Anomalous thermal expansion and chiral phonons in BiB3O6

Abstract

The origins of anomalous thermal expansion in the chiral monoclinic solid α-BiB3O6 have been studied through ab initio calculations. Positive and negative axial thermal expansion are shown to be driven by librations of borate units, elastic anisotropy, and most notably by chiral acoustic phonons involving elliptical revolutions of bismuth atoms. The chirality of the lattice gives rise to these modes by allowing the transverse acoustic branches to have opposite circular polarizations, only one of which couples strongly to the lattice strains. These results further understanding of relationships between crystallographic symmetry and physical properties.The monoclinic α phase of bismuth borate (BiB 3 O 6 ), in addition to having promising applications in nonlinear optics [1,2] and quantum computing [3,4], possesses the unusual physical properties of uniaxial negative thermal expansion (NTE) [5,6] and negative linear compressibility (NLC) [7,8] (Fig. 1). The chiral C2 space group adopted by α-BiB 3 O 6 [6] has unusually low symmetry for an NTE material [9, 10], or indeed more generally for an inorganic solid. The chirality of α-BiB 3 O 6 permits it to have chiral phonons, i.e., phonons with a circular polarization and pseudoangular momentum [11][12][13]. Phonon chirality has been shown to affect the anharmonic properties of phonons through the phonon Hall effect [11], and through modification of symmetry constraints for scattering [14], but these previous studies were limited to 1D and 2D materials. The effects of phonon chirality in a 3D crystal are studied here through their relationship to the related anharmonic property of thermal expansion [15].The thermal expansion of α-BiB 3 O 6 is highly anisotropic, with large NTE along a and large positive thermal expansion along b [5,6]. Such behaviour is characteristic of flexible framework materials, i.e., materials which have a mixture of compliant and stiff directions. Indeed, α-BiB 3 O 6 is also very elastically anisotropic: in the ac plane the ratio of Young's moduli between the stiffest and most compliant direction (Y max /Y min ) is 25 (Fig. 1, top); in the ab plane Y max /Y min = 15 (Fig. 1, bottom) [5]. By these standards, α-BiB 3 O 6 is an extraordinarily flexible inorganic material; it can be compared to the colossal NTE material Ag 3 [Co(CN) 6 ], for which Y max /Y min = 6.0 [16,17], and to ZnAu 2 (CN) 4 , which exhibits extreme NLC and has Y max /Y min = 3.8 [18].Axial NTE has been studied extensively in the tetragonal, orthorhombic, and hexagonal crystal families due to the appearance of anomalously large-magnitude thermal expansion [17], connections with ferroelectricity [19,20], and the use of chemical control to achieve zero thermal expansion [21]. However, NTE is extremely rare in monoclinic and triclinic crystals [9,10]. Outside of α-BiB 3 O 6 , c a a b c FIG. 1. At left, the structure of α-BiB3O6 is shown in the ac plane (top) and the ab plane (bottom), with bismuth atoms coloured in magenta and borate units coloured in green [6]. At right, the indica...

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“…It has been shown that chiral phonons can couple with circularly polarized light and valley electrons and result in chiral selective optical transitions [10][11][12][13]. And it was proposed that chiral phonons can make important contributions to the thermal conductivity [14], phononic Hall effect [15,16], orbital magnetization [17][18][19], and anomalous thermal expansion [20]. Most recently, the concept of chiral phonons has been extended to three-dimensional (3D) systems, enabling propagating chiral phonons [21].…”