Engineering the magnetic order in epitaxially strained Sr1−xBaxMnO3 perovskite thin films

Chemical doping and epitaxy can be used to tailor the magnetoelectric properties of multiferroic thin films, such as SrMnO3. Here, we study the dependence of the magnetic order temperatures of Sr1−xBaxMnO3 thin films on epitaxial strain and Ba content. Combining low-energy muon spin spectroscopy and scanning transmission electron microscopy, the broadness of the magnetic transition is attributed to the presence of a Mn-O-Mn angle gradient along the out-of-plane direction. We also demonstrate that the unit cell volume is the key parameter to determine the Neel temperature in Sr1−xBaxMnO3 thin films showing G-type antiferromagnetic order. The occurrence of a simultaneously ferroelectric and ferromagnetic ground state at high strain levels is suggested for the Sr0.8Ba0.2MnO3 thin film deposited on TbScO3.

Research on multiferroics (materials showing two or more ferroic orders) has been mainly focused on the design and study of magnetoelectric materials with an effective coupling between these orders that would allow commuting the conjugate fields and so controlling the magnetic response by applying an electric field and vice versa. A strong magnetoelectric coupling at room temperature is a basic requirement for introducing these materials into novel devices with potential applications in the field of spintronics, data storage, and sensors. [1][2][3] Sr 1−x BaxMnO 3 (SBMO) perovskites stand out as promising multiferroic materials due to the strong coupling between polar instability, spin order, and lattice expected in these compounds. The expansion of the lattice by either epitaxial strain engineering or chemical pressure (replacing Sr with Ba) favors noncentrosymmetric distortions. [4][5][6][7][8][9] This was experimentally confirmed by turning bulk centrosymmetric SrMnO 3 (SMO) into polar in strained (strain ≥ 1.7%) epitaxial thin films, 10,11 and by inducing ferroelectricity in bulk SBMO for x > 0. 4. 12,13 The coupling between lattice and spin enables a moderate epitaxial strain to modify the magnetic interactions and eventually the magnetic ground states in SMO. 6,8,9,11,14 Indeed, a crossover from G-type to C-type antiferromagnetic order was proposed by different groups at a critical tensile strain of 1.6% 6 or ≈3%. 9 The magnetic order strongly couples with the polar instability since both are driven by the Mn cation, [5][6][7]12,13,15 thus giving rise to a strong magnetoelectric coupling. 16,17 According to the observations previously reported, epitaxial films of SBMO perovskite are ideal candidates for tailoring the magnetoelectric coupling by modifying the magnetic and electrical ARTICLE scitation.org/journal/apm properties through the accurate control of Ba content and epitaxial strain. The perovskite phase in epitaxial SBMO films was synthesized for the first time by Langenberg et al. with Ba contents in the range of 0.2 ≤ x ≤ 0.5 on different perovskite substrates. 18 The combination of epitaxial strain and chemical pressure yields severe structural changes in SBMO in which much larger tetragonal distortions can be imposed than in bulk specimens. 18 Magnetoelectric coupling in bulk SBMO was indirectly observed by Sakai et al. by measuring the decrease in the tetragonality on the onset of the paramagnetic (PM) to antiferromagnetic (AF) transition. 12 For strained SMO thin films, a decrease in the emitted second harmonic signal, proportional to the square of the electric polarization, was also observed at the PM-AF transition. 10 Recently, our group has demonstrated the existence of a strong spin-phonon coupling at the Néel temperature (TN) in epitaxial Sr 0.6 Ba 0.4 MnO 3 thin films. 19 Moreover, we have found that the dielectric constant drops by up to 50% when the AF order emerges and, more important, this coupling between magnetism and dielectric properties can be tuned from ≈18% to ≈50% by appropriately selecting both Ba-content and epitaxial strain. 20 To date, most studies on the dependence of the magnetic order temperature (T order ) with the Ba content of SBMO have been done in bulk samples, 12,13,21 obtaining a decrease in TN with increasing x. Regarding the impact of strain, Maurel et al. reported the decrease in TN with the epitaxial strain in SMO thin films. 14 Recent ab initio calculations predicted that Sr 0.5 Ba 0.5 MnO 3 becomes ferromagnetic above a critical value of tensile epitaxial strain 8 and simultaneously ferromagnetic and ferroelectric at large enough compressive strain. 22 In this letter, we report on a comprehensive investigation of the magnetic order of SBMO perovskite epitaxial thin films by combining the Ba content and epitaxial strain. For this purpose, we have selected films with Ba compositions x = 0, 0.2, 0.4, and 0.5 grown on two different substrates: (LaAlO 3 ) 0.3 -(Sr 2 AlTaO 6 ) 0.7 (LSAT) and TbScO 3 (TSO). For a given substrate, Ba doping induces changes in both the cell volume and strain, which allows studying the dependence of T order on both parameters.
Films of single-phase SBMO perovskite were grown by pulsed laser deposition (PLD) onto (001)-oriented single-crystal substrates of LSAT and TSO, which have pseudocubic lattice parameters a ≈ 0.387 nm and a ≈ 0.396 nm, respectively. The growth, perovskite phase stability, and structure were reported elsewhere. 18 The thickness of the films was limited to 10 nm, assuring that all of them were fully strained. The structure, crystal quality, and epitaxial coherence of the films were evaluated using x-ray diffraction (XRD) and scanning transmission electron microscopy (HAADF-STEM).
Symmetric θ/2θ XRD scans measured with monochromatic Cu-Kα 1 radiation around the pseudocubic 002 reflection allowed us to obtain the out-of-plane (c) lattice parameter of the films; see Figs. 1(a) and 1(b). The resulting structural parameters are listed in Table I. Figures 1(c) and 1(d) display the dependence of the cell volume (V) and the tetragonality (c/a) on the Ba-content (x) for the films grown on LSAT and TSO, respectively. For the films grown on LSAT, a change in the tetragonality from c/a < 1 (tensile strain, for x = 0 and x = 0.2) to c/a > 1 (compressive strain, for x = 0.4) is induced by increasing the Ba content. For the films deposited on TSO, c/a increases by increasing the Ba doping but remains always below 1 (tensile strain). As expected, the progressive replacement of Sr 2+ cations (with ionic radius r = 1.44 Å in octahedral coordination 23 ) with the larger Ba 2+ cations (r = 1.60 Å) produces a gradual expansion of the unit cell volume for the films deposited on both substrates.

ARTICLE
scitation.org/journal/apm  (4) Low-energy muon spin spectroscopy (LE-µSR) 24,25 was used to determine T order in all the previous films. This technique was successfully applied before in strained multiferroic SMO thin films. 14 T order was determined from temperature scans in a weak transverse magnetic field (wTF) of Bext = 10 mT applied perpendicular to the initial muon spin polarization and to the film surface. The data presented here were obtained with a muon implantation energy Eimp = 1 keV. This energy yields a mean implantation depth of the muon of about 5 nm and approximately 80% of the muons stopped in the SBMO films. In a wTF, the time evolution of the muon spin polarization is described by the relaxation function 26 where f T TF and fL TF reflect the fraction of the muons having their spin initially transverse and longitudinal to the local magnetic field (B l ) direction, respectively, γµ is the gyromagnetic ratio of the muon, λ T and λL are the relaxation rates, and is a phase offset. The fitting of the relaxation function Gx(t) was performed using the musrfit program. 27 Above T order , f T TF is the full asymmetry since only Bext is present inside the sample. Below T order , the superposition of the small external Bext and the internal AF magnetic fields leads to a strong dephasing of the signal, so f T TF decreases to a level corresponding to the nonmagnetic fraction plus the background level.
A decrease in f T TF demonstrates static magnetism (see Ref. 14 for details).
Figures 2(a) and 2(b) display the transverse fraction f T TF as a function of temperature in the 10 nm-thick SBMO films on LSAT and TSO, respectively. The data are normalized to the values in the paramagnetic regime at 300 K. The magnetic transition temperature is evidenced by the decrease in the transverse fraction f T TF (T)/f T TF (300 K) at the ordering temperature. T order is obtained by fitting the derivative curve of the data with a Gaussian curve and taking its center as T order . 14 The corresponding values for T order are listed in Table I. Interestingly, as clearly observed in Fig. 2, the magnetic transition is broader in the films with the largest strain levels (x = 0 on LSAT, and x = 0.2 on TSO), whereas it is sharper for the films with lower strain (x = 0.4 on LSAT; x = 0.5 on TSO). This broad decay has been previously observed in SMO films, and it was attributed to the existence of a distribution of ordering temperatures. 14 In order to ascertain whether there is a similar effect in the films studied here, we have used aberrationcorrected scanning transmission electron microscopy (STEM). For these experiments, we have selected two samples grown on LSAT:  Figures 3(a) and 3(b) display the HAADF images (left panels) and geometrical phase analysis (GPA) relative deformation maps (right panels) of the SMO/LSAT and SB20MO/LSAT films viewed along the [110] zone axis, respectively. In both cases, the HAADF images show their very high crystal quality and the absence of structural defects within the film and at the interface with the substrate. The GPA in-plane relative deformation maps (εxx = a film − a subs /a subs , where a film and a subs are the film and substrate in-plane lattice parameters, respectively) confirm that both films are fully strained, with no color variation between the substrate (reference lattice) and the film. The out-of-plane deformation maps, defined by the out-ofplane film (c film ) and substrate (c subs ) lattice parameters (εzz = c film − c subs /c subs ), unveil different strain states in both films: The SMO/LSAT film presents a compressive strain gradient (from εzz ≈ −0.5 to εzz ≈ −2%), i. e., a gradual decrease in the c-parameter away from the interface (from c film = 0.3849 nm to c film = 0.3807 nm), whereas the SB20MO/LSAT film has a uniform deformation (εzz ≈ −1.6%). It is worth noting that the drop of the deformation values in the last unit cells near the surface in the films is due to damage caused by the sample preparation. Guzmán et al. demonstrated that this strain gradient is concomitant with a graded distribution of oxygen vacancies and additional out-of-plane polar distortions, which helps to accommodate the epitaxial strain at very low thickness. The additional off-centering of Mn cations, along the [001] axis, causes that the Mn-O-Mn bond-angle (α) departs from the 180 ○ ranging from α ≈ 178 ○ ± 3 ○ close to the film-substrate interface to α ≈ 172 ○ ± 3 ○ at the film surface. 15 This gradient in α causes a variation of the superexchange paths that can yield local changes in TN, which in turn gives rise to the broad magnetic transition observed in this sample. On the contrary, the SB20MO/LSAT film displays a uniform out-of-plane strain, and thus a constant Mn-O-Mn bond angle (α = 180 ○ ) is observed within the experimental error. 15 This evidence explains the uniform magnetic transition temperature (i.e., the sharp transition) measured by LE-µSR in this sample.
The values of T order in the SBMO films determined from wTF LE-µSR measurements as a function of the Ba content and the epitaxial strain induced by the LSAT and TSO substrates are shown in Figs. 4(a) and 4(b), respectively. Although a systematic theoretical study of the magnetic ordering as a function of the Ba content and strain is lacking, several first-principles calculations on the strain dependence of the magnetic ground state of SMO and Sr 0.5 Ba 0.5 MnO 3 6,8,9,22 have been performed. According to those studies, the predicted magnetic ground state at a low strain level (below 2% 6 or 3% 9 in SMO and below 3.5% in Sr 0.5 Ba 0.5 MnO 3 8 ) is G-type AF for both compounds. The predictions for the SMO system were confirmed in our previous experimental work. 14 The SBMO films grown on LSAT are below that critical strain level (<3.5%), and so G-type AF order is expected. This assumption is confirmed by the experimental results: a monotonous decrease in TN on increasing Ba doping is observed in the films grown on LSAT [ Fig. 4(a)], which is a similar behavior to the one obtained in bulk samples 12,13,21 showing G-type AF magnetic order. The SBMO films deposited on TSO [ Fig. 4(b)] present a higher strain level than those on LSAT for the same Ba content. It is worth noting that the calculations mentioned before predict changes in the magnetic ground state depending on the tensile strain level. Thus, different AF orders for SMO (G-type, C-type, and A-type) have been predicted by increasing tensile strain. 6,9 Above a critical value of tensile strain (3.2% 6 or 4% 9 ), a ferromagnetic (F) ground state is expected. This transition between AF (G-type) and F magnetic order driven by the strain was also predicted in Sr 0.5 Ba 0.5 MnO 3 and SMO. 8 The critical tensile strain needed to induce such an AF-F transition depends on the method used to perform the calculations: 5.2% and 3.5% for the sPBEsol and PBE+U+J methods for Sr 0.5 Ba 0.5 MnO 3 , respectively, and 6.8%, 4.8%, and 3.2% for the sPBEsol, PBE+U+J, and sPBE+Ueff methods for SMO, respectively. Note that the critical strain values are lower as Ba content increases. 8 Moreover, Lee and Rabe showed that for all the AF orders, the value of TN either decreases or remains constant by increasing the tensile strain, whereas the value of the ferromagnetic Curie temperature strongly increases by increasing the strain. 6 These predictions could explain the strong rise observed in T order by increasing the strain (decreasing Ba content) in the SBMO films deposited on TSO substrates: from 118(3) K and 124(4) K for strain values of 1.82% and 0.94% (x = 0.4 and 0.5, respectively) to 187(5) K for 3.39% (x = 0.2). This behavior suggests a transition between an AF (G-type) order (low strain, high Ba content) to an F order (high strain, low Ba content). The experimental value of the tensile strain needed to induce such possible AF-F transition (≈3.3%) is in good agreement with the theoretical values determined by Lee and Rabe 6 and Chen and Millis 8 and a slightly lower than those predicted by Edström and Ederer. 9 Moreover, the theoretical models predict the coexistence of a ferroelectric/ferromagnetic ground state at high strain levels, increasing the interest of this compound. Unfortunately, the direct proof of this hypothesis using conventional magnetometric techniques was hindered by the huge paramagnetic signal arising from the substrate.
To unify the dependence of TN on strain and Ba content in these films, we propose a model based on previous results on bulk materials. 21 According to the authors, TN decreases on increasing the ionic radius of the A-site cation, which induces a change in the unit cell volume. It is noteworthy that in the present work, the unit cell volume is being modified by both Ba doping and epitaxial strain. The values of T order determined from wTF-µSR measurements are plotted in Fig. 4(c) as a function of the room temperature unit-cell volume for the SBMO films deposited on TSO and LSAT substrates with Ba content ranging from x = 0 to x = 0.5. The values of TN obtained by Maurel et al. for the x = 0 films grown on SrTiO 3 and LaAlO 3 are also displayed. 14 The figure shows a monotonic decrease in TN as a function of the unit cell volume for those films with Gtype AF order, regardless of the Ba content or the substrate used. Such behavior evidences a direct link between the two parameters in these AF films. On the other hand, the samples which do not follow such trend are the SMO films grown on SrTiO 3 (for which a C-type AF order was proposed 14 ) and the x = 0.2 film on TSO. As mentioned above, our experimental results suggest that a plausible F order may occur in the SB20MO film deposited on TSO although an AF-type order different from G cannot be completely ruled out. All things considered, the unit cell volume, which determines the Mn-O-Mn distance, is the relevant parameter controlling TN in SBMO thin films with G-type AF order. Taking into account that the unit cell volume can be modified by either epitaxial strain or the Ba content, the results shown in Fig. 4(c) indicate that both chemical strain and lattice strain are equivalent/exchangeable when determining the magnetic properties of the films with G-type AF order.
First-principle calculations have established a complex interplay between lattice strain, oxygen stoichiometry, and functional properties in AMnO 3 manganites, A being an alkaline-earth atom. 28 It is thus essential to rule out the possible influence of oxygen ARTICLE scitation.org/journal/apm vacancies or other extrinsic effects on the strain in our films. As explained before, an indirect analysis of the oxygen content carried out in SMO/LSAT films 15 revealed a gradient in the vacancies distribution, which originates a volume inhomogeneity of about ±0.8% with respect to the average value. This corresponds to a volume variation of ±0.4 Å 3 , which is approximately accounted for by the error bar in the determination of T N (see Table I). Therefore, the impact of cell volume change induced by moderate amount of oxygen vacancies on the Néel temperature is within the experimental error.
Regarding the Ba doped films, X-ray absorption spectroscopy (XAS) measured in the SBMO sample that is most prone to have oxygen vacancies due to its large tensile strain and the low oxygen pressure during growth (i.e., 50% Ba-content film grown on the GdScO 3 substrate) 18 indicated the residual occurrence of Mn 3+ within the experimental error. Thus, we can conclude that the majority presence of Mn 4+ is a general feature in all our SBMO films. Also, the distribution of the polar domains should be considered when analyzing the effect of strain on T N in these films. A thorough study of their size and distribution was done in a 20-nm thick SMO/LSAT film. A combination of second harmonic generation (SHG) experiments and electrostatic force microscopy 10 showed the presence of micrometric-size polar domains, elongated along the cubic directions and markedly nonperiodical, which explains why we could not detect them by XRD. The polar axis lies in the film plane, equally probable along the ⟨110⟩ directions, as is also expected for the rest of the films analyzed in this work. 29 This was indeed confirmed by ABF-STEM direct imaging of cross sections of a Sr 0.7 Ba 0.3 MnO 3 film grown on TSO. 20 In spite of these observations, the epitaxial growth of the SBMO films on LSAT and TSO substrates is always cube-on-cube and is governed by the A cations of the ABO 3 perovskite structure (Sr/Ba in the films and La/Sr or Tb in the substrates), while the polar behavior arises from the shifts of Mn and O relative to that frame. 15,20 In conclusion, the existence of polar domains and domain walls has no influence in the determination of the epitaxial strain.
In summary, we have performed a systematic study of the dependence of the magnetic order temperatures in epitaxial SBMO thin films on the epitaxial strain and Ba content. From the experimental results, two main conclusions can be obtained: First, we reveal that the broadness of the magnetic transition occurring in the highly strained films is associated with a distribution of magnetic order temperatures within the film. This is due to the mechanism followed by these compounds to accommodate large epitaxial strain values, which yields a gradient in the out-ofplane lattice parameter along thickness and, therefore, a gradual change in the Mn-O-Mn bond angles. Second, we have found a clear correlation between TN and the unit cell volume in the G-type AF films. This evidences that the Mn-O-Mn ionic distance, the gradual increase of which weakens the magnetic interaction, is the relevant parameter when it comes to determining the magnetic order temperature in SBMO films. Finally, from the comparison of the experimental results with different theoretical calculations performed until now, we suggest that a possible ferromagnetic order could emerge in the highly strained SB20MO film on TSO which could coexist with a ferroelectric order, making this material promising for both basic studies and technological applications. This work has been supported by the Spanish Ministry of Science through Project Nos. MAT2017-82970-C2-1-R and MAT2017-82970-C2-2-R and by the Aragon Regional Government through Project Nos. E13_17R and E28_17R (Construyendo Europa desde Aragón). The LE-µSR measurements have been performed at the Swiss Muon Source SµS at the Paul Scherrer Institut, Villigen, Switzerland. The diffraction and microscopy studies have been conducted in the Laboratorio de Microscopías Avanzadas (LMA) at the Instituto de Nanociencia de Aragón (INA), Universidad de Zaragoza. The authors acknowledge the LMA-INA for offering access to their instruments and expertise.