Symmetry replication and toroidic effects in the multiferroic pyroxene<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mtext>NaFeSi</mml:mtext></mml:mrow><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mtext>O</mml:mtext><mml:mn>6</mml:mn></mml:msub></mml:mrow></mml:math>

Mettout, B.; Tolédano, Pierre; Fiebig, Manfred

doi:10.1103/physrevb.81.214417

Cited by 25 publications

(26 citation statements)

References 19 publications

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“…In the helical phase, neighboring moments along the chain are thus nearly perpendicular. It is remarkable that the second magnetic transition in natural NaFeSi 2 O 6 is described by the same irreducible representation of the paramagnetic group; the helical transition is thus a repetition of the same scheme [24], but similar cases are known [32].…”

Section: Discussion Of the Magnetic Structure And Of The Multifermentioning

confidence: 94%

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Magnetic structure and multiferroic coupling in pyroxeneNaFeSi2O6

et al. 2015

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By comprehensive neutron diffraction measurements we have studied the magnetic structure of aegirine (NaFeSi 2 O 6 ) in and above its multiferroic phase. Natural aegirine exhibits two magnetic transitions into incommensurate magnetic order with a propagation vector of k inc = (0, ∼ 0.78,0). Between 9 and 6 K, we find a transverse spin-density wave with moments pointing near the c direction. Below 6 K, magnetic order becomes helical and spins rotate in the ac plane. The same irreducible representation is involved in the two successive transitions. In addition, the ferroelectric polarization P appearing along the b direction cannot be described by the most common multiferroic mechanism but follows P ∝ S i × S j . Synthetic NaFeSi 2 O 6 does not exhibit the pure incommensurate helical order but shows coexistence of this order with a commensurate magnetic structure. By applying moderate pressure to natural aegirine, we find that the incommensurate magnetic ordering partially transforms to the commensurate one, underlining the nearly degenerate character of the two types of order in NaFeSi 2 O 6 .

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Section: Discussion Of the Magnetic Structure And Of The Multifermentioning

confidence: 94%

“…In the synthetic sample, a single muon-oscillation frequency indicates commensurate order, while the natural sample exhibits more complex magnetic order [23]. The symmetry breaking in NaFeSi 2 O 6 was studied theoretically by Mettout et al [24] who propose the replication of a single-order parameter as the origin of the two transitions.…”

Section: Introductionmentioning

confidence: 98%

Magnetic structure and multiferroic coupling in pyroxeneNaFeSi2O6

et al. 2015

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“…NaFeSi 2 O 6 A phenomenological model of phase transitions in NFSO was suggested earlier using the order parameters belonging to the wave vector (0, 0.77, 0) [54]. In contrast, we now build a model assuming the instability in the k = (0, 1 4 , 0) point of the Brillouin zone, which is close to the equivalent vector (0, 0.23, 0), and account for the spatial modulation by considering the Lifshitz invariants allowed for the respective order parameters.…”

Section: Pyroxenes Nafesi 2 O 6 and Nafege 2 Omentioning

confidence: 99%

“…It can be shown that the y components of iron spins transform according to Λ 1 , whereas the x and z components according to Λ 2 . In the magnetically ordered phases the spins are confined to the ac crystal plane [52,54]. Thus, the magnetic order is described by IR Λ 2 .…”

Section: C2/c Cmcmmentioning

confidence: 99%

Interpretation of magnetoelectric phase states using the praphase concept and exchange symmetry

Ter-Oganessian¹,

Sakhnenko²

2013

J. Phys.: Condens. Matter

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Abstract. The majority of magnetoelectric crystals show complex temperaturemagnetic field or temperature-pressure phase diagrams with alternating antiferromagnetic incommensurate, magnetoelectric, and commensurate phases. Such phase diagrams occur as a result of successive magnetic instabilities with respect to different order parameters, which usually transform according to different irreducible representations (IR) of the space group of the crystal. Therefore, in order to build a phenomenological theory of phase transitions in such magnetoelectrics one has to employ several order parameters and assume the proximity of various instabilities on the thermodynamic path. In this work we analyze the magnetoelectrics MnWO 4 , CuO, NaFeSi 2 O 6 , NaFeGe 2 O 6 , Cu 3 Nb 2 O 8 , α-CaCr 2 O 4 , and FeTe 2 O 5 Br using the praphase concept and the symmetry of the exchange Hamiltonian. We find that in all the considered cases the appearing magnetic structures are described by IR's entering into a single exchange multiplet, whereas in the cases of MnWO 4 and CuO by a single IR of the space group of the praphase structure. Therefore, one can interpret the complex phase diagrams of magnetoelectrics as induced by a single IR either of the praphase or of the symmetry group of the exchange Hamiltonian. Detailed temperature-magnetic field phase diagrams of MnWO 4 and CuO for certain field directions are obtained and the magnetic structures of the field-induced phases are determined.

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“…Today, the range of static toroidal systems under study includes various compounds 34,35 , boracites 36 , pyroxines 37 and olivines 38 , metals 39 , glasses 40 , ferroelectric nanoscale disks and rods 27 , molecular magnets 41,42 . However, unambiguous observations of long-range toroidal order have proven challenging due to the weak, short-range interactions between toroidal dipoles and the requirement of simultaneously breaking both space and time reversal symmetry to demonstrate its existence 18 .…”

Section: Static Toroidal Multipolesmentioning

confidence: 99%

Electromagnetic toroidal excitations in matter and free space

et al. 2016

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The toroidal dipole is a localized electromagnetic excitation, distinct from the magnetic and electric dipoles. While the electric dipole can be understood as a pair of opposite charges and the magnetic dipole as a current loop, the toroidal dipole corresponds to currents flowing on the surface of a torus. Toroidal dipoles provide physically significant contributions to the basic characteristics of matter including absorption, dispersion, and optical activity. Toroidal excitations also exist in free-space as spatially and temporally localized electromagnetic pulses propagating at the speed of light and interacting with matter. We review recent experimental observations of resonant toroidal dipole excitations in metamaterials and the discovery of anapoles, non-radiating current configurations involving toroidal dipoles. While certain fundamental and practical aspects of toroidal electrodynamics remain open for the moment, we envision that exploitation of toroidal response can have important implications for the fields of photonics, sensing, energy and information. IntroductionThe interactions of electromagnetic radiation with matter underpin some of the most important technologies today -from telecommunications to information processing and data storage; from spectroscopy and imaging to light-assisted manufacturing. Our understanding and description of the electromagnetic properties of matter traditionally involves the concept of electric and magnetic dipoles, as well as their more complex combinations, known as multipoles. Introduced by Maxwell and Lorentz and later refined by Jackson and Landau, this framework, termed the multipole expansion, is central in physics and is being routinely applied in the study of optical, condensed matter, atomic, nuclear phenomena and beyond 1 . Within this framework, electromagnetic media can be represented by a set of point-like multipole sources [2][3][4][5] . The commonly used set of multipoles comprises the electric and magnetic families, which can be represented by oscillating charges and loop currents respectively. Dynamic toroidal multipoles constitute a third independent family of elementary electromagnetic sources, rather than an alternative multipole expansion or higher-order corrections to the conventional electric and magnetic multipoles (see tutorial inset I).Introduced in 1958 by Y. B. Zeldovich, toroidal moments have been considered in systems of toroidal topology (see Fig. 1) and studied in the context of nuclear 6 , atomic 7 , and molecular physics 8 , classical electrodynamics 9,10 , and solid state physics 3 . In the field of electromagnetism, in particular, a number of works have led to the development of a complete theoretical framework for toroidal electrodynamics [11][12][13][14][15] and the prediction of exotic effects, including dynamic non-radiating charge current configurations 10 and non-reciprocal interactions 9 . Following recent experimental observations of toroidal contributions in the response of materials across the electromagnetic spectrum, dyn...

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Symmetry replication and toroidic effects in the multiferroic pyroxeneNaFeSi2O6

Cited by 25 publications

References 19 publications

Magnetic structure and multiferroic coupling in pyroxeneNaFeSi2O6

Magnetic structure and multiferroic coupling in pyroxeneNaFeSi2O6

Interpretation of magnetoelectric phase states using the praphase concept and exchange symmetry

Electromagnetic toroidal excitations in matter and free space

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