Magnetic point groups and space groups

We review the notion of magnetic symmetry of finite structures as well as infinite periodic and quasiperiodic crystals. We describe one of the most direct consequences of having magnetic symmetry in crystals which is the extinction of magnetic Bragg peaks in neutron diffraction patterns. We finish by mentioning the generalization of magnetic groups to spin groups and color groups.Comment: Written for the Encyclopedia of Condensed Matter Physics. Contains 2 color figures - gray scale version available from the author's website: http://www.tau.ac.il/~ronlif

Comment on "Quantum Quasicrystals of Spin-Orbit-Coupled Dipolar Bosons"

In a recent Letter, Gopalakrishnan, Martin, and Demler [Phys. Rev. Lett. 111 (2013) 185304] show that quasi-two-dimensional dipolar Bose gases, subject to a Rashba spin-orbit coupling, exhibit a variety of spatially ordered, or crystalline, ground states, including a pentagonal quasicrystal. Indeed, as the authors say, realizing quasicrystalline condensates would provide new ways to explore the physics of quasicrystals, and in particular to study the quantum dynamics of their unique collective phason modes. Yet, the authors conclude that "there are typically additional phasons in quantum-mechanical quasicrystals, when compared with their classical equivalents." In this Comment I review the notion of phason modes in quasicrystals, and explain why their number does not depend on whether they are classical or quantum

Lattice Color Groups of Quasicrystals

Lattice color groups are introduced and used to study the partitioning of a periodically- or quasiperiodically-ordered set of points into N symmetry-related subsets. Applications range from magnetic structure to superlattice ordering in periodic and quasiperiodic crystals.Comment: 5 pages, 1 color figure. Uses World Scientific style file: sprocl.sty. Final version to appear in the Proceedings of the 6th International Conference on Quasicrystals, Tokyo, Japan, May 26-30, 199

Magnetic quasicrystals: What can we expect to see in their neutron diffraction data?

The theory of magnetic symmetry in quasicrystals is used to characterize the nature of magnetic peaks, expected in elastic neutron diffraction experiments. It is established that there is no symmetry-based argument which forbids the existence of quasiperiodic long-range magnetic order. Suggestions are offered as to where one should look for the simplest kinds of antiferromagnetic quasicrystals.Comment: 4 pages. Submitted to Materials Science and Engineering