Strain-driven noncollinear magnetic ordering in orthorhombic epitaxial YMnO3 thin films

YMnO3 thin films X. Marti, V. Skumryev, V. Laukhin, R. Bachelet, C. Ferrater, M. V. García-Cuenca, M. Varela, F. Sánchez, and J. Fontcuberta Institut de Ciència de Materials de Barcelona (ICMAB-CSIC), Campus UAB, 08193 Bellaterra, Spain Institució Català de Recerca i Estudis Avançats, Lluís Companys 23, 08010 Barcelona, Spain Dept. Física, Universitat Autònoma de Barcelona, Campus UAB, 08193 Bellaterra, Spain Dept. Física Aplicada i Òptica, Universitat de Barcelona, Martí i Franquès 1, 08028, Barcelona, Spain


I. INTRODUCTION
Multiferroic materials are being intensively investigated due to their potential application in spintronics. Particularly relevant is the recent discovery that pronounced dielectric anomalies or even ferroelectricity can be obtained, in the so-called improper ferroelectrics, subsequent to magnetic ordering ͑see for instance Ref. 1͒. In this case, either particular noncollinear magnetic structures ͑such as spiral order͒ or even collinear ordering can lead to ferroelectricity. The best known examples for this class of materials are probably the antiferromagnetic orthorhombic manganites ͑o-RMnO 3 ͒ where, depending on the Mn-O-Mn bond angle, different magnetic structures can be obtained ranging from collinear ͑E-type AFM͒ such as observed in TmMnO 3 ͑Ref. 2͒ or HoMnO 3 ͑Ref. 3͒ to sinusoidal or spiral as in YMnO 3 ͑Ref. 4͒ or TbMnO 3 ͑Ref. 5͒ respectively. Ferroelectricity has been observed in all of them. Apart from these, let's call them intrinsic ferroelectrics, some particular type of domain walls, as recently emphasized by Komskii, 1 can also be the source of electric polarization and, in antiferromagnets, lead to magnetic frustration and, eventually, to some ferromagnetic response. This novel approach may have profound implications as it may constitute a new way to obtain improper ferroelectric and, if domain walls in antiferromagnets were a source of incomplete magnetic compensation, ferromagnetism, and ferroelectricity would be intimately linked.
From these considerations it follows that epitaxial thin films of antiferromagnetic o-RMnO 3 oxides offer unique opportunities to tailor the magnetic structure eventually breaking antiferromagnetic ordering and lowering its symmetry or even engineering crystal domains and/or magnetic domain walls. Indeed, recent results in o-RMnO 3 thin films [6][7][8][9][10][11][12][13] brought the unexpected observation of spontaneous magnetization, in the following labeled as weak-ferromagnetism ͑w-FM͒, in what it was supposed to be antiferromagnetic compounds. However, the understanding and control of this w-FM has remained elusive: whereas earlier reports suggested strain-driven effects, [6][7][8][9] it has also been claimed that it could be originated from symmetry breaking at domain walls. 13 The observation of w-FM in these materials may point to the occurrence or modification of an eventual magnetoelectric coupling. However, the lack of a detailed understanding of the observed w-FM may have hampered its exploitation to induce magnetoelectric response.
Here we will show that by an appropriate use of epitaxial strain, the magnetic properties of o-YMnO 3 can be gradually tuned into a spin-canted away from the b-axis magnetic structure. In this manuscript we follow different strategies to allow fine tuning of structural parameters and structural strain: ͑i͒ film-thickness variation, ͑ii, iii͒ growth and annealing conditions and ͑iv͒ chemical composition ͑Co substitu-tion͒. As 3d 6 -Co 3+ ions have the same magnetic moment as 3d 4 -Mn 3+ cations but smaller ionic radius, partial substitution of Mn by Co is an additional fine-tuning tool for the shrinking of unit cell and of the magnetic interactions. It will be shown that the ͑ferro͒magnetic response, that is the occurrence of a finite net magnetic moment, does not correlate with the film roughness thus denying spin incomplete magnetic compensation at grain boundaries as a source of w-FM. Detailed data analysis, particularly the observed magnetic anisotropy, indicates that ferromagnetic response arises from strain-unbalanced antiferromagnetic structure. Therefore, it follows that epitaxial strain can be used to induce and tailor the ferromagnetic response in otherwise antiferromagnetic materials, thus opening a way to obtain magnetic structures susceptible of tunable magnetoelectric coupling. In fact, in a subset of the samples presented here, indications of magne-toelectric coupling have been already reported. 14 Our findings, which specifically refer to o-YMnO 3 , are not, however, restricted to this oxide as other oxide thin films of the same o-RMnO 3 family are expected to display a similar response.

II. EXPERIMENTAL
Thin films were deposited on ͓001͔ and ͓110͔-oriented SrTiO 3 ͑STO͒ substrates by pulsed laser deposition. A KrF excimer laser beam ͑repetition rate of 5 Hz͒ was focused on stoichiometric YMnO 3 ͑YMO͒ and YMn 0.95 Co 0.05 O 3 ͑YMCO͒ targets placed at a distance of 5 cm of the substrate. Samples were grown at 785°C and P O2 in the 0.1-0.3 mbar range. By changing the number of laser pulses, samples with different thickness ͑30-140 nm͒ were obtained. Details on YMO samples can be found elsewhere. 8,15 Film thickness ͑t͒ was determined by x-ray reflectivity. X-ray diffraction ͑XRD͒ measurements were carried out with a Philips' Material Research Diffractometer. Magnetic data were obtained using a superconducting quantum interference device by Quantum Design. Atomic force microscopy images were obtained with PicoSPM from Molecular Imaging. Figure 1͑a͒ shows the / 2 XRD scan for one illustrative YMCO sample, showing only ͑00l͒ peaks ͑Pbnm setting of YMO͒ with no traces of other phases and/or orientations. -scan ͓Fig. 1͑b͔͒ reveals that the film is epitaxial. The splitting observed in the zoom of -scan ͓Fig. 1͑c͔͒ indicates the presence of two in-plane crystal domains, 90 degrees inplane rotated, with the epitaxial relationships ͓100͔YMCO ʈ ͓110͔STO and ͓010͔YMCO ʈ ͓110͔STO. The same crystal domain structure was observed in all YMCO and YMO films. 15 We previously reported 8 that lattice parameters and cell volume of YMO films change progressively with oxygen pressure during growth or increasing thickness. Here we will show that lattice parameters of YMO can be changed also by Co-doping. The reciprocal space maps around the ͑208͒ and ͑028͒ reflection for two pairs of YMO and YMCO samples having roughly the same thicknesses ͑ϳ140 nm͒ but grown under distinct P O2 ͑0.3 and 0.1 mbar͒ are shown in Fig. 2 ͑panels a and b, respectively͒. Lines in Fig. 2 indicate the corresponding position of bulk ͑208͒ and ͑028͒ reflection of YMO. 16 We discuss first data corresponding to films prepared at the highest P O2 ͓Fig. 2͑a͔͒. Regarding the in-plane directions, it turns out that, in both compounds, the ͑208͒ reflections appear at the bulk position, thus indicating that the cell along a is fully relaxed. In contrast, when scanning along the in-plane direction, it appears that the ͑028͒ reflections are shifted toward higher Q values. It indicates that both YMO and YMCO films have smaller b parameters than bulk YMO; therefore their unit cells are compressively strained along b. Regarding the out-of-plane direction, data in Fig. 2͑a͒ indicate that the ͑208͒ and ͑028͒ reflections of both YMO and YMCO appear at smaller values than bulk, thus indicating an expansion of the c parameter. In summary, the epitaxial strain is anisotropic being tensile along ͓001͔, compressive along ͓010͔ and negligible along ͓100͔. By comparing data in Fig. 2 for YMCO and YMO films, it is observed that shorter b and larger c and are obtained by partial Co-substitution. As a result of the changes in the lattice parameters, the unit cell volume V c ͑YMCO͒ is smaller than that of V c ͑YMO͒. For instance, for samples in Fig. 2͑a͒, V c ͑YMCO͒ = 223.19 Å 3 and V c ͑YMO͒ = 224.37 Å 3 , both visibly smaller ͑compressed͒ than the YMO bulk value ͓226.47 Å 3 ͑Ref. 16͔. Inspection of data of YMO and YMCO films prepared at 0.1 mbar ͓Fig. 2͑b͔͒ indicate the very same trend although obviously the cell parameters are different. Therefore, varying film thickness, 8 growth conditions ͑P O2 ͒ and Co-substitution, the cell parameters and unit cell volume can be varied at whish.

A. Tuning the lattice parameters
Post-growth annealing of the thin films is an alternative method to modify the unit cell parameters. Annealings effects under air or Ar atmosphere were tested on a YMO film relatively thin ͑30 nm͒ grown at 0.1 mbar P O2 . A first anneal- ing step ͑Anneal 1͒ was performed on air during 12 h at 800°C; in a second annealing step ͑Anneal 2͒ the very same sample was annealed again for 2 h but in Ar atmosphere ͑0.1 mbar͒ at 700°C. The reciprocal space maps around the ͑208͒ and ͑028͒ YMO reflections were recorded after each annealing step and are shown in Fig. 3. The bulk positions for the displayed diffraction spots are signaled by vertical and horizontal lines. The vertical dashed line is a guide for the eye. Data show that the a-and b-cell-parameter do not change appreciably by air annealing ͑Anneal 1͒ and remain closely coincident with those of the as-grown YMO film ͑top panels in Fig. 3͒ and bulk YMO. In contrast, the c cell parameter slightly shortens and approaches the bulk value; in overall the unit cell is somewhat compressed ͑0.05%͒. Both oxygen uptake and plastic relaxation may contribute to the observed behavior. A later reducing ͑Ar atmosphere͒ annealing process ͑Anneal 2͒ of the same sample promotes an expansion of the b-axis whereas the others ͑a and c͒ remain virtually constant and thus some expansion of the unit cell ͑0.72%͒ occurred suggesting that desorption of oxygen may have occurred leading to an expansion of the unit cell volume. In short, film annealing under distinct atmospheres provides an additional tuning tool to modulate the cell parameters of YMO perovskite.

B. Magnetic properties versus lattice parameters
We now focus on the magnetic properties of the YMCO films. Detailed results on strained YMO films can be found elsewhere. 8 Field-cooled ͑FC͒ and zero-field cooled ͑ZFC͒ magnetization measurements have been performed in the 150 K to 5 K temperature range with 500 Oe magnetic field applied in-plane of the sample. In Fig. 4͑a͒ we include the FC data for selected samples ͑samples are labeled by the corresponding V c ; the corresponding thickness ͑t͒ and used P O2 values, indicated in the caption͒. The ZFC branches are shown, for sake of clarity, only for two samples. Thermal ZFC-FC hysteresis is well evident at low temperature revealing the occurrence of net magnetization below the antiferromagnetic ordering temperature signaled by a kink well visible at T N Ϸ 40 K. Data in Fig. 4͑a͒ clearly shows that the low-temperature FC magnetization, is much enhanced as V c shrinks. This behavior resembles the trend we reported for the pure YMO films 8 where a correlation of net ferromagnetic moment with the strain of the b parameter was found. To further determine if the distortion along the modulation direction of the antiferromagnetic structure ͑b-axis͒ is the only relevant parameter accounting for the observed response, we compare in Fig. 5͑a͒ the FC magnetization at 25 K ͑measured at 500 Oe͒ versus b-and c-lattice parameters; a is not discussed because, as shown above, for YMCO films, and in agreement with previous results for YMO, 8 it remains constant. Data in Fig. 5͑a͒ shows that for both c-and b-parameters ͑top and bottom panels respectively͒, a monotonic increase of the magnetization is observed as b shrinks or c increases, indicating that the more distorted the unit cell is, the stronger is the ͑ferro͒magnetic response. However, comparison of data for YMO and YMCO in Fig. 5͑a͒ ͑bot-tom͒ display distinct slopes in ͑M͑25 K, 500 Oe͒ versus b͒ thus indicating that the observed w-FM is not solely determined by the length of the b-axis. Most naturally, the contribution of the modification of c ͑expansion͒ and a ͑constant͒ axis upon epitaxial and chemical strain should be also included to get a measure of the overall distortion of the unit cell. Note that the ground magnetic structures in bulk o-RMnO 3 are essentially determined by the Mn-O-Mn bonding angle and subsequent modification of the strength of the competing magnetic interactions which should be modified through changes in both b and c lattice parameters. Therefore, we chose the unit cell volume as the simplest parameter to include all structural distortions and we plot in Fig. 5͑b͒ M͑25 K, 500 Oe͒ ͑accounting for net magnetic moment͒ versus V c ͑accounting for unit cell distortion͒. Collapsing of all data ͑corresponding to YMO, YMCO films of different thicknesses and growth conditions͒ onto a single curve strongly indicates that the overall distortion of the unit cell is determining the induced ferromagnetism rather than the simple shrinking of the b-axis. Therefore we conclude that the observed w-FM results from unbalanced magnetic Mn-O-Mn͑Co͒ interactions by modification of bond length topology along b and c due to epitaxial strain or chemical pressure. It is worth mentioning that since unit cell volume for all films is slightly smaller than the bulk, the eventual presence of oxygen vacancies are not expected to play a major role. The annealing experiments discard absolutely oxygen vacancies as cause of the observed w-FM. FC magnetization curves ͑H ʈ = 500 Oe͒ measured for an YMO sample before and after the annealing described in the previous section are given in Fig. 4͑b͒. Data show that, upon the Anneal 1 process ͑air, 800°C͒, the magnetization slightly reduces as a result of the tiny changes in the lattice parameters. More noticeable is the drastic reduction of susceptibility and thus of w-FM after Anneal 2 process ͑Ar, 700°C, favoring the creation of oxygen vacancies͒. In correspondence to the visible expansion of the unit cell ͑Fig. 3͒, there is drop of over 60% of the magnetization. Importantly, the magnetic and structural data of these annealed films fall just on top of the data shown in Fig. 5͑b͒ for all films. We must therefore conclude that irrespective of the method used to tune the lattice parameters ͑thickness and P O2 , 8 chemical pressure or annealing͒ the ferromagnetic response is ruled by the unit cell distortion.

C. Magnetic properties versus surface morphology
Next, aiming to discriminate among strain and surface or domain boundaries as a source of w-FM by spin disorder, as suggested in Ref. 13, we compare the magnetic properties of films having distinct morphologies. Topographic images of representative YMCO and YMO films are shown in Figs. 6͑a͒ and 6͑b͒, respectively. Magnetometry revealed that the magnetization of the YMCO sample ͑0.84 emu/ cm 3 ͒ is significantly smaller than in the YMO sample ͑3.11 emu/ cm 3 ͒. Both images display morphology of a dense granular system with a significant quantitative difference: YMCO films are formed by smaller grains and thus the grain density and the density of grain boundaries are definitely larger than in YMO. If disorder at grain boundaries or surfaces were relevant sources of net magnetization, one would expect M to increase with grain density and roughness. The dependencies

D. Magnetic anisotropy
Finally, we focus on the anisotropy of the magnetic response. In the simplest antiferromagnetic picture, a drop of magnetization below T N should occur if the measurement is performed with H applied along the antiferromagnetic axis whereas magnetization should remain constant if H is applied perpendicular to this axis. In YMO, according to neutron diffraction experiments, 4 the spins are confined along the ͓010͔ direction with a sinusoidal modulation of their amplitude. We recall here that our films contain two-type of in-plane domains with ͑a , b͒ axis rotated in-plane by 90°. In this situation, when measuring in the plane of the sample along the two edges of the substrate ͓͑100͔ STO ͒, H will be applied along the ͓110͔ direction of YMO, that is 45°away from the spin modulation axis ͑b͒. On the other hand, in the out-of-plane measurements, H is applied along the ͓001͔ YMO direction which is perpendicular to the b direction. Figures  7͑a͒ and 7͑b͒ display the ZFC-FC curves for the most strained YMO sample we produced. 8 Notice that here magnetic moment rather than magnetization is displayed to emphasize that the features described below are a genuine experimental observation, not affected mass or volume normalization. Panels ͑a͒ and ͑b͒ correspond to the in-plane and out-of-plane measurements, respectively, and are sketched in Fig. 7͑e͒. Data show that in both measurements the ZFC-FC curves split at around T N ϳ 40 K indicating that the magnetic ordered state is not purely antiferromagnetic but a net magnetic moment is present along the two measured directions. However, data shows a clear FC drop in the measurement with H applied partially containing the ͓010͔ direction ͓Fig. 7͑a͔͒ that resemble a measurement of a pure antiferromagnet when H is along the antiferromagnetic axis. Although data supports the canted scenario sketched in Fig.  7͑e͒, in the set of films discussed so far is not possible a conclusive measurement with H applied solely along the ͓010͔ direction due to the mixed contribution of two in-plane crystal domains. To circumvent this problem we prepared strained single domain films on STO͑110͒ substrates. Details on the growth and structural characterization of similar films are described elsewhere. 15 In these films, ͑100͒-textured, the ͓010͔ and ͓001͔ directions are contained in the plane of the sample. Measurements along ͓010͔ and ͓001͔ directions with H applied in the plane of the sample are plotted in Figs. 7͑c͒ and 7͑d͒, respectively. There is a perfect match between the ZFC and FC magnetic moment curves when H is applied along the ͓010͔ direction ͓Fig. 7͑c͔͒ indicating the absence of remanent net magnetic moment along the mentioned direction. In all, data in Fig. 7 clearly show that the net magnetic moment is only observed when the magnetic field is applied perpendicular to the spin-modulation, ͓010͔, direction.
The average departure of the magnetic moment away from the b-axis ͑canting angles͒ can be estimated from the measured remnant magnetization in the in-plane and out-ofplane configurations. Two magnetic loops corresponding to two ͑001͒-oriented samples with different unit cell volumes are shown in the inset of Fig. 8. In this plot, the magnetic field is applied along the ͓110͔ direction. A larger remnant magnetic moment is found for the smaller unit cell support- ing that the ferromagnetic response is increased by the unit cell contraction, also in agreement with our previous hypothesis based on the temperature dependence of the magnetization. From the values of the remnant magnetization and assuming that the total moment in the Mn 3+ atoms is 4 B , the component of magnetization along the ͓100͔ and ͓001͔ directions, perpendicular to the b axis, can be found by trigonometry. Notice the choice of polar ͑͒ and azimuthal ͑͒ angles definitions according to the sketch in Fig. 7͑e͒. Using the measurements with the magnetic field applied along the ͓110͔ direction, we estimate that the polar canting angle is higher than 1.2°in the most ferromagnetic sample. Data for the complete set of samples is shown in Fig. 8 where both the canting angle and the remnant magnetization are shown as a function of the unit cell volume. As shown in Fig. 8 Fig. 8͒ for the azimuthal canting angle. To conclude, magnetic anisotropy observed in the YMO films can be explained by a canting of the spins away from the ͓010͔ direction. Before concluding we would like to stress that the observed anisotropic magnetic response, or more precisely, the observation of a net magnetization for a particular direction of the in-plane applied magnetic field, would not be expected if the finite remanent magnetization were produced by randomly distributed grain or domain boundaries.

IV. SUMMARY AND CONCLUSIONS
Using epitaxial strain and chemical pressure a substantially wide range of unit cell distortions in o-YMnO 3 has been achieved. We have shown that the observed net magnetic moment depends on the unit cell distortion involving both b and c distances which promote the occurrence of an uncompensated spin arrangement. Single domain fully textured YMO films have provided a unique opportunity to explore the magnetic anisotropy of the films, to demonstrate the intrinsic nature of the net magnetic moment and to show that it is related to spin canting out of the b-axis. More distortion implies larger ferromagnetic response; antiferromagnetism is recovered as lattice parameters tend to bulk. Therefore new, noncollinear magnetic structures have been stabilized by strain-driven distortions of the unit cell. Our findings provide a rationale to describe the observation of ferromagnetic response in o-YMnO 3 films, reported also in other orthorhombic manganites thin films. On these grounds, the strain-induced changes in the films would certainly resound on the dielectric properties as we have reported in an earlier work. 14 ACKNOWLEDGMENTS Financial support by the Ministerio de Ciencia e Innovación of the Spanish Government ͑Project Nos. MAT2008-06761-C03 and NANOSELECT CSD2007-00041͒ and Generalitat de Catalunya ͑Grant No. 2009 SGR 00376͒ are acknowledged. 1 D. Khomskii, Physica ͑Amsterdam͒ 2, 20 ͑2009͒.