Tilted Magnetic Anisotropy with In‐Plane Broken Symmetry in Ru‐Substituted Manganite Films

Controlling the magnetic anisotropy of materials is important in a variety of applications including magnetic memories, spintronic sensors, and skyrmion‐based devices. Ru‐substituted La0.7Sr0.3MnO3 (Ru‐LSMO) is an emerging material, showing tilted magnetic anisotropy (TMA) and possible nontrivial magnetic topologies. Here anisotropic in‐plane magnetization is reported in moderately compressed Ru‐LSMO films, coexisting with TMA. This combination is attractive for technological applications, such as spin‐orbit torque (SOT) based devices and other spintronic applications. A microstructural analysis of films of this material is presented, and Ru single ion anisotropy and strain‐induced structural mechanisms are found to be responsible for both the in‐plane anisotropy and the TMA. The manifestation of these properties in a correlated oxide with Curie temperature near room temperature highlights an attractive platform for technological realization of SOT and other spintronic devices. Illustrating the mechanisms behind these properties provides the necessary engineering space for harnessing these phenomena for practical devices.


Introduction
Mixed-valence manganites such as La 0.7 Sr 0.3 MnO 3 (LSMO) have attracted significant attention owing to the emergence of colossal magnetoresistance (CMR), metal-insulator transitions, ferromagnetism, high spin polarization near the Fermi level, and high DOI: 10.1002/aelm.[3][4][5] This system provides a textbook example of the complexity of structure-property relationships in correlated oxide systems, where small structural details can result in dramatic changes in the macroscopic behavior.][9][10] The microstructure plays a crucial role in the manifestation of magnetic anisotropy, and therefore epitaxial strain provides a direct route for tuning the magnetic properties. [11]In addition, the steps and terraces on vicinal substrates can break the fourfold rotational symmetry and reduce it into twofold symmetry, thereby affecting the growth mechanism and modifying the microstructure; this can lead to the manifestation of in-plane uniaxial magnetic anisotropy. [8,10]These structural details and the resulting magnetic anisotropy can have a crucial impact on various magnetic anisotropy-based devices.Furthermore, atomic substitution can play a significant role in epitaxial strain engineering, thereby affecting the magnetic anisotropy of a film.
[13] In addition to the strong perpendicular magnetization component, anisotropic in-plane magnetization is required for cutting edge applications such as deterministic perpendicular SOT devices. [11,12]ere we report TMA with strong perpendicular magnetization and anisotropic in-plane magnetization in 10% Ru-LSMO films.By detailed microstructural analysis, we unveil the microstructural origin of the observed magnetic anisotropy.We observe and analyze a 1D periodic structural modulation in a 48 nm 10% Ru-LSMO film.The relations between strain, microstructure and magnetism are discussed, illustrating the role of Ru and strain-induced structural mechanisms behind the TMA with anisotropic in-pane magnetization.While this material shows a Curie temperature near room temperature, which is attractive for practical applications, the study of the mechanisms of the magnetic anisotropy was carried out at low temperature (30 K) where the various mechanisms are most distinct and easy to analyze.
Ru-substituted LSMO gained significant attention recently, following a report of non-trivial magnetic topologies, [7] which are the consequences of tilted magnetic anisotropy.In this work, we report the first observation of anisotropic in-plane magnetization in Ru-LSMO; we complement this observation with a microstructural analysis of the films.By analyzing the microstructure, we elucidate the role of Ru and strain-induced structural mechanisms that drive the magnetic anisotropy.TMA with strong perpendicular magnetization and anisotropic in-plane magnetization makes Ru-LSMO an attractive candidate for SOT technology.Altogether, these benefits are encompassed within a wellestablished, high Curie temperature host material system of LSMO.

Magnetic Anisotropy
This study is based on 10% Ru-LSMO epitaxial films, focusing on a 48 nm ('thick') film, which is compared to a 10.5 nm ('thin') reference film.Both films were epitaxially grown on a (LaAlO 3 ) 0.3 (Sr 2 AlTaO 6 ) 0.7 (LSAT) substrates (see Experimental Section for details), resulting in moderate in-plane compressive strain (see Section 2.2).The temperature dependence of the magnetization (M-T curves, Figure 1a,b) and magnetic fielddependent magnetization loops (M-H curves, Figure 1c) along the main lattice directions show that a 48 nm 10% Ru-LSMO film has strong perpendicular magnetization as well as anisotropic inplane magnetization.This suggests that the easy axis of magnetization is tilted from the surface normal, indicating the existence of TMA.We note that the in-plane projection of the easy axis does not lie along the main in-plane lattice directions.From the M-H curves (Figure 1c, inset), the ascending order of magnetocrystalline anisotropy energy (E) can be estimated as: 100] pc , where "pc" stands for pseudocubic lattice coordinates.Henceforth, we use the notation for the in-plane ([100], [010]) and the perpendicular ([001]) pseudocubic directions.
While TMA is also observed in a thin (10.5 nm) 10% Ru-LSMO film, at this lower thickness the M-T and M-H behavior (Figure S1, Supporting Information) indicate that the magnetization anisotropy between the two main in-plane lattice directions is significantly diminished.In addition, we note the flattening of the [100] pc M-T curve of the thick 10% Ru-LSMO below ≈200 K, which includes a slight downturn (Figure 1a) that is reproducible at higher magnetic fields (Figure 1b).While further analysis is required to clarify the origins of this small feature, we observe it only in the sample featuring a 1D periodic structural modulation (to be discussed later on), suggesting a possible correlation.Furthermore, we rule out any significant contribution of shape anisotropy by comparing the [001] pc M-H curves of a thick (48 nm) and a thin (10.5 nm) 10% Ru-LSMO films from 0 T to 3 T (Figure S3, Supporting Information).
We further note that the M-H loops do not meet at the higher fields (up to ± 3 T) even though the loops close at ≈0.3 T, which indicates that the anisotropy of magnetization, both in-plane and  out-of-plane, persists to high magnetic fields. [14]This implies that anisotropic orbital magnetic moment plays a significant role here. [15,16]These results attest to the role of strong spin-orbit coupling of Ru ions, [14] together with the orbital anisotropy originated by the monoclinic structure and the in-plane structural modulation, on the overall magnetic anisotropy (to be discussed in Section 2.3).
Altogether, we observe a TMA with strong perpendicular magnetization and anisotropic in-plane magnetization in both the thick and thin Ru-LSMO films; however, anisotropy of the inplane magnetization in the thin film is negligible compared to that of the thick film.To explain these observations, we first study the microstructure of these films in Section 2.2, and then in Section 2.3 we combine magnetism and microstructure to explain the origins of magnetic anisotropy.

Microstructure
To understand the structural origins of the observed TMA, offspecular XRD reciprocal space maps (RSMs) of a thick (48 nm) 10% Ru-LSMO film were acquired at room temperature.The results (Figure 2) suggest that the main Bragg peaks of the film and the corresponding Bragg peaks of the substrate have the same in-plane momentum transfer Q || , confirming coherent growth of fully-strained Ru-LSMO films (see Figure S4, Supporting Information for the 2- Bragg peaks).Bulk LSMO has a rhombohedral crystal structure with a pseudocubic lattice parameter of 3.874 Å, which is only slightly larger than the lattice parameter of 3.868 Å of the cubic LSAT substrate. [17]The substitution of Mn by Ru increases the lattice parameter, resulting in increased compressive strain (to be discussed later). [17]he second key observation from Figure 2 is that the (0 1 3) pc film peak ((Q 013 ) ⊥ = 0.7638 Å (−1) ) has shifted upward and the (0 −1 3) pc film peak ((Q (0-13) ) ⊥ = 0.7584 Å (−1) ) has shifted downward with respect to the (± 1 0 3) pc film peaks (( 1) ).The Q ⊥ position of the (± 1 0 3) pc film peaks is indicated by a dashed line for clarity.This behavior is consistent with in-plane crystallographic symmetry breaking, such as an orthorhombic distortion in the case of SrRuO 3 (SRO). [18]e upward shift of the (0 1 3) pc peak and downward shift of the (0 −1 3) pc peak with respect to the (± 1 0 3) pc peaks imply that the (010) pc planes have tilted toward [0 −1 0] c with respect to (010) c ("c" indicates the substrate's cubic coordinates) by an angle , [19] where tan  = 90°+  that is the angle between [010] pc and [001] pc (Figure 3a).The in-plane symmetry breaking of the Ru-LSMO film is therefore ascribed to a monoclinic distortion, consistent with previous observations for LSMO. [20,21]he third observation from Figure 2 is the emergence of satellite film peaks along a specific direction.The satellites are distinct around the (± 1 0 3) pc film peaks, whereas no satellites are observed around the (0 ±1 3) pc peaks.This RSM feature is explained by a periodic structural modulation, and its exclusive appearance along the [100] pc direction indicates the existence of a 1D periodic structural domain array along or near this axis (Figure 3b). [10,20,21]ltogether, the RSM analysis of the 48 nm 10% Ru-LSMO film points to a compressively-strained, coherent monoclinic (distorted orthorhombic) crystal structure (Figure 3a) with a 1D crystallographic domain structure along [100] pc (Figure 3b).In monoclinic notation (subscript m), [110] In the interest of simplicity, we will continue with the "pc" notation.These microstructural details play a key role in the magnetic anisotropy, to be discussed in the Section 2.3.
During the coherent film growth, the biaxial compressive strain applied to the film by the substrate compresses the Ru-LSMO pseudocubic unit cells along [100] pc and [010] pc and hence expands the unit cells along [001] pc .This leads to the distortion of the lattice by tilting and rotating the MnO 6 and RuO 6 octahedra, resulting in monoclinic unit cells (Figure 3a), with the monoclinic angle  m being less than 90°.This interpretation agrees well with previous observations of similar lattice distortions and monoclinic unit cell formation in compressively strained LSMO films on LSAT substrates. [20,21][23][24]  In addition to its lattice parameter mismatch with LSAT, the rhombohedral (bulk) LSMO unit cell further features a lattice angle mismatch with the cubic LSAT substrate.The lattice parameter mismatch induces biaxial compressive strain on the Ru-LSMO unit cells, whereas the lattice angle mismatch induces shear strain.The angle  m becomes less than 90°to accommodate the lattice parameter mismatch [20] ; the estimated value of  m is 88.92°, with  = 0. = 3.9411 Å) is the perpendicular distance between the (001) pc planes.The LSMO film grown on LSAT substrate is slightly strained compressively (−0.155%), [17] producing  m ≈89.72°, [20] whereas the 10% Ru-LSMO films grown on LAST substrate experience moderate compressive strain (−0.41%), [17] leading to a lower angle  m .The monoclinic unit cells of Ru-LSMO can release a small amount of shear strain along [010] pc /[1 −1 0] m by changing the angle of  m , resulting in an octahedral tilt.However, shear strain accumulates as the thickness of a Ru-LSMO film increases.To release this shear strain, periodic structural lattice modulation of the film occurs along the lattice direction [100] pc , at the cost of deviation of the angle ( pc ) between [001] pc and [100] pc from 90°.This occurs while keeping the (100) pc planes perpendicular to the substrate's surface plane (001) c (Figure 3b), [10,20,21] resulting in satellite peaks in the films (Figure 2).We note that the variation of the angle  pc is the key reason behind the broadening of the satellites (see Figure S5, Supporting Information and the discussion therein).The lattice modulation along [100] pc induces periodic shifting of the centers of the pseudocubic unit cells with periodicity  along the lattice direction [001] pc (Figure 3b).The separation between the main peak (violet arrow in Figure 2) and satellite peaks (red arrows in Figure 2) of 48 nm 10% Ru-LSMO film in reciprocal space is Δ Q ∥ = 0.0045 Å −1 , yielding a 1D structural modulation period of  = (ΔQ ∥ ) −1 = 22 nm ± 6 nm in real space (accounting for satellite broadening, see Figure S5, Supporting Information and discussion therein).
The Ru-LSMO (± 1 0 3) pc main Bragg peaks are much more intense than their satellites, indicating that some volume of the film does not undergo the periodic lattice (Figure This is explained by the structural modulation starting above a critical thickness, releasing the (thickness-dependent) elastic energy.Indeed, an RSM analysis of 10.5 nm 10% Ru-LSMO film does not show any satellite features (Figure S6, Supporting Information) while retaining the monoclinic crystal structure.In addition, similarly to the 48 nm film, the 10.5 nm film has strong perpendicular magnetization component (Figure S1, Supporting Information), but it exhibits only weakly anisotropic in-plane magnetization.This suggests that the periodic structural domains are not necessary for the strong perpendicular component of magnetization, but they do play a role in the anisotropic in-plane magnetization, to be discussed in the Section 2.3.The emergence of such lattice modulation, only above a critical thickness, has been reported in LSMO films, [21,25,26] in good agreement with our observation.1D periodic structural modulation has also been reported in LaCoO 3 , showing such modulation in the entire film thickness. [10]ubstrate miscut can play a significant role in the manifestation and orientation of such structural modulations in complex oxide films.To determine the miscut angle and the miscut direction, rocking curve measurements were performed on the LSAT substrate Bragg peaks (Figure S7, Supporting Information).The measured miscut angle of the substrate is 0.1°, and the step direction is 8°± 5°clockwise with respect to [010] c .Therefore, the 1D periodic structural modulation occurs along the terraces, and the structural domains are perpendicular to the terraces.This picture is consistent with step-edge nucleation during the initial stage of the film growth. [21]he kind of structural modulation we observe in the Ru-LSMO films at room temperature has been observed in LSMO films on SrTiO 3 (STO) substrates as well. [25]In the case of STO substrates, the structural modulation disappears at low temperatures due to the structural phase transition (≈105 K) and phonon softening in STO. [25]However, unlike the case of LSMO on STO, the pattern of structural modulation of LSMO films on LSAT subtrates does not change with the temperature. [25]ven the possibility of minute structural variations of LSAT substrates, expected at ≈150 K, [27] has no expression in the M-T behavior of Ru-LSMO films (Figure 1; Figure S1, Supporting Information), thus validating the room temperature structural features of Ru-LSMO films at the low temperatures as well.

Microstructural Origins of the Magnetic Anisotropy
Having characterized the microstructure of the Ru-LSMO films, we now describe the microstructural mechanisms of their magnetic properties.The monoclinic (distorted orthorhombic) crys-tal structure reported here hosts the Glazer octahedral tilt system a + a − c − , similarly to compressively strained LSMO and SRO films. [20,23,28]Therefore, we begin by considering two related magneto-crystalline anisotropy archetypes that host the same octahedral tilt system (a + a − c − ) as the present case: pc in SRO films, when both are under compressive strain and the monoclinic lattice direction [110] m is along [001] pc . [21,23,29,30]As shown in Figure 1, the anisotropy energy in the present case is E [001]pc < E [010]pc < E [100]pc , which suggests that the present Ru-LSMO system behaves more closely to SRO than to LSMO, but with the distinct practical advantage of the much higher Curie temperature of LSMO.We will describe the atomic mechanisms of these archetypes, and from them we propose a mechanism for the presently observed TMA in Ru-LSMO.
On one hand, LSMO films with the a + a − c − tilt system were shown to induce weakly anisotropic in-plane magnetization, with [100] pc being magnetically easier than [010] pc . [21]In contrast, SRO films with the same tilt system exhibit TMA with strong perpendicular magnetization and anisotropic in-plane magnetization, with [010] pc being magnetically easier than [100] pc . [23]This comparison therefore suggests that the Ru ions have single ion anisotropy in the Ru-LSMO films and the single ion anisotropy in the Ru ions is induced by compressive strain.Moreover, the Ru single ion anisotropy plays a key role in the strong perpendicular magnetization of the 10% Ru-LSMO films. [7]This in turn implies that compressive strain, together with strong spin orbit coupling (SOC) of Ru ions, induces a preferred orientation of the Ru spins (to be discussed later), which then governs the orientation of Mn spins.The octahedral rotation (discussed in the next paragraph) that influences the Ru-Mn and Mn-Mn interactions further plays an important role behind the TMA in Ru-LSMO films.
While in-phase octahedral rotations enhance e g -e g orbital overlap, the out-of-phase rotations enhance six out of nine t 2g -t 2g orbital overlaps. [21,23]The Mn-Mn magnetic interaction in LSMO is based on the overlap of the e g orbitals, whereas the Ru-Ru magnetic interaction in SRO is based on the overlap of the t 2g orbitals.The octahedral rotation c − about the [001] pc is out-of-phase in both LSMO and SRO films, but strong perpendicular magnetization is observed only in SRO.The in-plane magnetic easier axis of LSMO films is the axis ([100] pc ) around which the octahedral rotation (a + ) is in-phase, whereas the in-plane magnetic easier axis of SRO films is the axis [010] pc around which the octahedral rotation (a − ) is out-of-phase.The octahedral rotation induced orbital anisotropy, together with spin-orbit coupling (SOC), induce two opposite orders of magneto-crystalline anisotropy energy in these examples: pc in SRO films (both compressively strained).This difference is rooted in the different dominant orbitals (and their overlap): e g in LSMO versus t 2g in SRO.
Here the 10% Ru-LSMO films (Figure 1; Figure S1, Supporting Information) exhibit the same order of magneto-crystalline anisotropy energy as observed in SRO films, opposite to the LSMO case.This suggests that the orbital anisotropy of the Ru 4d t 2g orbitals and their interaction with Mn 3d t 2g orbitals play a crucial role in the magnetic behavior of Ru-LSMO films.Indeed, it has recently been suggested that an antiferromagnetic interaction between Ru and Mn ions via t 2g orbital overlap governs the magnetic properties of Ru-LSMO films. [17]However, the influence of microstructure of the Ru-LSMO films on the Ru-Mn t 2g interaction has never been discussed.We therefore propose that the monoclinic crystal structure together with the octahedral tilt system a + a − c − create the playground for Ru-Mn t 2g interactions in 10% Ru-LSMO films, where the single ion anisotropy of the Ru ions dictates the spin orientation of Mn ions and determines the order of magneto-crystalline anisotropy energy here as The Ru ion is the magnetic anisotropy by playing a dual role.First, the substitution of Mn by Ru increases the compressive strain that induces t 2g orbital anisotropy by driving the monoclinic a + a − c − tilt structure, resulting in both inplane and out-of-plane orbital anisotropy.The Ru 4d orbitals have an order of magnitude stronger SOC compared to the Mn 3d orbitals. [31,32]When strained, the RuO 6 octahedra are expected to translate their local orbital preference to the Ru spins via the strong SOC of Ru ions, more effectively than the MnO 6 octahedra with the weaker SOC of Mn ions.Second, the Ru spins govern the Mn spins via Ru-Mn t 2g interactions. [17]The spatial distribution of the Ru 4d orbitals is wider than that of the Mn 3d orbitals, making Ru-Mn interactions stronger than Mn-Mn interactions (both of which occur via the oxygen anion) in Ru-LSMO.Moreover, the additional compressive strain induced by Ru substitution further increases the Ru-Mn interaction.Overall, the strain induced single ion anisotropy in Ru ions the magnetic anisotropy in 10% Ru-LSMO films via Ru-Mn t 2g interactions.
Having discussed the role of Ru in magnetic anisotropy, we now consider the 1D periodic structural modulation (Figure 3b), and its role in the anisotropic in-plane magnetization.This structural modulation appears in the thick Ru-LSMO film where the anisotropy of in-plane magnetization is relatively strong (Figure 1), compared to the thin Ru-LSMO film (Figure S1, Supporting Information) where the 1D structural modulation is absent (Figure S6, Supporting Information).The weaker anisotropy of the in-plane magnetization is therefore ascribed to the monoclinic structure that exists in both films, as discussed earlier.
The stronger anisotropy of in-plane magnetization in the thick film therefore shows correlation with the existence of the structural modulation.We ascribe the increased anisotropy of in-plane magnetization in the thick Ru-LSMO film to the additional outof-phase octahedral rotation a − around the [010] pc axis as a result of the periodic variations in the angle  pc (Figure 3b).
From the above discussion, we note that Ru plays an important role in the manifestation of TMA with strong perpendicular magnetization in Ru-LSMO.However, this raises a question whether the TMA observed here can be explained purely by strain.TMA with strong perpendicular magnetization in LSMO, with the effective magnetic anisotropy energy in the order of 10 5 J m −3 , [33,34] can be achieved without Ru substitution, albeit with high compressive strain (−2.2%) using LaAlO 3 (LAO) substrates. [33]However, in the 10% Ru-LSMO films with a moderate compressive strain (−0.41%) on LSAT substrates, the TMA with strong perpendicular magnetization having same order (≈10 5 J m −3 ) of effective magnetic anisotropy energy is observed here (Figure S1, Supporting Information and discussion therein).This comparison illustrates that strain alone cannot account for the observed TMA, highlighting the importance of Ru in translating the orbital anisotropy into magnetic anisotropy through strong SOC and more spread-out 4d orbitals.Ru substitution significantly enhances the strain induced perpendicular magnetization.From a practical perspective, high strain is less desirable as it limits growth, thickness, and processing parameter space.
We now briefly highlight a possible technological implementation of the observed TMA in the 10% Ru-LSMO films.Fieldfree perpendicular magnetization switching through SOT holds promise for future low-power non-volatile magnetic memories.[37][38] Therefore, materials that have tilted magnetic anisotropy (TMA) with a strong perpendicular magnetization component are of considerable advantage for such devices.For example, strong perpendicular magnetization of SRO was recently utilized to demonstrate deterministic perpendicular magnetization switching through SOT in an all-oxide heterostructure at 70 K. [13,14,23] However, the low Curie temperature (T C ) of SRO is a major hurdle toward practical realization.Nakamura et al. showed that 10% Ru substitution in the high-T C material LSMO supports strong perpendicular magnetization up to much higher temperatures, but the in-plane anisotropy of magnetization was not addressed.Along with a strong perpendicular magnetization, anisotropic in-plane magnetization is crucial for deterministic perpendicular magnetization switching through SOT. [11,12]Moreover, the Curie temperature of the manganites can be engineered to be above the room temperature. [39]herefore, the strong perpendicular magnetization along with the anisotropic in-plane magnetization in 10% Ru-LSMO could be utilized to fabricate the SOT switching devices, which could work much closer to (and potentially above) room temperature, paving the way toward practical applications.

Conclusion
We report TMA with strong perpendicular magnetization and anisotropic in-plane magnetization in 10% Ru-LSMO films under moderate compressive strain.The microstructure of the Ru-LSMO films was analyzed and correlated with observed magnetic anisotropy.We show how Ru magnifies the impact of strain, explaining the possible microstructural origin of magnetic anisotropy.We further illustrate how shear strain relaxation occurs above a critical thickness via the formation of 1D periodic structural modulation, which in turn plays a prominent role in the manifestation of anisotropic in-plane magnetization.Demonstrating and understanding the microstructural origin of TMA with strong perpendicular magnetization and anisotropic in-plane magnetization in 10% Ru-LSMO paves the way toward the realization of practical oxide-based room temperature spintronic memories.

Experimental Section
Thin Film Growth: Ru-LSMO films were epitaxially grown on LSAT (001) substrates (Crystec GmbH) using pulsed laser deposition (PLD).The substrates were held at 650 °C and the target was ablated using a KrF laser with a fluence of 2.4 J cm −2 at a repetition rate of 3-5 Hz.The oxygen pressure was maintained at ≈0.13 mbar during growth, and it was increased to 100 mbar after growth while the samples were cooled down at a rate of 10 °C min −1 .
Study of Magnetic Properties: Temperature and field-dependent magnetization measurements were performed using a superconducting quantum interference device (SQUID) magnetometer in a magnetic properties measurement system (MPMS3, Quantum Design).
Structural Characterization of the Films: X-ray diffraction (XRD) measurements were performed at room temperature using a Rigaku SmartLab diffractometer with Cu K radiation ( = 1.54 Å) and a 2-bounce incident monochromator.

Figure 1 .
Figure 1.Magnetic properties of a 48 nm 10% Ru-LSMO film.Magnetization as a function of temperature (M-T) under a) 0.1 T and b) 0.5 T along the main pseudocubic lattice directions.Before each M-T measurement, the sample was field cooled and the measurement was performed during warm up under the corresponding magnetic field.The M-T curves under 0.5 T (above the coercive fields) reveal the nature of magnetic anisotropy in the range of temperatures.c) Magnetic field-dependent magnetization (M-H) loops at 30 K; before each M-H measurement, the sample was zero field cooled to 30 K. The inset shows these loops extended to ± 3 T.

Figure 3 .
Figure 3. Schematic microstructure of 10% Ru-LSMO film coherently grown on LSAT.a) Schematic (magnified) relationship between monoclinic unit cell and pseudocubic unit cells of a 10% Ru-LSMO film on a vicinal LSAT substrate.b) 1D periodic structural modulation of a thick 10% Ru-LSMO film on a vicinal LSAT substrate.The substrate has a miscut angle of 0.1°with the step edge direction being 8.0°clockwise from the lattice direction [010] c .