minimum. An important role of the charge transfer term was suggested for the chemical reaction; this was in agreement wit...

Magnetic Ordering of Eu(1−x)GdxS

Abstract: Solid solutions of ferromagnetic EuS and antiferromagnetic GdS maintain the rock salt structure for all compositions. Metallic behavior occurs due to the replacement of Eu2+ by Gd3+ which contributes conduction electrons to the lattice and this strongly influences the magnetic properties. Initially there is a sharp increase in Tc and θ going from Tc = 16.5K, θ = 19K (pure EuS) to Tc = 49K, θ = c53K (x = .03, Eu(1−x) GdxS). Between x = .40 to .60 a reduced moment ferromagnetism is found but θ now becomes negative indicating that antiferromagnetic exchange is also present. The complex magnetic behavior of the intermediate compositions can be interpreted as a canted or spiral magnetic structure which minimizes the exchange energy of the competing ferro‐ and antiferromagnetic ion systems. Compositions with x>.80 are antiferromagnetic. For such concentrations the paramagnetic Curie constant is anomalously large showing a moment 0.1 to 0.2μB greater than the 7μB normally found for Eu2+ or Gd3+. This we attribut...

Magnetic transition in ising systems of triplet ions with zero field splittings

Abstract: An Ising system of triplet ions (S=1) has been studied using a Monte Carlo technique. The triplet is assumed split into a singlet and a doublet, even in the absence of a magnetic field, by a single ion splitting D. The ions are arrayed on a NxN square lattice with periodic boundary conditions, and a ferromagnetic coupling J acts only between nearest neighbors. We have found that the groundstate is non‐magnetic and there is no transition to an ordered state when the ratio of the single ion splitting to maximum exchange energy is greater than 0.5 (i.e. y = D/4J > 0.5). For γ<0.5 a low temperature ferromagnetic state is stable. The dependence of the critical temperature on γ is found to be similar to that predicted by molecular field theory although the Monte Carlo critical temperatures are substantially lower. For a narrow range of γ (0.473<γ<0.5) the transition to the paramagnetic state is 1st order; for lower values of γ the phase change is 2nd order.

Theory of NMR Line Shape of Alternate Linear Chains of Inequivalent Nuclei Coupled by Indirect Exchange Interaction

Abstract: The NMR spectrum of a linear chain containing two types of spin 12 nuclei, with slightly different chemical shifts, and coupled by a scalar exchange interaction between nearest neighbors, is examined theoretically. Analytical expressions for the first even moments of the spectrum are given and the dependence of the moments on the number of spins in the chain is analyzed. After a brief review of the Liouville representation, a Green's function theory in this representation is developed allowing the study of the line shape. It is shown that in the central region of the spectrum, one obtains an approximately Lorentzian shape whose width is calculated for a weak field experiment. The theory also provides an approximate value for the line intensity at the center of the spectrum for an arbitrary resonance frequency.