Spin-phonon interaction increased by compressive strain in antiferromagnetic MnO thin films

Out-of plane lattice constant, strain, thickness and sample homogeneity of all thin films were determined using XRD at 300 K. In-plane strain and lattice parameters of two MnO(1 1 0) films with thicknesses 26.5  ±  0.3 nm and 18  ±  1 nm were also measured.

Fluence of the laser affected the XRD patterns of films (figure 1(a)). As fluence was increased to 2 J cm⁻², a second phase (Mn₃O₄) emerged, possibly because the increased energy effected the ionization of Mn atoms. Pure MnO phase was obtained by reducing fluence below1.5 J cm⁻². As film thickness was decreased, the 2θ angle of the MnO 0 0 2 peak decreased (figure 1(b)); this change implies an out-of plane expansion of the lattice parameters of MnO with reducing film thickness. This expansion might be a result of increasing in-plane compressive strain due the lattice mismatch between MnO and MgO. One can also imagine that the observed lattice expansion is caused by point defects (like oxygen vacancies), but in this theoretical case all lattice parameters should increase, which was not confirmed, because we see in-plane compressive strain induced by a mismatch between MnO and MgO. The compressive strain is confirmed in the next paragraph by observation of phonon stiffening with the reduced film thickness. Theoretical lattice mismatch between film and substrate is relatively high (about 5%), therefore the strain rapidly decreases with increasing film thickness, because the critical thickness for total relaxation decreases as theoretical lattice mismatch increases [30]. Growth in vacuum also causes the relaxation of film as there is no decelerating force to reduce the energy of ablated species which, in turn, provides driving force for the surface diffusion.

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In 26.5 nm-thick MnO/MgO (1 1 0), the two RSMs around the peak positions in the 2 2 4 diffraction (figure 2(a)) had very different intensities of substrate and layer peaks, so the RSMs were measured independently, then combined into one image that has a common scale. The double peak at 2 2 4 coordinates of MgO substrate is due to the CuKα₁₂ doublet of the incident radiation. After a processing of the layer peak, the coordinates of the focal point L_lay and H_lay were obtained and the corresponding values of d_1 1 0 and d_0 0 1 could be derived. The value of d_1 1 0 can be compared with its value that was obtained by direct measurement using a symmetrical 2θ/θ scan. Figures 2(b) and (c)) show diffractions 2 2 0, 2 0 0 and 0 2 0. These scans lead directly to the d_1 1 0, d_1 0 0 and d_0 1 0 lattice parameters. MnO (1 1 0) film thickness (26.5 nm) was determined from x-ray reflectivity shown in figure 2(d)). The same procedure was used for second MnO (1 1 0) film with thickness 18 nm.

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The ω rocking scan around MnO (0 0 2) peak (inset of figure 1(b)) yields additional information on the structural features of the grown films. The shapes of the curves changed as film thickness d changed. Films that had d  =  17 and 10 nm showed a combination of two components, a broad component and a narrower component that has width of less than 0.15°. Films that had d  =  28 and 34 nm showed a simple broad peak. The two components imply the existence of two different structural correlation lengths throughout the films [31]. The sharper peak reveals an atomically long range-ordered area. The emergence of the broad component shows the formation of sub-grains (mosaic structure); this process breaks the long-range atomic arrangement. However, as d decreases, the width of broad peak increases and the sharp peak appeares and intensifies. These changes indicate the spread of the long-range ordered phase and reduction in mosaic sizes. Threading dislocations become increasingly common as d increases [31]; they can disrupt a long-range ordered area by forming subgrain boundaries (forming mosaic structure), so this process may cause the development of the broad peak. The increase in strain relaxation as d increases might be a result of an emergence of dislocations at the interface between the film and the substrate as well. All lattice parameters in two MnO (1 1 0) films were determined from the RSM: 26.5 nm-thick film had c  =  4.409  ±  0.003 Å and a  =  b  =  4.455  ±  0.001 nm; 18-nm-thick MnO (1 1 0) film had c  =  4.390  ±  0.005 Å and a  =  b  =  4.460  ±  0.002 Å. Bulk MnO has a  =  4.445 Å [12], so in both (1 1 0) films the c parameter is smaller than in the MnO bulk and a, b parameters are slightly larger than in the bulk MnO. It means that the strain is anisotropic in the (1 1 0) plane of the film. Shorter c axis lies in the (1 1 0) plane and it is under compressive strain. a and b axes are perpendicular to c axis, but they are oriented obliquely (approx. 45°) to the film plane. For that reason the a and b lattice parameters are larger.

To determine how the strain affects lattice dynamics, IR spectra of the films with various thicknesses grown on MgO substrates with (0 0 1) and (1 1 0) orientations were measured. Selected examples of the room-temperature reflectance spectra are shown in figure 3. Besides strong phonon response of MgO substrate (frequencies of MgO excitations are marked by arrow), reflection peaks from MnO phonons are seen near 285 cm⁻¹. Phonon frequencies in the films correspond to reflectance maxima [32], whereas in bulk substrate, transverse optical phonon frequency corresponds to the low-frequency edge of the reflection band [1, 19]. Multiphonon excitation frequency in the MgO substrate corresponds to the feature near 650 cm⁻¹ (arrow, figure 3(a)). Near-normal IR reflectivity gives only in-plane response, so we cannot see phonons polarized perpendicularly to the film plane, i.e. in the [0 0 1] direction. As a result of the epitaxial strain in the film induced by the lattice mismatch between the MgO substrate and MnO film, this phonon can have different frequency than phonons polarized in the (0 0 1) plane. Intensity of the MnO IR reflection peak increased as the thickness of the films was increased. According to our XRD measurement, strain is relaxed in 34 nm-thick MnO (0 0 1) film, because its out-off plane lattice constant is the same as in the bulk MnO. Nevertheless, the strain is present in thinner films and increases as thickness is reduced.

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IR spectra of the MgO (1 1 0) substrate (figure 3(b)) are the same as in the (0 0 1) plane (figure 3(a)) because MgO is cubic. Nevertheless, the spectra of MnO (1 1 0) thin films grown on MgO (1 1 0) (figure 3(b)) are completely different than of MnO (0 0 1) films (figure 2(a)), because the (1 1 0) oriented substrate induces anisotropic in-plane strain, and the MnO phonon has already split at RT. The splitting decreases as the thickness of the MnO (1 1 0) films increases (figure 3(b)), because the strain decreases as film thickness increases but remains also in the 65 nm thick film, where 10 cm⁻¹ splitting was observed (the thinnest 18 nm film exhibits splitting 42 cm⁻¹ at RT—see insets of figure 3(b)). Note that according to our XRD measurements, the out-of-plane strain in (0 0 1) oriented MnO film relaxed already in 34 nm thick film, but its RT phonon frequency (282 cm⁻¹) is 12 cm⁻¹ higher than that of the MnO bulk sample (270 cm⁻¹) [2] giving evidence in some small in-plane compressive strain which enhances the phonon frequency in the film.

The intensities of the reflection peaks are increased in polarized spectra of MnO (1 1 0) (figure 3(b), inset), because these modes are selectively excited, whereas in the unpolarized spectrum, both modes are simultaneously excited. The phonon polarized along [0 0 1] has higher frequency than the mode polarized perpendicularly to [0 0 1], because the c lattice parameter is smaller than a and b lattice parameters (see XRD results). It is well known that phonon frequencies generally increase with lattice compression (spring constant between atoms increases), while they decrease with lattice expansion [28, 33].

IR reflectance spectra of the film are highly sensitive to crystal structure and phase impurities in the film. One film had a completely different IR spectrum (figure 3(c)) than other films. Two reflection minima appear in the reststrahlen band of MgO near 470 and 598 cm⁻¹, and correspond to phonons in Mn₃O₄ [34]. The film probably contains more Mn₃O₄ phase than MnO, so the MnO reflection band near 280 cm⁻¹ is weak and smeared due to its high damping (caused by film inhomogenity) and low intensity. Mn₃O₄ phase impurity was also confirmed by independent XRD measurement (figure 1(a)).

Temperature dependence of IR reflectance spectra of selected samples are shown in figure 4 and the temperature evolution of MnO phonon frequencies is plotted in figure 5. In MnO/MgO (0 0 1) films, a doubly-degenerate E_u phonon splits into a doublet below T_N. In the paramagnetic phase, MnO phonon frequency increases with the biaxial compressive strain in the film due to increase in spring constants between atoms. As figure 5(a) shows, the frequency of TO phonon mode in MnO (0 0 1) films with different thickness is above 282 cm⁻¹ at RT which is at least 12 cm⁻¹ higher than that of the bulk value. This frequency increases as film thickness decreases which demonstrates the effect of compressive strain on the frequency of TO phonon mode. It is worth mentioning that the phonons are doubly degenerate at RT in all three selected (0 0 1) oriented films (i.e. they have the same frequencies along a and b crystallographic directions). This shows that in-plane strain is homogeneous in paramagnetic phase of MnO (0 0 1) films. If the strain would be anisotropic, the phonon should split.

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The phonon splits in AFM phase below T_N indicating reduction of crystal symmetry. The highest phonon splitting (~30 cm⁻¹) was observed in the thinnest film (thickness  =  17 nm), because its compressive strain was highest; this splitting was 20% higher than that of the bulk MnO in which the splitting is 25 cm⁻¹ [1, 3].

Luo et al [11] theoretically predicted and Kant et al [3] experimentally confirmed a linear relation between exchange-driven phonon splitting $\Delta \omega$ and non-dominant exchange interaction J₁. They found $\hbar \Delta \omega =\beta {{J}_{1}}{{S}^{2}}$. Since the phonon splitting is 20% larger in strained film, J₁ should be also 20% larger. This observation confirms theoretical calculations of Fischer et al [23], who predicted that J₁ should increase with reduced lattice constant. Interestingly, superexchange interaction J₂ or possible banding of the Mn–O–Mn bond angle has no influence on phonon splitting (see Kant et al [3]). Our observed 20% enhanced phonon splitting give evidence that biaxial compressive strain significantly strengthens the magnetic exchange interaction J₁.

The phonon behavior in MnO/MgO (1 1 0) is qualitatively different than in MnO (0 0 1). Due to anisotropic biaxial strain in the film, the phonon has already split in the paramagnetic phase at RT. The splitting is huge: 34 cm⁻¹ in 26.5 nm-thick film and 42 cm⁻¹ in 18 nm-thick film. The splitting increases as film thickness decreases because the reduction in thickness increases its strain-induced in-plane anisotropy. Since at high temperatures the lattice parameters usually reduce linearly on cooling, but at lower temperatures thermal contraction reduces and finally almost stops below ~50 K, reciprocal behavior of phonon frequencies is usually observed; phonons harden on cooling, but their frequencies ω_TO have tendency to saturation at low temperatures. This temperature dependence can be described by the formula [33]

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle {{\omega }_{{\rm TO}}}\left(T \right)={{\omega }_{0}}\left(1-\frac{c}{\exp \left(\frac{{{\theta }_{{\rm D}}}}{T} \right)-1} \right)\nonumber \end{align}$$

where ω₀ indicates the eigenfrequency at 0 K, c is a mode dependent scaling factor and θ_D marks the Debye temperature.

The expected temperature changes of phonon frequencies in MnO (1 1 0) are indicated by dashed lines in figure 5(b). Thermal contraction causes that the phonon polarized in [0 0 1] direction hardens slightly on cooling towards T_N, but exchange coupling occurs below T_N so the frequency increases greatly at lower temperatures. The phonons polarized perpendicularly to [0 0 1] split below T_N and the splitting again increases with increase in strain (and decrease in film thickness), to 14 cm⁻¹ in 18 nm-thick film. The splitting between two lowest frequency phonons is the same as in the bulk MnO although a and b lattice parameters are slightly larger in MnO(1 1 0) film than that of the bulk (section 3.1. XRD), and therefore one can expect that the exchange coupling could be reduced in ab plane as Fischer et al [23] predicted. Nevertheless, one has to admit that the accuracy of determination of the mode near 275 cm⁻¹ is limited (±2 cm⁻¹), due to its low intensity and high damping, so the determined phonon splitting of the two lowest-frequency phonons (figure 5(b)) has the same error bar. Total splitting between the highest-frequency and lowest-frequency phonons extends up to 55 cm⁻¹, which is 120% more than that of the bulk MnO.

Kant et al [3] discovered linear dependence between value of phonon splitting and non-dominant exchange coupling constant J₁ in various transition metal monoxides and Cr spinels. If we assume that compressive strain enhances exchange coupling in our films, because magnetic Mn ions will be mutually closer, and moreover, the size of phonon splitting gives information about the exchange coupling constant J₁, then we are able to estimate it from the linear plot published by Kant et al [3]. In figure 6 we show Kant's data together with our observed phonon splitting in 17 nm MnO (0 0 1) film under expectation of linear dependency of the phonon splitting on exchange coupling. In case of MnO film grown in (1 1 0) direction we have to admit that the phonon splitting was already observed in paramagnetic phase without influence of J₁. This anisotropic strain-induced splitting causes ambiguity to determine the pure effect of magnetic exchange interaction on phonon splitting. Therefore, the real value of J₁ in MnO (1 1 0) film is still unclear, but in MnO (0 0 1) film the phonon splitting is clearly 20% higher and therefore also J₁ should be 20% higher than that of the MnO bulk.

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Wan et al [24] predicted that the compressive strain should enhance J₁ and could even induce ferroelectricity in MnO film under compressive strain more than 4%. Note that our thinnest MnO (1 1 0) film exhibits compressive strain 1.4%, which is far below theoretical critical strain, which could induce the ferroelectricity in this material. We performed dielectric measurement (10 Hz–1 MHz) of the most strained 18 nm thin MnO (1 1 0) film with deposited interdigital electrodes (gaps 10 µm). Dielectric capacity taken down to 8 K did not reveal any dielectric anomaly characteristic for spin-order-induced (i.e. improper) ferroelectric phase transition. It is also worth noting that Wan et al [24] calculated J₁ in bulk MnO and obtained 1.4 meV, which is in qualitative agreement with Kant's value in [3] and in figure 6.

At RT, the two phonons observed in MnO (1 1 0) films can be explained by tetragonal symmetry (bulk MnO is cubic), which is in agreement with our XRD data. Three phonons observed at low temperatures give evidence for lower symmetry, but our IR spectra cannot be used to distinguish whether the AFM phase is orthorhombic, monoclinic or even trigonal; additional structural studies are required. Note that also low-temperature structure of MnO bulk is still unclear, older paper refined it as rhombohedral [12–15], but newer papers claim centrosymmetric C2/m or polar C2 monoclinic structures [16, 17]. Unfortunately, our IR data cannot reveal whether the AFM phase is polar or nonpolar. This determination requires further dielectric, Raman and second-harmonic studies, which are in progress.

Finally we can summarize that IR reflectance spectroscopy is a highly sensitive tool for study of strain, temperature and magnetic order influences on phonons in MnO thin films (thickness down to 17 nm) grown on MgO substrates. Investigation of phonons in ultrathin films is rather rare in literature [28], because most of substrates have rich phonon structure (e.g. scandates), conductivity (films with bottom electrodes or semiconducting substrates) or high and strongly temperature dependent reflectivity (e.g. SrTiO₃) which strongly reduce IR response of the thin films and do not allow accurate determination of phonon parameters in the ultrathin films. MgO substrate is very suitable for IR studies, because it is cubic, insulating with simply one optical phonon and therefore its IR reflectance spectra are highly sensitive on phonons in the ultra-thin films. In addition to exchange-driven phonon splitting in MnO below T_N, further phonon splitting was observed in the paramagnetic phase in anisotropically strained MnO (1 1 0) films grown on MgO (1 1 0). The phonon splitting in compressively strained MnO (0 0 1) film is 20% higher than that of the bulk MnO, so the nearest neighbor exchange-coupling constant J₁ should be also enhanced 20%. In anisotropic MnO (1 1 0) film the splitting is even 120% higher than that of the bulk, but since some splitting is present already in paramagnetic phase, we cannot clearly determine value of J₁ from the phonon splitting. Nevertheless, our observation supports a theoretical prediction [11] that phonon splitting is caused by the exchange coupling. Our most important observation is that epitaxial strain can strengthen exchange coupling at least in strained MnO (0 0 1) films. These films under compressive strain  >4% should be studied to test whether spin-order-induced ferroelectricity occurs, as predicted theoretically by Wan et al [24]. To prevent strain relaxation in such highly strained films, epitaxial superlattices of MnO with some other monoxide with smaller lattice constant should be prepared and studied.