3D oxygen vacancy distribution and defect-property relations in an oxide heterostructure

Oxide heterostructures exhibit a vast variety of unique physical properties. Examples are unconventional superconductivity in layered nickelates and topological polar order in (PbTiO3)n/(SrTiO3)n superlattices. Although it is clear that variations in oxygen content are crucial for the electronic correlation phenomena in oxides, it remains a major challenge to quantify their impact. Here, we measure the chemical composition in multiferroic (LuFeO3)9/(LuFe2O4)1 superlattices, mapping correlations between the distribution of oxygen vacancies and the electric and magnetic properties. Using atom probe tomography, we observe oxygen vacancies arranging in a layered three-dimensional structure with a local density on the order of 1014 cm−2, congruent with the formula-unit-thick ferrimagnetic LuFe2O4 layers. The vacancy order is promoted by the locally reduced formation energy and plays a key role in stabilizing the ferroelectric domains and ferrimagnetism in the LuFeO3 and LuFe2O4 layers, respectively. The results demonstrate pronounced interactions between oxygen vacancies and the multiferroic order in this system and establish an approach for quantifying the oxygen defects with atomic-scale precision in 3D, giving new opportunities for deterministic defect-enabled property control in oxide heterostructures.

Line 163, "The latter carry a negative charge of about 12μC/cm 2 , which is partially compensates the positive charge associated with the oxygen vacancies".Could the authors illuminate the origin of '12μC/cm 2 '?Is there any experimental evidence of electron transfer from LuFe2O4-x layer to the middle LuFeO3 layers as shown in Fig. 3d?

Reviewer #3 (Remarks to the Author):
This work is dedicated to further investigation of multiferroic nanocomposites LuFeO3/LuFe2O4.In the current research the stoichiometry of nanocomposites was, for the first time, investigated at nanoscale with the technique of the Atomic Probe Tomography and this gives the great value to this research.The reported results discover the approach to easily (in comparison to the titrimetric methods) and quantitatively determine the the concentration of oxygen vacancies.In fact, this seems to be the only technique applicable to thin films.However, I have several concerns which I state below: 1) My first and greatest is that the concentration of the oxygen vacancies in LuFe2O4 is stated to correspond to the stoichiometry LuFe2O3.5, which means that all the iron atoms have been reduced from +3 to +2.As far as I know, the greatest extent to which LuFe2O4 structure could be reversibly reduced is LuFe2O3.935[1].If reduced further, it should decompose to Lu2O3 and FeO.Of course the reported data might be explained by the fact of epitaxial stabilization, however I would recommend a careful recalculation.Just in case.
2) The procedure of deriving the value of polarization of the LuFe2O4 layer from the vacancy concentration remains unclear to me.Despite the reported polarization value is quite close to the one that was reported previously [2], the commonly accepted conception is such that the charge order manifests in LuFe2O4 due to the valance ordering of iron ions in the stoichiometric LuFe2O4 (Fe+3/Fe+2=1) and not due to the presence of oxygen vacancies.In fact, it is thought that thanks to the variable valance of iron, LuFe2O4 remains neutral in chemical sense even when the vacancies or additional oxygen atoms are being inserted into the structure.In this scenario even if LuFe2O3.5 does exist in the investigated material, charge ordering couldn't have existed in such compound.Thus it might be helpful to think about the systematic orientation of ferroelectric domains in h-LuFeO3 layers from the interfacial strain point of view, since the ferroelectricity in this compound is known to be greatly affected by the nanoscale deformations.
3) Authors state that lutetium and iron APT-derived profiles perfectly correspond to those predicted for the ideal structure of LuFe2O4.However figures 2 and 2S clearly show that lutetium content is somewhat reduced and greatly shifted down from the sample surface compare to the ideal profile.I can't help but notice that the the minimum of the oxygen content is shifted in the opposite direction.I feel that it should not be regarded as a mere coincidence and must be discussed in the manuscript.4) Like the authors I have no doubt in the fact that oxygen vacancies have great influence on the ferroelectric and magnetic properties of this material.However I feel that the information that is presented in this particular manuscript is not enough to lay down the assertion that the one-to-one correlation between the vacancy density and ferroelectric and magnetic properties.I would suggest authors to concentrate on the fact of application of the APT technique itself, not on the interrelation between ferroelectricity/magnetism and density of the oxygen vacancies since those still appear to be unclear.
In overall, I think that this research bears a great experimental importance demonstrating the application of the APT for the quantitative chemical composition profiling of thin-film nanocomposites.My personal recommendation is to publish it after a thorough revision.

REVIEWER COMMENTS
We greatly appreciate the time and efforts the reviewers have invested in carefully reading and commenting on our work.In the following, we answer to all points raised by the three reviewers and, in accordance with their comments, have improved our article (for convenience, all changes are marked in the revised manuscript and SI in yellow).

Reviewer #1 (Remarks to the Author):
General remark: "The authors describe the measurements of chemical elements using the atom probe tomography and electrical polariza�on using the electron microscopy.They correlate the polariza�on patern with the so-called oxygen vacancy order.The conclusion is quite ques�onable, however.There are problems for both experimental and theore�cal aspects."General answer: We thank the reviewer for carefully reading the manuscript, reflec�ng on the details, and providing construc�ve feedback.We respond to the reviewer's comments point by point in the following.
Remark 1.1: "On the experimental aspect, there are seven LuFe2O4 layers, but only two layers are analyzed, making the presented results lacking sta�s�cal meaning." Answer 1.1: We should start by saying that we took great care to present sta�s�cally meaning full results.For each of the analyzed layers, an area of about 20 x 20 nm 2 was analyzed, containing > 10 5 atoms.This analysis gives sta�s�cally robust and meaningful results, clearly proving a significant enhancement in the density of oxygen defects in the LuFe2O4 layers rela�ve to the LuFeO3 layers (also reflected by the error bars in Figure 2a).We specifically selected the two layers men�oned by the reviewer for the in-depth analysis as they are the most well-defined ones in the data set with a spacing of about 7 nm rela�ve to the neighboring ones.This spa�al separa�on allows for a reliable characteriza�on of individual layers within the resolu�on of the APT experiment, without the risk of intermixing effects caused by close-by layers.Importantly, the quan�fica�on of oxygen vacancies at the different interfaces -which is the main results of this work -is not to be confused with emergent layer-to-layer varia�ons.The later are not in the focus of this work, and we agree with the reviewer that their quan�fica�on would require the analysis of a much larger set of layers.Mo�vated by comment reviewer's comment, we measured addi�onal samples, looking at other welldefined LuFe2O4 layers that allow for a reliable APT analysis (see Figure R1). Figure R1a,b shows the results obtained from two APT needles extracted at different posi�ons from the same superla�ce sample as discussed in the main text.We consistently observe a sta�s�cally significant accumula�on of oxygen vacancies at the LuFe2O4 layers as reflected by the error bars.Furthermore, we expanded our inves�ga�ons to LuFeO3/LuFe2O4 superla�ces with a larger separa�on between the LuFe2O4 layers.Here, the same effect is observed at the LuFe2O4 layers, i.e., an oxygen deple�on and an increase in Lu and Fe concentra�on.Thus, we can safely conclude that oxygen vacancies accumulate at the LuFe2O4 layers, and we emphasize that the extracted numbers are sta�s�cally meaningful and significant as indicated by the respec�ve error bars.Changes to the manuscript 1.1:In the revised manuscript, we clarify on page 6, line 124, that the results for each LuFe2O4 layer are sta�s�cally meaningful, wri�ng "For each layer, more than 10 5 atoms are measured, over an area of 20 x 20 x 5 nm 3 , providing local error es�mates for the concentra�ons on the order of 0.3 at.%".Furthermore, we expanded Supplementary Figure S2, where we present the new APT measurements as seen in Figure R1.We also explicitly men�on now on page 6, line 144, that the quan�fica�on of sample-specific layer-to-layer varia�ons go beyond the scope of this work.In Figure 2c, we increased the pixel volume over which we average to 6 nm 3 , containing more than 10 3 atoms each, giving sta�s�cally significant varia�ons for lateral varia�ons within the LuFe2O4 layers.Remark 1.2: "On the theore�cal aspect, the charge state of oxygen vacancies is simply neglected, which is not acceptable for insula�ng oxides, in par�cular ferroelectric proper�es are major concerns in the manuscript."Answer 1.2: We agree that this is an important aspect and that a careful analysis of the impact of the oxygen charge state improves the study.Hence, to identify differences for charged and neutral oxygen vacancies, we performed additional DFT calculations considering the lowest energy crystal structure of the (LuFeO3)3/(LuFe2O4)1 superlattice (obtained from DFT and STEM 1 , see Figure R2a).The defect formation energy for a single oxygen vacancy in a  charge state is defined as ∆  =    −  0 +  O +   , where  O and   denote the chemical potential of oxygen and the electronic chemical potential (Fermi energy), respectively (computational details are provided in Methods).The calculated total energies of the supercell with and without an oxygen vacancy are denoted as    and  0 , respectively.
The additional DFT results are presented in Figure R2b,c, showing that the formation energy for a single oxygen defect in the Lu planes is generally higher than in Fe planes.Furthermore, the formation of charged defects is energetically favorable in LuFe2O4 compared to LuFeO3, yielding an energy reduction of 64 meV.The stability of a charged oxygen vacancy is significantly enhanced compared to a neutral oxygen vacancy in the non-polar LuFe2O4 layer compared to the polar counterpart (0.02 → 1.00 eV).
Thus, in agreement with the APT experiments, the DFT results show that an accumulation of oxygen vacancies in the LuFe2O4 layer is energetically favorable.
Concerning ferroelectricity, we note that the comparison of the optimized crystal structures before and after the formation of charged oxygen vacancies reveals a maximum reduction of the Lu displacement ∆ ~ 0.1 Å.This displacement is not expected to have a measurable effect on the ferroelectric properties.In summary, the extended DFT analysis clarifies that an oxygen vacancy forma�on in the LuFe2O4 layers is energe�cally favorable compared to the LuFeO3 layers.The energy costs for charged oxygen vacancies are lower than for neutral ones, and the defect forma�on has no significant impact on the polar displacements that give rise to ferroelectricity.

Changes to the manuscript 1.2:
The addi�onal DFT results are included in the revised main manuscript, where Figure R2 replaces the previous Figure 3.We specifically address the oxygen charge state on line 150 on page 7.

Reviewer #2 (Remarks to the Author):
General remark: "The oxygen vacancies have a very important impact on the proper�es of the oxide heterostructures, but quan�fying their impact is a big challenge.In the present work, the atom probe tomography (ATP) combined DFT method was used to quan�fy the oxygen vacancies in the (LuFeO3)9/(LuFe2O4)1 heterostructures.This work is exci�ng and suitable for the Journal a�er addressing the following comments" General answer: We greatly appreciate the reviewer's very posi�ve feedback and address all her/his construc�ve technical remarks in our point-by-point below.
Remark 2.1: In Fig. 1a, the arrow of polariza�on (P) is not consistent in the HAADF-STEM (head to head) and crystal structure (tail to tail), please confirm that.Answer 2.1: We thank the reviewer for poin�ng this out.The direc�on was indeed wrong and has been corrected in the revised manuscript.

Remark 2.2:
In lines 161 and 163, there are two 'The later', which is very confusing for the reader, please include more detailed informa�on.Answer 2.2: Agreed.We have revised the sentence accordingly.
Remark 2.3: Line 163, "The later carry a nega�ve charge of about 12μC/cm 2 , which is par�ally compensates the posi�ve charge associated with the oxygen vacancies".Could the authors illuminate the origin of '12μC/cm 2 '?

Changes to manuscript 2.3:
We have corrected the sentence and added a reference for the spontaneous polariza�on.
Remark 2.4: Is there any experimental evidence of electron transfer from LuFe2O4-x layer to the middle LuFeO3 layers as shown in Fig. 3d?
Answer 2.4: Our APT experiments cannot show such electron transfer directly.Going beyond previous EELS experiments, however, by applying APT we are able to measure an oxygen vacancy accumula�on at the LuFe2O4 layers.This accumula�on -together with the reported stability of head-to-head walls in the LuFeO3 layers -represents first experimental evidence for the electron-transfer hypothesis proposed in ref. 1 , and it is fully consistent with published first-principle calcula�ons 1 and our new DFT results, revealing that charged oxygen vacancies are energe�cally favorable in the LuFe2O4 layer (please see answer 1.2 for details).Changes to manuscript 2.4: In the revised manuscript, we clarify on page 8, line 170, that the electron transfer has not been measured directly and discuss how it is inferred from the accumula�on of oxygen vacancies and DFT calcula�ons, the stability of head-to-head walls in the LuFeO3 layers, and the system's propensity to form charged oxygen defects in the LuFe2O4 layers.

Reviewer #3 (Remarks to the Author):
General remark: "This work is dedicated to further inves�ga�on of mul�ferroic nanocomposites LuFeO3/LuFe2O4.In the current research the stoichiometry of nanocomposites was, for the first �me, inves�gated at nanoscale with the technique of the Atomic Probe Tomography and this gives the great value to this research.The reported results discover the approach to easily (in comparison to the �trimetric methods) and quan�ta�vely determine the the concentra�on of oxygen vacancies.In fact, this seems to be the only technique applicable to thin films.In overall, I think that this research bears a great experimental importance demonstra�ng the applica�on of the APT for the quan�ta�ve chemical composi�on profiling of thin-film nanocomposites.My personal recommenda�on is to publish it a�er a thorough revision."General answer: We greatly appreciate the reviewer's posi�ve feedback and that she/he feels that the APT experiments give great value to the research on nanocomposites.In the following, we respond to all the reviewer's comments.

Remark 3.1:
My first and greatest is that the concentra�on of the oxygen vacancies in LuFe2O4 is stated to correspond to the stoichiometry LuFe2O3.5, which means that all the iron atoms have been reduced from +3 to +2.As far as I know, the greatest extent to which LuFe2O4 structure could be reversibly reduced is LuFe2O3.935[1].If reduced further, it should decompose to Lu2O3 and FeO.Of course the reported data might be explained by the fact of epitaxial stabiliza�on, however I would recommend a careful recalcula�on.Just in case.Answer 3.1: We agree that this is an important point and we considered it carefully.Please note that the work by Semine et al. addresses the equilibrium thermodynamics of a homogenous material, implying an ergodic state where the global ground state can be reached.In that case, no spatial gradients exist in the chemical potential of any species and, opposite to our material, the oxygen vacancy concentration is uniform.This situation is very different from the (LuFeO3)3/(LuFe2O4)1 superlattice we study, which is not in a global equilibrium state and was not grown by an equilibrium method.For example, LuFeO3 is not a stable bulk compound and cannot be synthesized bulk material.In addition to the superlattice's nonequilibrium state, epitaxy -as mentioned by the reviewer -potentially plays an additional role in stabilizing LuFe2O3.5 as the mechanical clamping imposed by the substrate in epitaxy suppresses nucleation of a secondary phase.We are thus confident, that the superlattice can locally accommodate a reduction to LuFe2O3.5 without decomposing into Lu2O3 and FeO.We also double-checked that our analysis is correct: The reported stoichiometry LuFe2O3.935 for bulk corresponds to a decrease in oxygen concentration of 0.4 at.% relative to LuFe2O4 3 .In contrast, we consistently measure a substantially larger drop for the LuFe2O4 layers in both (LuFeO3)9/(LuFe2O4)1 and (LuFeO3)15/(LuFe2O4)1 superlattices, approaching a peak value of about 1 at.%(see, e.g., Figure 2b).This difference already demonstrates that, locally, the reduction exceeds the literature value reported for bulk systems.
Assuming that this drop is associated with a one-unit-cell thick LuFe2O4 layer (which is justified based on the excellent agreement between the model and the measured Lu and Fe concentration profiles), we find LuFe2O3.835.This estimate, however, does not account for the resolution of the APT experiment, which leads to a broadening of the minimum in the oxygen concentration profile (to around 2 nm), whereas TEM shows that the actual thickness of the LuFe2O4 layer is about 0.5 nm.To correct for this effect, we integrate over the oxygen concentration profile, which gives the stoichiometry LuFe2O3.5.Changes to the manuscript 3.1: For transparency, we now give more details in the methods to clarify how the local stoichiometry was determined, in addi�on to a men�on in the main text (page 6, line 133).Furthermore, we explicitly discuss that the values locally measured for the unit-cell-thick LuFe2O4 layers exceed the limit previously reported for bulk systems, which is consistent with the inherent metastable state of a superla�ce in local -but not global -equilibrium and, possibly, further promoted by epitaxial stabiliza�on.Remark 3.2.1:The procedure of deriving the value of polariza�on of the LuFe2O4 layer from the vacancy concentra�on remains unclear to me.Answer 3.2.1:The ferroelectric polariza�on we are referring to is the spontaneous polariza�on of the (LuFeO3)3 layers (P = 6.5 μC/cm 2 , ref. 2 ).It is established that the polariza�on vectors form a tail-to-tail configura�on (←→) at the (LuFe2O4)1 layers, leading to a polar discon�nuity, equivalent to a nega�ve bound 2P = 13 μC/cm 2 , that requires screening.This is consistent with the measured accumula�on of oxygen vacancies (= posi�ve charges).
Changes to manuscript 3.1: We have now made it more clear in the discussion on page 8, line 174, that the interface bound charges at the (LuFe2O4)1 layers originate from the (LuFeO3) layers.
Remark 3.2.2:Despite the reported polariza�on value is quite close to the one that was previously [2], the commonly accepted concep�on is such that the charge order manifests in LuFe2O4 due to the valance ordering of iron ions in the stoichiometric LuFe2O4 (Fe+3/Fe+2=1) and not due to the presence of oxygen vacancies.In fact, it is thought that thanks to the variable valance of iron, LuFe2O4 remains neutral in chemical sense even when the vacancies or addi�onal oxygen atoms are being inserted into the structure.In this scenario even if LuFe2O3.5 does exist in the inves�gated material, charge ordering couldn't have existed in such compound.Answer 3.2.2:We feel that there is misunderstanding concerning the origin of ferroelectricity in the (LuFeO3)15/(LuFe2O4)1 superla�ce.Please note that we do not claim that LuFe2O4 is ferroelectric.As reported in Mundy et al. 1 , ferroelectricity arises from the geometrically driven improper ferroelectric order in LuFeO3, manifes�ng in the characteris�c up-up-down = +P and down-down-up = -P displacement paterns of the Lu atoms we show in Figure 1a.The one unit-cell-thick LuFe2O4 layers represent the magne�c cons�tuent in the ar�ficial mul�ferroic superla�ce.
Remark 3.2.3:Thus it might be helpful to think about the systema�c orienta�on of ferroelectric domains in h-LuFeO3 layers from the interfacial strain point of view, since the ferroelectricity in this compound is known to be greatly affected by the nanoscale deforma�ons.Answer 3.2.3:It is correct that strain gradients can, in principle, lead to a movement of the topological vor�ces in hexagonal LuFeO3 and affect the domain structure (see, e.g., Holtz et al. 4 , where related effects for isostructural hexagonal manganites are discussed).While we cannot exclude that strain plays a role for the domain forma�on, it cannot explain how the fully charged head-to-head and tailto-tail 180° walls are stabilized.The associated diverging electrosta�c poten�als are energe�cally extremely costly and require screening, which we demonstrated is achieved via the accumula�on of oxygen vacancies, clarifying how the system stabilizes its unusual domain structure.

Remark 3.3:
Authors state that lute�um and iron APT-derived profiles perfectly correspond to those predicted for the ideal structure of LuFe2O4.However figures 2 and 2S clearly show that lute�um content is somewhat reduced and greatly shi�ed down from the sample surface compare to the ideal profile.I can't help but no�ce that the minimum of the oxygen content is shi�ed in the opposite direc�on.I feel that it should not be regarded as a mere coincidence and must be discussed in the manuscript.

Answer 3.3:
The reviewer is correct that there are shi�s in the O and Lu concentra�on profiles, which we atribute to delayed or preferen�al evapora�on effects of ionic species 5,6 during the APT analysis.
It is well-established that elements which require a higher electric field to be evaporated (high-field elements, here: Lu) are retained on the surface, whereas elements that require a lower electric field (low-field elements, here: O) evaporate earlier.This effect leads to biases in the reconstruc�on, and it is visible as small spa�al shi�s of a few Ångstrøm in the composi�onal profile.
To corroborate our conclusion and gain addi�onal insight, we analyze the field evapora�on behavior of the superla�ce by considering the charge-state-ra�o (CSR) evolu�on as shown in Figure R3.The CSR is directly related to the electric field strength during the APT analysis and, hence, sensi�ve to field evapora�on artefacts.
Figure R3 shows an increased ionic density at the LuFe2O4 layers, which is well-known to arise in APT due to an overall lower field evapora�on (we note that this increase does not directly translate into a higher ionic density).Most importantly, the LuFe2O4 layers have no detectable impact on the CSR profile, which reflects that the electric field strength is largely constant throughout the superla�ce.
The data shows that there is no substan�al difference in the field evapora�on of the LuFeO3 and LuFe2O4 layers, excluding field evapora�on artefacts beyond subtle atomic shi�s, consistent with the systema�c shi�ing of low-field O and high-field Lu seen in Figure 2 and S2, as well as the new datasets in Figure R1.

Figure R1 :
Figure R1: Analyses of representative LuFe2O4 layers in two different superlattices: Data for (LuFeO3)9/(LuFe2O4)1 is shown in a and b, and for (LuFeO3)15/(LuFe2O4)1 in c and d.Dotted lines and symbols represent the experimental data, whereas solid lines represent concentrations expected for defect-free DFT-based models.All data sets consistently show oxygen depletion compared to the DFT-based models, corresponding to an accumulation of oxygen vacancies, accompanied by fluctuations in the Fe/Lu ratio.

Figure R2 :
Figure R2: Defect formation energy for oxygen vacancies in LuFe2O4 and LuFeO3.a, Crystal structure of the (LuFeO3)3/(LuFe2O4)1 superlattice, demonstrating tail-to-tail and head-to-head ferroelectric domain walls.b, The formation energy of oxygen vacancy at the oxygen-rich limit and for   = 0 (which corresponds to valence band maximum). O •• |  2  4 ( O •• | L 3 ) and  O × |  2  4 ( O × |  3 ) corresponding to oxygen vacancy in 2+ and neutral charge state at the LuFe2O4 (LuFeO3) layer, respectively.We conducted calculations for   = 6.5 eV at the Fe 3d orbital and the corresponding band gap is   = 0.9 eV.c, The formation energy of  O •• |  2  4 charged oxygen vacancy as a function of oxygen partial pressure and temperature.

Figure R3 :
Figure R3: CSR analysis of the superlattice system, using the Fe charge state (black line).The vertical dashed lines indicate the position of the LuFe2O4 layers, obtained by considering the ionic density profile (red line), which can detect very subtle changesto the electric field evaporation criteria.Importantly, the CSR analysis does not identify any substantial changes to the electric field strength, which rules out any major artefacts stemming from changes to the field evaporation criteria.
Compared to neutral defects in LuFe2O4,  O X � LuFe 2 O 4 , the formation of charged defects,  O •• | LuFe 2 O 4 , is about 1 eV lower in energy.The stability range of  O •• | LuFe 2 O 4 as a function of oxygen partial pressure and temperature is displayed in Figure R2c, considering both oxygen-rich and oxygen-poor conditions.Going beyond the superlattice structure in Figure R2a (i.e., non-polar with asymmetric down-up-up and down-up-down Lu displacement patterns), we also calculated formation energy of an oxygen vacancy at the polar LuFe2O4 and LuFeO3 configurations, where Lu ions move symmetrically around both the Fe bi-and single-plane.The calculations reveal: (i) Irrespective of the LuFe2O4 layer being polar or non-polar, the formation of  O •• | LuFe 2 O 4 is always the energetically most favorable defect.(ii)