scholarly journals A historical introduction to the symmetries of magnetic structures. Part 1. Early quantum theory, neutron powder diffraction and the coloured space groups

2017 ◽  
Vol 32 (2) ◽  
pp. 148-155 ◽  
Author(s):  
Andrew S. Wills

This paper introduces the historical development of the symmetries for describing magnetic structures culminating in the derivation of the black and white and coloured space groups. Beginning from the Langevin model of the Curie law, it aims to show the challenges that magnetic ordering presented and how different symmetry frameworks were developed to meet them. As well as explaining core ideas, later papers will show how the different schemes are connected. With these goals in mind, the maths related is kept to the minimum required for clarity. Those wishing to learn more details are invited to engage with the references. As well as looking back and reviewing the development of magnetic symmetry over time, particular attention is spent on explaining where the concept of time-reversal has been applied. That time-reversal has different meaning in classical and quantum mechanical situations, has created confusions which continue to propagate.

2014 ◽  
Vol 70 (a1) ◽  
pp. C518-C518
Author(s):  
Brian VanLeeuwen ◽  
Mantao Huang ◽  
Daniel Litvin ◽  
Venkatraman Gopalan

This work follows from the recent introduction of the rotation-reversal operation intended to be analogous to the time-reversal operation used to describe the symmetry of magnetic structures. As a second independent antisymmetry operation, this operation "doubles" the antisymmetry of the magnetic space groups, hence the term double antisymmetry. Supposing the consideration of both rotation-reversal and time-reversal symmetry, it was found that there are 17,803 types of symmetry that a crystal could exhibit; the 1,651 magnetic space group types being a subset of these, just as the 230 crystallographic space group types are a subset of the magnetic space group types. In addition to discussing the methods applied to determine these types, describing their properties, and listing their symmetry diagrams (available online), the implications for symmetry constraints in magnetic structure determination will be explored.


2012 ◽  
Vol 45 (6) ◽  
pp. 1236-1247 ◽  
Author(s):  
Samuel V. Gallego ◽  
Emre S. Tasci ◽  
Gemma de la Flor ◽  
J. Manuel Perez-Mato ◽  
Mois I. Aroyo

MAGNEXTis a new computer program available from the Bilbao Crystallographic Server (http://www.cryst.ehu.es) that provides symmetry-forced systematic absences or extinction rules of magnetic nonpolarized neutron diffraction. For any chosen Shubnikov magnetic space group, the program lists all systematic absences, and it can also be used to obtain the list of the magnetic space groups compatible with a particular set of observed systematic absences. Absences corresponding to specific ordering modes can be derived by introducing effective symmetry operations associated with them. Although systematic extinctions in neutron diffraction do not possess the strong symmetry-resolving power of those in nonmagnetic crystallography, they can be important for the determination of some magnetic structures. In addition,MAGNEXTprovides the symmetry-adapted form of the magnetic structure factor for different types of diffraction vectors, which can then be used to predict additional extinctions caused by some prevailing orientation of the atomic magnetic moments. This program, together with a database containing comprehensive general information on the symmetry operations and the Wyckoff positions of the 1651 magnetic space groups, is the starting point of a new section in the Bilbao Crystallographic Server devoted to magnetic symmetry and its applications.


2014 ◽  
Vol 70 (a1) ◽  
pp. C520-C520
Author(s):  
Vaclav Petricek ◽  
Michal Dusek

The concept of Shubnikov (magnetic) symmetry becomes frequently used for description, solution and refinement of magnetic structures. Its growing importance is connected with the ease of application to various classes of magnetic structures having the translation periodicity identical, commensurate or incommensurate with the nuclear one. Recently generalized superspace approach [1] for incommensurately modulated magnetic structures allows for combination of nuclear and magnetic modulations. This unified description helps fully understand e.g. multiferroic phases. The program Jana2006 (http://jana.fzu.cz) combines the concept of Shubnikov (super)space groups with the representational analysis based on the decomposition of the magnetic configuration space into basis modes, which transform according to different physically irreducible representations (irreps) of the space group of the paramagnetic phase [2]. Moreover, Jana2006 can launch the recently developed program ISODISTORT [3] to obtain similar but more general analysis. The generalized symmetry concept facilitates data processing where symmetry related reflections for single crystal data can be merged and the list of generated reflections for powder data can be reduced to independent ones. Another benefit concerns calculation of magnetic structure factors, stability of refinement and logical way to describe twin domains. Unlike in the Fullproff program [6], Jana2006 can combine the nuclear and magnetic scattering internally without necessity to introduce two phases. It can also calculate magnetic structures with modulated parent phase where the modulation appears before the magnetic phase transition. The lecture shows manifold possibilities how to refine modulated magnetic structures from various experiments. Several recently solved magnetic structures will be presented.


Author(s):  
Kees Wapenaar ◽  
Joost van der Neut ◽  
Evert Slob

In wave theory, the homogeneous Green’s function consists of the impulse response to a point source, minus its time-reversal. It can be represented by a closed boundary integral. In many practical situations, the closed boundary integral needs to be approximated by an open boundary integral because the medium of interest is often accessible from one side only. The inherent approximations are acceptable as long as the effects of multiple scattering are negligible. However, in case of strongly inhomogeneous media, the effects of multiple scattering can be severe. We derive double- and single-sided homogeneous Green’s function representations. The single-sided representation applies to situations where the medium can be accessed from one side only. It correctly handles multiple scattering. It employs a focusing function instead of the backward propagating Green’s function in the classical (double-sided) representation. When reflection measurements are available at the accessible boundary of the medium, the focusing function can be retrieved from these measurements. Throughout the paper, we use a unified notation which applies to acoustic, quantum-mechanical, electromagnetic and elastodynamic waves. We foresee many interesting applications of the unified single-sided homogeneous Green’s function representation in holographic imaging and inverse scattering, time-reversed wave field propagation and interferometric Green’s function retrieval.


2020 ◽  
Author(s):  
Tobias Gasser ◽  
Alexander Thoeny ◽  
Andrew Fortes ◽  
Thomas Loerting

Abstract We here report ex situ calorimetry and high-resolution neutron powder diffraction data of a novel ice polymorph produced at 1.8 GPa and recovered to ambient pressure at 80 K. Ice XIX, previously called ice β-XV by us, is shown to be partially hydrogen-ordered and crystallising in a √2 x √2 × 1 supercell with respect to the parent ice VI phase. Our powder data match two nearly degenerate structural models in space-groups \(P\stackrel{-}{4}\) and Pcc2, in which the water molecules are partially antiferroelectrically ordered. Key to the synthesis of deuterated ice XIX is the use of DCl as dopant and the use of a D2O/H2O mixture, where the small H2O fraction nucleates ice XIX. This provides the basis to study the first order-order transition known in ice physics, from ice XIX to its sibling ice XV at ambient pressure. It proceeds via a transition state, ice VI‡, which contains a disordered H-sublattice, whereas both ice XIX and ice XV are fully crystalline.


Author(s):  
Morton Keller ◽  
Phyllis Keller

Harvard’s evolution from a Brahmin to a meritocratic university involved alterations in its governance as well as the makeup of its students and faculty. The cozy, we-happy-few atmosphere of the past began to give way to more professional administration. As a chemist accustomed to overseeing a laboratory and working systematically on problems, Conant rejected Eliot’s and Lowell’s style of running the University “largely ‘under their hats.’ ” His close associate Calvert Smith recalled that he devoted the pre-World War II years to seeking “a modus operandi adaptable to the present size and complexity of the institution, which at the same time still fitted in with the traditional precedents.” But the embedded culture of a venerable, decentralized university made change difficult. Looking back in 1952, Conant concluded that administration at Harvard was not very different from what it had been in Lowell’s day. He saw the central administration “as a sort of holding company responsible for the activities of some 20-odd operating companies.” There were occasional ineffective attempts to draw up a Harvard organizational chart, but as Corporation Secretary David Bailey conceded, “the difficulties of setting down complex relationships in black and white have always prevented their being cast in final form.” The University, he thought, “is suffering from acute decentralization.” For all his commitment to institutional change, Conant relied as did his predecessors on graduates of the College with strong institutional loyalties. When he assumed office in 1933, he brought in Jerome Greene to be both his and the Corporation’s secretary. Until his retirement in 1943, this consummate civil servant was Conant’s closest counselor on alumni and other matters. Greene’s successor was A. Calvert Smith, a classmate of Conant. Smith had strong public relations skills, honed by several decades in the wilds of New York’s investment and banking world, not unlike Greene’s background. Soon after he came into office Conant made John W. Lowes, the son of Higginson Professor of English John Livingston Lowes, his financial vice president. But it was not easy to work this new position into the existing Harvard structure, especially with power-seeking Treasurer William Claflin on the scene. When Lowes left for military service in September 1941, Conant told him his position would not exist when he returned.


2014 ◽  
Vol 70 (a1) ◽  
pp. C516-C516
Author(s):  
Dmitry Khalyavin

Geometrical frustration, related to the specific topology of certain crystal structures, plays a crucial role in forming exotic magnetic ground states. The presence of frustrated spins often leads to the suppression of long-range magnetic ordering and promotes short-range correlations due to fluctuations between nearly or totally degenerate ground states. The well-known structural topologies causing the presence of geometrical frustration are the three-dimensional pyrohlore and two-dimensional Kagome lattices. Compounds whose structural motif embraces these lattices are of great interest as model systems and have been the focus of numerous studies. In some cases, frustration is partially or entirely released by structural distortions through a strong magnetoelastic coupling and long-range magnetic order is established at a finite temperature. In the resulting distorted phases, complex noncollinear or partially disordered spin configurations can be observed. The phase transitions to the ordered state are quite often first order and may involve several irreducible representations of the paramagnetic space group and sometimes, like in the case of ZnCr2O4, even several propagation vectors which do not belong to the same star. The approach to determine magnetic structures in these systems, based on representation theory, should take into account the coupling free-energy invariants relating the magnetic and structural order parameters. Application of magnetic space groups and superspace groups is especially useful and can be efficiently combined with the representation theory. Based on specific examples, I will demonstrate how both approaches can be combined to provide symmetry constraints sufficient to solve complex magnetic structures in some geometrically frustrated systems.


2007 ◽  
Vol 76 (18) ◽  
Author(s):  
Jian Liu ◽  
Xiang-Yuan Cui ◽  
Peter A. Georgiev ◽  
Ian Morrison ◽  
D. Keith Ross ◽  
...  

2016 ◽  
Vol 119 (5) ◽  
pp. 053901 ◽  
Author(s):  
Harikrishnan S. Nair ◽  
Tapan Chatterji ◽  
C. M. N. Kumar ◽  
Thomas Hansen ◽  
Hariharan Nhalil ◽  
...  

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