DyFe₂O₄: A new trigonal rare-earth ferrite grown by molecular-beam epitaxy

In the quest for new functional materials, trigonal and hexagonal oxides are relatively unexplored and show great promise as there are many unexplored phases with similar lattice parameters that could be combined epitaxially to form new heterostructures. Trigonal and hexagonal rare-earth ferrites are of particular interest because both high-temperature ferrimagnetism and ferroelectricity are exhibited in this class of materials, making them potentially relevant to technology. An exciting new method of creating multiferroic materials by combining rare-earth ferrites into superlattices has been demonstrated using h-LuFeO₃ for its geometric ferroelectric properties and LuFe₂O₄ for its ferrimagnetism.¹ We believe exploring the phase space of hexagonal and trigonal oxides could lead to interesting new material discoveries.

The trigonal RFe₂O₄ phase with space group $R3̄m$ can be formed in bulk with R rare earths ranging on the periodic table from holmium to lutetium (as well as Y, Sc, and In).^2–7 The phase has a layered structure along the c axis with one layer of rare-earth atoms in octahedral oxygen coordination followed by two layers of iron atoms oxygen coordinated in trigonal bi-pyramids, as shown in Fig. 1(a). The irons are in a low oxygenated state with an equal mix of 2+ and 3+ valences. The spins on the iron atoms in the trigonal plane result in a frustrated ferrimagnet with a net moment along the c axis and a transition temperature around 220–250 K.^2,8–11 The RFe₂O₄ phase is more stable for rare earths with smaller atomic radii, and LuFe₂O₄ is believed to be the most stable^4,5 as lutetium has the smallest ionic radius of the rare-earth lanthanides. It is thought that dysprosium is too big to accommodate both the octahedral coordination of the dysprosium atoms and the trigonal bipyramid coordination of the iron atoms to form a DyFe₂O₄ phase that is isostructural with the known trigonal RFe₂O₄ phases.^4,5 The ionic radius of dysprosium 3+ in octahedral coordination is 0.912 Å, which is significantly larger than holmium at 0.901 Å,¹² the largest ion to form RFe₂O₄ in bulk. DyFe₂O₄ has never been synthesized before and is not bulk stable. Indeed, the only known ternary phases in the Dy-Fe-O system are DyFeO₃ and Dy₃Fe₅O₁₂.^3–5,13,14 Dysprosium has been substituted into the phase by doping YFe₂O₄ to form Y_0.95Dy_0.05Fe₂O₄, which was shown to increase the ferrimagnetic transition temperature from 230 K to around 270 K.¹⁵ 

Two key questions related to the quest of synthesizing DyFe₂O₄ are (1) how metastable is DyFe₂O₄ and (2) what reaction pathway might lead to its realization. According to the Materials Project,¹⁶ the enthalpy of DyFe₂O₄ (mp-756971) at T = 0 and P = 0 lies 104.92 meV/atom above the enthalpy of a mixture of stable phases (i.e., 104.92 meV/atom above the convex hull of thermodynamic stability at T = 0 and P = 0). For comparison, a recent analysis of over 5500 metastable oxides in the Materials Project concluded that the median enthalpy above the convex hull of those phases that have been experimentally realized is 15 meV/atom and that the 90th percentile of enthalpies above the convex hull of oxides that have been synthesized is 62 meV/atom.¹⁷ The calculated metastability of 106 meV/atom thus puts DyFe₂O₄ at the high end of what might be achievable and makes it an interesting example to see if epitaxial stabilization^18–23 can be used to make it following the “principle of remnant metastability” for what metastable phases can be synthesized.¹⁷ Interestingly, the other RFe₂O₄ phases (which are bulk stable) also have similarly high calculated enthalpies above the complex hull, as demonstrated in Fig. 2, along with values for the structurally similar P6₃cm phase.^16,24 Most of the other RFe₂O₄ are only calculated to be slightly more stable than DyFe₂O₄ with ErFe₂O₄ at 100.78 meV/atom, TmFe₂O₄ at 100.26 meV/atom, and LuFe₂O₄ at 101.70 meV/atom.

Epitaxial stabilization is a powerful method for the synthesis of metastable oxides.²³ It has been used to extend the range of rare earths that can be synthesized with hexagonal RMnO₃ and RFeO₃ structures; these structures are quite similar to the DyFe₂O₄ phase that are the subject of this study. This extension beyond the stable and metastable phases that have been achieved by bulk methods is via two approaches: (i) epitaxial growth of RMnO₃ and RFeO₃ thin films on commercially available substrates with structural similarities, but not isostructural, and (ii) growth on single crystals of isostructural compounds. The former approach enabled the growth of metastable hexagonal RMnO₃ with R = Sm to Gd^25,26 as well as metastable hexagonal RFeO₃ with R = Eu to Lu²⁷ and Sc.^28,29 The latter approach enabled thicker films of hexagonal RMnO₃ with R = Sm to Gd to be grown.³⁰ None of the aforementioned metastable compounds have been synthesized by bulk techniques. Nonetheless, hexagonal RInO₃ with R = Eu to Ho and Y³¹ is bulk stable with dysprosium forming as DyInO₃ with similar coordination, as in these hexagonal phases as well as DyFe₂O₄.

Motivated by the prior success of epitaxial stabilization to achieve new hexagonal RMnO₃ and RFeO₃ phases,^25–28 we apply this method and are able to synthesize hexagonal DyFe₂O₄ by oxide molecular-beam epitaxy (MBE). The films are shown to be epitaxial and single-phase. Although our approach is to grow DyFe₂O₄ on a commercially available substrate with structural similarities, but not isostructural, interestingly, a single monolayer of hexagonal DyFeO₃ is seen to form between the commercially available substrate and the overlying DyFe₂O₄ film.

One challenge when growing thin films of trigonal oxides is substrate selection as there are a limited number of commercially available substrates that are chemically and structurally compatible. For trigonal oxides, hexagonal substrates or the (111) face of cubic substrates can be used. Consideration also had to be taken into account for what substrates could act as an oxygen source, e.g., SrTiO₃^32–35 and YSZ^36,37 are notorious, as the iron in DyFe₂O₄ is in an Fe^2.5+ oxidation state. A (111) MgAl₂O₄ substrate was selected to grow (001)-oriented DyFe₂O₄ because of these criteria as well as previous success synthesizing epitaxial LuFe₂O₄.¹¹ Unfortunately, the lattice mismatch is quite large at about −7.3% with the DyFe₂O₄ [100] aligned along MgAl₂O₄ $21̄1̄$⁠, as shown in Fig. 1(c). The large mismatch suggests the film will relax right away by the introduction of dislocations and minimal homogeneous strain will be retained in the film. The aforementioned lattice mismatch, $asub−afilmafilm$⁠,³⁸ where a_sub is the relaxed lattice constant of the substrate and a_film is the relaxed lattice constant of the film, was estimated in two ways. The first way involved measuring the a lattice parameter of the epitaxial DyFe₂O₄ films by x-ray diffraction. The observed result differed greatly (>7%) from the underlying substrate, consistent with the film relaxing immediately. The second method involved an extrapolation of the trend in the a lattice parameter of the known RFe₂O₄ phases. Both methods agreed within 0.1%.

Thin films of DyFe₂O₄ were grown by MBE in a Veeco GEN ten chamber. Previous work showed that other RFe₂O₄ phases including In Fe₂O₄ and LuFe₂O₄ could be grown by adsorption control with the indium oxides and iron oxides acting as the volatile species, respectively.^11,39 Here, we use shuttering to assist in the deposition after the “growth window”—the range of oxygen pressure and substrate temperature within which DyFe₂O₄ formed by adsorption-controlled growth—was determined. The best conditions were found to be at a substrate temperature around 775 °C, an oxygen background partial pressure around 8 × 10⁻⁸ Torr, and a growth rate of about 3.5 Å/min. The substrate temperature was measured by an optical pyrometer with a measurement wavelength of 980 nm focused on a platinum layer deposited on the backside of the substrate. The background oxygen partial pressure was determined by a residual gas analyzer located at the wall of the chamber. Similar to the growth of LuFe₂O₄,¹¹ it was found that when the oxygen pressure was too low or the substrate temperature too high, precipitates of FeO would form, while if the oxygen was too high or the substrate temperature too low, precipitates of Fe₃O₄ would form. These extra phases could be observed as extraneous spots using reflection high-energy electron diffraction (RHEED) during growth. An example of a RHEED pattern taken during the growth of a phase-pure DyFe₂O₄ film is shown in Fig. 3(a). After growth, the films were cooled to 250 °C in the same oxygen pressure as used during film growth. If the oxygen was turned off at higher temperature, precipitates of Fe–O compounds could be seen to form by RHEED. Once the optimal substrate temperature, oxygen background partial pressure, and growth rate were established, the shutter time for dysprosium was adjusted to precisely correspond to one monolayer to decrease the amount of h-DyFeO₃ that formed. The unwanted h-DyFeO₃ impurity phase could be detected by x-ray diffraction by both distinct x-ray peaks at the expected position for h-DyFeO₃ when a large amount was formed or by a broadening of the DyFe₂O₄ peak and shifting toward higher 2θ when a smaller amount was formed, which we expect was due to syntactic intergrowths in which some of the Fe-O bilayers of DyFe₂O₄ were replaced by the Fe-O monolayers of h-DyFeO₃. Additionally, as has been previously seen in adsorption controlled growth of LuFe₂O₄,¹¹ excess iron above the 1:2 (R:Fe) stoichiometric ratio is needed during deposition to create a stoichiometric film. In DyFe₂O₄, a ratio of ∼1:2.5 was found to be ideal. This is significantly different from the adsorption-controlled growth of LuFe₂O₄ where a ratio of 1:4 was used,¹¹ although in DyFe₂O₄, we are also using shuttering to supply the atomic fluxes separately. If less iron than this ∼1:2.5 ratio was added, more DyFeO₃ would grow; however, if more iron was added, intergrowths of other iron oxide phases such as Fe₃O₄ were seen to form unlike during the deposition of LuFe₂O_4.

The films were grown to a total thickness of ∼30 nm. A few attempts were made to grow significantly thicker films (∼50 nm) using similar growth conditions, but phase-pure films (by XRD) of DyFe₂O₄ could not be stabilized. This suggests that the considerable metastability of DyFe₂O₄ significantly limits the thickness of films that can be grown. As shown in Fig. 3(b), 30 nm thick films of DyFe₂O₄ could be synthesized with no impurity phases detectable by XRD. Nonetheless, the Bragg peaks of DyFe₂O₄ in the θ–2θ scan do appear asymmetric, which could indicate the presence of DyFeO₃ intergrowths,^40,41 or this could be caused by other inhomogeneous disruptions to the structure such as variation in oxygenation. As a consequence of the large lattice mismatch between the substrate and film, the film relaxes right away, which is reflected in a large full width at half maximum (FWHM) of 1.36° of the ω rocking curve of the 003 peak of a 30 nm thick film [Fig. 3(c)]. ϕ scans revealed that although the films are aligned out of plane, the in-plane films contain 60° (which is symmetrically equivalent to 180°) rotation twins, resulting in the doubling of the number of expected peaks in the ϕ scan [Fig. 3(d)] compared to what an untwinned single crystal would show. One of the twins does align with DyFe₂O₄ [100] parallel to MgAl₂O₄ $211̄$ as expected, with the other twin being 60° rotated with DyFe₂O₄ [100] along MgAl₂O₄ $12̄1$⁠, as in Fig. 1(c).

Scanning transmission electron microscopy (STEM) images further elucidate the microstructure of the non-bulk stable ordered DyFe₂O₄ phase that has formed. After growth, the air-exposed DyFe₂O₄ sample was first coated with a carbon layer to protect it during the focused-ion beam specimen preparation process. Figure 4 displays two STEM images showing the clear formation of the epitaxial structure resulting in bright dysprosium planes between double layers of Fe–O planes as expected for this phase. On the wider view STEM image in Fig. 4(b), we see that the majority of the film is in the DyFe₂O₄ phase although there is a small amount of h-DyFeO₃ forming near the interfaces. The structure of h-DyFeO₃ is very similar to DyFe₂O₄ but has only one Fe–O layer between puckered DyO₂ layers instead of the two Fe–O layers of DyFe₂O₄. This structural similarity allows for epitaxial integration (or syntactic intergrowths) without disrupting the rest of the DyFe₂O₄ film.

Hexagonal DyFeO₃ (h-DyFeO₃) is itself not bulk stable. The stable polymorph of DyFeO₃ is an orthorhombic perovskite structure. Nevertheless, h-DyFeO₃ has been epitaxially stabilized before^42,43 and appears to be a strong competitor in this system as films were observed to preferentially form in a mixture of DyFe₂O₄ and h-DyFeO₃ if there was any excess dysprosium or higher levels of oxygen. Rather than considering the metastability vs the convex hull of bulk stable phases, i.e.,

we see that what becomes relevant in this thin film system involving the substrate interface is the convex hull involving decomposition into epitaxially stabilized phases, i.e.,

Usually, the Fe₃O₄ on the right-hand side of Eq. (2) is not incorporated into the film due to the adsorption-controlled growth regime utilized for film synthesis. Nonetheless, if the oxygen is increased above the adsorption-controlled window, precipitates of Fe₃O₄ are seen to form in the film. In the similar system of LuFe₂O₄, although phase-pure LuFe₂O₄ was able to be deposited by MBE,¹¹ other groups could only find growth regimes where a mixture of LuFe₂O₄ and h-LuFeO₃ would form.⁴⁴ The a lattice parameter of h-DyFeO₃ is effectively smaller⁴² than that of DyFe₂O₄ and should therefore have a smaller misfit strain with the MgAl₂O₄ substrate, which could be encouraging its growth as the first interfacial layer. Even though the growth conditions were optimized for DyFe₂O₄ within the film, the fact that we see single layers of h-DyFeO₃ along both interfaces of an otherwise pure DyFe₂O₄ film indicates the thermodynamic stability regime near the interfaces, due to strain or surface adsorption, could be less favorable for DyFe₂O₄ formation and the single layers of h-DyFeO₃ could be helping to facilitate DyFe₂O₄ formation throughout the rest of the film.

The lattice parameters of the DyFe₂O₄ films were calculated from x-ray diffraction and yield a = 3.540 ± 0.007 Å and c = 24.90 ± 0.06 Å. The c lattice parameter was calculated using Nelson–Riley plots⁴⁵ of the first four 003l film peaks and then averaged over five films. The a lattice parameter was then calculated using the c lattice parameter found for a particular film and the location of the off-axis 011 peak of that same film and then averaged over four films. When these values are compared to the trends of the other rare earths in the RFe₂O₄ phase⁶ (Fig. 5), we find that the a lattice parameter of our films is as expected and falls nicely on the linear trend line with minimal error, but the c lattice parameter is larger than what is expected from the trend (24.71 Å) and is instead similar to what is found in HoFe₂O₄ or ErFe₂O₄. It was also seen that when x is increased in LuFe₂O_4+x, the distance between rare-earth planes also increases,⁴⁶ leading to an increase in the c lattice parameter as we also see in our DyFe₂O₄ films. In addition, when dysprosium was doped into Y_1−tDy_tFe₂O_4+x, it was noted that as the amount of dysprosium was increased (t), the amount of excess oxygen (x) also increased, and stoichiometric samples were not able to be synthesized for t > 0.05.¹⁵ It thus appears that we are also likely seeing this effect of over oxygenation in our DyFe₂O₄ films. This leads us to conclude that although it is possible to incorporate dysprosium into the non-bulk stable structure of DyFe₂O₄, the larger ionic radius of dysprosium in this metastable structure leads to non-stoichiometry due to over oxygenation: DyFe₂O_4+x.

Although unintended, the ability of oxygen non-stoichiometry to lower the formation energy of the metastable phase we targeted is not unexpected. Oxygen excess or oxygen vacancies often arise when thin films containing multivalent species are strained as a way for the system to lower its overall energy.⁴⁷ For example, oxygen vacancies are induced and order in epitaxial La_0.5Sr_0.5CoO₃ films in response to substrate-imposed strains.⁴⁸ The oxygen content of (La, Sr)₂CuO_4+δ films can be modulated by substrate-imposed strain in combination with the oxygen activity in the growth or annealing environment.⁴⁹ Even in bulk, the ability of the oxygen content of a material to change in response to stress—an effect known as chemical expansion⁴⁹—is also common in multivalent systems.⁵⁰ In the present case, DyFe₂O_4+x, the oxidation state of the iron is between 2+ and 3+. This flexibility of the iron oxidation state in combination with the stress-free boundary condition of thin films in the out-of-plane direction provides an opportunity for the system to reduce its free energy.

The RFe₂O₄ phase⁴⁶ as well as the similar RMnO₃ phase^51,52 have both been suggested as promising materials for oxygen storage because of their ability to accommodate large amounts of excess oxygen and cycle it through their structures reversibly. As DyFe₂O_4+x appears to show an affinity for excess oxygen as the most stable state, it may play an interesting role in helping to understand the basic science behind these phases’ unique oxygen accommodating properties.

In conclusion, using MBE, the non-bulk stable phase of (001) DyFe₂O₄ was synthesized by epitaxial stabilization on (111) MgAl₂O₄ substrates. Although a new phase was synthesized, it appears to contain significant point defect densities; the increased c lattice parameter leads us to believe an increase in oxygenation is unavoidable in this rather metastable structure when synthesized by these methods. The unique abilities of MBE to use epitaxial stabilization in combination with a very tunable growth window (precise control of atomic flux, temperature, and background oxygen pressure) allowed us to find a growth regime where the barrier to formation for RFe₂O₄ was low enough that with just one last unintentional thermodynamic tuning parameter, oxygen stoichiometry, the phase was stabilized. It is possible that with a better matched substrate, a thick h-DyFeO₃ buffer layer, or precise annealing, this last imperfection could be eliminated and a stoichiometric DyFe₂O₄ revealed. If over oxygenation persists in this compound, it may open questions about what is truly accessible for other possible remnant metastable phases, as well as provide insight into the oxygen storage capacity of RFe₂O₄ compounds.

We acknowledge helpful discussions with Kristin Persson and Matt Horton. This work was supported by the U.S. Department of Energy, Office of Science, Basic Energy Sciences under Award No. DE-SC0002334. Sample preparation was in part facilitated by the Cornell NanoScale Facility, a member of the National Nanotechnology Coordinated Infrastructure (NNCI), which was supported by the National Science Foundation (Grant No. NNCI-1542081). This work made use of the Cornell Center for Materials Research Shared Facilities, which are supported through the NSF MRSEC program (No. DMR-1719875).

The data that support the findings of this study are available from the corresponding author upon reasonable request.