Broken symmetries, non-reciprocity, and multiferroicity

Abstract

The interplay of space and time symmetries, ferroic properties, chirality and notions of reciprocity determines many of the technologically important properties of materials such as optical diode effect, e.g., in polar ferromagnet FeZnMo 3 O 8 . We illustrate these concepts, including the non-reciprocal directional dichroism, through a number of practical examples. In particular, the conditions for non-reciprocity of ferro-rotational order are discussed and the possible use of linear optical gyration is suggested as a way to detect ferro-rotational domains. In addition, we provide the means to achieve high-temperature optical diode effect and elucidate multiferroic behaviors as a result of helical vs. cycloidal spins. Finally, we identify different entities behaving similarly under all symmetry operations, which are useful to understand non-reciprocity and multiferroicity in various materials intuitively.npj Quantum Materials (2018) 3:19 ; doi:10.1038/s41535-018-0092-5 When the motion of an object in one direction is different from that in the opposite direction, it is called a non-reciprocal effect. 1The object can be an electron, a phonon (lattice wave), a magnon (spin wave), or light in crystalline solids, and the best known example is that of non-reciprocal charge transport (i.e., diode) effects in p-n junctions, where a built-in electric field (E) breaks the directional symmetry. The polarization (P) of ferroelectrics can also act like the built-in electric field, so bulk ferroelectric diode (and photovoltaic) effects can be realized.2 Certainly, both E and P are polar vectors, and behave identically under various symmetry considerations. In addition to p-n junctions, numerous technological devices such as optical isolators, spin current diodes or metamaterials utilize non-reciprocal effects. In this perspective, we will discuss how non-reciprocal effects can arise from broken symmetries in various crystalline materials, especially multiferroics.Multiferroics are materials where ferroelectric and magnetic orders coexist, and space inversion and time reversal symmetries are simultaneously broken.3 Thus, multiferroics are often good candidates for non-reciprocal effects. Magnetic order naturally breaks time reversal symmetry, and a magnetic lattice, combined with a crystallographic lattice, can break space inversion symmetry, leading to multiferroicity, called magnetism-driven ferroelectricity. In this perspective, two types of magnetism-driven ferroelectricity will also be considered in terms of various symmetries.Symmetry governs physics, in particular a broken symmetry leads to a phase transition. (ref. 4 and references therein). There are five important symmetries relevant to crystalline materials, namely translational, rotational, mirror reflection, space inversion and time reversal. Note that these symmetries are not completely independent; for example, space inversion operation is equivalent to a 180°rotation about the vertical axis plus a mirror reflection about the horizontal mirror plane. Full th...

SOS: symmetry-operational similarity

“…1(a) depicts structural ferro-rotation with P and M (or in E and H), and structural chirality with broken space inversion and ferro-rotation without broken space inversion are discussed in detail in ref. [15].…”

“…Certainly, both E and P are polar vectors, and behave identical under various symmetry operationssimilar with the identical behavior of magnetic field (H) and magnetization (M). In addition to p-n junctions, numerous technological devices such as optical isolators, spin current diodes or metamaterials do utilize nonreciprocal effects.Multiferroics, where ferroelectric and magnetic orders coexist, has attracted an enormous attention in recent years because of the cross-coupling effects between magnetism and ferroelectricity, and the related possibility of controlling magnetism with an electric field (and vice versa) [13][14][15]. Magnetic order naturally breaks time reversal symmetry, and a magnetic lattice, combined with a crystallographic lattice, can have broken space inversion symmetry, leading to multiferroicity, called magnetism-driven ferroelectricity.…”

“…Multiferroics, where ferroelectric and magnetic orders coexist, has attracted an enormous attention in recent years because of the cross-coupling effects between magnetism and ferroelectricity, and the related possibility of controlling magnetism with an electric field (and vice versa) [13][14][15]. Magnetic order naturally breaks time reversal symmetry, and a magnetic lattice, combined with a crystallographic lattice, can have broken space inversion symmetry, leading to multiferroicity, called magnetism-driven ferroelectricity.…”

Spin-wave directional anisotropies in antiferromagnetic Ba3NbFe3Si2O14

“…[10] An example of anisotropic excitations in bulk materials are spin waves in low crystallographic symmetry crystals [11][12][13][14] where magnons propagating in differing directions have dissimilar velocities. Such excitations have been defined as non reciprocal [15,16] given that the motion in one direction differs from that in the opposite [17] in the presence of broken time reversal symmetry. [18] Other directional anisotropies have been reported in optical measurements where the response depends on the direction of the incident probing beam [19] resulting in contrasting absorption for counter propagating beams.…”

Magnetic monopoles and toroidal moments inLuFeO3and related compounds

“…These states support a rich landscape of topological defects and elementary excitations that may enable novel devices [2,3]. Particular attention was concentrated on magnetic toroidal order [4,5] and magnetic monopoles [6][7][8] that give rise to peculiar magnetoelectricity, non-reciprocal effects [9] and also lead to peculiar excitations and dynamics in spin ice [10,11]. One of the reasons for such a variety of properties in these systems is the coupling between magnetic and electric degrees of freedom, i.e.…”