Tilting and Distortion in the Multiferroic Aurivillius Phase Bi6Ti3Fe1.5Mn0.5O18

Aurivillius structured Bi6Ti3Fe1.5Mn0.5O18 (B6TFMO) has emerged as a rare room temperature multiferroic, exhibiting reversible magnetoelectric switching of ferroelectric domains under cycled magnetic fields. This layered oxide presents exceptional avenues for advancing data storage technologies owing to its distinctive ferroelectric and ferrimagnetic characteristics. Despite its immense potential, a comprehensive understanding of the underlying mechanisms driving multiferroic behavior remains elusive. Herein, we employ atomic resolution electron microscopy to elucidate the interplay of octahedral tilting and atomic-level structural distortions within B6TFMO, associating these phenomena with functional properties. Fundamental electronic features at varying bonding environments within this complex system are scrutinized using electron energy loss spectroscopy (EELS), revealing that the electronic nature of the Ti4+ cations within perovskite BO6 octahedra is influenced by position within the Aurivillius structure. Layer-by-layer EELS analysis shows an ascending crystal field splitting (Δ) trend from outer to center perovskite layers, with an average increase in Δ of 0.13 ± 0.06 eV. Density functional theory calculations, supported by atomic resolution polarization vector mapping of B-site cations, underscore the correlation between the evolving nature of Ti4+ cations, the extent of tetragonal distortion and ferroelectric behavior. Integrated differential phase contrast imaging unveils the position of light oxygen atoms in B6TFMO for the first time, exposing an escalating degree of octahedral tilting toward the center layers, which competes with the magnitude of BO6 tetragonal distortion. The observed octahedral tilting, influenced by B-site cation arrangement, is deemed crucial for juxtaposing magnetic cations and establishing long-range ferrimagnetic order in multiferroic B6TFMO.

Possibilities for ferrimagnetic order may arise from cation disorder (e.g., configurations analyzed by density functional theory in this study and referenced work 4 ), potential uncompensated antiferromagnetically coupled spins, or variations in the valence states of magnetic cations.These scenarios would be reflected in unsaturated magnetization-magnetic field (MH) hysteresis loops, distinct from the saturated MH loops observed in ferromagnets.
The primary challenge in experimentally distinguishing between ferromagnetism and ferrimagnetism lies in the relatively low magnetic moment of the B6TFMO thin films compared to the diamagnetic background originating from the substrate.This complicates the accurate estimation of small differences in saturation and unsaturation.Nevertheless, the maximum observed moment from experiments at a field strength of 5 T and a temperature of 5K is 3.01 µB/formula units (f.u.) (19 emu/cc) 1 , which is close to the range of theoretical moments calculated for ferromagnetic alignment, spanning from 3.16 to 8.34 µB/f.u.(depending on the valences and high-spin or low-spin configuration of Mn 3+ /Mn 4+ and Fe 3+ ).Consequently, in previous experimental analyses, B6TFMO was designated as ferromagnetic based on these findings.

Magnetic Cation Partitioning within the B6TFMO Aurivillius Phases
Below the ferroelectric transition temperature, a strong bond is formed between the bismuth cation in the [Bi2O2] 2+ interface layer and an apex oxygen of the adjacent perovskite layer within the Aurivillius structures.As well as having an inductive effect on the B-O bond distances in the layer direction (c-axis) 5 and prompting ferroelectricity via a polar displacement of ions perpendicular to the layer direction, the shorter Bi-O bond (e.g.2.42 Å compared with 2.65 Å in Bi4Ti3O12) shears the perovskite layer, resulting in tilting and rotation of the BO6 octahedra 6,7 .The presence of the [Bi2O2] 2+ interface layers interleaved within the structure imparts an elastic strain energy gradient through the Aurivillius layers, due to layer mismatch between the differing lateral dimensions of the [Bi2O2] 2+ layers (a = 3.80 Å) compared to the perovskite lattice layers (a = 3.89 Å) 8 .In addition, the layer of oxygen anions in the [Bi2O2] 2+ interface layer provides electrostatic energy variations within the Aurivillius structure.For the case of B6TFMO, substitution of Ti/Fe with magnetic Mn and Fe cations (necessary to achieve the m = 5 multiferroic phase), results in an even more complex bonding environment for the transition metal cations at the available perovskite-type B-sites of the Aurivillius phase structure (see Figure 1 of the Main Text).Atomic resolution energy dispersive X-ray analysis studies have revealed that cation partitioning occurs in B6TFMO due to elastic strain and electrostatic energy contributions, which vary as a function of distance from the [Bi2O2] 2+ fluorite-type layers 3,[8][9][10][11][12] .This partitioning is revealed as a preference for Mn to locate predominantly in the center perovskite layers within the five-layered perovskite block enabling an increase in the probability of nearest-neighbor magnetic interactions in the center layer by up to 90 % compared to a scenario where the magnetic cations are randomly distributed over the five available B-sites in a perovskite block 3 .Electron microscopy 3 and density functional theory (DFT) 4 studies demonstrate that the inclusion of manganese within the B6TFMO structure is crucial to promoting long-range ferrimagnetic order.Note that detailed micro-and nano-structural analysis, combined with rigorous statistics (confidence level ≥99.5%), conclude that ferrimagnetic/ferromagnetic secondary phase impurities do not influence the ferrimagnetic/ferromagnetic behavior 13 .

Analysis of STEM-EELS spectra
Titanium is the most abundant B-site cation in B6TFMO, therefore the Ti L2,3-edge is the most intense peak in the EELS spectra.There is a ~18 ± 4 % decrease in the amount of Ti at the center layers compared to the outer layers.The decrease in the Ti L2,3-edge intensity from outer to center perovskite layer in the EELS data (SI Figure S1 (a)) is consistent with the decrease in Ti B-site occupancy observed in previous analysis by the HAADF-STEM EDX technique 3 , confirming the preference for Ti to partition towards the outer layers in B6TFMO.Both Fe L2,3-edge and Mn L2,3edge demonstrate a preference for the Fe and Mn cations to partition towards the intermediate and center layers, as shown in SI Figure S1 (g) and (e) by the increase in intensity from the outer layers towards the center layers of these edges.Although the signal-to-noise ratio was too low to reliably quantify the intensity changes, this observation confirms previous EDX observations of a significant increase in the B-site proportion of Mn 3 in the center layers, confirming a distinct preference for partitioning of magnetic Mn towards the center perovskite layers.
The O K-edge within B6TFMO provides electronic information on the bonding between O and its neighboring cations.Typically, in the O K-edge fine structure for metal oxides, much information can be gained about the local geometry of the complex 14,15 .The most intense component of the O K-edge in the data collected in SI Figure S1 (c-d), which is not zero-loss aligned, is at an energy of ~522 eV and gives information on the unoccupied O 2p states, which hybridize with the B-site metal cation 3d states.First, we observe an energy splitting of ~2 eV in the O K-edge due to the weak hybridization between the transition metal cation 3d t2g orbitals (lower peak) with the O 2p orbitals, and the more strongly hybridized 3d eg orbitals (higher peak) with the O 2p orbitals.This splitting could also have a contribution from the interactions between the O 2p and Bi 5d/p states 16,17 .The second broad feature at ~532 eV in our spectra of the O K-edge is attributed to the O 2p hybridization with the 4s and 4p states in the metal cations along with covalent bonding in Bi.Given that B6TFMO is a complex multi-cation oxide, it should be noted that the individual contributions of Ti, Mn and Fe to the O K-edge structure would be difficult to deconvolute.In our analysis, we did not differentiate any significant changes to the O K-edge structure in the EELS spectra as measured from the outer, intermediate or center perovskite layers and taking into account that B6TFMO is a complex multi-cation oxide, it would be difficult to deconvolute the individual contributions of Ti, Mn and Fe to the O K-edge structure.While peak splitting can be observed within the O K-edge as shown in Figure S1 (c, d), the splitting between the t2g and eg peaks is not as well defined compared to the splitting within the Ti L2,3-edge demonstrated in SI Figure 1 (a-b).Accordingly, the Ti L2,3-edge was selected for further investigation of the electronic structure and subtle chemical bonding changes through the B6TFMO structure, that is from the interface of the [Bi2O2] 2+ -perovskite interface to the center of the perovskite block.
In previous works 1,3,4 , we have demonstrated that the presence of Mn is key to the ferrimagnetic/ferromagnetic behavior observed within B6TFMO.EELS analysis in this work (SI Figure S1 (e-f)) confirms the previous EDX observations of the partitioning of Mn cations towards the center perovskite layers.Previous Density Functional Theory (DFT) calculations 4 indicate that magnetization values in B6TFMO are highly dependent on the increased nearest neighbor magnetic interactions resulting from this Mn partitioning.Considering the Goodenough−Kanamari rules, [18][19][20] ferromagnetic coupling could be created through Fe 3+ −O−Mn 4+ (d 5 /d 3 configurations) super-exchange or Mn 3+ −O−Mn 4+ (d 4 /d 3 configurations) double-exchange interactions.Ideally, EELS analysis would enable determination of the oxidation state of Mn within B6TFMO in order to determine the precise mechanism for ferromagnetic exchange 21,22 .However, due to the comparatively low concentration of Mn (~1.7%) within B6TFMO's total composition, the Mn L2,3-edge had a relatively low intensity compared to Ti, Fe and O signals within our data sets.The low signal to noise ratio within the Mn L2,3-edge meant that the structural features characteristic of the different Mn oxidation states could not be observed, and it was not possible to determine the exact oxidation state of the Mn cation.The Fe cation oxidation state was confirmed by the presence of a shoulder at ~699 eV just after the edge onset in the L3 signal.This initial feature is ~1 eV before the maximum peak, at ~700 eV, and the shape seen in SI Figure S1 (g-h) is characteristic of Fe 3+ and is consistent with the literature [23][24][25][26] .S1. Data from which the average change in crystal field splitting (Δ) for the Ti 4+ L3 edge is calculated.Eleven EELS data sets were used to calculate the average Δ value.Each data set had two eg values for the outer perovskite layer and one eg value for the center layer, therefore for each data set, two Δ values were obtained (twenty-two data sets were obtained in total).The t2g peak value remains the same for the EELS spectra moving from the outer to the center perovskite layers while the eg peak value changes.The change in Δ moving from the outer to the center perovskite layers for the Ti 4+ L3 peak was calculated by subtracting the outer perovskite layer Ti 4+ L3 eg peak value from the center perovskite Ti 4+ L3 eg layer value.Note that Configuration: b is slightly (0.18 meV/atom) lower in energy relative to Configuration: a.In fact, there are many possible atomic and magnetic configurations for Mn and Fe atoms to be placed in real samples.While we present two possible configurations within this study, we propose that the antipolar Ti displacement along c-direction within each perovskite block will be observed irrespective of the atomic and magnetic configurations of Mn and Fe atoms.

Octahedral tilting in Aurivillius phase systems
It has been proposed 28,29 that symmetry lowering in the Aurivillius phases is caused by tilting of the oxygen octahedra around the a-axis (tilt mode designated by the irreducible representation (irrep) notation  3 + ), rotations of the oxygen octahedra around the c-axis (irreps  2 + ,  1 − ), (shown in SI Figure S6), and the polar cation motions along the a-axis (irrep  5 − ), which when coupled together contribute to a material's ferroelectric ground state.Goldschmidt's tolerance factor 30 , , where   ,   and   are the ionic radii of the oxygen, A-site and B-site ions respectively, has been used to deduce that t < 1 would promote a perovskite system with an instability towards an octahedral tilting distortion 5,31,32 .This tolerance factor can also be applied to the Aurivillius phases, where octahedral tilting is commonly observed 5,7,10,28,33 due to divergences between the A-O and B-O interatomic distances.
Research on the m = 3 phase, Bi4Ti3O12 (BTO), has shown the importance of analyzing the contributions of the light oxygen atoms to denoting the symmetry and space group of the material.
In the 1990s it was proposed that above the Curie temperature (Tc) ~675 o C, BTO adopts the aristotype I4/mmm structure, while at RT a subgroup of Fmmm: B1a1 is present [34][35][36] .However, theoretical calculations found no triggering mechanism to support a single transition from the I4/mmm to B1a1 space group 29 , leading researchers to revisit the BTO system in 2019 7 , where an intermediate paraelectric phase above Tc was discovered corresponding to the irrep  2 + mode, P4/mbm (SI Figure S6).The BTO case highlights the significance of the oxygen octahedral tilting on the resultant symmetry and polar properties of the Aurivillius structure and demonstrates that visualization of the light atoms is critical for correct structural characterization of a material.It has also been found for the higher phase m = 4 systems 33 , Bi5Ti3FeO15 and SrBi4Ti4O15 that at RT the A21am space group is present, which allows movement of the oxygen atoms and BO6 octahedral tilting, rather than the once proposed Fmm2 space group 37 .Analysis on the m = 3 and m = 4 systems shows the advantages neutron diffraction has over X-ray diffraction, as in these systems the additional symmetry lowering arises from displacements of the oxygen atoms via octahedral tilting, which do not give rise to strong reflections within X-ray diffraction patterns.
Of the five-layered Aurivillius phases that have been investigated, one of the most compositionally similar materials to B6TFMO is Bi6Ti3Fe2O18, where García-Guaderrama et al. 38 deduced the space group to be F2mm via synchrotron X-ray powder diffraction, which did not detect tilting of the TiO6 octahedra.However, samples of the five layered Aurivillius system A2Bi4Ti5O18, substituted by Ca, Sr, Pb or Ba at the A-sites, were refined to the orthorhombic B2eb space group in a neutron diffraction study by Ismunandar et al. 5 .The tolerance factors were calculated to be 0.97, 1.0, 1.02 and 1.06 for Ca, Sr, Pb or Ba substituted structures, respectively, with an increase in the degree of octahedral tilting corresponding with a decrease in the tolerance factor, as shown in Table S2 of the SI.Among the compositions within this m = 5 system previously characterized 5 by neutron diffraction, Ca2Bi4Ti3O18 displays the highest orthorhombic distortion (t = 0.97), and exhibits tilt angles of 11 o for center, 10 o for intermediate and 7 o for outer perovskite octahedra, as illustrated in SI Table S2.
The calculation of the Goldschmidt tolerance factor 30 for B6TFMO results in a value of 0.95.
This tolerance factor of < 1 indicates that octahedral tilting within B6TFMO is favorable.

Figure S1 .
Figure S1.Atomic resolution STEM EELS spectra of outer, intermediate, and center perovskite

Figure S2 .
Figure S2.Further examples of plots from EELS data sets to support Figure 2 (d) in the main

Figure
Figure S3.a) STEM-HAADF image of five-layered B6TFMO overlaid with polarization vector

Figure S4 .
Figure S4.This is supplementary information to Figure 3 in the main text (Configuration: a).All

Figure S5 .
Figure S5.We consider another configuration (Configuration: b) of atoms and magnetic moments

Figure S6 .
Figure S6.Illustration of individual tilt modes found in three-layered Aurivillius phases.

Figure S7 . 5 (
Figure S7.Projected images down [100] used to approximate tilt angles associated with anti-phase tilting of perovskite octahedra, correlated with the irrep  3 + mode.Given that positions of the perovskite A-site bismuth atoms coincide with positions of apex oxygen atoms, accurate O-B-O

Figure S8 .
Figure S8.The positions of all oxygen and B-site atoms can be accurately measured from the DFT

Figure S9 .
Figure S9.The positions of all oxygen and B-site atoms can be accurately measured from the DFT

Figure S10 .
Figure S10.For Configuration: a, we also consider U values of 4.0 eV and 3.0 eV for Fe and Mn,