Showing papers on "Exchange interaction published in 1969"

Exchange Interaction in Alloys with Cerium Impurities

Abstract: Starting with the Anderson model for the $4{f}^{1}$ configuration of cerium, the transformation of Schrieffer and Wolff is performed, taking into account combined spin and orbit exchange scattering. The resultant interaction Hamiltonian differs qualitatively from the conventional $s\ensuremath{-}f$ exchange interaction. The Kondo effect, the spin-disorder resistivity, the Ruderman-Kittel interaction, and the depression of the super-conducting transition temperature with impurity concentration are worked out for alloys containing cerium impurities on the basis of this new interaction.

Magnetic Properties of Cobalt and Nickel Dichalcogenide Compounds with Pyrite Structure

Abstract: The magnetic properties of dichalcogenide compounds, CoS 2 , CoSe 2 , NiS 2 , NiSe 2 and the system Co(S x Se 1- x ) 2 , were studied by means of magnetic measurement, neutron diffraction and NMR. The exchange interaction J s w of the ferromagnetic CoS 2 ( T c =124°K, θ p =220°K, p eff =1.76µ B , n =0.84µ B and H i =52 kOe) was estimated to be 24 cm -1 per Copair from the analysis of spin wave theory. While, CoSe 2 ( T N =90°K, θ p =-160°K and p eff =1.72µ B ) showed an antiferromagnetic spin ordering with MnSe 2 type. NiS 2 (θ p =-740°K and p eff =2.48µ B ) had no magnetic ordering even at 4.2°K. NiSe 2 exhibited weak constant paramagnetism with metallic conductivity. In Co(S x Se 1- x ) 2 , (0≤ x ≤1), the magnetic properties and the magnetic phase diagram were determined, and this system showed to have “low spin state” with 1µ B per Co. Some discussions were given from the theoretical stand points.

Anisotropy in Two-Center Exchange Interactions

Abstract: The exchange interaction between electrons on two different centers is developed in a bipolar series of angular momentum operators. In contrast to the isotropic Hamiltonian commonly used to represent this interaction, we find that all forms of anisotropic terms are needed, antisymmetric as well as symmetric ones. The degrees of the anisotropy assume all values commensurate with the angular momenta of the electrons. Beside the Dzyaloshinsky-Moriya term ${\mathrm{S}}_{1}$\ifmmode\times\else\texttimes\fi{}${\mathrm{S}}_{2}$, two-center exchange interactions contain antisymmetric anisotropies of higher degrees. For ions with strong orbital contributions to their magnetic moments, anisotropic exchange does not enter merely as a perturbation, and we find that the magnitudes of the symmetric and antisymmetric anisotropies are as large as the isotropic part of the exchange interaction. Explicit expressions containing radial integrals are derived for the coefficients representing the anisotropy in the exchange interaction. These anisotropy coefficients are related to the more conventional exchange constants; we also find the number of independent parameters needed to describe two-center exchange interactions for various situations. The coefficients of anisotropy representing the exchange interaction between ions with $N$ equivalent electrons are related to the coefficients for the interaction between ions with one electron. Although anisotropic superexchange is not considered in detail, both the form of the Hamiltonian representing this interaction, and also the number of independent parameters in the Hamiltonian, immediately follow from the Hamiltonian for the two-center exchange interaction.

Magnetoresistance in Chalcogenide Spinels

Abstract: The consequences of a simple type of exchange interaction between charge carriers in a broad energy band and localized magnetic moments will be discussed for a ferromagnetic semiconductor. The interaction causes (1) a splitting of the energy band into two bands for the different spin directions, (2) spin disorder scattering of the charge carriers. The calculated temperature and field dependence of the magnetoresistance are compared with experimental data of CdCr2Se4. The magnetoresistance of compounds MeCr2S4, Me=Fe, Co, Cd was measured. For n‐type CdCr2S4 and for p‐type FeCr2S4 and p‐type CoCr2S4, the magnetoresistance −Δρ/ρ0 was found to be 0.78, 0.05, and 0.05, respectively, at 12 kOe near Tc, whereas n‐type FeCr2S4 and CoCr2S4 show no effect. The magnetoresistance of the system Fe1−xCdxCr2S4 was also measured. The temperature dependence of the polar magneto‐optical Kerr effect of CdCr2Se4 is discussed in connection with the described model for the energy bands.

Stress-Induced Exchange Splitting of Hyperbolic Excitons in GaAs.

Abstract: Evidence for the existence of hyperbolic excitons has been obtained from a study of the effects of compressive uniaxial stresss on optical structure of GaAs at 77\ifmmode^\circ\else\textdegree\fi{}K using a double-beam wavelength-modulation technique. We have observed a polarization-dependent splitting of this structure which cannot be accounted for on the basis of one-electron band theory but is explained by including the electron-hole exchange interaction. An estimate of an effective radius of \ensuremath{\cong}10 \AA{} for the electron-hole interaction has been made.

Partial Quenching of Rare Earth Moment in Cubic Laves Intermetallic Compounds

Abstract: Measurements of the low‐temperature (0.1° to 1.0°K) heat capacities of several cubic Laves intermetallic compounds containing praseodymium indicate the presence of a substantial nuclear hyperfine contribution to the specific heat. It is possible to relate the magnitude of this contribution to the magnetic moment carried by the Pr3+ ion in each of the materials studied. The moments deduced in this way are PrNi2, 0.582±0.006; PrCo2, 2.18±0.05; PrAl2, 2.65±0.03 μB. These are each significantly less than the free Pr3+ ionic moment of 3.20 μB. The results are discussed in terms of a theory of Bleaney and it is concluded that the crystalline electric field is the same in PrCo2 and PrNi2, the large moment in the former being due to a larger exchange interaction. In the case of PrAl2, the data indicate an accidental degeneracy in the crystalline field ground state.

Absence of ferromagnetism or antiferromagnetism in the isotropic Heisenberg model with long-range interactions

Abstract: It is shown that the isotropic Heisenberg model with an exchange interaction J(R) cannot be ferromagnetic or antiferromagnetic if the spherical model with an interaction|J(R)| does not exhibit a phase transition. From this result it follows that the isotropic Heisenberg model with J(R) = A/|R|d+σ (where d is the dimensionality of the lattice, A > 0 and σ > 0) cannot be ferromagnetic for d or= d.

Metamagnetism in the perovskite compound Gd2CoMnO6

Abstract: The compound Gd2CoMnO6 crystallizes with the orthorhombic perovskite structure and is isomorphous with GdFeO3. A crystal structure refinement shows that the Mn3+-O2−-Mn3+ bond angles are ∼ 145° and that the distortion from cubic symmetry is considerable. A spontaneous moment of 5 e.m.u./g develops below 115°K due to the exchange interactions between near neighbouring Mn3+ ions. Below 115°K a field induced metamagnetic transition to a state with a moment of 20 e.m.u./g is also observed and this transition is depressed in temperature by 1°c for 360 oe applied field. The metamagnetism is accounted for on the basis of a transition between an uncompensated anti-ferromagnetic and a ferromagnetic state which is observed in Gd2CoMnO6 due to a change in sign of the Mn3+-O2−-Mn3+ exchange interaction originating from Jahn-Teller electronic ordering in Mn3+ ions. This ordering is favoured at low temperatures and introduces a negative contribution to the exchange interaction.

Exchange Interactions and Magnetic Susceptibilities of Ni2+ in KMgF3 and K2MgF4

Abstract: Magnetic susceptibilities of KMg (1- x ) Ni x F 3 and K 2 Mg (1- x ) Ni x F 4 (0≦ x ≦0.121) have been measured in the temperature range from 1.6°K to 300°K, and the exchange interactions between neighboring Ni 2+ ions have been evaluated. The analysis of the data has been made on the assumption that Ni 2+ ions distribute randomly in Mg 2+ sites and form various types of clusters coupled by the exchange interactions. In KMgF 3 , the nearest-neighbor exchange J 1 is 110±10°K and the next-nearest-neighbor exchange J 2 is 0.5±0.1°K, where an exchange interaction between neighboring spins s i and s j is written as J ( s i · s j ). In K 2 MgF 4 , J 1 is 120±10°K. The intraplane next-nearest-neighbor exchange J 2 and the interplane-nearest-neighbor exchange J 3 can not be determined uniquely, but the most probable values are \(J_{2}{\cong}0.5\)°K and \(J_{3}{\cong}0\). The Van Vleck paramagnetic susceptibilities of Ni 2+ in both salts have been found to be 2.83×10 -4 cgsemu/mol within the experimental errors of 10%.

Magneto-optical effects and a Monte Carlo calculation for dysprosium aluminium garnet

Abstract: The optical absorption spectrum of the antiferromagnet dysprosium aluminium garnet has been studied both above and below its Neel temperature (25 °K) Shifts and splittings of the absorption lines are interpreted in terms of magnetic interactions and, in particular, the finite shifts above TN are attributed to the presence of magnetic short-range order A Monte Carlo calculation provides quantitative confirmation of these ideas The value obtained for the nearest-neighbour exchange interaction is equivalent to an enhancement of the nearest-neighbour dipolar interaction by a factor 147, which is in good agreement with a value obtained by other authors Further studies of the spectrum as a function of external field give a direct indication of the dominance of nearest-neighbour interactions in this substance, and also some insight into the form of the small non-dipolar interaction, which is clearly not of the simple Heisenberg JijSi Sj form

Local Electron Distribution in the Singlet Ground State Due to the s-d Exchange Interaction

Abstract: On the basis of the theory of singlet ground state for a localized spin developed so far, the total charge and spin localized around the impurity are calculated in detail. It is shown that for ¢a-component associated with the localized up-spin state half of a down-spin electron and half of an up-spin hole are trapped by the impurity. This leads to a conclusion with the aid of the Friedel sum rule that a phase shift of the conduction electrons at the Fermi level is ±n/2. It is further shown in general that the localized charge in the ground state completely vanishes for the present s-d exchange Hamiltonian. 111 non-magnetic metals forms a singlet (non-degenerate) state coupled with the conduction electrons by the s-d exchange interaction. In this singlet state, the spins of the. conduction electrons are localized around the impurity spin, and form a singlet bound state with it. The energy of the singlet ground state is lower by the binding energy IE I than the normal-state energy JE which can be obtained by the usual perturbation calculation which starts from the doubly degenerate free state of a localized spin and the conduction electrons. Our theory dealing with the present system consisting of a localized spin and the conduction electrons is based on the perturbation method.*> It starts from a singlet state in which one electron (or hole) excited above (or below) the Fermi sea is coupled with the localized spin instead of starting with the doubly degenerate free state, and calculates the ground-state energy and the wave function (and also other quantities) perturbed by the s-d exchange interaction in a power series of the exchange coupling among which the most divergent terms are retained. As particularly shown in a previous paper by the present authors,7) the charge density at the impurity center which is :finite in the start­ ing approximation completely vanishes in the :final stage of pertu:rbation. This fact indicates that the localized charge around the impurity vanishes and only the spin-correlation density remains to be localized. The main purpose of this paper is to calculate the total localized charge

Magnetic Properties of Low Dimensional Spin Systems

Abstract: Using the method of the two-time Green's function, both static and dynamic properties of low dimensional spin systems with an anisotropic exchange interaction were investigated. It was shown that the magnetic behaviours of one- and two-dimensional spin systems are considerably different from those of the usual three-dimensional systems. That is, the transi­ tion temperature is lower than that expected from the magnitude of the coupling constant when an anisotropy is small enough. The short range order is developed more remarkably in the neighbourhood of the transition temperature. The damping constant increases in both ferro- and antiferromagnet with decreasing temperature owing to the anomalous growth of fluctuation. At the same time a broad shoulder is developed in the line shape, which may be considered as indicating quasi-collective modes of motion which persist in the paramag­ netic phase.

Exchange Interactions in Mn[Sc2]S4

Abstract: One possible explanation for the rapid development of antiferromagnetism in the system MnCr2S4–MnInCrS4 is the existence of antiferromagnetic interactions among the A‐site Mn. The normal spinel MnSc2S4 was prepared and studied to determine the actual magnitude of A‐A interactions in sulfide spinels. The cubic lattice parameter is a=10.615 A with u=0.381. Magnetic susceptibility measurements showed this material to be an antiferromagnet with a Neel temperature below 4.2°K and with a θ‐parameter of about −21°K. The magnitude of the Mn–Mn exchange interaction was determined by fitting the susceptibility data from 15° to 295°K to the [3, 3] Pade approximant to the Rushbrooke‐ Wood series expansion. The value of the Mn–Mn exchange constant was found to be J/k=−0.80°K. The use of Pade approximants rather than the truncated series itself greatly improves the applicability of the power series expansions at temperatures comparable to or below the value of the θ‐parameter.

The Theory of Josephson Tunneling

Abstract: I’ll begin by making an analogy between the long-range spatial order of a solid and the long-range phase order of a superconductor. The first question which one might ask is, how does a short-range force produce long-range order? In a solid the typical range of the interatomic forces are of the order of the interatomic spacings. However, once a part of the crystal forms the continued propagation of the order is established in a step-wise manner with the arrangement of the occupied sites legislating the arrangement of the subsequent level through the short-range interactions. In the case of a superconductor we are dealing with an interaction whose “range” is associated with the retarded nature of the phonon-exchange interaction and may “extend”† on the order of v F /ω D ≈ 10−5 cm. The attractive nature of this interaction leads to the formation of pairs which are spread out over a coherence length ξ of order 10−4 cm. Now, the center-of-mass coordinates of some 106 pairs lie in a sphere of diameter ξ. In order for each of the pairs to have the optimum space-time correlations necessary to take advantage of the attractive phonon exchange interaction, it is necessary that they all have the same center-of-mass momentum.

Magnetic Properties of the Oxygen Molecule in Solid Oxygen‐Argon Mixtures

Abstract: Recent neutron diffraction and crystallographic studies of the magnetically ordered phase (≤24°K) of solid oxygen have aroused new interest in magnetic exchange interactions between oxygen molecules. The interpretation of the magnetic ground state in the pure oxygen system is difficult because multiple solid‐phase transitions and the narrow range of temperatures over which each phase is stable prevent a determination of the magnitude of the exchange interaction. We report here on magnetic susceptibility studies of O2‐A solid mixtures which exist from 0°–70°K in a single hcp phase for O2 concentrations in argon ranging from 20%–50% and in a single fcc phase from 0%–20%. The measurements can be quantitatively interpreted using a statistical molecular field theory of disordered solid‐solutions. We find θ/c≅60∘K, where θ is the ``statistical'' Curie‐Weiss temperature and c is the concentration of O2 in A. This is comparable to the paramagnetic Curie‐Weiss temperature θ=50°–60°K observed in pure liquid and γ...

Theory of Magnetic Excitations in FeCl2 and CoO

Abstract: A theory has been developed whereby single‐ion effects in a magnet may be treated exactly providing an RPA is made to the exchange interaction. The method is applied to FeCl2 and CoO, both of which have unquenched orbital angular momentum, a factor which might complicate conventional approaches. For FeCl2 the available data on static properties and the AFMR can be explained. In addition to the AFMR, there are many lines predicted, but experiments are lacking. Measurements on CoO can also be accounted for, but there is a serious lack of interpretable data on absorptions to test the theory.

Magneto-Optical Investigation of Trivalent Dysprosium in Gadolinium Trichloride

Abstract: The optical absorption spectrum of 2% Dy3+ in the ferromagnet GdCl3 has been investigated and found to exhibit line shifts and splittings below the Curie temperature (2.2°K), which are attributable to magnetic dipole and exchange interaction between the various states of Dy3+ and the ordered Gd3+ system. These effects have enabled the exchange field to be measured for a number of different J multiplets, at the lowest temperature obtainable (1.35°K). The exchange field is found to be reasonably constant within a particular multiplet, but the variation between multiplets is more complex than the simple model would indicate. The temperature dependence of the shifts and splittings suggests that the optical effects are a measure of the long-range, rather than the short-range order, although the latter cannot be entirely ruled out.

The Hyperfine Field of Praseodymium Implanted in Iron

Abstract: It is well known that the magnetic properties of rare earth impurities in crystals are due to the localized character of the 4 f electrons The degeneracy of the | L , S > ionic levels may be lifted by the exchange interaction between the rare earth and the host or by crystal field effects, and the level sequence depends on which of these mechanisms dominates (see, for example, Campbell, this volume, p 131) Experiments on various rare earth ions implanted into Fe, Co and Ni have shown that the exchange mechanism is important in ferromagnetic transition metal hosts (Grodzins, Borchers & Hagemann 1966; Boehm, Hagemann & Winther 1966) where the main contribution to the hyperfine field is due to the orbital momentum L of the 4 f shell, but there is no reason to expect that crystal field effects are negligible in all cases In fact, at very low temperatures, the hyperfine field, which is proportional to the average of the ground state, may be rather sensitive to the relative strength of the two mechanisms This is shown by the measurement, reported here, of the hyperfine field at Pr in Fe, using nuclear orientation

Effect of Copper Layers on the Coercive Force of Permalloy Films

Abstract: Three mechanism of the effect of a copper layer on the coercive force of films are studied in this work: variation in the “roughness” of the substrate; diffusion of the copper into the permalloy; variation in the energy of exchange interaction between permalloy films separated by a copper layer. It is found, that an increment of the coercive force (ΔHc) with time is directly proportional to the effective diffusion depth, Δd. The results of experimental investigations on the condensation of metallic film make it possible to single out the following stages of this process: the formation of stable nuclei, the coalescence of discrete nuclei to a continuous layer; the growth of crystallites with a further increase of the thickness of continuous films. Observation of structures of interlayers under an electron microscope indicates that in wide ranges of thickness and deposition temperatures the interlayer consists of individual stable nuclei. The presence of exchange interaction between separated magnetic layers due to their direct contact makes it possible to explain the experimental results. [Russian Text Ignored].

Dynamic Behavior of a Near‐Ising System Near the Critical Point

Abstract: Applying the master equation to an Ising model, equations of motion are obtained for the average of a single spin and for the average of a pair of spins. These equations relax to equilibrium values that predict a self‐consistency relationship among the internal field, temperature, and exchange energy. The critical temperature obtained is that of the Bethe approximation, and is extended to include a static external field in the magnetization direction. With this, the relaxation of an Ising model near the Curie temperature has been investigated in a self‐consistent manner. The results are similar to those of Suzuki and Kubo, but in the Bethe approximation instead of the Bragg‐Williams approximation, and hence predict the relaxation of the correlation as well. In particular we studied a nearly Ising spin system that is a system with relatively small isotropic transverse coupling. An oscillating, linear, and external magnetic field applied transverse to the strongly coupled direction of the spins leads to low...