Magnetic Energy Constants of Dipolar Lattices

Sauer, J. A.

doi:10.1103/physrev.57.142

Cited by 87 publications

(21 citation statements)

References 3 publications

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“…Therefore, even if the ferromagnetic state may be more stable than the paramagnetic one, at least in the absence of demagnetizing field, it does not mean that another type of spin ordering is not more stable. Indeed, the magnetization is not the only factor in determining the local internal field as shown first by Sauer [22] who computed the energies of certain intuitively selected dipole arrays and found that ordered arrays of zero net magnetization (antiferromagnets) may have widely different energies, some of them lower than that due to the Lorentz field. The question then arose of identifying the actual magnetic order in the ground state of a pure dipole system for a given network (periodic or random) of moments (single-or multi-valued).…”

Section: The Mean-field Approximationmentioning

confidence: 99%

Magnetic Ordering due to Dipolar Interaction in Low Dimensional Materials

Panissod

Drillon

2001

Magnetism: Molecules to Materials IV

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In the quest towards the development of new materials, in which the dimensions of the building units do not exceed a few atoms in at least one direction of the spaceorganic magnets built of spin chains or lamellae, for instance, or magnetic dots, wires and multilayers -the scientists are currently facing the influence of through-space interactions of dipolar origin. Basically, the concept of dipolar interaction is very familiar in solid state physics, and its manifestations at the macroscopic scale are well described in many textbooks [1], and actually used for magnetic applications. However, at the atomic scale, this interaction is mostly negligible and, when it occurs, the magnetic ordering is controlled by the quantum exchange mechanism which usually prevails in 3D networks.In this chapter, we demonstrate that the dipole-dipole interaction may have a foremost importance when considering low dimensional magnetic materials, made of strongly correlated objects of dimensionality zero (0D), one (1D) or two (2D) interacting through a weak interaction of dipolar origin. The aim is not to provide an exhaustive review on the dipolar interaction effects in magnetic materials but rather an outlook, both theoretical and experimental, on the magnetic ordering of 0D to 2D units embedded in higher dimensionality systems.From a fundamental viewpoint, magnetic ordering due to pure dipole-dipole interaction is a clean phase transition problem since the related Hamiltonian does not involve any adjustable parameter: unlike the exchange-coupled systems, one cannot change the form and the magnitude of the interaction in order to improve the agreement between theory and experiment. Therefore, experimental observations provide a direct answer for testing the models used to predict the magnetic structure and the ordering temperature, if observed.From the applied physics viewpoint, the pure dipole-dipole interaction is essentially an academic problem as long as only ionic/atomic moments are involved. Indeed the expected dipolar ordering temperature is of the order of µM s /k B (M s is the saturation magnetization and µ the individual moment) that is at most a few Kelvin for rare earth compounds. Nevertheless, there is nowadays a large renaissance of interest for pure dipole systems that involve not individual atomic moments but magnetic assemblies comprising a large number of strongly exchange coupled atomic moments. Indeed the magnetic ordering temperature for such systems can be much higher than in classical dipole systems because the magnetic moment µ of the objects Magnetism: Molecules to Materials IV. Edited by Joel S. Miller and Marc Drillon

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Section: The Mean-field Approximationmentioning

confidence: 99%

Magnetic Ordering due to Dipolar Interaction in Low Dimensional Materials

Panissod

Drillon

2001

Magnetism: Molecules to Materials IV

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“…The system we consider has the practical advantages of the high energy scale for spin-dependent phenomena (set by dipolar interactions) and the new physics associated with the longranged nature of the dipole interactions. Experimental realization of the system will give insight into several open questions in condensed matter physics including competition between ferro and antiferroelectric orders in crystals [19,20] and systems with frustrated spin interactions [21].…”

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confidence: 99%

Quantum Magnetism with Multicomponent Dipolar Molecules in an Optical Lattice

et al. 2006

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We consider bosonic dipolar molecules in an optical lattice prepared in a mixture of different rotational states. The 1/r 3 interaction between molecules for this system is produced by exchanging a quantum of angular momentum between two molecules. We show that the Mott states of such systems have a large variety of quantum phases characterized by dipolar orderings including a state with ordering wave vector that can be changed by tilting the lattice. As the Mott insulating phase is melted, we also describe several exotic superfluid phases that will occur.

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“…In Paper I of this series, 47 we compared the dipolar and quadrupolar energy expressions against analytic expressions for ordered dipolar and quadrupolar arrays. 39,[60][61][62] In this work, we used the multipolar Ewald sum as a reference method for comparing energies, forces, and torques for molecular models that mimic disordered and ordered condensed-phase systems. The parameters used in the test cases are given in Table I.…”

Section: Methodsmentioning

confidence: 99%

Real space electrostatics for multipoles. II. Comparisons with the Ewald sum

Lamichhane

Newman

Gezelter

2014

The Journal of Chemical Physics

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We report on tests of the shifted potential (SP), gradient shifted force (GSF), and Taylor shifted force (TSF) real-space methods for multipole interactions developed in Paper I of this series, using the multipolar Ewald sum as a reference method. The tests were carried out in a variety of condensed-phase environments designed to test up to quadrupole-quadrupole interactions. Comparisons of the energy differences between configurations, molecular forces, and torques were used to analyze how well the real-space models perform relative to the more computationally expensive Ewald treatment. We have also investigated the energy conservation, structural, and dynamical properties of the new methods in molecular dynamics simulations. The SP method shows excellent agreement with configurational energy differences, forces, and torques, and would be suitable for use in Monte Carlo calculations. Of the two new shifted-force methods, the GSF approach shows the best agreement with Ewald-derived energies, forces, and torques and also exhibits energy conservation properties that make it an excellent choice for efficient computation of electrostatic interactions in molecular dynamics simulations. Both SP and GSF are able to reproduce structural and dynamical properties in the liquid models with excellent fidelity.

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Magnetic Energy Constants of Dipolar Lattices

Cited by 87 publications

References 3 publications

Magnetic Ordering due to Dipolar Interaction in Low Dimensional Materials

Magnetic Ordering due to Dipolar Interaction in Low Dimensional Materials

Quantum Magnetism with Multicomponent Dipolar Molecules in an Optical Lattice

Real space electrostatics for multipoles. II. Comparisons with the Ewald sum

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