Magnetically ordered quasicrystals: enumeration of spin groups and calculation of magnetic selection rules

Lifshitz, Ron; Mandel, Shahar Even-Dar

doi:10.1107/s0108767303026746

Cited by 22 publications

(17 citation statements)

References 47 publications

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“…The set of all rotations satisfying (4) forms the point group of the crystal, and along with the corresponding phase functions completely characterizes its space group [13][14][15][17][18][19].…”

Section: Quasicrystals-terminology and General Frameworkmentioning

confidence: 99%

Soft quasicrystals–Why are they stable?

Lifshitz

Diamant

2007

Philosophical Magazine

104

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In the last two years we have witnessed the exciting experimental discovery of soft matter with nontrivial quasiperiodic long-range order-a new form of matter termed a soft quasicrystal. Two groups have independently discovered such order in soft matter: Zeng et al. [Nature 428 (2004) 157] in a system of dendrimer liquid crystals; and Takano et al. [J. Polym. Sci. Polym. Phys. 43 (2005) 2427] in a system of ABC star-shaped polymers. These newly discovered soft quasicrystals not only provide exciting platforms for the fundamental study of both quasicrystals and of soft matter, but also hold the promise for new applications based on self-assembled nanomaterials with unique physical properties that take advantage of the quasiperiodicity, such as complete and isotropic photonic band-gap materials. Here we provide a concise review of the emerging field of soft quasicrystals, suggesting that the existence of two natural length-scales, along with 3-body interactions, may constitute the underlying source of their stability. BackgroundThe discovery of quasicrystals by Shechtman more than two decades ago We know today that quasicrystals are more common than one had originally expected. Scores of binary and ternary metallic alloys are known to form quasicrystalline phases [22]-mostly with icosahedral or decagonal point-group symmetry-and more are being discovered all the time. Nevertheless, it is only in the last couple of years that quasicrystals have been discovered (independently) in two 1

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Section: Quasicrystals-terminology and General Frameworkmentioning

confidence: 99%

Soft quasicrystals–Why are they stable?

Lifshitz

Diamant

2007

Philosophical Magazine

104

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“…11 Furthermore, the static spin structure factor exhibits magnetic selection rules that impose a shift of reciprocal space indices. 10 The resulting neutron-diffraction pattern 10 can be accounted for by analysis 12 of the quasicrystal spin group, 13 also applicable to frustrated classical models on the octagonal tiling with longrange exchange interactions. 14 While static properties of the Heisenberg antiferromagnet on the octagonal tiling are thus well studied, little is known about the spectral properties of these systems.…”

Section: Introductionmentioning

confidence: 99%

Quantum fluctuations and excitations in antiferromagnetic quasicrystals

Wessel

Milat

2005

Phys. Rev. B

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We study the effects of quantum fluctuations and the excitation spectrum for the antiferromagnetic Heisenberg model on a two-dimensional quasicrystal, by numerically solving linear spin-wave theory on finite approximants of the octagonal tiling. Previous quantum Monte Carlo results for the distribution of local staggered magnetic moments and the static spin structure factor are reproduced well within this approximate scheme. Furthermore, the magnetic excitation spectrum consists of magnonlike low-energy modes, as well as dispersionless high-energy states of multifractal nature. The dynamical spin structure factor, accessible to inelastic neutron scattering, exhibits linear-soft modes at low energies, self-similar structures with bifurcations emerging at intermediate energies, and flat bands in high-energy regions. We find that the distribution of local staggered moments stemming from the inhomogeneity of the quasiperiodic structure leads to a characteristic energy spread in the local dynamical spin susceptibility, implying distinct nuclear magnetic resonance spectra, specific for different local environments.

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“…5c,d of Ref. [5]) and theoretical prediction [9], while the intensity map of the configuration Fig. 2a is almost structureless.…”

Section: (B) They Occur With Relative Frequenciesmentioning

confidence: 73%

“…The Bragg reflexes found in our study select a subset of the wave vectors given in Ref. [9] where n 1 + n 2 + n 3 + n 4 is odd. Peaks with n 1 + n 2 + n 3 + n 4 even are extinct.…”

Section: (B) They Occur With Relative Frequenciesmentioning

confidence: 99%

“…According to the nomenclature of Ref. [9], the following wave vectors can be identified: (1, 0, 0, 0), (1, −1, 1, 0), (3, −2, 1, 1), (3, −1, −1, 2), (1, 1, −1, 0), (1, 0, 1, −1), (0, 2, −1, 0), (0, 0, 1, −2), (−1, 0, 1, −3), (0, 2, −2, 1), (0, 1, −2, 2). Hence, the noncollinearity of the spin structure gives rise to selection rules different from those of collinear models [5,7].…”

Section: (B) They Occur With Relative Frequenciesmentioning

confidence: 99%

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Noncollinear Magnetic Order in Quasicrystals

2004

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Based on Monte-Carlo simulations, the stable magnetization configurations of an antiferromagnet on a quasiperiodic tiling are derived theoretically. The exchange coupling is assumed to decrease exponentially with the distance between magnetic moments. It is demonstrated that the superposition of geometric frustration with the quasiperiodic ordering leads to a threedimensional noncollinear antiferromagnetic spin structure. The structure can be divided into several ordered interpenetrating magnetic supertilings of different energy and characteristic wave vector. The number and the symmetry of subtilings depend on the quasiperiodic ordering of atoms.PACS numbers: 71.23. Ft, 75.50.Ee, 75.10.Hk, 75.70.Ak The last few years have shown a boom in investigations of the spin order in antiferromagnetic films [1,2] motivated by the dramatic changes in the magnetic properties of such systems induced by frustration. In contrast to the rather well studied spin structure of antiferromagnets on periodic lattices, the antiferromagnetic ordering of quasicrystals is subject of ongoing scientific debate. Whereas an experimental finding of long-range antiferromagnetic order in rare-earth icosahedral quasicrystals [3] turned out to be an artefact [4], theoretical models that deal with magnetism on quasicrystals [5] are known to exhibit long-range magnetic order. Recent inelastic neutron scattering experiments on the Zn-Mg-Ho icosahedral quasicrystal [6] revealed a very peculiar diffuse scattering pattern with icosahedral symmetry at temperatures below 6K. Such a pattern, in principle, can originate from a noncollinear spin arrangement first suggested by Lifshitz from pure geometrical considerations [7][8][9]. However, real-space magnetic configurations leading to those long wave vector correlations remain obscure despite recent interesting results for quantum spins [5]. Thus, the knowledge about the spin structure on quasiperiodic tilings is of basic importance for experiments as well as for theoretical predictions of new phenomena, which can be expected due to nontrivial frustration effects [15].The patterns found in our theoretical study provide an explanation for the origin of the antiferromagnetic modulations observed experimentally in Ref. [6]. While the spin order in antiferromagnets is usually characterized by a periodic modulation described by wave vectors on the order of inverse atomic distances, the spin order in antiferromagnetic quasicrystals admits three-dimensional noncollinear structures consisting of several interpenetrating subtilings with longer wave vectors. Here we report on the details of the low-temperature antiferromagnetic ordering and the map of the local frustration for the octagonal tiling.(a) We discuss the antiferromagnetic Hamiltonianwhere S i is a three-or two-dimensional unit vector in the case of classical vector or xy-spins, and S z i is equal to ±1 in the case of Ising spins (so S x i = S y i = 0); i, j denotes the nearest neighbor pairs. For an antiferromagnetic system, the exchange parameter J i...

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Magnetically ordered quasicrystals: enumeration of spin groups and calculation of magnetic selection rules

Cited by 22 publications

References 47 publications

Soft quasicrystals–Why are they stable?

Soft quasicrystals–Why are they stable?

Quantum fluctuations and excitations in antiferromagnetic quasicrystals

Noncollinear Magnetic Order in Quasicrystals

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