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The present article highlights the lattice-imperfection and compositional origins of the nonlinear optical response in bismuth-substituted iron garnet films. In particular the roles of lattice mismatch strain and micro-strain on second harmonic generation in (Bi,Y)3(Fe,Ga)5O12 films are elucidated based on experimental findings. It is found that lattice mismatch strain drives the second harmonic signal in (Bi,Y)3(Fe,Ga)5O12 films, in agreement with theoretical predictions; however micro-strain was found not to correlate significantly with the second harmonic signal at the micro-strain levels present in these samples. The present study also elaborates on the influence of the film’s constitutive elements and finds the nonlinear response to increase with yttrium concentration.
©2010 Optical Society of America
1. Introduction
Ultra high sensitivity delivered by second harmonic generation (SHG) has proven to be a versatile tool for the exploration of magnetized surfaces and buried interfaces of metallic and non-metallic materials with a centrosymmetric bulk crystal structure [1]. In addition SHG has been suggested as a non-destructive technique for optical memory read-out in magneto-optic memory storage [2]. A number of articles have reported on the nonlinear response in liquid-phase-epitaxial (LPE) grown iron garnet films, [3–5] and on strain-induced effects from magnetic-nonmagnetic interfaces [6, 7]. This problem is of interest because magnetic garnets are centrosymmetric and for crystals with inversion symmetry the quadratic susceptibility is identically zero. To observe nonlinear magneto-optical effects in centrosymmetric materials requires a lack of inversion symmetry, making the study of strained epitaxial films of particular interest. The bulk bismuth-substituted iron garnet is characterized by the cubic centrosymmetric space group Ia3d (Oh 10). However, various studies done in the past on structural and magnetic properties of epitaxially grown magnetic iron garnet films have revealed that the films lose their cubic symmetry and transform to uniaxial or orthorhombic symmetry [8–10]. This lowering of crystallographic symmetry of the film can be assigned to its growth anisotropy, lattice mismatch between film and substrate, crystallographic orientation of the substrate and applied magnetic field. Pisarev et. al. [11] have reported the lowering of symmetry in epitaxial magnetic garnet thin films stemming from the elastic deformation caused by lattice mismatch between film and substrate and growth-induced gradients of the film’s lattice constant. These authors point out that lattice mismatch, film composition and substrate orientation are the main factors affecting the inversion centers, leading to polar point groups where the operation of inversion is forbidden. Yet they note that more systematic studies of SHG in magnetic garnet films as a function of lattice mismatch, composition, etc are needed. We attack this problem by inducing strain via lattice mismatch between film and substrate, and by the generation of compositional gradients in the bismuth component of epitaxially-grown films.
In a medium with broken space-inversion and time-reversal symmetry the total quadratic nonlinear polarization of the medium (in electric dipole approximation) is given by
Where, Pcryst (2ω) is the crystallographic contribution and Pmagn (2ω) is the magnetic contribution. Aktsipetrov and co-workers studied the magnetic and non-magnetic (crystallographic) origin of the nonlinear response in centrosymmetric magnetic garnets films [12], and Gridnev et al [3], reported on the effect of bismuth substitution on the second harmonic response in yttrium iron garnets films. However, to date no detailed systematic investigation of the effect of film strain, and the systematic inclusion of lattice mismatch strain, strain gradients and fluctuations, and bismuth substitution on the nonlinear response in this material system has been conducted. Here we study the incorporation of internal stresses due to lattice mismatch and micro-strain in sputter-deposited bismuth-substituted iron garnet (Bi,Y)3(Fe,Ga)5O12 films for their impact on SHG. Radio-frequency (RF) sputter deposition allows the incorporation of Bi and the generation of strain gradients. This is of particular interest since the presence of strain gradients and strain fluctuations, generally referred to in the literature as micro-strain, as well as the presence of lattice mismatch strain have been reported to contribute to the nonlinear response in magnetic garnets and other materials [13–15]. In the present work we study their effect and that of composition on thirteen samples on the second harmonic response of bismuth-substituted iron garnet films.
2. Experimental background
Second harmonic generation in magnetically ordered dielectrics facilitates the study of magnetic symmetries, structures, interactions and buried interfaces as well as determination of in-plane magnetization components [16–19]. Bismuth-substituted yttrium iron garnet films are a model system for magnetically ordered dielectric materials [20–23]. The results presented here are based on the analysis of thirteen (Bi,Y)3(Fe,Ga)5O12 (Bi:YIG) films, grown under similar sputter-deposition conditions (Argon flow rate: 20sccm; substrate holder temperature: 550°C; RF power density: 4.6W/cm2) in a two-target RF magnetron sputtering system. These Bi:YIG films range in thickness from 300nm to 1200nm, and were sputter-deposited at a working pressure of 22 ± 1 milli-Torr (starting base pressure ~ 10-6-10-7 Torr) on 1cm2 pieces of (111)-oriented single crystal Tb3Ga5O12 (TbGG) and Gd3Ga5O12 (GGG) substrates, using radio frequency (RF) magnetron sputtering. The targets used are two inches in diameter and a quarter-inch in thickness, with stoichiometric compositions Bi0.8Y2.2Fe1Ga4O12 and Bi0.8Y2.2Fe4.8Ga0.2O12.
Crystallinity and epitaxial quality of the films was confirmed using X-ray diffraction (XRD) analysis. In the XRD plots for these samples, an asymmetry and broadening in the film peak signal was recognized as the manifestation of strain variations across the film (micro-strain) and crystallite size. Elemental compositions of the Bi:YIG films were investigated using Rutherford Backscattering Spectrometry (RBS) [24]. The refractive indices of the films were measured using a prism coupler. Second harmonic generation measurements were carried out by excitation with a femto-second Ti:Sapphire laser (pulse duration 80fs, λ = 800nm). Measurement of the films’ nonlinear response was done in reflection geometry in the absence of an external magnetic field, with an experimental set-up shown schematically in Fig. 1 (a). The azimuthal angular dependence of the SHG intensity for a typical Bi:YIG sample is shown in Fig. 1(b). Experimental data were approximated by the expression (a+b·Sin(3φ+c))2 with an error of about 18% in the measured SHG signals. The curves agree with theoretical calculations for an SHG signal reflected from (111)-oriented single crystals [25]. The SH intensity measured in PS-geometry has no isotropic contribution which indicates that the surfaces of the films’ are atomically flat.
Fig. 1. (a) Experimental setup for SHG measurement, (b) Azimuthal angular dependences of the SHG intensity for p-in, p-out (closed circles) and for p-in, s-out (open circles) polarization combinations
3. Types of strain and strain determination
In thin epitaxially-grown films a major part of the strain is caused by lattice mismatch between film and substrate. This lattice-mismatch strain (ε) in the Bi:YIG films is calculated through the expression ε = (af-as)/as, where af and as are the film- and substrate-lattice constants in the normal direction to the plane of the film, respectively. Lattice-mismatch strain deforms the cubic structure of the iron garnet unit cell under study, lowering its inversion symmetry and producing strain-induced SHG. A second source of nonlinear response in the Bi:YIG films can be traced to strain and compositional gradients, dislocations and strain fluctuations (denoted as micro-strain). Micro-strain is explored in the present work by X-ray line profile analysis. In the XRD plots peak broadening and distortions gauge the effect of strain variations and crystallite size present in the film. Strain variations stem from compositional gradients, strain relaxation across the thickness and dislocations.
Since the films deposited for this project are very thin compared to the substrate, the crystalline structure of the mono-crystal substrate is not deformed much and is used as an internal standard for instrumental resolution. A careful analysis was conducted in which distorted film peaks were treated with symmetrical Pearson VII profiles, as shown for example in Fig. 2. The film peak (to the left) of a typical sample is fitted by two Pearson VII profiles. To calculate the effect of strain gradients, fluctuations and particle size on XRD profile broadening a simplified Williamson-Hall fit was applied to two lattice-plane peaks (444 and 888) parallel to film surface. The strain values for each fitted peak are extracted from the slope of the line passing through the origin of a standard (FWHM) * Cosθ = 4ε’Sinθ plot, in the Williamson-Hall plot. Here FWHM is the full-width-half-maximum (in radians) of the fitted profiles, corrected for instrumental resolution, ε’ is the micro-strain and θ is the XRD incidence angle. Since only two points (corresponding to 444 and 888 peaks) were accessible to us by XRD for the Bi:YIG samples, the micro-strain was extracted by a straight-line fit through the origin; hence the form of the simplified expression relating FWHM to ε’ given above. This method is equivalent to taking the average of the contributions to the line profile broadening for both 444 and 888 profiles, and folds in all contributions to the broadening but folds out instrumental resolution.
Fig. 2. Peak fit of (444) sample peak of a typical sample using symmetrical Pearson VII profiles. The profiles near 50.14° correspond to the film and the one near 51.14° to the substrate. Each profile has two peaks corresponding to XRD Kα1 and Kα2 lines.
Lattice mismatch strain was found to show an inverse relation to the films’ deposition rate, thus providing a means for strain control during the deposition process. Of the two targets used in the film growth process in our magnetron sputtering system, those samples grown under a lower target-magnetic-field and larger target-substrate separation evinced higher lattice mismatch strain as compared to samples grown under higher (two times) target-magnetic field and lower target-substrate separation, providing another handle for strain control in the film fabrication. In-situ post-annealing of one of the films yielded a reduced lattice mismatch strain (least among all the samples).
4. Strain and elemental concentrations
In this section the compositional and crystallographic origin of lattice mismatch strain and micro-strain within a film are explored. An absolute difference in the film and substrate lattice parameters produces lattice mismatch strain in the film, with highest influence near the film-substrate interface. To calculate the micro-strain and compositional variations in the film, XRD peak profiles were analyzed and the Bi:YIG samples were scanned for depth profiles of the constitutive elements using Rutherford Backscattering Spectrometry (RBS). The compositional analysis of a typical film reveals that bismuth concentrations deviate from their stoichiometric value in (Bi,Y)3(Fe,Ga)5O12, as shown in Fig.3. This is because bismuth has a lower surface binding energy and liable to be preferentially sputtered. Variations in the Bi concentration cause gradient/displacement in elemental concentrations across the film thickness.
In all the samples, a lessening trend in Bi concentration towards the surface of the film is observed, as shown in Fig. 3; however the concentrations of other elements (Y, Fe, Ga and O) stay more or less constant with depth. A possible explanation for the decreasing Bi concentration towards the surface could be imputed to in-situ annealing of the growing Bi:YIG film. The diffusion of Bi, with relatively larger ionic radius (Bi3+) in the Bi:YIG, towards the interface brings about an atomic rearrangement and renders an overall least strained crystallography in the film. This relative displacement of the elements causes local stress generation, which along with dislocations and stacking faults produces micro-strain (strain gradients and fluctuations) across the film thickness. This micro-strain, however, turns out to be an order of magnitude smaller than the lattice mismatch strain. The gradient in Bi concentration across the thickness noted here generates micro-strain which contributes to the removal of inversion symmetry in the film and enables the observed second harmonic generation. The average elemental concentrations, thickness and the average values of two types of strains corresponding to each film are presented in Table I.
Table I. Elemental atomic concentrations and strain values of the Bi:YIG samples
Average elemental concentrations were plotted against the mean micro-strain and lattice mismatch strain. It was found that Bi and Y concentrations exhibit a monotonic relation with lattice mismatch strain as shown in Fig. 4(a), (b), while no correlation with micro-strain is seen in Fig. 4(c), (d). In Figs. 4, 5 and 6, each data point is labeled by its corresponding Bi:YIG sample number as given in column one of Table I.
It was observed that the elements in the dodecahedral site (Bi and Y) of the garnet influence the lattice mismatch strain. An increase in Bi concentration causes a decrease in lattice mismatch strain, while growing the Y concentration supports the lattice mismatch strain, as seen in Fig. 4(a), (b), respectively. As depicted in Fig. 4(c), (d), the micro-strain value does not show any clear dependence on Bi and Y concentration.
Fig. 4. Plot of Bi concentration Vs lattice mismatch strain (a), Y concentration Vs lattice mismatch strain (b), Bi concentration Vs micro-strain (c), Y concentration Vs micro-strain (d).
A thorough study of the dependence of elemental composition on strain value reveals that no interesting trend is seen with gallium, iron and oxygen under the range of elemental concentrations explored here. So it can be concluded that Bi and Y concentrations from sample to sample result in different lattice mismatch strain value to each sample; however, variations in these elemental concentrations do not show any systematic influence over the average micro-strain in the film
5. Second harmonic generation and strain
A theoretical analysis of the effect of strain on SHG in magnetic films on nonmagnetic substrates has been performed by Lyubchanskii et al [13]. These authors examine the contribution of lattice misfit and dislocation strains on SHG, using a nonlinear photoelastic tensor. Strain enters into the second-order nonlinear optical susceptibility tensor via the expression given in Eq. (22) below.
Where pijklm and ulm(r) are the nonlinear photoelastic tensor and the strain tensor, respectively. The strain tensor ulm(r) is given by Eq. (3).
Here θ(z) is the Heaviside step function; hc is the critical thickness of the film, the thickness above which misfit dislocations will appear and contributes to the nonlinear polarization. ulm (1)(r) and ulm (2)(r) represent the lattice mismatch and micro-strain components of the strain tensor, respectively. Summation over repeated indices applies.
In the present study, the effects of individual strain components as well as of their convolution in the form of sum and product on the film’s SHG signal were tested experimentally. The Bi:YIG films grown over (111)-oriented GGG substrate are expected to acquire a non-centrosymmetric point group 3m (C3v) [11]. This lowering in the symmetry is primarily due to the presence of lattice mismatch strain and Bi concentration gradients in our samples. This non-centrosymmetric structure of the Bi:YIG films manifested by missing inversion centers produce the observed second harmonic generation from these samples. Lyubchanskii et al predict that the p-polarized SHG signal is an indication of the presence of both strain components and depends additively on both contributions [13]. SHG measurements were done in the absence of an external magnetic field, under near-zero spontaneous (or static) magnetization. Under these conditions a crystallographic contribution to the nonlinear polarization is expected to dominate, as suggested by Eq. (1). It was also verified that no significant SHG contribution is produced by the single-crystal GGG and TbGG substrates, so that the measured signal is due to the presence of the deposited film only. As seen in Fig. 5(a) the second harmonic response for p-in, p-out polarization combination (PP geometry) for the system of samples in our study shows a monotonic dependence on the average lattice mismatch strain value, while no noticeable dependence on the micro-strain is seen in Fig. 5(b). The second harmonic intensity is normalized to the optical transmittance of the second harmonic wave (λ=400nm) in the film, to take into account losses of the SH radiation near film-substrate interface.
Fig. 5. Normalized SHG signal (PP geometry) dependence on the lattice mismatch strain (a), dependence on the micro-strain (b). A second power allometric fit to lattice mismatch dependence is plotted in (a).
The clear trend exhibited in Fig. 5(a) indicates that the SHG signal strongly correlates with changes in lattice mismatch strain, while the absence of a monotonic trend with micro-strain in Fig. 5(b) is evidence that the SHG is less sensitive to strain fluctuations at the level of micro-strain present in our samples. The convolution of strain components in the form of their sum shows a slightly degraded but similar trend as that for the lattice-mismatch, with the dominant contribution coming from the latter. A strain product convolution is not predicted by theory and does not fit the experimental data well.
Hence from Fig. 5 it could be said that control of the second harmonic signal in the set of Bi:YIG samples analyzed in these experiments stems mainly from the lattice mismatch strain. This observation partly abides by the prediction of Ref [13], that both strain components contribute. The lower sensitivity of the SHG signal to micro-strain in the film could be ascribed to the fact that micro-strain is an order of magnitude smaller than the lattice mismatch strain. At the same time, the factors engendering micro-strain (varying elemental displacement, strain gradients, dislocations, local stresses, etc) might contribute differently and be distributed unevenly in different samples leading to a random net contribution to the second harmonic signal.
The plots in Fig. 6 display the dependence of SHG signal on Bi and Y concentration. From these plots it is evident that the normalized second harmonic signal decreases with increasing Bi concentration, while it increases with an increase in Y concentration.
Fig. 6. Normalized SHG signal (PP geometry) dependence on the Bi concentration (a), dependence on the Y concentration (b).
A clear conclusion can be drawn from Figs. 4, 5 and 6, that the Y concentration in the film supports the lattice mismatch, which in turn enhances the second harmonic signal in the film, while the Bi concentration acts adversely to the lattice mismatch and results in a weaker nonlinear response in the film. The micro-strain value does not show any interesting trend with second harmonic intensity, and neither does it show any dependence on average Bi and Y concentration in the film.
6. Conclusions
A detailed study of the second harmonic response as a function of strain in bismuth-substituted yttrium iron garnet films shows a strong dependence on lattice mismatch strain. The nonlinear response increases with strain. Bismuth and yttrium concentrations correlate with strain in the material, thus affecting the second harmonic response. It is found that an increase in yttrium atomic concentration in the dodecahedral site of the (Bi,Y)3(Fe,Ga)5O12 garnet film leads to an enhancement in second harmonic generation, while an increase in bismuth concentration produces an adverse effect. Inversion centers in the structure of Bi:YIG film grown over (111)-oriented GGG substrate are prevented by the combined effects of lattice-mismatch strain and compositional gradients.
Acknowledgments
This material is based upon work supported by the National Science Foundation under Grant No. 0709669 and Russian Foundation for Basic Research No. 07-02-91352-NSF. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the supporting agencies.
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