Epitaxial strain and the magnetic properties of canted antiferromagnetic perovskite NaNiF 3 thin ﬁlms

The perovskite crystal structure is known to exhibit a multitude of interesting physical phenomena owing to the intricate coupling of the electronic and magnetic properties to the structure. Fluoro-perovskites offer an alternative chemistry to the much more widely studied oxide materials which may prove advantageous for applications. It is demonstrated here for the ﬁrst time that the antiferromagnetic perovskite ﬂuoride, NaNiF 3 , can be synthesized in thin ﬁlm form. The ﬁlms were grown via molecular beam epitaxy on SrTiO 3 (100) substrates to produce high quality epitaxial ﬁlms in the thickness range of 5 – 50 nm. The Pnma structure of the ﬁlms was conﬁrmed by x-ray diffraction. There was a decrease in the out-of-plane lattice spacing from the bulk value corresponding to a maximum strain of 1.7 % in the thinnest ﬁlm. Canted antiferromagnetism was measured in all ﬁlms using magnetometry and a negative change in the antiferromagnetic ordering temperature of ∆ T N = - 9.1 ± 0.7 K was observed with increasing strain.

The perovskite crystal structure is known to exhibit a multitude of interesting physical phenomena owing to the intricate coupling of the electronic and magnetic properties to the structure. Fluoro-perovskites offer an alternative chemistry to the much more widely studied oxide materials which may prove advantageous for applications. It is demonstrated here for the first time that the antiferromagnetic perovskite fluoride, NaNiF 3 , can be synthesized in thin film form. The films were grown via molecular beam epitaxy on SrTiO 3 (100) substrates to produce high quality epitaxial films in the thickness range of 5 -50 nm. The Pnma structure of the films was confirmed by x-ray diffraction. There was a decrease in the out-of-plane lattice spacing from the bulk value corresponding to a maximum strain of 1.7 % in the thinnest film. Canted antiferromagnetism was measured in all films using magnetometry and a negative change in the antiferromagnetic ordering temperature of ∆T N = -9.1 ± 0.7 K was observed with increasing strain.

I. INTRODUCTION
Perovskite materials host a huge variety of interesting properties ranging from high temperature superconductivity 1 , ferroelectricity 2 , piezoelectricity 3 to both ferro-and antiferromagnetic order as well as metal-to-insulator transitions 4 . The flexibility of the bond angles within the perovskite crystal leads to an intimate connection between its exact structure and its electronic and magnetic properties. In turn, this results in the potential for high tunability of physical properties within composition ranges, heterostructures or via externally applied stimuli (such as electric field or strain), providing an exciting playground for fundamental science as well as diverse functionality.
There have been extensive studies on the oxide perovskites over the years but the fluoro-perovskites have received little attention, in comparison. Recently, fluoro-perovskites have been suggested as potential electrode materials in Li/Naion rechargeable batteries, demonstrating more robust chemistry and performance than their oxide counterparts. 5,6 Hollow microspheres of NaNiF 3 (NNF), the material of the current study, were shown to have outstanding electrode material properties. 7 Fluoroperovskites have also been proposed as an alternative candidate in the search for multiferroicity i.e. the simultaneous existence of long-range magnetic order and ferroelectricity. 8 Strained NaMnF 3 in particular was postulated to be magnetoelectric, where the magnetism and ferroelectricity are coupled and can be controlled by either an applied electric or magnetic field. [9][10][11][12] Much like the oxide compounds, it is desirable to create thin film samples to integrate into devices. It is important therefore to understand whether the fluoro-perovskites retain their physical properties in thin film form. NaNiF 3 (NNF) shares the same crystal structure as NaMnF 3 but is not predicted to be ferroelectric according to theoretical calculations. 9 In bulk form, NNF was found to be a G-type antiferromagnet using neutron diffraction 13 with a weak ferromagnetic component along the b direction due to anti-symmetric exchange or the Dzyaloshinskii-Moriya interaction (DMI). 14 the canted antiferromagnetic fluoride, NiF 2 16 and not the commonly considered non-centro symmetric crystals such as the B20 compounds of MnSi 17 and FeGe 18 which are currently popular material hosts for magnetic spin textures known as skyrmions; possible future technologically viable data storage bits. 19 DMI is also present in centrosymmetric crystals when the ionic environment inversion symmetry is broken, such as is the case for the magnetic fluorides NiF 2 and NaNiF 3 .
In bulk form, NNF has a distorted perovskite crystal structure with an orthorhombic Pnma space group symmetry. The bulk values of the lattice constants are reported as a = 5.361 Å, b = 7.688 Å and c = 5.524 Å. 21 The crystal structure can be seen in Fig. 1a-c. The distortion from an ideal perovskite structure, such as that of SrTiO 3 (STO), shown in Fig. 1e and f, comes from a shift of the Na atoms in the a − b plane (Fig. 1b) and a tilting of the NiF 6 octahedra (Fig. 1c). The tilt angle has been measured in the bulk material as 11 • using x- ray diffraction measurements, and although this value is quite large, the distortion of the octahedra was found to be relatively small with the Ni-F-Ni bond angles within the octahedra remaining close to orthogonal. 22

A. Thin film growth
The NNF thin films were grown on pre-polished single crystal (001) STO substrates (a = 3.905 Å) by molecular beam epitaxy (MBE) in the thickness range 5 -50 nm. A standard procedure to obtain an atomically flat and TiO 2 -terminated substrate surface was used which consisted of two thermal annealing steps and a deionized water treatment. 23 The substrates were heated to 250 • C and annealed for one hour to remove surface contaminants before growing at the same temperature. The correct stoichiometry was achieved by codepositing NaF and NiF 2 using effusion cells in an ultra-high vacuum chamber with base pressure p = 3 × 10 −9 Torr and typical growth rates of 0.009 nm/s.

B. Structural and magnetic characterization
Structural characterization was carried out via X-ray diffraction (XRD) using a Rigaku Smartlab 3 kW sealed tube x-ray source with a Ge(220) crystal monochromator optimized for Cu K α radiation (λ = 0.15406 nm). We also carried out in-situ analysis of the substrate and film surfaces using reflection high energy electron diffraction (RHEED) STAIB RH 15 system with an operating voltage of 15 keV corresponding to ≈ 0.01 nm de Broglie wavelength and a current of 1.5 A. In addition, we carried out ex-situ analysis of the thickness and surface roughness using X-ray reflectivity (XRR) and the surface morphology was studied by atomic force microscopy (AFM) on an Asylum Cypher S using tapping mode in air or a controlled N 2 atmosphere. Elemental analysis was carried out using a LEO VP1400 scanning electron microscope (SEM) with an Oxford x-ray spectrometer for electron dispersive x-ray spectroscopy (EDS). Measurements were taken with a beam energy of 25 keV and the spectra were averaged over five scans.
Magnetization measurements were performed using a Magnetic Properties Measurement System (MPMS) based on a superconducting quantum interference device (SQUID) sensor from Quantum Design.

A. Structural properties
The out-of-plane XRD is shown in Fig. 2a and confirms all the films are single phase and have the expected Pnma structure. Only peaks related to the NNF and STO substrate were observed as labelled in the figure. An enlarged plot in Fig. 2b shows the clear shift to the right with decreasing thickness of the NNF (202)/(040) peak. In the pseudo-cubic (pc) unit cell of NNF, the corresponding lattice parameters are a pc = c pc = a 2 0 + c 2 0 /2 = 3.849 Å and b pc = b 0 /2 = 3.844 Å. When grown on STO it would have a lattice mismatch strain of ≈ 1.44% if the growth is oriented along the [010] orientation, with the long b axis out of the plane and the ac plane at 45 • to the cubic STO (Fig. 1d, red unit cell). By comparison, the strain for [101]-oriented growth, with the long b-axis in the plane (Fig. 1d, blue unit cell), is also tensile but slightly increased, ≈ 1.56%. These two most favorable growth orientations are indistinguishable in the out-of-plane XRD, a fact encountered when growing NaMnF 3 on STO previously. 11 We used χ − Φ measurements to determine the dominant growth direction. A schematic illustrating both axes with respect to the sample plane is shown in Fig. 2e  The peak positions were fitted to a gaussian line shape to extract the exact 2θ position in order to calculate the out-ofplane crystallite coherence, ξ OOP using the Scherrer equation: where κ is the shape factor taken to be 0.9 24 , λ is the wavelength of the x-rays (λ Cu K-α = 0.15406 nm), FWHM is the full width half maximum of the fitted 2θ peak and θ is half of the fitted center of the peak. The thickness dependent coherence is plotted in Fig. 2c and shows that all films grown are coherent throughout their entire thickness up to 30 nm where it then starts to decrease. All thicknesses were measured directly by fitting the XRR data and the fully coherent linear relation has been plotted as a black line in the figure.
To characterize the strain in the films, the fitted 2θ positions were converted to their corresponding out-of-plane d hkl spacing, assuming both growth directions, and subsequently compared to that of bulk NNF 25 to calculate the out-of-plane strain, ε ⊥ : where d hkl is the measured interplanar spacing and d bulk hkl is the bulk value calculated using lattice constants from the literature. 21 We calculated this strain to be tensile (positive) and to decrease as the thickness of the film increases, by 1.2% over the thickness range measured, as shown in Fig. 2d. The strain values saturated for the thickest films, 40 and 50 nm. Additional characterization of the in-plane crystallographic order was done via rocking curves shown in Supplementary S1.

B. Surface roughness
In-situ RHEED analysis revealed a high level of in-plane order at the surface as shown by the diffraction patterns in Fig. 3a-j. The sharp rods indicate high in-plane crystal order and also that the surfaces of the films were smooth. The topography of each film was also measured ex-situ using AFM, shown in Fig. 3k-o. The underlying terraces from the STO are visible in all samples indicating the growth was extremely smooth. Spots on the surface were confirmed using scanning electron microscopy-electron dispersive x-ray spectroscopy (SEM-EDS) as excess NaF, although this did not seem to affect the structural or magnetic properties of the underlying material. X-ray reflectivity (XRR) was used as an additional method to determine the sample roughness (ex-situ) which is shown in Fig. 4a where the data points were fitted using the GenX software. 26 All samples show Kiessig oscillations that extend to high angle and the fitted roughnesses were between 0.27 and 0.56 nm. These values have been plotted with the root mean square roughness extracted from the AFM data ( Fig. 3k-o) and are shown in Fig. 4b. The roughness parameters, as determined by the two methods, are in good agreement for the 10, 20 and 30 nm films but the value from XRR is consistently lower than that of the AFM. The 10, 20 30 nm film are fairly free of defects, as seen in Fig. 3 (l) -(n), meaning the defects present are most likely only weakly interacting with the x-rays. The discrepancy arises as XRR is more sensitive to the roughness within the terraces, which have an approximate step size equal to the STO lattice constant of 0.39 nm, as this is where the material is deposited. The AFM is also sensitive to the roughness between the terraces which can be much larger than along the terraces as is shown and discussed in more detail in Supplementary S2.

C. Magnetic properties
The magnetisation was measured via zero-field-cooled and field-cooled (ZFC-FC) measurements as shown for the 20 nm film in Fig. 5a. The sample was first cooled in zero field (H = 0 Oe) to T = 5 K, after which a measurement field of H = 1 kOe was applied and the magnetic moment was measured while warming up to 300 K (ZFC portion of the curve). The measurement was than continued whilst cooling back down to 5 K to obtain the field-cooled portion of the curve. Subsequently, the field was set to zero and the magnetic moment was measured whilst warming back to room temperature, resulting in the thermo-remanent magnetization (TRM) plotted in Fig. 5b. The sharp increase in the susceptibility in the the ZFC data at T N , shown more clearly in the inset of Fig. 5a, is a  (i.e. weak ferromagnetism). 15 Similar behavior has also been observed in NaMnF 3 thin films. 11 The weak ferromagnetic moment is due to the canting of the Ni spins away from the antiferromagnetic axis ( Fig. 5c and d) and is shown as an increase in the magnetic signal as the temperature is reduced in the FC magnetisation and TRM measurement. The magnetic structure only allows canting along the b axis and is such that the canted moment for the [101]-growth direction would have a net magnetisation in-plane whereas for the [010]-growth direction it would be out-of-plane, as illustrated in Fig. 5c and d. The TRM measurements for different in-plane angles and the out-of-plane orientation of the field are shown in Fig. 5b. The data show a larger TRM moment in-plane which is in agreement with the predominant growth orientation being [101] found from XRD. We see no discernible difference between the magnetisation for the 0, 45 and 90 • in-plane orientations (Fig. 5b) which supports the in-plane x-ray φ scans and the orthogonal twinning of the [101]-oriented crystal. In the magnetic measurement the ratio of the in-plane to out-ofplane magnetization is ≈ 28.5 % (assuming equal proportion of twinned domains in the plane), which is slightly higher than the ratio of (010)/(101) domains found in the in-plane XRD measurements which was 20%. This difference could be due to a small angular misalignment in the SQUID giving an inplane component during the out-of-plane measurement. The spontaneous magnetic moment of the NNF corresponds to a tiny fraction of the Ni 2+ ion moment (assuming 2.0µ B per Ni) and was found to be 0.07 ±0.02 µ B /f.u. (using the average M TRM (T = 5 K) value for all films except 5 nm). We also assumed that as the thin film sample is twinned inplane we only measure half of the true bulk value in one crystalline in-plane direction. This corresponds to an upper limit of 3.5±0.7% Ni 2+ ion moment. This is in good agreement with the 3% value found in the bulk. 21 The small contribution from the (010) domains should act to reduce the measured value. It is worth noting here that if the mechanism for the canting is antisymmetric exchange, then it has been proposed that the canting angle has no temperature dependence, whereas the single ion anisotropy model does predict a tem-perature dependence. 13 All samples showed a qualitatively similar behaviour except the 5 nm film as shown in Fig. 6a. The thinnest film had a large ferromagnetic signal which was present up to the highest temperature measured. There was a ≈ 0.5 emu/cc = 0.01 µ B /f.u. change in the ZFC-FC magnetisation at T = 146.4 K which we attribute to NNF. The antiferromagnetic Néel ordering temperature, T N , was measured for the other samples as the point where the spontaneous canted moment disappeared in the TRM, as shown in Fig. 6b. We observe a thickness dependence, as shown in Fig. 6c, with a change of ∆T N = -9.1 ± 0.7 K as the film thickness is reduced from 50 nm to 5 nm. There is a sharp change between 5 and 20 nm into a gradual plateau between 40 and 50 nm, as shown by the red curve in Fig. 6c which correlates with the calculated strain, plotted by the blue curve. Both show a plateau at the high end of the thickness range. Beyond 30 nm the sample is no longer fully strained and it has relaxed, also indicated by the difference between the out-of-plane structural coherence length and film thickness, shown in Fig. 2c. The ordering temperature of the films approaches the bulk value as the strain is reduced, shown in Fig. 6d.
There are two mechanisms whereby tensile strain can be accommodated in perovskite materials, both are shown in the lower part of Fig. 6e. The magnitude of the tilt can change through rigid rotations of the NiF 6 octahedra where the intraoctahedral Ni-F distances remain unchanged but there is a change in the inter-octahedral bond angle, shown as α in the figure. 27 Alternatively, a change of the in-plane Ni-F bond lengths can occur and the octahedra are distorted. It is also possible to have a combination of both simultaneously. It is well known from the Goodenough-Kanamori rule that the magnetic superexchange interaction is antiferromagnetic for the 180 • transition metal-oxygen-transition metal bond angle. 28,29 A reduction in the bond angle has been shown to lower the Néel temperature in oxide perovskites and was attributed to the weakening of the Fe-O-Fe exchange interaction in the orthoferrites. 30 It is possible the reduction in T N observed here is due to the strain being accomodated in a similar way. There is a octahedral rotation about an axis parallel to the substrate plane (labelled β in the figure) and a corresponding decrease in α, away from the ideal antiferromagnetic 180 • Ni-F-Ni bond angle.

IV. CONCLUSION
In summary, highly ordered thin films of NaNiF 3 have been grown for the first time. The Pnma crystal structure was confirmed via XRD in the preferred [101] growth orientation. The films showed a reduction in the out-of-plane d spacing, which was sustained throughout the film in thicknesses up to 30 nm, after which the structure relaxed towards the bulk NNF as did the magnetic ordering temperature, T N . The canted antiferromagnetic order was confirmed via magnetometry and the measured value of magnetisation was in good agreement with the bulk value. We attribute the decrease in T N to increasing strain which can be accommodated via octahedral rotations, reducing the bond angle between octahedra and causing a corresponding reduction of the superexchange interaction across the Ni-F-Ni bonds. A detailed study of the strain-dependent bond angle is desirable which could be done using synchrotron XRD where there is sensitivity to the half order peaks created by the tilt pattern and changes can be quantified. 31 The presence of ferromagnetic behavior in the thinnest film warrants further investigation. Potential for magneto-electric coupling in strained fluoroperovskites is possible due to the predicted behavior of NaMnF 3 , which may manifest in electric field dependent exchange bias phenomena 32 and the feasibility of ultrafast and low power spintronic devices based on antiferromagnetic insulators. 33

ACKNOWLEDGMENTS
Funding provided by the University of California Multicampus Research Programs and Initiatives (grant MRP- . Some support at the initial stages of the project was provided by the National Science Foundation (grant 1434897).  25 . (e) The NNF crystal structure for the bulk (upper) and strained thin film (lower) with the two possible ways in which the octahedra can change (rotation or distortion) to accommodate a decrease in the out of plane spacing for the [101]-oriented growth.