Nearest-neighbour Exchange Interactions Research Articles

Microscopic spin-wave theory for yttrium-iron garnet films

Motivated by recent experiments on thin films of the ferromagnetic insulator yttrium-iron garnet (YIG), we have developed an efficient microscopic approach to calculate the spin-wave spectra of these systems. We model the experimentally relevant magnon band of YIG using an effective quantum Heisenberg model on a cubic lattice with ferromagnetic nearest neighbour exchange and long-range dipole-dipole interactions. After a bosonization of the spin degrees of freedom via a Holstein-Primakoff transformation and a truncation at quadratic order in the bosons, we obtain the spin-wave spectra for experimentally relevant parameters without further approximation by numerical diagonalization, using efficient Ewald summation techniques to carry out the dipolar sums. We compare our numerical results with two different analytic approximations and with predictions based on the phenomenological Landau-Lifshitz equation.

Energetic selection of ordered states in a model of the Er2Ti2O7 frustrated pyrochlore XY antiferromagnet

We consider the possibility that the discrete long-range ordered states of Er2Ti2O7 are selected energetically at the mean field level as an alternative scenario that suggests selection via thermal fluctuations. We show that nearest neighbour exchange interactions alone are not sufficient for this purpose, but that anisotropies arising from excited single ion crystal field states in Er2Ti2O7, together with appropriate anisotropic exchange interactions, can produce the required long range order. However, the effect of the single ion anisotropies is rather weak so we expect thermal or quantum fluctuations, in some guise, to be ultimately important in this material. We reproduce recent experimental results for the variation of magnetic Bragg peak intensities as a function of magnetic field.

Ann. Phys. 4/2008: Rigorous solution of a Hubbard model extended by nearest-neighbour Coulomb and exchange interaction on a triangle and tetrahedron

Ann. Phys. 4/2008: Rigorous solution of a Hubbard model extended by nearest-neighbour Coulomb and exchange interaction on a triangle and tetrahedron

Ann. Phys. 4/2008: Rigorous solution of a Hubbard model extended by nearest‐neighbour Coulomb and exchange interaction on a triangle and tetrahedron

Annalen der PhysikVolume 520, Issue 2-3 p. 64-64 Recent and forthcoming publication in Annalen der Physik Ann. Phys. 4/2008: Rigorous solution of a Hubbard model extended by nearest-neighbour Coulomb and exchange interaction on a triangle and tetrahedron First published: 04 February 2008 https://doi.org/10.1002/andp.200852002-302AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat Abstract Volume520, Issue2-3February 2008Pages 64-64 RelatedInformation

Max Planck – a life for thermodynamics

Annalen der PhysikVolume 520, Issue 2-3 p. 64-64 Recent and forthcoming publication in Annalen der Physik Ann. Phys. 4/2008: Rigorous solution of a Hubbard model extended by nearest-neighbour Coulomb and exchange interaction on a triangle and tetrahedron First published: 04 February 2008 https://doi.org/10.1002/andp.200852002-302AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Graphical Abstract Volume520, Issue2-3February 2008Pages 64-64 RelatedInformation

Magnetism and the effect of anisotropy with a one-dimensional monatomic chain of cobaltusing a Monte Carlo simulation

The magnetic properties of a one-dimensional (1D) monatomic chain of Co reported in aprevious experimental work are investigated by a classical Monte Carlo simulation based onthe anisotropic Heisenberg model. In our simulation, the effect of the on-site uniaxial anisotropy,Ku, on each individual Co atom and the nearest neighbour exchange interaction,J, are accounted for. The normalized coercivityHC(T)/HC(TCL) is found to show auniversal behaviour, HC(T)/HC(TCL) = h0(eTB/T−e) inthe temperature interval TCL<T≤TBCal, arising from the thermal activation effect. In the above expression,h0 is aconstant, TBCal is the blocking temperature determined by the calculation, andTCL is the temperature above which the classical Monte Carlo simulation gives a gooddescription of the investigated system. The present simulation has reproducedthe experimental features, including the temperature dependent coercivity,HC(T), and the angular dependence of the remanent magnetization,MR(θ, ϕ), upon the relativeorientation (θ, ϕ) of theapplied field H. In addition, the calculation reveals that the ferromagnetic-likeopen hysteresis loop is a result of a slow dynamical process atT<TBCal. The dependence of thedynamical TBCal on the fieldsweeping rate R, the on-siteanisotropy constant Ku, and the number of atoms in the atomic chain,N, has been investigated in detail.

On the Ising model for the simple cubic lattice

The Ising model was introduced in 1920 to describe a uniaxial system of magnetic moments, localized on a lattice, interacting via nearest-neighbour exchange interaction. It is the generic model for ...

Stability of Skyrmions in discrete arrays of spins with Heisenberg and truncated RKKY-interaction and single-spin anisotropy

In two-dimensional discrete classical spin arrays subject to ferromagnetic nearest-neighbour isotropic Heisenberg exchange interaction and single-spin anisotropy D localised single excitations of Skyrmion-type are studied. Following Abanov and Pokrovsky (AP) [Ar. Abanov, V.L. Pokrovsky, Phys. Rev. 58 (1998) R8889], also RKKY interaction is simulated by including antiferromagnetic next-nearest-neighbour interaction. Their stability is tested numerically by letting their energy relax. For the isotropic case ( D=0), the narrowing of single Skyrmions with larger radius is very slow. Excitations with easy axis anisotropy shrink in size much faster than in the isotropic case, whereas excitations with easy plane anisotropy are stable. Already RKKY interaction truncated to AF next-nearest-neighbour interaction stabilises Skyrmions to distinct radius in agreement with (AP), including also D=0 beyond their treatment.

Arithmetic logic unit of a computer based on spin-polarised single electrons

The design of an arithmetic logic unit (ALU) is presented using ‘single spin logic’ where classical binary bits 0 and 1 are encoded in orthogonal spin polarisations of single electrons hosted in semiconductor quantum dots. The logic signal (spin state) is transmitted from one spin to the next via nearest-neighbour exchange interaction. The ALU circuits are implemented by placing the quantum dots in specific geometric patterns on a wafer so as to realise the desired relationships between the input and output spin states.

Exchange Interactions in Bcc Co: Implications for Temperature Dependence of TMR

Yuasa recently constructed Co/MgO/Co magnetic tunneling junctions (MTJs) with bcc Co(100) electrodes. These MTJs exhibited a magnetoresistance ratio of 410% at room temperature, and 507% at 20 K. The weak temperature dependence in comparison to Fe based electrodes led them to speculate that the weak temperature dependence may be due to exceptionally strong exchange interactions in bcc Co. Here we report on a theoretical investigation of the nearest neighbour exchange interactions in bcc Co

Rigorous solution of a Hubbard model extended by nearest-neighbour Coulomb and exchange interaction on a triangle and tetrahedron

The Hubbard model extended by either nearest-neighbour Coulomb correlation and/or nearest neighbour Heisenberg exchange is solved analytically for a triangle and tetrahedron. All eigenvalues and eigenvectors are given as functions of the model parameters in a closed form. The groundstate crossings and degeneracies are discussed both for the canonical and grand-canonical energy levels. The grand canonical potential and the electron occupation of the related cluster gases were calculated for arbitrary values (attractive and repulsive) of the three interaction constants. In the pure Hubbard model we found various steps in the electron occupation higher than one. It is shown that the various degeneracies of the grand-canonical energy levels are partially lifted by an antiferromagnetic exchange interaction, whereas a moderate ferromagnetic exchange modifies only slightly the results of the pure Hubbard model. A repulsive nn Coulomb correlation lifts these degeneracies completely. The relation of the cluster gas results to extended systems is discussed.

Spin-transfer mechanism of ferromagnetism in polymerized fullerenes:Ab initiocalculations

A mechanism of the high temperature ferromagnetism in polymerized fullerenes is suggested. It is assumed that some of the C$_{60}$ molecules in the crystal become magnetically active due to spin and charge transfer from the paramagnetic impurities (atoms or groups), such as hydrogen, fluorine, hydroxyl group OH, amino group NH$_2$, or methyl group CH$_3$, dispersed in the fullerene matrix. The exchange interaction between the spins localized on the magnetically active fullerenes is evaluated using \textit{ab initio} calculations. The nearest neighbour and next nearest neighbour exchange interaction is found to be in the range $0.1\div 0.3 $ eV, that is, high enough to account for the room temperature ferromagnetism.

One‐dimensional XY antiferromagnetic Heisenberg model with nearest and next nearest neighbour exchange interactions

AbstractWe study the one‐dimensional anisotropic antiferromagnetic Heisenberg model with competing interactions using the self‐consistent harmonic approximation. The dispersion relation, the correlation function and the susceptibility are obtained for several values of the ratio δ = J2/J1 between the nearest (J1) and next nearest neighbour exchange interactions (J2). For δ &lt; 0.25, the pair correlation function decays monotonically and exponentially to zero and the susceptibility has a maximum value at q = π. For J2 &gt; 0.25J1, the exponential decay of the pair correlation is modified by an oscillatory behavior while the maximum of the susceptibility does not necessarily occur at q = π. Furthermore, the phase diagram of a system with weakly coupled chains is considered. (© 2005 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Thermal entanglement properties of small spin clusters

Exchange interactions in spin systems can give rise to quantum entanglement in the ground and thermal states of the systems. In this paper, we consider a spin tetramer, with spins of magnitude 1/2, in which the spins interact via nearest-neighbour, diagonal and four-spin interactions of strength J1, J2 and K respectively. The ground and thermal state entanglement properties of the tetramer are calculated analytically in the various limiting cases. Signatures of quantum phase transition (QPT) in terms of appropriate entanglement measures are obtained. The magnetic properties of a S = 1/2 AFM polyoxovanadate compound, V12, are well explained by spin tetramers with only nearest-neighbour exchange interactions. Treating the magnetic susceptibility chi as an entanglement witness (EW), an estimate of the lower bound of the critical entanglement temperature, T_c, above which the multipartite entanglement disappears in the experimental compound, is determined. A second EW based on energy provides an estimate of the entanglement temperature T_E, below which bipartite entanglement is certainly present in the system, is determined. The cases of the symmetric trimer and the tetrahedron are also considered.

Three-Dimensional Spin Fluctuations inNa0.75CoO2

We report polarized- and unpolarized-neutron scattering measurements of magnetic excitations in single-crystal Na0.75CoO2. The data confirm ferromagnetic correlations within the cobalt layers and reveal antiferromagnetic correlations perpendicular to the layers, consistent with an A-type antiferromagnetic ordering. The magnetic modes propagating perpendicular to the layers are sharp, and reach a maximum energy of approximately 12 meV. From a minimal spin-wave model, containing only nearest-neighbor Heisenberg exchange interactions, we estimate the interlayer and intralayer exchange constants to be 12.2+/-0.5 meV and -6+/-2 meV, respectively. We conclude that the magnetic fluctuations in Na0.75CoO2 are highly three dimensional.

Relaxation phenomena in the Blume–Emery–Griffiths model near the critical and multicritical points

AbstractThe relaxation behaviour of the Blume–Emery–Griffiths (BEG) model Hamiltonian with bilinear and biquadratic nearest‐neighbour ferromagnetic exchange interaction and crystal field interactions is studied by using the molecular field approximation (MFA) and Onsager's theory of irreversible thermodynamics. First the equilibrium behaviour and the phase diagrams of the model in MFA are given briefly in order to understand the relaxation behaviour. Then, Onsager theory is applied to the model and the set of linear differential equations, which is also called the kinetic or rate equations, is obtained. By solving these equations a set of relaxation times is calculated and examined for temperatures near the critical and multicritical points. It is found that one of the relaxation times (τ1) is sharply cusped at the triple and critical points, whereas it approaches infinity near the critical‐end point. On the other hand, the other relaxation time (τ2) displays a jump‐discontinuity behaviour at the triple and critical points but it has a cusp at the critical‐end point. A maximum of τ2 has also been observed above the critical‐end point. Moreover, similar calculations are performed for non‐zero magnetic field (H) to investigate the effect of H on relaxation times. (© 2003 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Ni(II)octadecylphosphonate: an inorganic/organic layered weak-ferromagnet

Ni[CH3(CH2)17PO3]·H2O was prepared and characterized by several techniques and the magnetic properties were measured by using a SQUID magnetometer. Preliminary refinement of the X-ray diffraction powder data by structure-less Le Bail fitting could be obtained and the compound was found to crystallise in the orthorhombic space group Pmn21 with a=5.478(7) Å, b=42.31(4) Å, c=4.725(3) Å. Ni(II)octadecyl phosphonate is lamellar and the structure consists of alternating inorganic and organic layers. The inorganic layers are interspersed by by-layers of the octadecyl substituent and van der Waals contacts are established between them. IR spectroscopy revealed all-trans configuration of the hydrocarbonic chain. A tilt angle of 48.2° between the chain axis and the (ac) plane could be estimated. The temperature dependence of the molar susceptibility plotted as 1/χ vs. T is linear above 100 K and it follows the Curie–Weiss law. The Curie, C, constant suggests the presence of Ni(II) ion in the S=1 spin state and the negative Weiss, θ, constant is indicative of antiferromagnetic nearest neighbour exchange interactions. Zero-field and field-cooled χ vs. T plots were then recorded. The plots show no overlap below 20 K, thus indicating that the compound is in an ordered magnetic state. The critical temperature has been located at the onset of the χ vs. T plot and was found to be TN=21 K. The magnetization vs. field plots, measured at different temperatures, provide the indication that the compound is a weak-ferromagnet below TN.

Spin waves in monolayer Fe films on stepped W surfaces

A theoretical study of the magnetic excitations of an iron monolayer grown on a stepped tungsten surface is presented. The theory includes contributions due to an applied field, exchange interactions and dipole interactions. The effects of nearest and next nearest neighbour exchange interactions are examined. Modes that become localized to the step edges are found for values of the wave vector close to the boundaries of the first Brilliouin zone.

Magnetization processes in quantum spin chains with regularly varying exchange interactions and fields

We consider the spin- 1 2 Ising chain in a transverse field with regularly alternating nearest neighbour exchange interactions and on-site fields. Using the Jordan–Wigner fermionization, Green functions approach and continued fractions we calculate exactly the thermodynamic functions of the model. We discuss the effects of regular alternation on the magnetic properties at zero temperature. We find that the qualitative behaviour of the magnetization and susceptibility (e.g., the number of plateau-like steps) strongly depends on the strength of nonuniformity.

Soliton diffusion on the classical, isotropic Heisenberg chain

: We investigate the diffusive motion of a solitary wave on a classical, isotropic, ferromagnetic Heisenberg spin chain with nearest-neighbour exchange interaction. The spins are coupled magnetically to Gaussian white noise and are subject to Gilbert damping. The noise induces a collective, stochastic time evolution of the solitary wave. Within a continuum version of the model we employ implicit collective variables to describe this stochastic behaviour. Thermally excited magnons are disregarded. We derive stochastic equations of motion for the collective variables and solve them numerically, in particular to obtain their variances as functions of time. These results are compared to data from spin dynamics simulations of a discrete chain. For some of the collective variables we find good agreement with respect to the long time behaviour, whereas for other variables the agreement is only qualitative; reasons for this are given. For shorter times we derive analytical expressions for the variances of the collective variables, which also agree well with spin dynamics.