Anharmonic lattice interactions in improper ferroelectrics for multiferroic design

Abstract

The design and discovery of new multiferroics, or materials that display both ferroelectricity and long-range magnetic order, is of fundamental importance for new electronic technologies based on low-power consumption. Far too often, however, the mechanisms causing these properties to arise are incompatible or occur at ordering temperatures below room temperature. One design strategy which has gained considerable interest is to begin with a magnetic material, and find novel ways to induce a spontaneous electric polarization within the structure. To this end, anharmonic interactions coupling multiple lattice modes have been used to lift inversion symmetry in magnetic dielectrics. Here we provide an overview of the microscopic mechanisms by which various types of cooperative atomic displacements result in ferroelectricity through anharmonic multi-mode coupling, as well as the types of materials most conducive to these lattice instabilities. The review includes a description of the origins of the displacive modes, a classification of possible non-polar lattice modes, as well as how their coupling can produce spontaneous polarizations. We then survey the recent improper ferroelectric literature, and describe how the materials discussed fall within a proposed classification scheme, offering new directions for the theoretical design of magnetic ferroelectrics. Finally, we offer prospects for the future discovery of new magnetic improper ferroelectrics, as well as detail remaining challenges and open questions facing this exciting new field.

First-principles reinvestigation of bulk WO3

“…Numerous first-principles studies were performed on WO 3 79 in order to characterize its electronic structure (bulk, thin films, 80 and cluster phases [35][36][37][38][39][40][41]), the role of oxygen vacancies 81 [42][43][44][45], and cation doping [46][47][48][49][50][51][52][53]. In this paper we do not 82 only focus on the electronic structure but also extensively 83 study the structural stabilities and metastabilities of the 84 various phases.…”

“…6). This additional mode appears 508 by anharmonic coupling between the R + 4 and M + 3 modes such 509 that the symmetry of the P nma structure allows the X + 5 mode 510 to develop even though the X + 5 mode is not unstable by itself 511 [79]. Similarly, we observe the apparition of several additional 512 modes in the P bcn, P 2 1 /n, P 2 1 /c, and P1 phases, which we 513 discuss in the next section.…”

Designing new ferroelectrics with a general strategy

“…But for the improper FEs, the FE mode is no longer the primary order parameter, i.e., the polarization is induced by one or two rotational modes. [13][14][15][16][17][18][19][20][21][22][23][24][25] To verify whether the ½111 -superlattice LaCoO 3 /LaAlO 3 is an improper FE or not, the stability of the FE mode will be examined. We adopt the ISOTROPY software 33 to obtain the symmetry-adapted phonon modes in the low-symmetry FE structure.…”

“…13,14 The free energy expansion in this system contains the coupling term (PQ 3 ) between the Q and P, indicating that the non-polar distortion Q must be reversed. 15 The hybrid improper ferroelectricity (HIF) was recently discovered in the artificial superlattice PbTiO 3 /SrTiO 3 , 16 where the ferroelectricity is induced by a trilinear coupling (PQ 1 Q 2 ) between the FE mode (P) and two oxygen octahedral rotational modes (Q 1 and Q 2 , respectively). The HIF was also found in the double-layered Ruddlesden-Popper (RP) perovskite A 3 B 2 O 7 (A=Ca, Sr; B=Mn,Ti), [17][18][19] the 1:1 A-cation ordering perovskite-type superlattice, [20][21][22][23] A-cation ordering RP NaRTiO 4 (R = Y, La, Nd, Sm-Ho), 24 the 2:2 B-cation ordered superlattice, 25 and metal-organic perovskite material.…”

To superspace and beyond

“…This is vital not only for correctly constructing the Landau-style free energy expansion as mentioned above, but also for identifying and predicting coupling mechanisms within the solid state that can give rise to unexpected physical properties. The recent resurgence of interest in improper ferroelectrics, where the polarization forms only a secondary order parameter of two antiferrodistortive primary order parameters, is a good example of this, and undoubtedly this has been driven to a great part by the ease with which such couplings can now be ascertained [see Benedek et al (2015) and Young et al (2015) for some recent review articles].…”