Showing papers on "Exchange interaction published in 1970"

Magnetic Structure of α-Mn

Abstract: A neutron diffraction study has been made on single crystal specimens of α-Mn at 4.4°K, 60°K, and several other temperatures. Five types of magnetic form factor were in turn employed in the analysis. The magnetic structure is described by a single non-collinear configuration throughout the temperature range below T N with relatively large magnetic moments in Sites I, II and small moments in Sites III, IV, irrespective of which form factor is chosen. The experimental results seem to favor a localized moment model rather than a spin density wave model. When the analysis is based on the localized moment model, moments of 1.9, 1.7, 0.6 and 0.2 5 µ B may be assigned to Site I, II, III, and IV, respectively at 4.4°K, and the spin density in the atom is a superposition of a positive 3d-density and a negative 4s-density. The dependence of the effective exchange interaction coefficient on the inter-atomic distance is discussed.

Exchange mechanisms in europium chalcogenides

Abstract: Superexchange mechanisms, which are mostly responsible for the nnn exchange constanIt I2 in Eu chalcogenides, are investigated in detail. In contrast with the usual 3d transition metal compounds, the Kramers-Anderson mechanism is estimated to be one order of magnitude too small to explain the experimental results due to a small 4f → 2p transfer energy. The mechanism by which a p electron is transferred to a 5d state through the d-f exchange interaction gives the correct order of magnitude for I2, with a negative sign, even though it is a sixth-order perturbation. The cross term between the above two mechanisms is shown to be nearly as important as the second mechanism and may have a positive sign. The indirect exchange mechanisms, in which the anion p level has no important role, are responsible for the nn exchange constant I1. The phonon-assisted mechanism proposed by Smit is estimated to be more than one order of magnitude smaller than the experimental value. The d-f mixing term is proved to be responsible for I1, in good agreement with experiment.

On the 90° Exchange Interaction between Cations (Cr3+, Mn2+, Fe3+ and Ni2+) in Oxides

Abstract: Some empirical relations between the bond angle (of M–O 2- –M) and the asymptotic Curie temperature (\(\varTheta\)) or Neel temperature ( T N ) are derived from data for oxides containing Cr 3+ , Mn 2+ , Fe 3+ or Ni 2+ ions. Further, these relations seem to be explained through assuming the presence of two types of exchange interactions; one is a 90° superexchange interaction which obeys the rule proposed by Kanamori and Goodenough, the other a direct exchange interaction which is sensitive to the overlap between neighboring two d e orbitals. In oxides containing Cr 3+ or Mn 2+ the above two types of exchange are effective, while in oxides containing Fe 3+ or Ni 2+ only the former (superexchange) effective.

Spin Ordering in a Spin-Pair System

Abstract: A new type of spin ordering in a spin-pair system is theoretically investigated. In the system, the intra-pair exchange interaction is antiferromagnetic and is much stronger than the inter-pair exchange interaction. In an external magnetic field, the excited triplet of the pair splits, and the lowest component of the triplet crosses the ground singlet at a certain magnitude of the field. In the vicinity of the point of level crossing, even the weak inter-pair exchange interaction causes a considerable amount of mixing between the singlet and the lowest component of the triplet. Due to the mixing, an ordering of the spin component perpendicular to the external field occurs. This ordering explains an anomaly which has been found by Haseda et al. in their experiment of cooling by adiabatic magnetization of Cu(NO 3 ) 2 2.5H 2 O.

Spin Ordering in a Spin-Pair System

Abstract: A new type of spin ordering in a spin-pair system is theoretically investigated. In the system, the intra-pair exchange interaction is antiferromagnetic and is much stronger than the inter-pair exchange interaction. In an external magnetic field, the excited triplet of the pair splits, and the lowest component of the triplet crosses the ground singlet at a certain magnitude of the field. In the vicinity of the point of level crossing, even the weak inter-pair exchange interaction causes a considerable amount of mixing between the singlet and the lowest component of the triplet. Due to the mixing, an ordering of the spin component perpendicular to the external field occurs. This ordering explains an anomaly which has been found by Haseda et al. in their experiment of cooling by adiabatic magnetization of Cu(NO 3 ) 2 2.5H 2 O.

New Approach to the Theory of Itinerant Electron Ferromagnets with Local‐Moment Characteristics

Abstract: The understanding of ferromagnets, like iron, which exhibit localized moment behavior above the Curie point yet show itinerancy has long stood as a major theoretical problem. An account will be given of recent progress on this problem which was achieved through functional integral methods. This technique transforms the interacting electron system into an average over a system of noninteracting electrons moving in a Gaussian‐weighted external ``magnetic'' field which acts only on the electronic spins. For a single magnetic impurity in a free electron metal, a single approximation allows one to go from Pauli paramagnetism to localized moment behavior in a smooth manner as the atomic exchange interaction is increased. The two impurity problem leads to an effective exchange coupling as in the Heisenberg model, which is antiferromagnetic for the nondegenerate orbital case studied here. Application of the technique to homogeneous systems leads to damped spin waves in the ferromagnet in lowest approximation.

Spin-Wave Dispersion Relations in Gadolinium

Abstract: Spin-wave dispersion relations have been measured in high-symmetry directions for metallic Gd. Analysis shows that at least five interplanar constants are required for a satisfactory fit to the data. The energy gap at $q=0$ is unmeasurably small. In the $c$ direction the measured dispersion curve gives directly the Fourier-transformed exchange interaction $J(0)\ensuremath{-}J(q)$. This exhibits no other extreme value except that at the origin.

Helical Spin Arrangement in Cubic FeGe

Abstract: The magnetic properties of single crystals of the cubic B20 modification of the metallic compound FeGe have been investigated by means of a vibrating-sample magnetometer and a torsion balance. Transition to an ordered spin structure occurs at 280 K. Magnetization curves below this temperature shown an almost linear field dependence for the [100], [111] directions with a field of about 2 kOe required for saturation at low temperatures, indicating a small magnetocrystalline energy compared to the exchange energy. The saturation moment as extrapolated to zero Kelvin corresponds to 1.0μB. A model with the spins forming a helical screw propagating in the [111] direction at zero field is proposed to explain the observed magnetic properties.

Evidence for an Exchange Coupling at the Interface between Two Ferromagnetic Films

Abstract: In a first part, we estimate the effect of dynamic pinning [C. F. Kooi, E. P. Wigen, M. R. Shanabarger, and J. V. Kerrigan, J. Appl. Phys. 35, 791 (1964)] due to two ferromagnetic layers upon the spin‐waves resonances in a sandwiched film having a higher magnetization, assuming the interface interaction energy to be of an exchange type. Experiments performed on epitaxial films of Permalloy, symmetrically coupled with two nickel layers of various thicknesses, exhibit results in excellent agreement with theory and provide a reproducible value of the interface energy which is one‐tenth of that of the bulk exchange energy.

Effect of Pressure on Curie Temperature of Calcogenide Spinels CuCr2X4(X=S, Se and Te)

Abstract: The pressure coefficient of the Curie temperature of CuCr 2 X 4 was obtained from the result of measurement of the variation with pressure in the self inductance of search coil wounded on the specimen vessel. The coefficients, d T c /d p , were founded to be -11.3×10 -4 °Kkg -1 cm 2 for CuCr 2 S 4 , -4.1×10 -4 °Kkg -1 cm 2 for CuCr 2 Se 4 and nearly zero for CuCr 2 Te 4 , respectively. If the main exchange interaction in a pair of Cr ions is thought to be the ferromagnetic superexchange of the Cr-X-Cr type and the antiferromagnetic direct interaction of the Cr-Cr type, it can be seen from the results of the present experiment that the direct Cr-Cr interaction is more sensitive to lattice compression than the superexchange Cr-X-Cr. The magnetic properties of those compounds are also reported.

The dependence of exchange energy on orbital overlap

Abstract: Several methods of estimating exchange energies have been tested for the interaction of two hydrogen atoms in 2s, 2p or hybrid valence states. The simplest relationship previously used, X = KS 2/R, does not give an accurate picture of the dependence on internuclear distance. A two-term expression X = S 2(AR -1 + BR -2) is considerably better but fails for the case of exchange between orthogonal orbitals (S = 0). An alternative expression in which C 0 - C is the penetration part of the two-electron coulomb integral, is just as accurate, contains no more constants and holds equally well for orthogonal and non-orthogonal orbitals. C 0 - C is a better measure of the net overlap of two orbitals than is the overlap integral S, because the latter is zero for orbitals which are orthogonal but nevertheless overlap. We have found no method of deducing the constants K, A or B other than by calculating the exchange energy exactly at one or two values of R.

Linear Chain Antiferromagnetism in Copper Benzoate

Abstract: Various magnetic properties of one dimensional antiferromagnet Cu(C6HsC00)2 ·3H20 were investigated by means of magnetic susceptibility, magnetic torque, NMR, and ESR measurements. The results show that this compound is one of the best one dimensional antiferromagnets known at present. An intrachain exchange interaction J/K was estimated to be -8. 6±1 °K while no second order phase change was found down to 1. 4 °K. ESR line width at room temperature was not explained by an usual treatment and an anisotropic exchange effect was newly taken into account. However, other anomalies of the line width such as the frequency, temperature, and angular dependences appeared at low temperature regions were not yet explained.

Tomonaga's model and the Kondo problem

Abstract: An expression for the free energy of thes-d-exchange Hamiltonian for the caseS=1/2 is derived using Tomonaga's model for the description of the free electrons. Thereby a formal equivalence can be established to the thermodynamics of a classical gas of charged particles distributed on a ring with alternating charges interacting via a log sin-potential. Although we are unable to calculate the free energy in a closed form, the result clearly indicates that as the exchange interaction changes sign the behavior of the free energy is changed significantly for low temperatures.

Transport in Gd‐Doped EuO

Abstract: Transport properties of 2% Gd‐doped EuO with Tc≈123°K have been investigated. The resistivity anomaly in the neighborhood of Tc can be explained satisfactorily by critical scattering theory. Estimates of the exchange interaction between conduction electrons and localized spins are found to vary from 4.9×10−2 eV in Gd :EuO to 4.3×10−2 eV in Gd :EuS.Transport properties of 2% Gd‐doped EuO with Tc≈123°K have been investigated. The resistivity anomaly in the neighborhood of Tc can be explained satisfactorily by critical scattering theory. Estimates of the exchange interaction between conduction electrons and localized spins are found to vary from 4.9×10−2 eV in Gd :EuO to 4.3×10−2 eV in Gd :EuS.

Fine-structure transitions in sodium--rare-gas collisions.

Abstract: An impact-parameter treatment is used to obtain cross sections for reactions such as Na 2P12/+He to Na2P32/+He. The coupled equations with and without rotational coupling are numerically solved. The reaction between this work and the Landau Zener formula is discussed. It is shown that rotational coupling cannot be neglected even at low velocities. The effect of repulsive exchange interaction is shown to be much more important, at temperatures exceeding 400 K, than Van der Waals interaction for Na-He collisions. At 400 K, the cross sections are 78 AA2 for Na-He, 68 AA2 for Na-Ne and 62 AA2 for Na-Ar.

Magnetic characteristics of lanthanide zinc (LnZn2) inter-metallic compounds☆

Abstract: The magnetic characteristics of LnZn2, with Ln = La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Ho, and Yb, have been studied from 4° to 300 °K. LaZn2 is a Pauli paramagnet. All the other compounds except SmZn2, EuZn2 and YbZn2 exhibit Curie-Weiss behavior from 100 ° to 300 °K, with paramagnetic moments in close agreement with those expected for free tripositive ions. The behavior of SmZn2 is due to the closeness of the multiplet spacing for the Sm3+ ion. The non-linearity of χ with T for EuZn2 and YbZn2 is ascribed to the variable valency of the lanthanide. Magnetic ordering is observed for all compounds except LaZn2, PrZn2 and YbZn2 at temperatures ranging from 7 °K (CeZn2) to 68 °K (GdZn2). NdZn2 and GdZn2 order ferromagnetically; the other six compounds order antiferromagnetically. PrZn2 becomes a Van Vleck paramagnet at low temperatures. The moment of Nd3+ is partially quenched by the crystal field. The magnetic behavior of the LnZn2 compounds can be understood in terms of the RKKY interaction. The effective s-f exchange interaction for GdZn2 is evaluated as 0.15 eV as compared with 0.09 eV obtained from esr (g-shift) measurements.

Spin Ordering and Thermodynamical Properties in Spin-Pair Systems under Magnetic Fields

Abstract: It has recently been shown that in spin-pair systems a new type of spin ordering occurs under magnetic fields. In the present paper, the spin ordering in general cases of the inter-pair exchange interaction and the thermodynamical properties of these systems are investigated on the basis of molecular field theory. Various types of spin ordering appear depending on the strength of the inter-pair exchange interaction and the external magnetic field. The specific heat originating from the short range order of spins in a one-dimensional lattice is also calculated for a purpose of comparison with experiments in Cu(N03)2 2. 5 HzO.

Effect of Single-Ion Anisotropy on Two-Spin-Wave Bound State in a Heisenberg Ferromagnet

Abstract: We consider the scattering of two spin waves in a uniaxial (easy axis) Heisenberg ferromagnet with single-ion anisotropy. The two-spin-deviation problem is solved exactly at zero temperature. We find (for $Sg\frac{1}{2}$), in addition to the usual two-spin-wave bound states, a new "single-ion bound state," in which at the zone corner the two spin deviations are on the same site. When the magnitude of the anisotropy is comparable to the exchange interaction, the single-ion bound state becomes the dominant feature of the bound-state spectrum. For arbitrary spin there is a critical anisotropy strength above which the single-ion bound state exists throughout the Brillouin zone. We conclude that the presence of single-ion anisotropy enhances the possibility of experimental observation of the bound states.

Contribution to the theory of a dilute Heisenberg ferromagnet

Abstract: A theory of a dilute Heisenberg ferromagnet is studied in two ways; the molecular field approximation and the Tyablikov approximation. By considering the Heisenberg model in the molecular field approximation, an expression for the averaged moment at any lattice site is obtained by the use of the diagram method. For a simple cubic crystal, numerical calcu­ lations of the averaged moment with a spin t host are presented. The Curie temperature depending on the concentration of magnetic atoms is presented. In the case of the molecular field approximation, it is shown that the critical concentration at which the ferromagnetic state disappears may not exist. By the use of the Green's function another method based on the Tyablikov approximation is formulated. The theory is a straightforward generalization of the previous paper published in Prog. Theor. Phys. 42 (1969), 477, to finite temperature range. The existence of the critical concentration is also indicated. In a previous paper (referred to as K) /) we have developed a spin-wave theory of a dilute Heisenberg ferromagnet by the use of the Green's function method. For simple lattices with nearest-neighbour interactions, a general forma­ lism of the Green's function was expressed in terms of a function of the con­ centration of magnetic elements. The expression for the energy was applied to determine the critical concentration for which the ferromagnetic ground state is unstable with respect to the formation of long-wavelength spin waves. The critical concentration is defined as the minimum concentration of magnetic atoms, arranged at random in a non-magnetic lattice, for which ferromagnetism will occur. Ferromagnetism is caused by exchange interaction for a greater part between neighboring atoms, and it seems there is no need to have a rigorous periodicity in the distribution of magnetic atoms. For this reason, as was firstly suggested by Gubanov, 2 ) amorphous or vitreous ferromagnets can exist at tem­ peratures low enough so that when they contain the right atoms we have reason to believe they will be ferromagnetic. In this paper, we intend to generalize the previous theory to finite tempera­ ture range in order to obtain the Curie point depending on the concentration of magnetic elements. From this approach, it seems to be possible to clarify the existence of ferromagnetism in the amorphous or vitreous states. Experimentally there are some publications opening the possibility of ferromagnetism in amor­ phous or vitreous states. 3 )

Anomalies and Bound State Due to the Anisotropic s-d Exchange Interaction

Abstract: The Kondo problem for the anisotropic s-d exchange interaction is investigated in de­ taiL The scattering amplitude of a conduction electron is calculated in the most divergent approximation (Abrikosov's approximation). The importance of some types of terms over­ looked in the previous work by Miwa and Nagaoka is pointed out. By changing the degree of anisotropy of the exchange integral the behaviors of the obtained scattering amplitude­ especially the divergence difficulties-are examined. To see physical meaning of the diver­ gence difficulties the problem of the existence of the bound state realized as the ground state of this coupled many-body system is discussed by extending the Yosida-Okiji-Yoshimori theory to the anisotropic case. It is shown that the exact solution of the bound state can be obtained also for the anisotropic s-d interaction, and that the divergence difficulties stated above are closely connected with the existence of the bound state.

Anomalous Temperature Dependence of Exchange Interactions in K 2 CuCl 4 2H 2 O and K 2 CuCl 4 2D 2 O

Abstract: Exchange interactions between two dissimilar Cu 2+ ions in K 2 CuCl 4 2H 2 O and K 2 CuCl 4 2D 2 O were investigated by means of electron paramagnetic resonance (EPR). The measurements were done in the frequency range from 9.3 to 65.8 GHz between 10° and 370°K. An amalgamated single line was observed below 200°K but the line splits into two lines near room temperatures. Considering the frequency and temperature dependence of the phenomenon, it is concluded that the exchange interaction depends strongly on temperature. The magnitude of the exchange interaction J / k (°K) varies from 0.3 to 0.08 between 4° and 300°K. Similar temperature dependence was obtained in K 2 CuCl 4 2D 2 O and the exchange interaction in this compound was found to be about 0.02°K larger than of K 2 CuCl 4 2H 2 O.

Effect of exchange on magnetostatic modes

Abstract: : When surface spin pinning is included in the thin-film magnetostatic-mode eigenvalue problem, exchange must be included even when the exchange energy is negligible. The magnetization is changed drastically in general, but the intensities and frequencies are essentially the same as for the pure magnetostatic modes (exchange constant D = 0 and no explicit pinning mechanism). (Author)

Direct Exchange between d Electrons

Abstract: The empirical data necessary to determine all the parameters in the exchange interaction between a pair of orbitally degenerate ions do not exist for any system. Given this paucity, we have resorted to using the best available theoretical estimates of the two-center exchange integrals for $d$ electrons which have been calculated for particular cases of cobalt atoms and ions. With these data we have quantitatively substantiated the recent assertions made about the importance of anisotropic and higher-degree isotropic-exchange interactions. We demonstrate that a bilinear scalar spin hamiltonian is totally inadequate to describe exchange interactions in systems containing orbitally degenerate ions. The higher-degree isotropic terms considerably alter the positions of the centers of gravity of the energy levels of exchange-coupled pairs. We estimate that the exchange interaction accounts for 25% of the discrepancy between the spin-orbit coupling constant $\ensuremath{\lambda}$ required to explain the magnon spectra of cobalt in KCo${\mathrm{F}}_{3}$ and the $\ensuremath{\lambda}$ for free cobalt ions. For orbitally degenerate ions in magnetically inequivalent sites, it is shown that antisymmetric exchange is as large as the symmetric terms.

Role of the Ytterbium Spins in the Spin Reorientation in YbFeO3

Abstract: The spin‐reorientation transition in YbFeO3 is explained by including the rare earth‐iron exchange interaction in a spin‐wave model, without resorting to a temperature‐dependent iron anisotropy. In a four‐sublattice model (2 Fe and 2 RE) the iron spins are coupled to each other and to the RE spins by both symmetric and antisymmetric exchange. There are four modes at k=0. Two of these modes reduce to those of the iron‐only model in the absence of the RE spins. Another mode has the frequency of a single RE spin in the exchange field of the iron sublattices. The fourth mode goes to zero frequency when the Fe‐RE interaction cancels the iron anisotropy, resulting in a spin‐reorientation transition. Measurements of far‐infrared absorption spectra of YbFeO3 have been made and confirm many aspects of the model. The similarities between the spin‐reorientation transitions in different orthoferrites suggest that a similar model may be valid for all.