On the ground state of crystals with dipole-dipole and exchange interactions

Niemeyer, Th.

doi:10.1016/0031-8914(72)90260-1

Cited by 53 publications

(4 citation statements)

References 8 publications

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“…They found that the quantum-mechanical energy of the ferromagnetic state is sufficiently less than the classical energies of other arrays to suggest that ferromagnetism will occur for spins greater than 5/2 in the fcc and 6 in the bcc lattice. Later quantum calculations [33][34][35] confirmed the predictions of the classical theory.…”

Section: Crystalline 3d Systems -The Cubic Casementioning

confidence: 58%

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: Crystalline 3d Systems -The Cubic Casementioning

confidence: 58%

Magnetic Ordering due to Dipolar Interaction in Low Dimensional Materials

Panissod

Drillon

2001

Magnetism: Molecules to Materials IV

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“…In the first approximation the orthorhombic Bravais lattice is considered in which all magnetic ions are equivalent. The ground state energy was estimated taking into account the dipole and exchange interactions and using the method in [34]. The Lorentz sphere was taken with a diameter of ∼260 Å.…”

Section: Parameters Of Magnetic Interactionsmentioning

confidence: 99%

Crystal structure and magnetic properties of potassium erbium double tungstate KEr(WO₄)₂

Borowiec¹,

Dyakonov²,

Woźniak³

et al. 2007

J. Phys.: Condens. Matter

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Results of structural, magnetic and specific heat investigations of the potassium erbium double tungstate, KEr(WO 4 ) 2 , are presented. Potassium erbium doubletungstate KEr(WO 4 ) 2 single crystals have been grown by the top-seeded solution growth method (TSSG) and modified Czochralski techniques. It crystallizes in the monoclinic crystal structure (C2/c space group). The unit cell contains four formula units and is described by parameters a = 10.615(2) Å, b = 10.316(2) Å, c = 7.534(2) Å, β = 130.73(3) • . From the x-ray diffraction measurements the fractional atomic coordinates, displacement parameters and interatomic distances have been determined.The specific heat C(T ) of the KEr(WO 4 ) 2 crystal has been measured over a temperature range of 0.6-300 K. The susceptibility has been studied at T = 0.25-4.0 K. The magnetic phase transition was observed at a temperature of 0.48 K. The magnetization has been measured in the temperature region from 4.2 to 60 K and in magnetic field up to 1.6 T. A strong anisotropy of magnetic properties was found. The temperature and field dependences of susceptibility and magnetization data were used for both elucidation of character of the magnetic ordering and calculation of the exchange and dipole-dipole interaction energies as well as for determination of the possible magnetic structure of KEr(WO 4 ) 2 .

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“…ies [10][11][12][13][14][15] and have been found to correctly describe many substances whose thermodynamic properties are determined mostly by magnetic dipole-dipole interactions [16]. On the other hand, ideal lattices with electric dipole-dipole interactions have not found, until now, any applications to real systems due to the presence of close packing in molecular crystals that hinders free rotation of molecular dipoles [17].…”

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Endohedral fullerites: A new class of ferroelectric materials

Ciosłowski¹,

Nanayakkara²

1992

Phys. Rev. Lett.

103

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Endohedral fullerites, composed of periodic lattices of endohedral complexes with polar molecules trapped inside the Ceo cluster, constitute a new class of ferroelectric materials and the first practical realization of ideal electric dipolar lattices. In these substances, interactions between the partially screened and freely rotating dipole moments of the guest molecules give rise to dipole-ordered low-temperature phases. The respective transition temperatures for the endohedral fullerites with LiF, LiCl, NaF, and NaCl as the guest molecules are estimated to be at 25, 36, 51, and 60 K, 64.60.Cn, 65.4aHq The known ferroelectric materials are traditionally divided into two classes that reflect the mechanisms responsible for the transitions to the low-temperature phases [1]. The first class encompasses many ionic crystals in which the individual ions move in potentials with several closely spaced minima. In these displacive-type ferroelectrics, of which barium titanate BaTiOa is a well-known example, the high-temperature phase is associated with the vibrationally averaged positions of ions, whereas the low-temperature (anti)ferroelectric phase corresponds to ions at the individual minima of the potential energy hypersurface. On the other hand, in the order-disorder-type ferroelectrics, such as potassium dihydrogen phosphate KH2PO4, the appearance of the low-temperature phase is directly linked to an order-disorder transition that often involves infinite networks of hydrogen bonds.In this Letter, we predict the existence of a new class of ferroelectric materials composed of the endohedral complexes [2] in which polar molecules are trapped inside the Ceo cluster. Although macroscopic quantities of these endohedral fullerites [3] have yet to be isolated, there is a plethora of both direct and indirect experimental evidence that confirms their existence. In particular, endohedral complexes with one [4,5] or two [6] noble gas atoms (He, Ne, and Ar) as the guests have been observed in collisional insertion experiments. Complexes with metals such as La, Ni, Na, K, Rb, and Cs [7] have also been detected among the products of laser or arc ablation of graphite rods impregnated with metal salts. Even more notably, in a very recent publication, endohedral complexes (primarily of the C60 cluster) with small polar molecules (including CaCl, CeCl, NaCl, and Nal) have been reported [8].Previous calculations [2(b)] demonstrated the absence of any significant (the activation energy of ca. 20 cal/ mol) barriers to rotation for sufficiently small guest molecules inside the Ceo cage. This observation, together with the fact that the cage screens the dipole moments of the guest molecules only partially [2,9], means that the endohedral fullerites can be regarded as the first practical realization of ideal electric dipolar lattices. The dipolar lattices have been the subject of several theoretical stud-

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On the ground state of crystals with dipole-dipole and exchange interactions

Cited by 53 publications

References 8 publications

Magnetic Ordering due to Dipolar Interaction in Low Dimensional Materials

Magnetic Ordering due to Dipolar Interaction in Low Dimensional Materials

Crystal structure and magnetic properties of potassium erbium double tungstate KEr(WO₄)₂

Endohedral fullerites: A new class of ferroelectric materials

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On the ground state of crystals with dipole-dipole and exchange interactions

Cited by 53 publications

References 8 publications

Magnetic Ordering due to Dipolar Interaction in Low Dimensional Materials

Magnetic Ordering due to Dipolar Interaction in Low Dimensional Materials

Crystal structure and magnetic properties of potassium erbium double tungstate KEr(WO4)2

Endohedral fullerites: A new class of ferroelectric materials

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Crystal structure and magnetic properties of potassium erbium double tungstate KEr(WO₄)₂