Epitaxial strain and the magnetic properties of canted antiferromagnetic perovskite NaNiF₃ thin films

Perovskite materials host a huge variety of interesting properties ranging from high temperature superconductivity,¹ ferroelectricity,² and piezoelectricity³ 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 fluoroperovskites have received little attention, in comparison. Recently, fluoroperovskites have been suggested as potential electrode materials in Li/Na-ion rechargeable batteries, demonstrating more robust chemistry and performance than their oxide counterparts.^5,6 Hollow microspheres of NaNiF₃ (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 NaMnF₃, 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.^9–12 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 fluoroperovskites retain their physical properties in thin film form.

NaNiF₃ (NNF) shares the same crystal structure as NaMnF₃ 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 diffraction¹³ with a weak ferromagnetic component along the b direction due to the antisymmetric exchange or the Dzyaloshinskii-Moriya interaction (DMI).^14,15 Coincidentally, DMI was first proposed in the canted antiferromagnetic fluoride, NiF₂,¹⁶ and not the commonly considered noncentrosymmetric crystals such as the B20 compounds of MnSi¹⁷ and FeGe¹⁸ that 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 NiF₂ and NaNiF₃.

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 Figs. 1(a)–1(c). The distortion from an ideal perovskite structure, such as that of SrTiO₃ (STO), shown in Figs. 1(e) and 1(f), comes from a shift of the Na atoms in the a–b plane [Fig. 1(b)] and a tilting of the NiF₆ octahedra [Fig. 1(c)]. The tilt angle has been measured in the bulk material as 11° using x-ray diffraction (XRD) 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 

The NNF thin films were grown on prepolished 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 TiO₂-terminated substrate surface was used that consisted of two thermal annealing steps and a deionized water treatment.²³ The substrates were heated to 250 °C and annealed for 1 h to remove surface contaminants before growing at the same temperature. The correct stoichiometry was achieved by codepositing NaF and NiF₂ using effusion cells in an ultrahigh vacuum chamber with base pressure p = 3 × 10⁻⁹ Torr and typical growth rates of 0.009 nm/s.

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 = 0.154 06 nm). We also carried out in situ analysis of the substrate and film surfaces using a 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 N₂ 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.

The out-of-plane (OOP) XRD is shown in Fig. 2(a) and confirms that all the films are single phase and have the expected Pnma structure. Only peaks related to the NNF and STO substrate were observed as labeled in the figure. An enlarged plot in Fig. 2(b) shows the clear shift to the right with decreasing thickness of the NNF (202)/(040) peak. In the pseudocubic (pc) unit cell of NNF, the corresponding lattice parameters are $apc=cpc=a02+c02/2$ = 3.849 Å and b_pc = b₀/2 = 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. 1(d), red unit cell]. By comparison, the strain for [101]-oriented growth, with the long b axis in the plane [Fig. 1(d), 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 NaMnF₃ 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. 2(e) along with the extended phi range showing the STO (013) and NNF (222) diffraction peaks observed every 90°, indicating that the sample is twinned in the plane. Plotted in Fig. 2(f) is the NNF (222) peak intensity in a Φ scan with χ = 63.42° assuming the [010] growth direction and χ = 26.66°, assuming the [101] growth direction. We determined the predominant growth direction to be [101] with orthogonal twinning in-plane and a much smaller contribution from [010] domains (between 0% and 20% for all samples).

The peak positions were fitted to a Gaussian line shape to extract the exact 2θ position in order to calculate the out-of-plane 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 (⁠$λCuK−α$ = 0.154 06 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. 2(c) 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 NNF²⁵ to calculate the out-of-plane strain, $ε$_⊥,

where d_hkl is the measured interplanar spacing and $dhklbulk$ 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. 2(d). 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 Fig. S1 of the supplementary material.

In situ RHEED analysis revealed a high level of in-plane order at the surface as shown by the diffraction patterns in Figs. 3(a)–3(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, as shown in Figs. 3(k)–3(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. 4(a), where the data points were fitted using the GenX software.²⁶ All samples show Kiessig oscillations that extend to high angles, 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 [Figs. 3(k)–3(o)] and are shown in Fig. 4(b). 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, and 30 nm films are fairly free of defects, as seen in Figs. 3(l)–3(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 shown and discussed in more detail in Fig. S2 of the supplementary material.

The magnetization was measured via zero-field-cooled and field-cooled (ZFC-FC) measurements as shown for the 20 nm film in Fig. 5(a). 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 then continued while 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 while warming back to room temperature, resulting in the thermoremanent magnetization (TRM) plotted in Fig. 5(b). The sharp increase in the susceptibility in the ZFC data at T_N, shown more clearly in the inset of Fig. 5(a), is a signature of canted antiferromagnetism (i.e., weak ferromagnetism).¹⁵ Similar behavior has also been observed in NaMnF₃ thin films.¹¹ The weak ferromagnetic moment is due to the canting of the Ni spins away from the antiferromagnetic axis [Figs. 5(c) and 5(d)] and is shown as an increase in the magnetic signal as the temperature is reduced in the FC magnetization 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 magnetization in-plane, whereas for the [010]-growth direction, it would be out-of-plane, as illustrated in Figs. 5(c) and 5(d). The TRM measurements for different in-plane angles and the out-of-plane orientation of the field are shown in Fig. 5(b). 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 magnetization for the 0, 45, and 90° in-plane orientations [Fig. 5(b)], which is in good agreement with the in-plane x-ray ϕ scans and the orthogonal twinning of the [101]-oriented crystal found. In the magnetic measurement, the ratio of the in-plane to out-of-plane 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 in-plane component during the out-of-plane measurement.

The spontaneous magnetic moment of the NNF corresponds to a tiny fraction of the Ni²⁺ ion moment (assuming 2.0 μ_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 in-plane, 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% Ni²⁺ 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 the antisymmetric exchange, then it has been proposed that the canting angle has no temperature dependence, whereas the single ion anisotropy model does predict a temperature dependence.¹³ 

All samples showed a qualitatively similar behavior except the 5 nm film as shown in Fig. 6(a). 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 magnetization 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. 6(b). We observe a thickness dependence, as shown in Fig. 6(c), with a change of ΔT_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. 6(c) that 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, as shown in Fig. 2(c). The ordering temperature of the films approaches the bulk value as the strain is reduced, as shown in Fig. 6(d).

There are two mechanisms whereby tensile strain can be accommodated in perovskite materials, and both are shown in the lower part of Fig. 6(e). The magnitude of the tilt can change through rigid rotations of the NiF₆ octahedra where the intraoctahedral Ni–F distances remain unchanged, but there is a change in the interoctahedral bond angle, as 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 accommodated in a similar way. There is a octahedral rotation about an axis parallel to the substrate plane (labeled β in the figure) and a corresponding decrease in α, away from the ideal antiferromagnetic 180° Ni–F–Ni bond angle.

In summary, highly ordered thin films of NaNiF₃ 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 films in thicknesses up to 30 nm, after which the structure relaxed toward the bulk NNF, as did the magnetic ordering temperature, T_N. The canted antiferromagnetic order was confirmed via magnetometry and the measured value of magnetization 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. The potential for magnetoelectric coupling in strained fluoroperovskites is possible due to the predicted behavior of NaMnF₃, which may manifest in electric field dependent exchange bias phenomena³² and the feasibility of ultrafast and low power spintronic devices based on antiferromagnetic insulators.³³ 

See the supplementary material for rocking curve XRD analysis of all films (Fig. S1) and an extended AFM survey of the 20 nm thick NNF film (Fig. S2).

Funding was provided by the University of California Multicampus Research Programs and Initiatives (Grant No. MRP-17-454963). Some support at the initial stages of the project was provided by the National Science Foundation (Grant No. 1434897).