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Magnetic anisotropies in ultrathin bismuth iron garnet films
Journal of Magnetism and Magnetic Materials 335 (2013) 139–143
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Journal of Magnetism and Magnetic Materials journal homepage: www.elsevier.com/locate/jmmm
Magnetic anisotropies in ultrathin bismuth iron garnet films Elena Popova a,n, Andres Felipe Franco Galeano b, Marwan Deb a, Be´ne´dicte Warot-Fonrose c,d, Hamid Kachkachi b, Franc- ois Gendron e, Fre´de´ric Ott f, Bruno Berini a, Niels Keller a a
Groupe d’Etude de la Matie re Condense´e (GEMaC), CNRS/Universite´ de Versailles-Saint-Quentin, 45 Avenue des Etats-Unis, 78035 Versailles, France Laboratoire PROce´de´s, Mate´riaux et Energie Solaire (PROMES), CNRS/Universite´ de Perpignan Via Domitia, 52 Avenue Paul Alduy, 66860 Perpignan, France c Centre d’Elaboration de Mate´riaux et d’Etudes Structurales (CEMES), CNRS, 29 rue Jeanne Marvig, 31055 Toulouse, France d Transpyrenean Associated Laboratory for Electron Microscopy (TALEM), CEMES-INA, CNRS–Universidad de Zaragoza, France and Spain e Institut des NanoSciences de Paris (INSP), CNRS/Universite´ Pierre et Marie Curie-Paris 6, 4 place Jussieu, Boˆıte courrier 840, 75252 Paris Cedex 05, France f Laboratoire Le´on Brillouin (LLB), CNRS/CEA, Bˆ atiment 563, CEA Saclay, 91191 Gif sur Yvette Cedex, France b
a r t i c l e i n f o
abstract
Article history: Received 16 October 2012 Received in revised form 21 January 2013 Available online 13 February 2013
Ultrathin bismuth iron garnet Bi3Fe5O12 films were grown epitaxially on (001)-oriented gadolinium gallium garnet substrates. Film thickness varied from two to three dozens of unit cells. Bi3Fe5O12 films grow pseudomorphically on substrates up to a thickness of 20 nm, and then a lattice relaxation occurs. Magnetic properties of the films were studied as a function of bismuth iron garnet thickness. The magnetization and cubic anisotropy decrease with decreasing film thickness. The uniaxial magnetocrystalline anisotropy is constant for all film thicknesses. For two unit cell thick films, the easy magnetization axis changes from in-plane to perpendicular to the plane direction. Such a reorientation takes place as a result of the competition of constant uniaxial perpendicular anisotropy with weakening film magnetization. & 2013 Elsevier B.V. All rights reserved.
Keywords: Bismuth iron garnet Ultrathin film Magnetization reorientation Magnetic anisotropy Pulsed laser deposition
1. Introduction Bismuth iron garnet (Bi3Fe5O12 or BIG) is a material with remarkable magneto-optic properties. It possesses the largest known Faraday rotation angle of polarized light. This material is therefore highly interesting for applications involving significant magneto-optic and non-reciprocal effects [1]. The integration of BIG into device heterostructures requires the thorough study of film properties, especially at low thicknesses. Magnetic anisotropies in ultrathin BIG films are particularly of interest for applications. Bismuth iron garnet without any rare-earth cation substitution can be synthesized only in thin film form by non-equilibrium growth techniques. Therefore, there is no reference for the ‘‘bulk’’ BIG properties. BIG is expected to have the same crystallographic and magnetic structures as those of another extensively studied magnetic garnet: Y3Fe5O12 or yttrium iron garnet (YIG). As yttrium iron garnet, BIG should belong to the O10 h (Ia3d) cubic space group and have a magnetization of around 5 mB/(formula unit) at 2 K. However, the magnetic moment measured for BIG thick films (thickness above 700 nm) prepared by different research groups has never exceeded 4.4 mB/(formula unit) [1–3]. There is no way to conclude whether the difference in expected and measured saturation magnetization originates from
n
Corresponding author. Tel.: þ33 139 254672; fax: þ33 139 254652. E-mail address: [email protected] (E. Popova).
0304-8853/$ - see front matter & 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jmmm.2013.02.003
structural modifications in thin film form or is intrinsic for this material. Consequently, the detailed study of BIG magnetic properties is of interest from fundamental point of view, as magnetic properties of this material are not completely understood. A series of completely bismuth substituted films of thickness ranging from 2.5 nm to 40 nm were grown on (001)-oriented gadolinium gallium garnet (GGG) substrates using pulsed laser deposition. Their structural, morphological and magnetic properties were studied. High magneto-optic signal of the films combined with high sensitivity of the ferromagnetic resonance allowed detailed study of magnetic properties of ultrathin BIG films. Theoretical calculations were performed to describe the observed magnetic properties of BIG ultrathin films.
2. Experimental details A series of BIG thin films was epitaxially grown on GGG(001) substrates. The mismatch between lattice parameters of BIG and GGG is about 2% and the first layers of the film undergo an inplane compressive stress. BIG thin film deposition was performed by pulsed laser ablation in an ultra-high vacuum chamber with base pressure of 6.7 10 7 Pa. The target was synthesized with a slight excess of bismuth (Bi/Fe ¼0.64) in order to compensate the cation loss during deposition due to bismuth volatility [4]. The films were grown using a 248 nm KrF laser having pulse duration of 20 ns.
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E. Popova et al. / Journal of Magnetism and Magnetic Materials 335 (2013) 139–143
Prior to the series deposition, a complete study of film properties was conducted in order to determine the best preparation conditions needed to obtain well crystallized and stoichiometric samples [1]. Samples were grown at a temperature of 950 K in oxygen pressure of 5 Pa, regulated by a flow meter. The laser frequency was set to 1 Hz. The fluence was maintained at about 2.1 J/cm2 for all depositions with a target to substrate distance of 5 cm. After the growth, each sample was cooled down in the oxygen atmosphere of 5 Pa and without any post-deposition annealing. The deposition rate was calibrated using a thicker sample and film thicknesses were verified ex situ by a Veeco Dektak profilometer. Reflection high energy electron diffraction (RHEED) from Staib Instruments was used in situ for structural characterization. X-ray diffraction (XRD) measurements were performed using Siemens D5000 and high resolution custom-designed 4-circles X-ray diffractometers. Room temperature Faraday rotation measurements were carried out using a custom-designed magneto-optical magnetometer in the field range 1.3 T to 1.3 T. Quantum Design superconducting quantum interference device (SQUID) magnetometer was used for the saturation magnetization measurement for the film of 350 nm in the field range [ 5 T to 5 T]. Ferromagnetic resonance (FMR) experiments were conducted in X-band on a Varian spectrometer operating at the frequency of 9.08 GHz in the field range [0 T–2 T] at 300 K. Atomic force microscopy (AFM) measurements were carried out with the help of a Bruker AFM setup in contact mode. High resolution transmission electron microscopy (HRTEM) analysis was performed using a Titan3 60– 300 kV microscope fitted with a spherical aberration corrector whose point resolution was equal to 80 pm. The cross-sectional specimens for TEM studies were cut along (010)GGG planes before thinning by tripod grinding and ion milling to attain the electron transparency.
Fig. 1. Lattice parameter of BIG/GGG(001) films determined from XRD and TEM measurements as a function of film thickness. The dashed line represents the expected BIG lattice parameter.
3. Results and discussions 3.1. Film structure and morphology The following epitaxial relation between films and substrates was deduced from RHEED and XRD measurements: (001)[100]BIG99(001)[100]GGG. The out-of-plane lattice parameter was calculated from XRD measurements in Bragg–Brentano configuration. Fig. 1 shows the out-of-plane lattice parameter as a function of film thickness. Due to the low diffraction peak intensity, it was impossible to determine with precision the lattice parameter for films thinner than 8 nm. Therefore, for the thinnest film, TEM images were used for the lattice size determination. The lattice parameter deduced from TEM measurements for the thickest film of the series is shown in Fig. 1 for comparison. Its value corresponds, within the error bars, to the one measured by XRD. Globally, the out-of-plane lattice parameter of BIG films increases by 0.4% with decreasing film thickness. Such an increase at low thicknesses is the consequence of the lattice volume preservation and the lateral compression of the lattice due to the lattice mismatch between the substrate and the film. Apparently, the lattice of the thickest film of the series is relaxed and close to the value estimated theoretically for BIG (Fig. 1). The state of relaxation of films was studied for films of different thicknesses. The corresponding rocking curves around (400) diffraction peak are shown in Fig. 2. For thicknesses below 20 nm a single narrow peak is observed with full width at half maximum (FWHM) of around 0.031. A second large peak with FWHM of 0.31 appears when the film thickness reaches 20 nm. The relative weight of this peak becomes higher as the thickness increases. These results can be interpreted taking into account the models of the epitaxial growth
Fig. 2. XRD rocking curves measured for four BIG/GGG(001) samples of different thicknesses. The curves are shifted along the Y-axis for clarity. Dashed lines represent zero counts for each curve.
in the presence of a lattice mismatch [5]. In the case of intermediate lattice mismatch of a few percents, the film will grow pseudomorphically with the substrate up to some critical thickness which is a function of the misfit. Homogeneous strain accumulates linearly with increasing film thickness and at some point the strain energy becomes greater than the energy of misfit dislocations. Then the commensurability breaks down and misfit dislocations are introduced. The homogeneous strain is replaced with periodic strain and film lattice becomes relaxed on average [5]. In the case of BIG growth on GGG, the narrow diffraction peak corresponds to pseudomorphic BIG film and the area of large peak is proportional to the relaxed part of the film which exhibits a larger mosaicity. Moreover, the pseudomorphic growth of BIG on the substrate with a mismatch induces a tetragonal distortion of the lattice for films of the thickness below 20 nm. The good crystallinity of films and their continuity down to a thickness of two unit cells was confirmed by high resolution transmission electron microscopy. Fig. 3 presents HRTEM image of the thinnest film of the series (nominal thickness of 2.5 nm). It is obvious that the film is perfectly crystallized with an abrupt interface with the substrate (showed by dashed line). Though the film roughness is relatively high, the film is continuous even at low thickness.
E. Popova et al. / Journal of Magnetism and Magnetic Materials 335 (2013) 139–143
141
Root-mean-square (rms) roughness as a function of film thickness was determined from AFM measurements (Fig. 4). It increases significantly with increasing film thickness for the low thicknesses and reaches the saturation value, which is below 10 nm, for films thicker than 150 nm [1]. This roughness, though relatively high, is still suitable for applications.
3.2. FMR and magnetization measurements Ferromagnetic resonance measurements were performed in the geometry presented in Fig. 5. The direction of applied magnetic field varied in and out of the sample plane. These configurations were used to probe various anisotropies of the system. Due to the presence of gadolinium, the substrate gives a strong paramagnetic contribution into overall FMR signal. This contribution does not depend on sample angle with respect to the applied field and can be easily eliminated. The bare substrate contribution was measured and subtracted. A single resonance line of BIG was observed for each sample at every angle between the direction of applied magnetic field and the [001] axis. The linewidth of resonance line varied with the sample thickness and was different for different applied field directions with respect to the sample plane. The largest linewidth for the field applied perpendicularly to the sample plane (E4.5 104 A/m) was measured for 8 nm thick film and the lowest (E4.8 103 A/m) for 350 nm thick film. Fig. 6 summarizes the dependence of the resonance field Hres on the outof-plane angle of the magnetic field for samples with different thicknesses. The perpendicular (yH ¼901) resonance field H? res decreases with decreasing film thickness, while the parallel
Fig. 5. FMR measurement geometry. H and M are applied magnetic field and magnetization of the film respectively. yH (yM) and fH (fM) are the out-of-plane angle and in-plane angle between the applied magnetic field (magnetization) direction and [001] film axis, respectively.
Fig. 6. Resonance field for BIG/GGG(001) films of different thicknesses as a function of the out-of-plane angle of the applied magnetic field. 99
Fig. 3. HRTEM cross-section image of BIG film with thickness of 2.5 nm grown on GGG(001) substrate. The dashed line represents BIG/GGG interface.
Fig. 4. rms roughness of BIG/GGG(001) films determined from AFM measurements as a function of film thickness. The roughness measured at 0 nm corresponds to GGG(001) substrate roughness.
(yH ¼01) resonance field Hres increases for the thinnest samples. Similarly to the case of polycrystalline films of yttrium iron garnet 99 [1], for the thinnest film Hres is higher than H? res . Due to different magnetic anisotropies and interactions in a magnetic film, the precession of magnetic spins takes place in an effective magnetic field Heff, which is different from the applied field H. The effective magnetic field corresponding to resonance fields presented in Fig. 6 can be estimated using Kittel’s formula [6] adapted for the case of a thin film: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi oJres ¼ g HJres ðHJres þHef f Þ o?res ¼ gðH?res Hef f Þ, ð1Þ where ores ¼2pfres, fres is the resonance frequency and g the gyromagnetic ratio. The deduced effective field is presented in Fig. 7. Heff decreases with decreasing film thickness, as observed for several other garnets, epitaxial [7] or polycrystalline [8]. For the thinnest film of 2.5 nm, Heff is negative, indicating the change in the easy axis direction of magnetization from parallel to perpendicular to the film plane. One of the causes that can favor this reorientation could be the slight change of demagnetizing factor due to the thinnest film morphology. However, results obtained previously for ultrathin garnet films [8,9] suggest that the change in demagnetizing field cannot be the only reason for this phenomenon. The effective anisotropy field includes, among other contributions, the film saturation magnetization MS. BIG saturation magnetization as a function of film thickness was deduced from the measured magneto-optic hysteresis loops (Fig. 7). A 350 nm-thick reference film was measured using the SQUID magnetometer. Similar to polycrystalline yttrium iron garnet films [8], magnetization of films decreases significantly with decreasing thickness, following the Heff(thickness)
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dependence (Fig. 7). For films thicker than 20 nm, the coercive field is around 6.5 103 A/m; for thinner films the coercive field is about two to three times smaller. The inset of Fig. 7 shows the Faraday rotation angle as a function of applied field for the thinnest sample of the series (2.5 nm). The measurement was performed at the wavelength of 450 nm. The linear paramagnetic contribution of the substrate was subtracted. The in-plane dependency of the resonance field is shown in 99 Fig. 8. The angular variation of Hres is due to the cubic anisotropy of films. It is usually weak in garnet films with respect to other types of anisotropy, such as shape and uniaxial ones. Apparently, the cubic anisotropy becomes weaker with decreasing thickness and disappears completely in the samples with thickness below 20 nm. These results are in agreement with the structural data that imply the lattice distortion for films thinner than 20 nm. Experimental results for Hres(yH,fH) were adjusted in order to determine the anisotropy contribution into effective field.
3.3. Comparison between experiment and calculations
where EZ is the Zeeman energy, Eu and Ec are the contribution of uniaxial and cubic anisotropy respectively, and Ed corresponds to the magnetostatic energy. Using spherical coordinates, Eq. (2) can be represented in the following form: E ¼ HmðeH UsÞK u Vðez UsÞ2 þK d Vs2z þ Ec ,
ð3Þ
where H is the applied field, m is the magnetic moment and Ku, Kd are the anisotropy constants, V is the sample volume, 99eH99¼1, eH ¼ f(yH,fH), 99s99 ¼1, s¼f(y,f). The first term in Eq. (3) is the Zeeman energy. The second term is the magnetocrystalline anisotropy energy with an unknown uniaxial anisotropy constant Ku. The third term corresponds to the magnetostatic anisotropy, with Kd ¼ m0M2s /2, which is proportional to sample magnetization and therefore known from magnetooptical measurements. It is assumed that demagnetizing factors have the following values: Nxx ¼Nyy ¼0 and Nzz ¼1, thus representing a film with smooth surface. The approximate effects of the surface roughness can be calculated using Ref. [11]:
ps2
,
FMR resonance field was calculated using the Vonsovskii formulation [10] with the following energy contributions:
Nxx ¼ N yy
E ¼ EZ þEu þ Ed þ Ec ,
where s is rms roughness, ls is roughness wavelength and t is the film thickness. For the 20 nm film, the measured rms roughness and roughness wavelength are around 2.8 nm and 25 nm respectively. Inserting these values in Eq. (4) gives Nxx ¼Nyy E0.049 and Nzz ¼1–(Nxx þNyy) E0.902. For 2.5 nm layer, the rms roughness is about 0.8 nm and the roughness wavelength is the same as for the thicker sample. Therefore, the demagnetizing factors are Nxx ¼Nyy E0.032 and Nzz E0.936. This indicates that the demagnetizing field direction is still perpendicular to the film plane and the smooth surface model can be used for a qualitative description of the system and to determine approximate values of the anisotropy. Taking into account that both magnetocrystalline and magnetostatic anisotropies induce the same easy axis direction, their joint contribution can be defined as an effective anisotropy Keff ¼Kd Ku, which represents the total uniaxial anisotropy of the film. Therefore, Eq. (3) can be rewritten in the following form:
ð2Þ
ls t
E ¼ HmðeH UsÞ þ K ef f VðeH UsÞ2 þEc Fig. 7. Saturation magnetization and effective field deduced from magneto-optic and FMR measurements (using Eq. (1)) respectively. The inset shows Faraday rotation measured by magneto-optical setup at 450 nm for the thinnest sample of 2.5 nm.
Fig. 8. Resonance field for BIG/GGG(001) films of different thicknesses as a function of the in-plane angle of the applied magnetic field. The continuous lines represent the fit.
ð4Þ
ð5Þ
In most cases, the ferromagnetic resonance calculation can be done analytically (see for example Ref. [12] for analytical expressions for FMR description in YIG films). However, an expression for the global minima can be found only for very specific configurations of the system; thus the need of a numerical approach in order to calculate said minima. Therefore, the resulting expressions for the resonance field are fitted to experimental measurements by using the robust estimation fitting algorithm [13]. The energy is minimized numerically using Monte Carlo simulation followed by the resolution of the Landau–Lifshitz equation for improved precision. Comparisons between resonance field calculations and experimental measurements show that cubic anisotropy decreases with decreasing thickness (Fig. 9) in agreement with structural data. However, this term is found to be between one and two orders of magnitude lower than all other anisotropies present in BIG films; hence it is not considered further in the fitting process. These comparisons show as well that Ku – and consequently the magnetocrystalline anisotropy – remains relatively constant for all thicknesses (Fig. 10, black line with circles). This means that the change in effective field comes mainly from the change in the demagnetizing field contribution and, more specifically, from changes in MS.
E. Popova et al. / Journal of Magnetism and Magnetic Materials 335 (2013) 139–143
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up to a thickness of 20 nm, inducing tetragonal lattice distortion and absence of cubic anisotropy. With increasing thickness (above 20 nm), a relaxed layer appears and the cubic anisotropy and magnetization increase. The perpendicular uniaxial anisotropy is constant for all film thicknesses. Due to the decrease of saturation magnetization with decreasing thickness, the easy magnetization axis changes direction from in-plane to out-of-plane for the two unit cells thick film. Such an easy axis reorientation was observed for polycrystalline yttrium iron garnet film for the thickness below 10 nm [8] and for the single crystalline films of samarium iron garnet grown on GGG(001) substrates below 30 nm [9]. The common reason for the easy axis reorientation is the decrease of saturation magnetization competing with the constant perpendicular uniaxial anisotropy.
References Fig. 9. Cubic anisotropy determined from the fit of experimental dependences presented in Fig. 8.
Fig. 10. Different anisotropies determined from the experimental data and the fit of experimental dependences presented in Fig. 6 using Eq. (5).
4. Conclusions A series of BIG films of different thicknesses was epitaxially grown on GGG(001) substrates. The film growth mode was pseudomorphic
[1] E. Popova, L. Magdenko, H. Niedoba, M. Deb, B. Dagens, B. Berini, M. Vanwolleghem, C. Vilar, F. Gendron, A. Fouchet, J. Scola, Y. Dumont, M. Guyot, N. Keller, Journal of Applied Physics 112 (2012) 093910. [2] V. Denysenkov, A. Jalali-Roudsar, N. Adachi, S. Khartsev, A. Grishin, T. Okuda, Materials Research Society Symposium Proceedings. 603 (1999) 107. [3] N. Adachi, V.P. Denysenkov, S.I. Khartsev, A.M. Grishin, Joural of Applied Physics 88 (2000) 2734. [4] B. Vertruyen, R. Cloots, J.S. Abell, T.J. Jackson, R.C. de Silva, E. Popova, N. Keller, Physical Review B. 78 (2008) 094429. [5] I.V. Markov, Crystal Growth for Beginners, Fundamentals of Nucleation, Crystal Growth and Epitaxy, second edition, World Scientific, Singapore, 2003. [6] C. Kittel, Physical Review 73 (1948) 155. [7] T. Takeuchi, N. Ohta, Y. Sugita, Journal of Magnetism and Magnetic Materials 31–34 (1983) 925. [8] E. Popova, N. Keller, F. Gendron, L. Thomas, M.-C. Brianso, M. Guyot, M. Tessier, S.S.P. Parkin, Journal of Vacuum Science and Technology A. 19 (2001) 2567. [9] H. Yamahara, M. Mikami, M. Seki, H. Tabata, Journal of Magnetism and Magnetic Materials 323 (2011) 3143. [10] S.V. Vonsovskii, Ferromagnetic Resonance: The Phenomenon of Resonant Absorption of a High-Frequency Magnetic Field in Ferromagnetic Substances, Pergamon Press, Oxford, 1966. ¨ [11] E. Schlomann, R.I. Joseph, Journal of Applied Physics 41 (1970) 1336. [12] S.A. Manuilov, A.M. Grishin, Journal of Applied Physics 108 (2010) 013902. [13] W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flannery, Numerical Recipes in C: The Art of Scientific Computing, Cambridge University Press, New York, 1992.
Contents lists available at SciVerse ScienceDirect
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Magnetic anisotropies in ultrathin bismuth iron garnet films Elena Popova a,n, Andres Felipe Franco Galeano b, Marwan Deb a, Be´ne´dicte Warot-Fonrose c,d, Hamid Kachkachi b, Franc- ois Gendron e, Fre´de´ric Ott f, Bruno Berini a, Niels Keller a a
Groupe d’Etude de la Matie re Condense´e (GEMaC), CNRS/Universite´ de Versailles-Saint-Quentin, 45 Avenue des Etats-Unis, 78035 Versailles, France Laboratoire PROce´de´s, Mate´riaux et Energie Solaire (PROMES), CNRS/Universite´ de Perpignan Via Domitia, 52 Avenue Paul Alduy, 66860 Perpignan, France c Centre d’Elaboration de Mate´riaux et d’Etudes Structurales (CEMES), CNRS, 29 rue Jeanne Marvig, 31055 Toulouse, France d Transpyrenean Associated Laboratory for Electron Microscopy (TALEM), CEMES-INA, CNRS–Universidad de Zaragoza, France and Spain e Institut des NanoSciences de Paris (INSP), CNRS/Universite´ Pierre et Marie Curie-Paris 6, 4 place Jussieu, Boˆıte courrier 840, 75252 Paris Cedex 05, France f Laboratoire Le´on Brillouin (LLB), CNRS/CEA, Bˆ atiment 563, CEA Saclay, 91191 Gif sur Yvette Cedex, France b
a r t i c l e i n f o
abstract
Article history: Received 16 October 2012 Received in revised form 21 January 2013 Available online 13 February 2013
Ultrathin bismuth iron garnet Bi3Fe5O12 films were grown epitaxially on (001)-oriented gadolinium gallium garnet substrates. Film thickness varied from two to three dozens of unit cells. Bi3Fe5O12 films grow pseudomorphically on substrates up to a thickness of 20 nm, and then a lattice relaxation occurs. Magnetic properties of the films were studied as a function of bismuth iron garnet thickness. The magnetization and cubic anisotropy decrease with decreasing film thickness. The uniaxial magnetocrystalline anisotropy is constant for all film thicknesses. For two unit cell thick films, the easy magnetization axis changes from in-plane to perpendicular to the plane direction. Such a reorientation takes place as a result of the competition of constant uniaxial perpendicular anisotropy with weakening film magnetization. & 2013 Elsevier B.V. All rights reserved.
Keywords: Bismuth iron garnet Ultrathin film Magnetization reorientation Magnetic anisotropy Pulsed laser deposition
1. Introduction Bismuth iron garnet (Bi3Fe5O12 or BIG) is a material with remarkable magneto-optic properties. It possesses the largest known Faraday rotation angle of polarized light. This material is therefore highly interesting for applications involving significant magneto-optic and non-reciprocal effects [1]. The integration of BIG into device heterostructures requires the thorough study of film properties, especially at low thicknesses. Magnetic anisotropies in ultrathin BIG films are particularly of interest for applications. Bismuth iron garnet without any rare-earth cation substitution can be synthesized only in thin film form by non-equilibrium growth techniques. Therefore, there is no reference for the ‘‘bulk’’ BIG properties. BIG is expected to have the same crystallographic and magnetic structures as those of another extensively studied magnetic garnet: Y3Fe5O12 or yttrium iron garnet (YIG). As yttrium iron garnet, BIG should belong to the O10 h (Ia3d) cubic space group and have a magnetization of around 5 mB/(formula unit) at 2 K. However, the magnetic moment measured for BIG thick films (thickness above 700 nm) prepared by different research groups has never exceeded 4.4 mB/(formula unit) [1–3]. There is no way to conclude whether the difference in expected and measured saturation magnetization originates from
n
Corresponding author. Tel.: þ33 139 254672; fax: þ33 139 254652. E-mail address: [email protected] (E. Popova).
0304-8853/$ - see front matter & 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jmmm.2013.02.003
structural modifications in thin film form or is intrinsic for this material. Consequently, the detailed study of BIG magnetic properties is of interest from fundamental point of view, as magnetic properties of this material are not completely understood. A series of completely bismuth substituted films of thickness ranging from 2.5 nm to 40 nm were grown on (001)-oriented gadolinium gallium garnet (GGG) substrates using pulsed laser deposition. Their structural, morphological and magnetic properties were studied. High magneto-optic signal of the films combined with high sensitivity of the ferromagnetic resonance allowed detailed study of magnetic properties of ultrathin BIG films. Theoretical calculations were performed to describe the observed magnetic properties of BIG ultrathin films.
2. Experimental details A series of BIG thin films was epitaxially grown on GGG(001) substrates. The mismatch between lattice parameters of BIG and GGG is about 2% and the first layers of the film undergo an inplane compressive stress. BIG thin film deposition was performed by pulsed laser ablation in an ultra-high vacuum chamber with base pressure of 6.7 10 7 Pa. The target was synthesized with a slight excess of bismuth (Bi/Fe ¼0.64) in order to compensate the cation loss during deposition due to bismuth volatility [4]. The films were grown using a 248 nm KrF laser having pulse duration of 20 ns.
140
E. Popova et al. / Journal of Magnetism and Magnetic Materials 335 (2013) 139–143
Prior to the series deposition, a complete study of film properties was conducted in order to determine the best preparation conditions needed to obtain well crystallized and stoichiometric samples [1]. Samples were grown at a temperature of 950 K in oxygen pressure of 5 Pa, regulated by a flow meter. The laser frequency was set to 1 Hz. The fluence was maintained at about 2.1 J/cm2 for all depositions with a target to substrate distance of 5 cm. After the growth, each sample was cooled down in the oxygen atmosphere of 5 Pa and without any post-deposition annealing. The deposition rate was calibrated using a thicker sample and film thicknesses were verified ex situ by a Veeco Dektak profilometer. Reflection high energy electron diffraction (RHEED) from Staib Instruments was used in situ for structural characterization. X-ray diffraction (XRD) measurements were performed using Siemens D5000 and high resolution custom-designed 4-circles X-ray diffractometers. Room temperature Faraday rotation measurements were carried out using a custom-designed magneto-optical magnetometer in the field range 1.3 T to 1.3 T. Quantum Design superconducting quantum interference device (SQUID) magnetometer was used for the saturation magnetization measurement for the film of 350 nm in the field range [ 5 T to 5 T]. Ferromagnetic resonance (FMR) experiments were conducted in X-band on a Varian spectrometer operating at the frequency of 9.08 GHz in the field range [0 T–2 T] at 300 K. Atomic force microscopy (AFM) measurements were carried out with the help of a Bruker AFM setup in contact mode. High resolution transmission electron microscopy (HRTEM) analysis was performed using a Titan3 60– 300 kV microscope fitted with a spherical aberration corrector whose point resolution was equal to 80 pm. The cross-sectional specimens for TEM studies were cut along (010)GGG planes before thinning by tripod grinding and ion milling to attain the electron transparency.
Fig. 1. Lattice parameter of BIG/GGG(001) films determined from XRD and TEM measurements as a function of film thickness. The dashed line represents the expected BIG lattice parameter.
3. Results and discussions 3.1. Film structure and morphology The following epitaxial relation between films and substrates was deduced from RHEED and XRD measurements: (001)[100]BIG99(001)[100]GGG. The out-of-plane lattice parameter was calculated from XRD measurements in Bragg–Brentano configuration. Fig. 1 shows the out-of-plane lattice parameter as a function of film thickness. Due to the low diffraction peak intensity, it was impossible to determine with precision the lattice parameter for films thinner than 8 nm. Therefore, for the thinnest film, TEM images were used for the lattice size determination. The lattice parameter deduced from TEM measurements for the thickest film of the series is shown in Fig. 1 for comparison. Its value corresponds, within the error bars, to the one measured by XRD. Globally, the out-of-plane lattice parameter of BIG films increases by 0.4% with decreasing film thickness. Such an increase at low thicknesses is the consequence of the lattice volume preservation and the lateral compression of the lattice due to the lattice mismatch between the substrate and the film. Apparently, the lattice of the thickest film of the series is relaxed and close to the value estimated theoretically for BIG (Fig. 1). The state of relaxation of films was studied for films of different thicknesses. The corresponding rocking curves around (400) diffraction peak are shown in Fig. 2. For thicknesses below 20 nm a single narrow peak is observed with full width at half maximum (FWHM) of around 0.031. A second large peak with FWHM of 0.31 appears when the film thickness reaches 20 nm. The relative weight of this peak becomes higher as the thickness increases. These results can be interpreted taking into account the models of the epitaxial growth
Fig. 2. XRD rocking curves measured for four BIG/GGG(001) samples of different thicknesses. The curves are shifted along the Y-axis for clarity. Dashed lines represent zero counts for each curve.
in the presence of a lattice mismatch [5]. In the case of intermediate lattice mismatch of a few percents, the film will grow pseudomorphically with the substrate up to some critical thickness which is a function of the misfit. Homogeneous strain accumulates linearly with increasing film thickness and at some point the strain energy becomes greater than the energy of misfit dislocations. Then the commensurability breaks down and misfit dislocations are introduced. The homogeneous strain is replaced with periodic strain and film lattice becomes relaxed on average [5]. In the case of BIG growth on GGG, the narrow diffraction peak corresponds to pseudomorphic BIG film and the area of large peak is proportional to the relaxed part of the film which exhibits a larger mosaicity. Moreover, the pseudomorphic growth of BIG on the substrate with a mismatch induces a tetragonal distortion of the lattice for films of the thickness below 20 nm. The good crystallinity of films and their continuity down to a thickness of two unit cells was confirmed by high resolution transmission electron microscopy. Fig. 3 presents HRTEM image of the thinnest film of the series (nominal thickness of 2.5 nm). It is obvious that the film is perfectly crystallized with an abrupt interface with the substrate (showed by dashed line). Though the film roughness is relatively high, the film is continuous even at low thickness.
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Root-mean-square (rms) roughness as a function of film thickness was determined from AFM measurements (Fig. 4). It increases significantly with increasing film thickness for the low thicknesses and reaches the saturation value, which is below 10 nm, for films thicker than 150 nm [1]. This roughness, though relatively high, is still suitable for applications.
3.2. FMR and magnetization measurements Ferromagnetic resonance measurements were performed in the geometry presented in Fig. 5. The direction of applied magnetic field varied in and out of the sample plane. These configurations were used to probe various anisotropies of the system. Due to the presence of gadolinium, the substrate gives a strong paramagnetic contribution into overall FMR signal. This contribution does not depend on sample angle with respect to the applied field and can be easily eliminated. The bare substrate contribution was measured and subtracted. A single resonance line of BIG was observed for each sample at every angle between the direction of applied magnetic field and the [001] axis. The linewidth of resonance line varied with the sample thickness and was different for different applied field directions with respect to the sample plane. The largest linewidth for the field applied perpendicularly to the sample plane (E4.5 104 A/m) was measured for 8 nm thick film and the lowest (E4.8 103 A/m) for 350 nm thick film. Fig. 6 summarizes the dependence of the resonance field Hres on the outof-plane angle of the magnetic field for samples with different thicknesses. The perpendicular (yH ¼901) resonance field H? res decreases with decreasing film thickness, while the parallel
Fig. 5. FMR measurement geometry. H and M are applied magnetic field and magnetization of the film respectively. yH (yM) and fH (fM) are the out-of-plane angle and in-plane angle between the applied magnetic field (magnetization) direction and [001] film axis, respectively.
Fig. 6. Resonance field for BIG/GGG(001) films of different thicknesses as a function of the out-of-plane angle of the applied magnetic field. 99
Fig. 3. HRTEM cross-section image of BIG film with thickness of 2.5 nm grown on GGG(001) substrate. The dashed line represents BIG/GGG interface.
Fig. 4. rms roughness of BIG/GGG(001) films determined from AFM measurements as a function of film thickness. The roughness measured at 0 nm corresponds to GGG(001) substrate roughness.
(yH ¼01) resonance field Hres increases for the thinnest samples. Similarly to the case of polycrystalline films of yttrium iron garnet 99 [1], for the thinnest film Hres is higher than H? res . Due to different magnetic anisotropies and interactions in a magnetic film, the precession of magnetic spins takes place in an effective magnetic field Heff, which is different from the applied field H. The effective magnetic field corresponding to resonance fields presented in Fig. 6 can be estimated using Kittel’s formula [6] adapted for the case of a thin film: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi oJres ¼ g HJres ðHJres þHef f Þ o?res ¼ gðH?res Hef f Þ, ð1Þ where ores ¼2pfres, fres is the resonance frequency and g the gyromagnetic ratio. The deduced effective field is presented in Fig. 7. Heff decreases with decreasing film thickness, as observed for several other garnets, epitaxial [7] or polycrystalline [8]. For the thinnest film of 2.5 nm, Heff is negative, indicating the change in the easy axis direction of magnetization from parallel to perpendicular to the film plane. One of the causes that can favor this reorientation could be the slight change of demagnetizing factor due to the thinnest film morphology. However, results obtained previously for ultrathin garnet films [8,9] suggest that the change in demagnetizing field cannot be the only reason for this phenomenon. The effective anisotropy field includes, among other contributions, the film saturation magnetization MS. BIG saturation magnetization as a function of film thickness was deduced from the measured magneto-optic hysteresis loops (Fig. 7). A 350 nm-thick reference film was measured using the SQUID magnetometer. Similar to polycrystalline yttrium iron garnet films [8], magnetization of films decreases significantly with decreasing thickness, following the Heff(thickness)
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dependence (Fig. 7). For films thicker than 20 nm, the coercive field is around 6.5 103 A/m; for thinner films the coercive field is about two to three times smaller. The inset of Fig. 7 shows the Faraday rotation angle as a function of applied field for the thinnest sample of the series (2.5 nm). The measurement was performed at the wavelength of 450 nm. The linear paramagnetic contribution of the substrate was subtracted. The in-plane dependency of the resonance field is shown in 99 Fig. 8. The angular variation of Hres is due to the cubic anisotropy of films. It is usually weak in garnet films with respect to other types of anisotropy, such as shape and uniaxial ones. Apparently, the cubic anisotropy becomes weaker with decreasing thickness and disappears completely in the samples with thickness below 20 nm. These results are in agreement with the structural data that imply the lattice distortion for films thinner than 20 nm. Experimental results for Hres(yH,fH) were adjusted in order to determine the anisotropy contribution into effective field.
3.3. Comparison between experiment and calculations
where EZ is the Zeeman energy, Eu and Ec are the contribution of uniaxial and cubic anisotropy respectively, and Ed corresponds to the magnetostatic energy. Using spherical coordinates, Eq. (2) can be represented in the following form: E ¼ HmðeH UsÞK u Vðez UsÞ2 þK d Vs2z þ Ec ,
ð3Þ
where H is the applied field, m is the magnetic moment and Ku, Kd are the anisotropy constants, V is the sample volume, 99eH99¼1, eH ¼ f(yH,fH), 99s99 ¼1, s¼f(y,f). The first term in Eq. (3) is the Zeeman energy. The second term is the magnetocrystalline anisotropy energy with an unknown uniaxial anisotropy constant Ku. The third term corresponds to the magnetostatic anisotropy, with Kd ¼ m0M2s /2, which is proportional to sample magnetization and therefore known from magnetooptical measurements. It is assumed that demagnetizing factors have the following values: Nxx ¼Nyy ¼0 and Nzz ¼1, thus representing a film with smooth surface. The approximate effects of the surface roughness can be calculated using Ref. [11]:
ps2
,
FMR resonance field was calculated using the Vonsovskii formulation [10] with the following energy contributions:
Nxx ¼ N yy
E ¼ EZ þEu þ Ed þ Ec ,
where s is rms roughness, ls is roughness wavelength and t is the film thickness. For the 20 nm film, the measured rms roughness and roughness wavelength are around 2.8 nm and 25 nm respectively. Inserting these values in Eq. (4) gives Nxx ¼Nyy E0.049 and Nzz ¼1–(Nxx þNyy) E0.902. For 2.5 nm layer, the rms roughness is about 0.8 nm and the roughness wavelength is the same as for the thicker sample. Therefore, the demagnetizing factors are Nxx ¼Nyy E0.032 and Nzz E0.936. This indicates that the demagnetizing field direction is still perpendicular to the film plane and the smooth surface model can be used for a qualitative description of the system and to determine approximate values of the anisotropy. Taking into account that both magnetocrystalline and magnetostatic anisotropies induce the same easy axis direction, their joint contribution can be defined as an effective anisotropy Keff ¼Kd Ku, which represents the total uniaxial anisotropy of the film. Therefore, Eq. (3) can be rewritten in the following form:
ð2Þ
ls t
E ¼ HmðeH UsÞ þ K ef f VðeH UsÞ2 þEc Fig. 7. Saturation magnetization and effective field deduced from magneto-optic and FMR measurements (using Eq. (1)) respectively. The inset shows Faraday rotation measured by magneto-optical setup at 450 nm for the thinnest sample of 2.5 nm.
Fig. 8. Resonance field for BIG/GGG(001) films of different thicknesses as a function of the in-plane angle of the applied magnetic field. The continuous lines represent the fit.
ð4Þ
ð5Þ
In most cases, the ferromagnetic resonance calculation can be done analytically (see for example Ref. [12] for analytical expressions for FMR description in YIG films). However, an expression for the global minima can be found only for very specific configurations of the system; thus the need of a numerical approach in order to calculate said minima. Therefore, the resulting expressions for the resonance field are fitted to experimental measurements by using the robust estimation fitting algorithm [13]. The energy is minimized numerically using Monte Carlo simulation followed by the resolution of the Landau–Lifshitz equation for improved precision. Comparisons between resonance field calculations and experimental measurements show that cubic anisotropy decreases with decreasing thickness (Fig. 9) in agreement with structural data. However, this term is found to be between one and two orders of magnitude lower than all other anisotropies present in BIG films; hence it is not considered further in the fitting process. These comparisons show as well that Ku – and consequently the magnetocrystalline anisotropy – remains relatively constant for all thicknesses (Fig. 10, black line with circles). This means that the change in effective field comes mainly from the change in the demagnetizing field contribution and, more specifically, from changes in MS.
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up to a thickness of 20 nm, inducing tetragonal lattice distortion and absence of cubic anisotropy. With increasing thickness (above 20 nm), a relaxed layer appears and the cubic anisotropy and magnetization increase. The perpendicular uniaxial anisotropy is constant for all film thicknesses. Due to the decrease of saturation magnetization with decreasing thickness, the easy magnetization axis changes direction from in-plane to out-of-plane for the two unit cells thick film. Such an easy axis reorientation was observed for polycrystalline yttrium iron garnet film for the thickness below 10 nm [8] and for the single crystalline films of samarium iron garnet grown on GGG(001) substrates below 30 nm [9]. The common reason for the easy axis reorientation is the decrease of saturation magnetization competing with the constant perpendicular uniaxial anisotropy.
References Fig. 9. Cubic anisotropy determined from the fit of experimental dependences presented in Fig. 8.
Fig. 10. Different anisotropies determined from the experimental data and the fit of experimental dependences presented in Fig. 6 using Eq. (5).
4. Conclusions A series of BIG films of different thicknesses was epitaxially grown on GGG(001) substrates. The film growth mode was pseudomorphic
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