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Interplay of shape and magnetocrystalline anisotropy in electrodeposited Fe3O4 films
Journal of Magnetism and Magnetic Materials 361 (2014) 107–111
Contents lists available at ScienceDirect
Journal of Magnetism and Magnetic Materials journal homepage: www.elsevier.com/locate/jmmm
Interplay of shape and magnetocrystalline anisotropy in electrodeposited Fe3O4 films Rui Wu a, Xue Gang Chen a, Jian Zhong Wei a, Yun Bo Yang a, Yuan Hua Xia a, Xiao Bai Ma a, Jin Bo Yang a,b,n a b
State Key Laboratory for Mesoscopic Physics, School of Physics, Peking University, Beijing 100871, PR China Collaborative Innovation Center of Quantum Matter, Beijing, PR China
art ic l e i nf o
a b s t r a c t
Article history: Received 30 January 2013 Received in revised form 18 December 2013 Available online 3 March 2014
Fe3O4 thin films have been grown on ITO glass substrates using an electrodeposition technique. The properties of the films can be tuned by changing the electric potential within 1.00 V to 1.22 V. Preferred crystalline orientation along 〈511〉 arises in the samples prepared with the potentials of 1.06 V to 1.08 V. An apparent decrease of the in-plane coercivity is found in these films with preferred orientation. A simple model considering the interplay of shape anisotropy and magnetocrystalline anisotropy, which leads to a weaker effective plane anisotropy in the oriented films, is given to explain the decrease of coercivity. & 2014 Elsevier B.V. All rights reserved.
Keywords: Fe3O4 Electrodeposition Thin film Magnetic anisotropy Interplay
1. Introduction Recently, half-metallic materials with 100% spin polarization including Fe3O4, CrO2, La0.7Sr0.3MnO3 and some other Heusler alloys have attracted considerable attention due to their potential applications in the spintronics, such as magnetic random access memory (MRAM) and spin valves [1–3]. Among these materials, Fe3O4 has the highest Curie temperature (858 K) and is therefore a suitable candidate for spintronics devices [4]. Many traditional methods, such as molecular beam epitaxy and electron beam evaporation, have been developed to prepare thin films for all kinds of applications. Among these methods, electrodeposition is a relatively simple method and can be applied to prepare magnetic films [5–7]. For magnetic materials, crystalline orientation plays an important role in the determination of the magnetic properties by affecting the magnetocrystalline anisotropy directions. In the constrained magnetic structures, such as thin films and nanorods, shape anisotropy may become dominant. The interplay of shape and other anisotropy provides a new route to tune the magnetic properties [8,9]. Experimentally, the microstructure including crystalline orientation can be tuned by the conditions used in the synthesis process of the
n Corresponding author at: School of Physics, Peking University, No. 5 Yiheyuan Road, Haidian District, Beijing 100871, PR China. Tel.: þ 86 10 62753459; fax: þ86 10 62751615. E-mail address: [email protected] (J.B. Yang).
http://dx.doi.org/10.1016/j.jmmm.2014.02.076 0304-8853 & 2014 Elsevier B.V. All rights reserved.
electrodeposition, for instance, to change the potential, current density and the composition of the bath [10–12]. In this paper, series of iron oxide films were electrodeposited on ITO glasses with the potential in the range of 1.00 to 1.22 V. It was found that the preferred orientation can significantly reduce the coercivity of the samples. The decrease of coercivity can be described by a model considering competition of the shape and magnetocrystalline anisotropies in the film. The magnetocrystalline anisotropy in these oriented films leads to an out-of-plane equilibrium magnetization, which reduces the local energy barrier when the magnetization of each grain is reversed.
2. Experimental details Thin films of iron oxide were prepared with a similar method reported by Kulp et al. [6]. The experimental setup was composed of an electrochemical studio (Chenhua CHI600D), a constant temperature water bath and a reaction beaker. The standard three-electrode mode was applied. The working electrode was ITO glass which was cleaned in the deionized water and then in the acetone with an ultrasonic cleaner for 5 min prior to use. A platinum wire was served as a counter electrode. In this work, all potentials are quoted relative to Ag/AgCl reference electrode. A Fe(III)–TEA solution composed of 0.048 M Fe2(SO4)3, 1 M NaOH and 0.1 M triethanolamine (TEA) was used by pouring the Fe2(SO4)3 powder slowly into the stirring solution of NaOH and TEA. The temperature of the electrolyte was kept at 80 1C
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R. Wu et al. / Journal of Magnetism and Magnetic Materials 361 (2014) 107–111
throughout the preparation process. Films were deposited with constant applied potentials ( 1.00 V to 1.22 V) and the process was terminated when the total charge was up to 1 C/cm2. The reaction process can be described by the following equations: FeðTEAÞ3 þ þ e - Fe2 þ þ TEA
ð1Þ
Fe2 þ þ 2FeðTEAÞ3 þ þ8OH - Fe3 O4 þ 2TEA þ 4H2 O
ð2Þ
X-ray diffraction (XRD) measurement was performed using a high-resolution Philips X’Pert X-ray diffractometer with a Cu Kα1,2 radiation resource (λ ¼1.54056 ˚). Scans were run from 151 to 801 2θ at a rate of 31/min with a step size of 0.031. The scanning electron microscope (SEM) was used to analyze surface morphology. The alternating gradient magnetometer (AGM) was used for magnetic measurements with external field parallel and perpendicular to the films.
〈400〉 and 〈511〉 can be seen, whereas the intensities corresponding to Miller indices 〈111〉 and 〈222〉 decrease significantly (Fig. 1). This indicates that there is a preferred orientation along 〈400〉 or 〈511〉 direction in the films deposited with potential from 1.06 V to 1.08 V. The FULLPROF program with a cubic model (space group Fd-3m) was used to refine the XRD data for those films deposited in the potential of 1.00 V to 1.16 V, where the main phase is Fe3O4 [13]. The preferred orientation of the 〈511〉 is further refined in order to quantitatively evaluate the preferred orientation in these samples using the function P hkl ¼ G2 þ ð1 G2 ÞexpðG1 α2hkl Þ
ð3Þ
P hkl is the peak intensity contribution of preferred orientation of 〈hkl〉 plane. αhkl is the acute angle between the scattering vector and the normal to the crystallites. G1 and G2 are refinable parameters. In our refinement, the factor G2 was fixed to 0, only the parameter G1 was refined. Fig. 2 shows the refined lattice parameters a0 and the preferred orientation parameter G1 of 〈511〉
3. Results and discussion Different colors are shown when films are deposited at different potentials. The films deposited in the potential of 1.00 to 1.04 V are black gray while those deposited in the potential of 1.06 to 1.08 V are bright gray and reflective like a mirror. Those deposited in the potential of 1.10 to 1.18 V are black at the beginning, and reddish brown afterwards when dried in the air. The films deposited at 1.20 V and above change their colors from translucent green to red when dried in the air. The colors of the films deposited in 1.06 to 1.08 V indicate well-formed texture which is in accordance with our XRD results. Between the depositing potentials of 1.06 and 1.08 V, an increase of the XRD peak intensity corresponding to Miller indices
Fig. 2. The lattice parameters (square) and the preferred orientation parameters of 〈511〉 (round) are given by the refinement of the XRD data. Lines are provided as a guide to the eye.
Fig. 1. Typical X-ray diffraction patterns of Fe3O4 films. Red symbols represent the experimental patterns, black lines represent the calculated ones while the blue curves at the bottom show the difference between experimental and calculated patterns. The vertical bars are Bragg peak positions. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
R. Wu et al. / Journal of Magnetism and Magnetic Materials 361 (2014) 107–111
orientation. The lattice parameters of the samples deposited at 1.00 V and 1.16 V are 0.84175 nm and 0.83920 nm, respectively. The lattice parameter shows a tendency of decrease with increasing potential. This is related to the nonstoichiometry of the Fe to O ratio in these samples. With the increasing potentials, the growth of the films becomes faster and leads to more cation vacancies in the films [14]. The preferred orientation parameter G1 of 〈511〉 increases and reaches its maximum at the vicinity of the potential 1.08 V. It indicates that films deposited in 1.06 to 1.08 V have a preferred orientation along 〈511〉. The intensity of the 〈400〉 peak has the similar behavior to that of the 〈511〉 peak in Fig. 1, which is reasonable with the fact that the angle between 〈511〉 and 〈400〉 directions is only 15.791. According to the SEM images, the potential has a notable effect on the film surface morphology. The films deposited in the potential range of 1.00 to 1.04 V show highly faceted and dense morphology (Fig. 3(a)). In the potential range of 1.06 to 1.08 V, the surface of the films exhibits rounded and featureless morphology (Fig. 3(b)), which is related to the preferred orientation. At the potential of 1.10 V and above, ferrihydrite nanoribbons begin to grow on the top of magnetite films (Fig. 3(c)). At 1.14 V, the film shows a magnetite-ferrihydrite bi-layer structure (Fig. 3(d)). Moreover, the grain size increases with the potential in the range of 1.00 to 1.10 V, which can be ascribed to the potential dependence of deposition efficiency. The thickness and grain size increase with the deposition efficiency during 1.00 to 1.10 V, although the total charge was kept constant for all samples. For films deposited with the potential higher than 1.10 V, bilayer structure formed and the thickness of the Fe3O4 layer was reduced. Then the average grain size reaches its maximum at 1.08 V. In order to study the magnetic properties of the films, hysteresis loops of the samples deposited in the potential range of 1.00 to 1.16 V were measured with AGM. As a result of dipolar interaction, the magnetization of the Fe3O4 films favors an in-plane orientation (Fig. 4), which is called dipolar anisotropy or shape anisotropy [15]. Hysteresis loops of different potential are given in Fig. 5. The saturation magnetization of the sample prepared at 1.08 V is calculated to be 88 emu/g with the thickness assumed to be 1.16 μm according to the total charge
109
transfer during the preparation. That is very close to the bulk magnetization of Fe3O4 (92 emu/g), indicating high deposition efficiency at 1.08 V. From the total magnetization of unit area (emu/cm2), the thickness of all these samples is calculated and
Fig. 4. Room temperature M–H hysteresis loops with H applied parallel and perpendicular to the Fe3O4 film surface (the sample is obtained at 1.02 V). The inset highlights the region at low field.
Fig. 5. The hysteresis loops of samples deposited at different potentials (left) and their coercivities (black square), calculated thickness (red circle) as a function of potential (right). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 3. SEM images of films deposited at (a) 1.00 V, (b) 1.08 V, (c) 1.10 V, and (d) 1.14 V.
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R. Wu et al. / Journal of Magnetism and Magnetic Materials 361 (2014) 107–111
shown in Fig. 5. The thickness of the samples prepared at 1.00 V and 1.16 V is estimated to be about 0.55 μm and 0.20 μm, respectively. The change of thickness with the potential is in accordance with the change of grain size obtained by SEM. The obtained coercivities of the films with the applied magnetic field parallel to the film surface are plotted as a function of the applied potentials in Fig. 5. The coercivity clearly shows a minimum at the vicinity of the potential 1.08 V, where the preferred orientation parameter of 〈511〉 reaches its maximum. Usually, the coercivity is affected by the grain size of the film. Multi-domain grain crystal will show much lower coercivity than that of single domain crystal. However, the change of coercivity shown here is not caused by the transition between multi-domain and single domain grains since the average grain size of the film is much larger than the size of a single domain (less than 50 nm). According to the orientation parameter shown in Fig. 2, it can be inferred that the coercivity decreases greatly when the preferred orientation parameter increases. The decrease of coercivities in these films with preferred orientation can be explained by a model considering the interplay of shape anisotropy (SA) and magnetocrystalline anisotropy (MA). In the films without preferred orientation, the in-plane shape anisotropy plays a major role; the random local magnetocrystalline anisotropy cancels each other giving zero macroscopic magnetocrystalline anisotropy. The free energy density can be described as the phenomenological expressions [16]
εs ¼ k0 þ k1 cos 2 θ
ð4Þ
In the film with preferred orientation, the magnetocrystalline contributions cannot cancel each other. For cubic crystal, the free energy density can be written as
εm ¼ k0' þk1' ðs2x s2y þ s2y s2z þ s2x s2z Þ þ k2' sx sy sz
ð5Þ
where k0,1 and k´0,1,2 are anisotropy constants and θ is the magnetization angle with respect to the film planesx,y,z are magnetization components with the relationship sx ¼ sin θ cos φ, sx ¼ sin θ sin φ, and sz ¼ cos θ, where θ and φare the magnetization angle with respect to film normal and xz plane,
respectively. Then, the total free energy can be expressed as
εa ¼ εs þ εm
ð6Þ
Bulk Fe3O4 has a cubic structure, with the 〈111〉 and 〈100〉 directions being easy and hard axes of magnetization, respectively [17]. The magnetocrystalline energy can be well described in Eq. (5) with k´1 o 0 and k´2 ¼0. Based on Eqs. (4)–(6), the free energy landscape and the equilibrium magnetization which lies in the local minimum of the free energy landscape were calculated and plotted in Fig. 6(a) and (b), giving an illustration to the relationship between the equilibrium magnetization direction and the ratio of shape anisotropy and magnetocrystalline anisotropy (k1 / | k´1|). In films prepared at 1.00 V and 1.16 V, stronger shape anisotropy is given by thinner thickness and at the same time the macroscopic magnetocrystalline anisotropy is reduced by randomness of orientation. Generally speaking, the randomness of the anisotropy will reduce the coercivity of the system of randomly oriented noninteracting single domain particles. It was calculated to be Hc ¼ 0.479 Hk and Hc 0.185 Hk with uniaxial anisotropy and cubic anisotropy (k´1 o0), respectively, where Hc and Hk are the coercive field and anisotropy field [18,19]. However, in the film with SA, not all the local magnetization of the grains can stay in local energy minimum. On the contrary, most of the local magnetization will stay apart from local energy minimum to in-plane direction and cannot reverse via local saddle points (Fig. 6(a), k1 / | k´1| ¼2.5), which will give a larger coercivity. In those films with 〈511〉 orientation, the equilibrium magnetization will not favor the in-plane direction any more due to the cubic property of the magnetocrystalline anisotropy with 〈111〉 direction easy axis in Fe3O4 and the reduced SA due to the increase of thickness (Fig. 6(b), k1 / | k´1| ¼0.4). Actually, the equilibrium magnetization will be lift close to 〈111〉 direction and closer to the saddle point of the energy landscape. This will cause a drastic decrease of local anisotropy energy barrier for reversing the magnetization. In another word, interplay between the two magnetic anisotropy contributions changes the route of the magnetization reversal,
Fig. 6. (a) Free energy landscape with major component of shape anisotropy (k1 / |k´1| ¼ 2.5) and (b) energy landscape of coexistence of shape and magnetocrystalline anisotropy k1 / |k´1| ¼ 0.4).
R. Wu et al. / Journal of Magnetism and Magnetic Materials 361 (2014) 107–111
resulting in a weaker effective anisotropy barrier and a lower coercivity in the oriented films. 4. Conclusions In summary, we have investigated the interplay between the shape anisotropy and the magnetocrystalline anisotropy in electrodeposited Fe3O4 films. The refinement of the XRD data shows that the films have preferred orientations along 〈511〉 at a potential around 1.08 V. The lattice parameter of the film decreases with increasing applied potentials due to that more cation vacancies produce at higher growing speed. It was found that the coercivity of the films reached its minimum at the potential around 1.08 V. An orientation-caused coercivity mechanism can be clearly observed in the experiment data. A simple model including interplay between shape anisotropy and magnetocrystalline anisotropy was introduced to give a quantitative explanation to the experimental results. The magnetocrystalline anisotropy emerging in the oriented films pulls the equilibrium magnetization away from the film plane, which reduces the local free energy barrier and coercivity. This provides a new route to tune the magnetic anisotropy in the Fe-oxide magnetic films. Acknowledgments This work has been supported by the National Natural Science Foundation of China (Grant nos. 51371009, 50971003 and 51171001), National Basic Research Program of China (No. 2010CB833104, MOST
111
of China), and National High Technology Research and Development Program of China (No. 2011AA03A403).
References [1] K. Nishimura, Y. Kohara, Y. Kitamoto, M. Abe, J. Appl. Phys. 87 (2000) 7121. [2] K. Schwarzt, J. Phys. F 16 (1986) L211. [3] J.-H. Park, E. Vescovo, H.-J. Kim, C. Kwon, R. Ramesh, T. Venkatesan, Nature 392 (1998) 794. [4] P. Sensor, A. Fert, J.-L. Maurice, F. Montaigne, F. Petroff, A. Vauress, Appl. Phys. Lett. 74 (1999) 4017. [5] S. Chatman, Adam J. G Noel, Kristin M. Poduska, J. Appl. Phys. 98 (2005) 113902. [6] E.A. Kulp, H.M. Kothari, S.J. Limmer, Chem. Mater. 21 (2009) 5022. [7] Rakesh V. Gudavarthy, S. Gorantla, G.J. Mu, Chem. Mater 23 (2017) (2011). [8] A. Brandlmaier, S. Geprägs, M. Weiler, A. Boger, M. Opel, Phys. Rev. B 77 (2008) 104445. [9] J. Sánchez-Barriga, M. Lucas, F. Radu, E. Martin, M. Multigner, P. Marin, A. Hernando, G. Rivero, Phys. Rev. B 80 (2009) 184424. [10] S. Yoshimura, S. Yoshihara, T. Shirakashi, E. Sato, Electrochim. Acta. 39 (1994) 589. [11] F. Maurer, J. Brötz, S. Karim, M.E.T. Molares, C. Trautmann, H. Fuess, Nanotechnology 18 (2007) 135709. [12] J. Fustes, A. Gomes, M.I. da Silva Pereira, J. Solid State Electrochem. 12 (2008) 1435. [13] J. Rodriguez-Carvajal, Program: FULLPROF, Version Feb-2007, 2007. [14] J.B. Yang, X.D. Zhou, W.B. Yelon, W.J. James, Q. Cai, K.V. Gopalakrishnan, S.K. Malik, X.C. Sun, D.E. Nikles, J. Appl. Phys. 95 (2004) 7540. [15] M.T. Johnsony, P.J.H. Bloemenzx, F.J.A. den Broedery, J.J. de Vriesz, Rep. Prog. Phys. 59 (1996) 1409–1458. [16] J.M.D. Coey, Magnetism and Magnetic Materials, Cambridge, New York (2009) 270. [17] G.F. Goya, T.S. Berquó, F.C. Fonseca, M.P. Morales, J. Appl. Phys. 94 (2003) 3520. [18] E.C. Stoner, E.P. Wohlfarth, Phil. Trans. R. Soc. Lond. A 240 (1948) 599. [19] N.A. Usov, S.E. Peschany, J. Magn. Magn. Mater. 174 (1997) 247.
Contents lists available at ScienceDirect
Journal of Magnetism and Magnetic Materials journal homepage: www.elsevier.com/locate/jmmm
Interplay of shape and magnetocrystalline anisotropy in electrodeposited Fe3O4 films Rui Wu a, Xue Gang Chen a, Jian Zhong Wei a, Yun Bo Yang a, Yuan Hua Xia a, Xiao Bai Ma a, Jin Bo Yang a,b,n a b
State Key Laboratory for Mesoscopic Physics, School of Physics, Peking University, Beijing 100871, PR China Collaborative Innovation Center of Quantum Matter, Beijing, PR China
art ic l e i nf o
a b s t r a c t
Article history: Received 30 January 2013 Received in revised form 18 December 2013 Available online 3 March 2014
Fe3O4 thin films have been grown on ITO glass substrates using an electrodeposition technique. The properties of the films can be tuned by changing the electric potential within 1.00 V to 1.22 V. Preferred crystalline orientation along 〈511〉 arises in the samples prepared with the potentials of 1.06 V to 1.08 V. An apparent decrease of the in-plane coercivity is found in these films with preferred orientation. A simple model considering the interplay of shape anisotropy and magnetocrystalline anisotropy, which leads to a weaker effective plane anisotropy in the oriented films, is given to explain the decrease of coercivity. & 2014 Elsevier B.V. All rights reserved.
Keywords: Fe3O4 Electrodeposition Thin film Magnetic anisotropy Interplay
1. Introduction Recently, half-metallic materials with 100% spin polarization including Fe3O4, CrO2, La0.7Sr0.3MnO3 and some other Heusler alloys have attracted considerable attention due to their potential applications in the spintronics, such as magnetic random access memory (MRAM) and spin valves [1–3]. Among these materials, Fe3O4 has the highest Curie temperature (858 K) and is therefore a suitable candidate for spintronics devices [4]. Many traditional methods, such as molecular beam epitaxy and electron beam evaporation, have been developed to prepare thin films for all kinds of applications. Among these methods, electrodeposition is a relatively simple method and can be applied to prepare magnetic films [5–7]. For magnetic materials, crystalline orientation plays an important role in the determination of the magnetic properties by affecting the magnetocrystalline anisotropy directions. In the constrained magnetic structures, such as thin films and nanorods, shape anisotropy may become dominant. The interplay of shape and other anisotropy provides a new route to tune the magnetic properties [8,9]. Experimentally, the microstructure including crystalline orientation can be tuned by the conditions used in the synthesis process of the
n Corresponding author at: School of Physics, Peking University, No. 5 Yiheyuan Road, Haidian District, Beijing 100871, PR China. Tel.: þ 86 10 62753459; fax: þ86 10 62751615. E-mail address: [email protected] (J.B. Yang).
http://dx.doi.org/10.1016/j.jmmm.2014.02.076 0304-8853 & 2014 Elsevier B.V. All rights reserved.
electrodeposition, for instance, to change the potential, current density and the composition of the bath [10–12]. In this paper, series of iron oxide films were electrodeposited on ITO glasses with the potential in the range of 1.00 to 1.22 V. It was found that the preferred orientation can significantly reduce the coercivity of the samples. The decrease of coercivity can be described by a model considering competition of the shape and magnetocrystalline anisotropies in the film. The magnetocrystalline anisotropy in these oriented films leads to an out-of-plane equilibrium magnetization, which reduces the local energy barrier when the magnetization of each grain is reversed.
2. Experimental details Thin films of iron oxide were prepared with a similar method reported by Kulp et al. [6]. The experimental setup was composed of an electrochemical studio (Chenhua CHI600D), a constant temperature water bath and a reaction beaker. The standard three-electrode mode was applied. The working electrode was ITO glass which was cleaned in the deionized water and then in the acetone with an ultrasonic cleaner for 5 min prior to use. A platinum wire was served as a counter electrode. In this work, all potentials are quoted relative to Ag/AgCl reference electrode. A Fe(III)–TEA solution composed of 0.048 M Fe2(SO4)3, 1 M NaOH and 0.1 M triethanolamine (TEA) was used by pouring the Fe2(SO4)3 powder slowly into the stirring solution of NaOH and TEA. The temperature of the electrolyte was kept at 80 1C
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R. Wu et al. / Journal of Magnetism and Magnetic Materials 361 (2014) 107–111
throughout the preparation process. Films were deposited with constant applied potentials ( 1.00 V to 1.22 V) and the process was terminated when the total charge was up to 1 C/cm2. The reaction process can be described by the following equations: FeðTEAÞ3 þ þ e - Fe2 þ þ TEA
ð1Þ
Fe2 þ þ 2FeðTEAÞ3 þ þ8OH - Fe3 O4 þ 2TEA þ 4H2 O
ð2Þ
X-ray diffraction (XRD) measurement was performed using a high-resolution Philips X’Pert X-ray diffractometer with a Cu Kα1,2 radiation resource (λ ¼1.54056 ˚). Scans were run from 151 to 801 2θ at a rate of 31/min with a step size of 0.031. The scanning electron microscope (SEM) was used to analyze surface morphology. The alternating gradient magnetometer (AGM) was used for magnetic measurements with external field parallel and perpendicular to the films.
〈400〉 and 〈511〉 can be seen, whereas the intensities corresponding to Miller indices 〈111〉 and 〈222〉 decrease significantly (Fig. 1). This indicates that there is a preferred orientation along 〈400〉 or 〈511〉 direction in the films deposited with potential from 1.06 V to 1.08 V. The FULLPROF program with a cubic model (space group Fd-3m) was used to refine the XRD data for those films deposited in the potential of 1.00 V to 1.16 V, where the main phase is Fe3O4 [13]. The preferred orientation of the 〈511〉 is further refined in order to quantitatively evaluate the preferred orientation in these samples using the function P hkl ¼ G2 þ ð1 G2 ÞexpðG1 α2hkl Þ
ð3Þ
P hkl is the peak intensity contribution of preferred orientation of 〈hkl〉 plane. αhkl is the acute angle between the scattering vector and the normal to the crystallites. G1 and G2 are refinable parameters. In our refinement, the factor G2 was fixed to 0, only the parameter G1 was refined. Fig. 2 shows the refined lattice parameters a0 and the preferred orientation parameter G1 of 〈511〉
3. Results and discussion Different colors are shown when films are deposited at different potentials. The films deposited in the potential of 1.00 to 1.04 V are black gray while those deposited in the potential of 1.06 to 1.08 V are bright gray and reflective like a mirror. Those deposited in the potential of 1.10 to 1.18 V are black at the beginning, and reddish brown afterwards when dried in the air. The films deposited at 1.20 V and above change their colors from translucent green to red when dried in the air. The colors of the films deposited in 1.06 to 1.08 V indicate well-formed texture which is in accordance with our XRD results. Between the depositing potentials of 1.06 and 1.08 V, an increase of the XRD peak intensity corresponding to Miller indices
Fig. 2. The lattice parameters (square) and the preferred orientation parameters of 〈511〉 (round) are given by the refinement of the XRD data. Lines are provided as a guide to the eye.
Fig. 1. Typical X-ray diffraction patterns of Fe3O4 films. Red symbols represent the experimental patterns, black lines represent the calculated ones while the blue curves at the bottom show the difference between experimental and calculated patterns. The vertical bars are Bragg peak positions. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
R. Wu et al. / Journal of Magnetism and Magnetic Materials 361 (2014) 107–111
orientation. The lattice parameters of the samples deposited at 1.00 V and 1.16 V are 0.84175 nm and 0.83920 nm, respectively. The lattice parameter shows a tendency of decrease with increasing potential. This is related to the nonstoichiometry of the Fe to O ratio in these samples. With the increasing potentials, the growth of the films becomes faster and leads to more cation vacancies in the films [14]. The preferred orientation parameter G1 of 〈511〉 increases and reaches its maximum at the vicinity of the potential 1.08 V. It indicates that films deposited in 1.06 to 1.08 V have a preferred orientation along 〈511〉. The intensity of the 〈400〉 peak has the similar behavior to that of the 〈511〉 peak in Fig. 1, which is reasonable with the fact that the angle between 〈511〉 and 〈400〉 directions is only 15.791. According to the SEM images, the potential has a notable effect on the film surface morphology. The films deposited in the potential range of 1.00 to 1.04 V show highly faceted and dense morphology (Fig. 3(a)). In the potential range of 1.06 to 1.08 V, the surface of the films exhibits rounded and featureless morphology (Fig. 3(b)), which is related to the preferred orientation. At the potential of 1.10 V and above, ferrihydrite nanoribbons begin to grow on the top of magnetite films (Fig. 3(c)). At 1.14 V, the film shows a magnetite-ferrihydrite bi-layer structure (Fig. 3(d)). Moreover, the grain size increases with the potential in the range of 1.00 to 1.10 V, which can be ascribed to the potential dependence of deposition efficiency. The thickness and grain size increase with the deposition efficiency during 1.00 to 1.10 V, although the total charge was kept constant for all samples. For films deposited with the potential higher than 1.10 V, bilayer structure formed and the thickness of the Fe3O4 layer was reduced. Then the average grain size reaches its maximum at 1.08 V. In order to study the magnetic properties of the films, hysteresis loops of the samples deposited in the potential range of 1.00 to 1.16 V were measured with AGM. As a result of dipolar interaction, the magnetization of the Fe3O4 films favors an in-plane orientation (Fig. 4), which is called dipolar anisotropy or shape anisotropy [15]. Hysteresis loops of different potential are given in Fig. 5. The saturation magnetization of the sample prepared at 1.08 V is calculated to be 88 emu/g with the thickness assumed to be 1.16 μm according to the total charge
109
transfer during the preparation. That is very close to the bulk magnetization of Fe3O4 (92 emu/g), indicating high deposition efficiency at 1.08 V. From the total magnetization of unit area (emu/cm2), the thickness of all these samples is calculated and
Fig. 4. Room temperature M–H hysteresis loops with H applied parallel and perpendicular to the Fe3O4 film surface (the sample is obtained at 1.02 V). The inset highlights the region at low field.
Fig. 5. The hysteresis loops of samples deposited at different potentials (left) and their coercivities (black square), calculated thickness (red circle) as a function of potential (right). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 3. SEM images of films deposited at (a) 1.00 V, (b) 1.08 V, (c) 1.10 V, and (d) 1.14 V.
110
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shown in Fig. 5. The thickness of the samples prepared at 1.00 V and 1.16 V is estimated to be about 0.55 μm and 0.20 μm, respectively. The change of thickness with the potential is in accordance with the change of grain size obtained by SEM. The obtained coercivities of the films with the applied magnetic field parallel to the film surface are plotted as a function of the applied potentials in Fig. 5. The coercivity clearly shows a minimum at the vicinity of the potential 1.08 V, where the preferred orientation parameter of 〈511〉 reaches its maximum. Usually, the coercivity is affected by the grain size of the film. Multi-domain grain crystal will show much lower coercivity than that of single domain crystal. However, the change of coercivity shown here is not caused by the transition between multi-domain and single domain grains since the average grain size of the film is much larger than the size of a single domain (less than 50 nm). According to the orientation parameter shown in Fig. 2, it can be inferred that the coercivity decreases greatly when the preferred orientation parameter increases. The decrease of coercivities in these films with preferred orientation can be explained by a model considering the interplay of shape anisotropy (SA) and magnetocrystalline anisotropy (MA). In the films without preferred orientation, the in-plane shape anisotropy plays a major role; the random local magnetocrystalline anisotropy cancels each other giving zero macroscopic magnetocrystalline anisotropy. The free energy density can be described as the phenomenological expressions [16]
εs ¼ k0 þ k1 cos 2 θ
ð4Þ
In the film with preferred orientation, the magnetocrystalline contributions cannot cancel each other. For cubic crystal, the free energy density can be written as
εm ¼ k0' þk1' ðs2x s2y þ s2y s2z þ s2x s2z Þ þ k2' sx sy sz
ð5Þ
where k0,1 and k´0,1,2 are anisotropy constants and θ is the magnetization angle with respect to the film planesx,y,z are magnetization components with the relationship sx ¼ sin θ cos φ, sx ¼ sin θ sin φ, and sz ¼ cos θ, where θ and φare the magnetization angle with respect to film normal and xz plane,
respectively. Then, the total free energy can be expressed as
εa ¼ εs þ εm
ð6Þ
Bulk Fe3O4 has a cubic structure, with the 〈111〉 and 〈100〉 directions being easy and hard axes of magnetization, respectively [17]. The magnetocrystalline energy can be well described in Eq. (5) with k´1 o 0 and k´2 ¼0. Based on Eqs. (4)–(6), the free energy landscape and the equilibrium magnetization which lies in the local minimum of the free energy landscape were calculated and plotted in Fig. 6(a) and (b), giving an illustration to the relationship between the equilibrium magnetization direction and the ratio of shape anisotropy and magnetocrystalline anisotropy (k1 / | k´1|). In films prepared at 1.00 V and 1.16 V, stronger shape anisotropy is given by thinner thickness and at the same time the macroscopic magnetocrystalline anisotropy is reduced by randomness of orientation. Generally speaking, the randomness of the anisotropy will reduce the coercivity of the system of randomly oriented noninteracting single domain particles. It was calculated to be Hc ¼ 0.479 Hk and Hc 0.185 Hk with uniaxial anisotropy and cubic anisotropy (k´1 o0), respectively, where Hc and Hk are the coercive field and anisotropy field [18,19]. However, in the film with SA, not all the local magnetization of the grains can stay in local energy minimum. On the contrary, most of the local magnetization will stay apart from local energy minimum to in-plane direction and cannot reverse via local saddle points (Fig. 6(a), k1 / | k´1| ¼2.5), which will give a larger coercivity. In those films with 〈511〉 orientation, the equilibrium magnetization will not favor the in-plane direction any more due to the cubic property of the magnetocrystalline anisotropy with 〈111〉 direction easy axis in Fe3O4 and the reduced SA due to the increase of thickness (Fig. 6(b), k1 / | k´1| ¼0.4). Actually, the equilibrium magnetization will be lift close to 〈111〉 direction and closer to the saddle point of the energy landscape. This will cause a drastic decrease of local anisotropy energy barrier for reversing the magnetization. In another word, interplay between the two magnetic anisotropy contributions changes the route of the magnetization reversal,
Fig. 6. (a) Free energy landscape with major component of shape anisotropy (k1 / |k´1| ¼ 2.5) and (b) energy landscape of coexistence of shape and magnetocrystalline anisotropy k1 / |k´1| ¼ 0.4).
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resulting in a weaker effective anisotropy barrier and a lower coercivity in the oriented films. 4. Conclusions In summary, we have investigated the interplay between the shape anisotropy and the magnetocrystalline anisotropy in electrodeposited Fe3O4 films. The refinement of the XRD data shows that the films have preferred orientations along 〈511〉 at a potential around 1.08 V. The lattice parameter of the film decreases with increasing applied potentials due to that more cation vacancies produce at higher growing speed. It was found that the coercivity of the films reached its minimum at the potential around 1.08 V. An orientation-caused coercivity mechanism can be clearly observed in the experiment data. A simple model including interplay between shape anisotropy and magnetocrystalline anisotropy was introduced to give a quantitative explanation to the experimental results. The magnetocrystalline anisotropy emerging in the oriented films pulls the equilibrium magnetization away from the film plane, which reduces the local free energy barrier and coercivity. This provides a new route to tune the magnetic anisotropy in the Fe-oxide magnetic films. Acknowledgments This work has been supported by the National Natural Science Foundation of China (Grant nos. 51371009, 50971003 and 51171001), National Basic Research Program of China (No. 2010CB833104, MOST
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of China), and National High Technology Research and Development Program of China (No. 2011AA03A403).
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