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Unraveling the origin of training in granular Co-CoO exchange bias systems with buried antiferromagnetic constituents
Journal of Magnetism and Magnetic Materials 478 (2019) 170–174
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Research articles
Unraveling the origin of training in granular Co-CoO exchange bias systems with buried antiferromagnetic constituents ⁎
E. Menéndeza, , L.E.S. Silvab, G. Johannb, J. Sorta,c, T. Diasb,
T
⁎
a
Departament de Física, Universitat Autònoma de Barcelona, Cerdanyola del Vallès, E-08193 Barcelona, Spain Federal University of Techonology – Paraná, Campus Dois Vizinhos, Estrada para Boa Esperança, km 04, PR, 85660-000 Dois Vizinhos, Brazil c Institució Catalana de Recerca i Estudis Avançats (ICREA), Pg. Lluís Companys 23, E-08010 Barcelona, Spain b
A R T I C LE I N FO
A B S T R A C T
Keywords: Magnetic properties of interfaces Magnetic anisotropy Micromagnetic simulations Exchange interactions: magnetically ordered materials Hysteresis in magnetism
Training is a common effect in exchange bias systems and accounts for the decrease of the exchange bias loop shift and coercivity with consecutively measured hysteresis loops until steady values. This is an ageing-like phenomenon that is related to the metastable state of the ferromagnetic/antiferromagnetic interface after field cooling. However, its origin still remains intriguing and not univoquely established. Here, by micromagnetic simulations considering discrete non-interacting antiferromagnetic grains embedded in a ferromagnetic matrix, it is demonstrated that the origin of training in granular Co-CoO exchange bias systems prepared by O ion implantation into Co thin films is linked to the perpendicular anisotropy of rotatable interface uncompensated spins. The simulations are compared to experimental data as reported in Physical Review B 89 (2014) 144407. The out-of-plane nature of the rotatable anisotropy of the system is also responsible for the magnetic reversal asymmetry between the first and the second magnetic reversals, evidencing the interconnection between training and magnetization reversal, suggesting that training effect and magnetization reversal asymmetry are ultimately interconnected through perpendicular anisotropy.
1. Introduction The magnetic interaction between a ferromagnet (FM) and the interfacial uncompensated spins (UCS) of an antiferromagnetic (AFM) material is the leading mechanism of exchange bias (EB) phenomenon [1–4]. The typical manifestations of EB are the horizontal displacement of hysteresis loops by a quantity called exchange bias field (HEB ) and an increase of coercive field (HC ) of the FM/UCS system. This effect is commonly established by cooling the system below the Néel temperature of the AFM under an applied magnetic field down to the working temperature. In general, EB systems also exhibit training effect which results in a decrease of HC and HEB upon successive magnetic cycles [5]. This effect depends on both the intrinsic properties of the AFM constituent, such as magnetic anisotropy, and the interactions between the FM and interfacial UCSs [6]. Training is commonly divided in athermal and thermal according the behavior of the UCSs during hysteresis loop measurements. Athermal training accounts for the abrupt reduction of HC and HEB between the first and the second consecutively measured hysteresis loops, whereas thermal training refers to the slight decreases in HC and HEB for the subsequent measurements, ultimately reaching steady values [7,8]. Regarding the latter type of training, Binek et al.
⁎
has derived an equation that describes it as a thermodynamically-governed spin relaxation at the interface towards the equilibrium configuration [9]. In polycrystalline heterosystems, finite temperature activates a fraction of the uncompensated spins which reorient when magnetic field is applied. These spins can find local or global minima and become compensated, i.e., not adding to bias anymore [7]. More recently, numerical simulations on Co/CoO bilayers demonstrated that training effect is not only governed by magnetic compensation but by the spread of easy axes distribution of highly anisotropic UCSs due to their coupling to the AFM matrix [10], relaxation of rotatable spins is the mechanism of thermal training in Fe3O2 thin films as well [11]. Conversely, athermal training occurs only during the first magnetization reversal and it is essentially temperature independent. Hoffman argued symmetry issues in the AFM (i.e., AFMs with multiple easy anisotropy axes) as its origin [12]. That is, upon field-cooling, a noncollinear configuration of the AFM is achieved which relaxes to an antiparallel arrangement after the first magnetization reversal. Brems et al. considered a single FM domain that interacts with UCSs with cubic anisotropy and found that the reorientation of the magnetization towards AFM easy axes different from the one closest to the induced by the field-cooling is responsible for training [13]. The authors also
Corresponding authors. E-mail addresses: [email protected] (E. Menéndez), [email protected] (T. Dias).
https://doi.org/10.1016/j.jmmm.2019.01.104 Received 30 November 2018; Received in revised form 21 January 2019; Accepted 29 January 2019 Available online 31 January 2019 0304-8853/ © 2019 Published by Elsevier B.V.
Journal of Magnetism and Magnetic Materials 478 (2019) 170–174
E. Menéndez et al.
the FM/AFM interface is considered granular, but the whole AFM and the FM counterparts. Our model considers UCSs which can interact laterally with FM grains and not only horizontally as it happens in bilayers. The results of the simulations were compared to the experimental results reported in Physical Review B 89 (2014) 144407 (Ref. [24]) on granular Co-CoO EB systems prepared by O ion implantation into Co thin films.
showed that the untrained state can be restored by applying a strong inplane magnetic field perpendicular to the direction in which EB was set. In the framework of a polycrystalline model for exchange bias, Harres and Geshev have demonstrated that athermal training arises from interactions between UCSs, regardless of their anisotropy [14]. Several models have been proposed to explain EB. However, a unified theory that, for example, not only explains the loop shift but also training is still lacking. Taking into account FM/AFM bilayers, for instance, Fulcomer and Charap considered that the AFM material is composed by an assembly of grains with distributed sizes and shapes coupled to a single FM [15]. This model properly describes the temperature dependence of HEB and HC , training effects, and blocking temperature (temperature above which EB vanishes). Stiles and McMichael have proposed that single-domain AFM grains can interact with the FM by both direct interfacial and spin-flop interactions [16]. They considered a rotatable anisotropy term, − MFM·HRA , in the total magnetic anisotropy in order to be able to explain the frequently observed isotropic resonance field shift in ferromagnetic resonance measurements, where HRA is the rotatable anisotropy field, which is practically parallel to the applied field Happlied , and MFM the saturation magnetization of the FM. Later on, another rotatable anisotropy term, proportional to − (MFM·Happlied)2 , was included in order to explain the HC enhancement [17]. This is ascribed to the additional uniaxial anisotropy sensed by the FM. Other attempts, such as the domain state model, mainly attribute EB phenomena to defect concentration in the AFM [18]. With the aim to go beyond systems with single FM layers and properly describe granular systems, Harres and Geshev,[19] based on the Fulcomer and Charap model, considered that a strong FM/AFM exchange interaction can break the FM into small-sized grains which interact with two types of UCSs. The first type corresponds to spins that virtually do not modify their magnetization during FM reversals (from now on referred as set). The exchange interaction between a set UCS and the adjacent ferromagnetic grain (Jset ) results in a torque that originates the shift. The second type of UCSs are the so-called rotatable (rot) spins, which contribute to HC by accompanying the FM magnetization reversal. This polycrystalline model has proved to be able to reproduce the coercivity of the loop taken in a direction perpendicular to the field applied during the cooling. It has also predicted that both anisotropy and exchange coupling magnitudes are needed in order to classify an UCS as set or rot spin. Highly anisotropic UCS enhances HC if the coupling with the FM grain is strong enough, while low-anisotropy spins pin the FM if the respective coupling is weak. However, as can be seen in Ref. [10], rot spins may play also a role in determining bias while thermal training. Even though EB was discovered in partially oxidized Co fine particles [1], the majority of EB investigations are based on thin films, such as bilayers or multilayers, due to the essential role of this effect in spintronics [20]. Recently, ion implantation has been shown as an alternative approach to form AFM oxides embedded in a FM matrix by, for instance, O ion implantation into Co thin films, resulting in multiple FM-AFM interfaces [21,22]. This overcomes conventional approaches such as surface oxidation by exposing the sample to air or to a controlled oxygen atmosphere, which result in ultra-thin AFM layers, due to the self-limiting nature of surface oxidation, and a single FM/AFM interface. Moreover, it has been demonstrated that the interplay between the intrinsic properties of the investigated materials and ion implantation allows for engineering systems with enhanced exchange bias properties and tunable magnetization reversal mechanisms. However, a suitable theoretical framework to model granular EB systems with discrete and buried AFM constituents, which is for instance crucial to understand systems such as those prepared by ion implantation, is still lacking [23,24]. In this work, we present a micromagnetic approach to numerically simulate the exchange bias properties of non-layered FM/AFM systems with multiple interfaces and buried AFM constituents. Namely, not only
2. Model Micromagnetic numerical simulations were carried out in a mesh composed by 256 × 256 × 5 (327,680) cells with an individual cell volume of 6 × 6 × 6 nm3 . From the total number of cells, approximately 2.4 × 105 form the AFM constituent. Limited size effects were avoided by repeating the system 10 times in both x and y directions. The total energy of the system is minimized when the normalized magnetization mj of the jth cell points towards a direction parallel to the effective field H eff, j acting on the cell. Ferromagnetic cells are affected by an effective field that takes into account the Zeeman term, magnetic anisotropy (in our case, uniaxial), and FM exchange interactions described by the exchange stiffness Aex . The AFM cells are not influenced by the Zeeman term. The demagnetizing field is not directly computed to the UCSs, but it is reflected in the uniaxial UCS anisotropy. The assumption of uniaxial anisotropy for the UCSs is in accordance with phenomenological computations that have demonstrated that a competition between magnetocrystalline and shape anisotropy is induced in non-interacting single-domain AFM grains [27]. The interfacial exchange fields added to H eff , due to FM/set and/or FM/rot coupling, are given by:
H exc,FM =
H exc,AFM =
2Ji (mFM − mAFM); μ0 δMFM
2Ji (mAFM − mFM). μ0 δMAFM
(1)
(2)
Eq. (1) accounts for the exchange interaction field acting on a FM cell, and Eq. (2) for an AFM cell. In both equations, Ji represents the exchange coupling constant (subscript i denotes either rot or set-type UCSs), MFM and MAFM are the FM and AFM saturation magnetizations, respectively, and μ0 is the vacuum permeability. The parameter δ is the range where Hexc,FM(AFM) acts, which is twice the cell size along the direction of contact. Eqs. (1) and (2) are applicable to any FM/AFM system regardless microstructure. To validate our granular model, we simulate the experimental results reported in Physical Review B 89 (2014) 144407 (Ref. [24]) on granular Co-CoO systems prepared by O ion implantation into Co thin films. We focus on the experimental conditions of the employed fluences and, specifically, on the sample implanted to a fluence of 5 × 1016 ions/cm2, which contains 8 at.% of O. In O-implanted Co thin films, the incorporation of O takes place mainly at the grain boundaries of the Co. Nonetheless, for this regime of fluences, AFM Co oxides are likely to grow in a discontinuous way, being rather isolated from each other [22,24]. In order to take into account that the AFM is discrete and its constituents might not interact among each other, the total simulation mesh has been divided into grains with a lateral size of approximately 12 nm using a 2D Voronoi tessellation. A fraction of these grains are considered either set or rot UCSs. It is important to note that the micromagnetic premise of continuous variation of magnetization is not satisfied at the vicinity of set UCSs. Thus, the validity of our model is achieved by taking the cosine between nearest-neighbors’ magnetization instead of ∇m2 , as the theory of magnetism proposes to describe the exchange energy between neighboring magnetic cells [28]. In contrast to most reported simulations on exchange-biased systems, our results do not emerge from interacting FM and AFM layers, but from discrete AFM constituents buried in a FM matrix. This is schematically depicted in Fig. 1, which shows the division of the sample into small-sized grains and the distribution of AFM grains inside a 171
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The ratio of rotatable and stable UCSs during the simulations has been fixed to 1:1, since it properly reproduces the experimental results. The number of set UCSs is related to the loop shift, whereas rot-type spins affects the drop in both HC and HEB between the first and the second loops.
3. Results and discussion We have checked the validity of our model by comparing the obtained micromagnetic simulations to previous reported experimental results corresponding to granular Co-CoO systems prepared by the implantation of O ions into 30 nm-thick Co thin films as presented in Ref. [24]. Specifically, we have focused on a sample implanted to a fluence of 5 × 1010 ions/cm2, which results in 8 at.% O. This sample shows rich EB phenomena, such as a large HEB , strong training effects and asymmetry between the first the and second magnetization reversals. During the simulations, the cobalt from FM cells is described with typical parameters found in the literature: exchange stiffness Aex = 13 pJ/m and MFM = 1.4 MA/m. Inside the AFM grains, the exchange stiffness was chosen to be 9 pJ/m, which is in accordance to values to CoO found in literature [29], and the interface UCSs are considered non-interacting. In order to equally divide the interfacial exchange energy between AFM and FM adjacent cells, MAFM = MFM has been taken for the uncompensated AFM spins. The saturation magnetization of the UCS (i.e. MAFM ) does not influence our results, since no Zeeman term was considered for the AFM counterpart. The uniaxial anisotropy constants as well as the easy-axes directions are free parameters used to fit the experimental data. The experimental curves were obtained by superconducting quantum interference device (SQUID) magnetometry at a temperature of 10 K upon field-cooling the sample from room temperature in an inplane magnetic field of 400 mT. As can be seen in Fig. 2, the experimental hysteresis loops evidence a pronounced training effect between the first (untrained) and the second (trained) cycles. The experimental data are compared to the average x component of the magnetization
Fig. 1. Schematic top view of the constituent distribution of the system used for the micromagnetic simulations. Uncompensated spins are represented by colorfilled areas in dark grey, while blank zones correspond to FM grains. Black lines are the grain boundaries. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
particulate FM film, modeling in first approximation the finite size and non-interacting nature of the experimental system. In contrast to CoCoO bilayers, which exhibit a single FM/AFM interface, each UCS of ion-implanted Co-CoO systems interacts with more than one FM grain via multiple FM/AFM interfaces. In Fig. 1, about 8% of the grains are considered either rot or set uncompensated spins since the data which are simulated correspond to an O-implanted sample with 8 at.% of O.
Fig. 2. First and second hysteresis loops obtained from the simulated x (black and blue lines) and y (red and green lines) components of magnetization together with the low-temperature experimental results (circles and squares correspond to the first and second loops, respectively) presented in Ref. [24] considering (a) Krot = 50 kJ/m3 , φrot = 0°; and (b) Krot = 21 kJ/m3 , φrot = 90°. Other parameters were fixed during simulations: KFM = 6.5 kJ/m3 , Kset = 1.8 MJ/m3 , φFM = φset = 90°, MFM = MAFM = 1.4 MA/m , Jrot = 1.20 mJ/m2 , and Jset = 0.80 mJ/m2 . The cartoons in each panel represent FM, set, and rot anisotropy directions. 172
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(〈m x 〉) as a function of the magnetic applied field Happlied (applied along x direction) resulting from our numerical simulations. In order to investigate the magnetization reversal mechanisms, the simulated inplane perpendicular average magnetization (〈m y 〉) is also shown in Fig. 2. The uniaxial anisotropy constants as well as their directions with respect to the polar angle (denoted by φ ) were varied in order to achieve the best agreement between the experimental and the numerically simulated results. While φ = 0° corresponds to the direction perpendicular to the plane of the film, φ = 90° corresponds to in-plane directions. The best fitting magnetization curves simulated through our model were obtained for in-plane FM and set anisotropies with KFM = 6.5 × 103 J/m3 and Kset = 1.8 × 106 J/m3, respectively. We have compared out-of-plane and in-plane rot spins’ anisotropy directions φrot = 0°, Krot = 5 × 10 4 J/m3; with (i) and (ii) φrot = 90°, Krot = 2.1 × 10 4 J/m3. In our model, KFM is kept non-refinable. The use of a lower Krot value when considering in-plane rather than out-of-plane allows for properly simulating the coercivities. That is, taking into consideration in-plane anisotropy and keeping Krot = 5 × 10 4 J/m3 rather than 2.1 × 10 4 J/m3 would result in much broader hysteresis loops. This is why, during the simulations, not only the anisotropy direction of rot UCSs was modified but also Krot value. As can be seen in Fig. 2(a), out-of-plane rotatable anisotropy (φrot = 0°) is required to satisfactory simulate the athermal training between the first and the second measured hysteresis loops. μ0 HC decays from 48 to about 35 mT (around 27% of its original value), while |μ0 HEB | drops from 65 to 49 mT (about 25% of its original value). This is in agreement with the already envisaged out-of-plane anisotropy of CoCoO granular and clustered systems [24,25]. The perpendicular anisotropy of rot UCSs can be partly linked to the O ion implantation since it tends to hybridize Co perpendicularly [30,31]. As a consequence of the field-cooling, most of the FM and the UCSs are metastably forced to be oriented in the direction of the applied magnetic field (i.e., in-plane). During the first reversal, the magnetic moments of rot UCSs reorient according to their anisotropy (perpendicular) and the closest FM moments follow this orientation due to their strong exchange interaction with rot spins, not contributing to the longitudinal magnetization (along x) and, thus, giving rise to training. Conversely, in Fig. 2(b) it is shown that, when in-plane rotatable anisotropy is considered during the simulation, no differences between 〈m x 〉1 and 〈m x 〉2 are observed and thus no training effect takes place for in-plane rot UCS anisotropy. In certain parallelism, perpendicular anisotropy has already been observed to rule exchange bias properties in other systems, such as Pt/Co/ Cu/IrMn and Pd/Co/IrMn [32,33]. The uniaxial anisotropy constants used are about two orders of magnitude lower than those reported in literature. The reduced value of KFM can be ascribed to both the presence of stacking faults in thin Co films and the coexistence of fcc and hcp phases of Co [10,24]. The reduced values of Kset and Krot are a consequence of the way we have described the system, since there is no antiferromagnetic matrix to build-up UCS anisotropies. The obtained effective coupling between CoO spins and the adjacent FM grains were Jset = 0.80 mJ/m2 and Jrot = 1.20 mJ/m2, which are in concordance with values reported in the literature [3,10]. Due to the morphology of the system, each UCS can interact with more than one FM grain, which increases the effective contact area when compared to FM/AFM bilayers. In our micromagnetic simulations, this is reflected in a larger amount of magnetic cells under the influence of exchange anisotropy. This results in low anisotropic UCSs adding to both bias and HC . Co-CoO exchange-biased systems prepared by low fluence O ion implantation exhibit magnetization reversal asymmetry between the first and the second magnetic reversals as it happens in Co/CoO films [24,26,36]. The first reversal is governed by domain wall nucleation and motion, whereas coherent rotation is the dominant mechanism in the subsequent reversals. Fig. 2 also shows the orthogonal in-plane component of the magnetic moment 〈m y 〉 of the first two hysteresis loops since it accounts for magnetization reversal mechanisms which
involve spin rotation. As it happens with training, the experimentally observed asymmetry between the first and the second reversals is only observed if perpendicular rot anisotropy is taken into account. That is, during the first reversal 〈m y 〉 is negligible, whereas for subsequent reversals this orthogonal contribution becomes significant in agreement with the fact that coherent rotation becomes enabled from the second reversal on. In order to investigate the influence of large magnetic fields on the system [34,35], we have performed simulations after applying an external field of 4 T along x , y and z directions were carried out to simulate the trained state. No significant differences have been observed between the hysteresis loops of the trained state simulated with maximum applied magnetic fields of 500 mT and 4 T. Out-of-plane contributions to the sample magnetization naturally arise in our simulations in agreement with the experimental results from Ref. [24]. Specifically, the polarized neutron reflectometry results indicate a loss of in-plane magnetization which scales with the number of measured loops, suggesting an increase of out-of-plane contributions which cannot be probed by this technique. Hence, we also simulate the evolution of the perpendicular component z for the first two hysteresis loops (Fig. 3). Upon field-cooling, magnetization remains in the plane of the sample. Thus, when initiating the first magnetic reversal, there is virtually no 〈mz 〉. However, when the applied field reaches a value of μ0 Happlied ≈ −80 mT, the magnetization of FM grains that interact with rot UCSs partially rotate towards the out-of-plane direction. After the first reversal, the z contribution remains and reinforces with consecutive reversals, in agreement with the loss of in-plane contributions with reversals envisaged by polarized neutron reflectometry in Ref. [24]. The field-cooling results in a metastable state with its magnetization frozen in the plane of the sample. With reversals, configurations with out-of-plane components arise because they are energetically favorable. As one can see in Fig. 3, the hysteretic behavior of 〈mz 〉 shows a vertical shift. This is due to the fact that FM moments that interact with rot UCSs rotate towards + z and, during the first reversal and from second reversal on, a fraction of these magnetic moments become frustrated, probably due to the interaction with other UCSs. It is worth mentioning that perpendicular magnetization goes to zero for |μ0 Happlied | > 500 mT as expected from fully saturated in-plane hysteresis. It should be noted that the noise of hysteresis loops of Fig. 3 is ascribed to the reduced quantity of FM cells which are influenced by the perpendicular anisotropy of the rot UCSs, since it is considered that the exchange interaction extends only to the first-neighbors. Perpendicular contribution to the effective field are small when compared to the inplane ones, as a consequence fluctuation of 〈mz 〉 can occur without
Fig. 3. Evolution of the out-of-plane magnetization during the untrained (black solid line) and first trained (dashed red line) magnetic cycles for simulations considering perpendicular rot anisotropy with Krot = 5 × 10 4 J/m3 . 173
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affecting significantly the effective field and, thus, the global energy.
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4. Summary and conclusions In summary, we have theoretically investigated using micromagnetic simulations the athermal training effect in granular Co-CoO exchange-biased systems prepared by ion implantation in Co thin films by comparing the simulations to the experimental results obtained in Physical Review B 89 (2014) 144407. Instead of a bilayer system, we have considered non-interacting and discrete AFM grains buried inside a FM thin film, successfully reproducing training and magnetization reversal asymmetry, whose origin and interdependence is linked to the perpendicular anisotropy of rotatable spins. Acknowledgements This work was supported by the Brazilian Foundation CNPq under Project Nos. 402013/2016-6 and 104289/2018-0, the Generalitat de Catalunya (2017-SGR-292) and the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 665919. T.D and G.J. thank the facilities of Laboratório de Pesquisa em Computação Aplicada (LPCA-UTFPR). Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, athttps://doi.org/10.1016/j.jmmm.2019.01.104. References [1] [2] [3] [4] [5] [6] [7] [8] [9]
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Research articles
Unraveling the origin of training in granular Co-CoO exchange bias systems with buried antiferromagnetic constituents ⁎
E. Menéndeza, , L.E.S. Silvab, G. Johannb, J. Sorta,c, T. Diasb,
T
⁎
a
Departament de Física, Universitat Autònoma de Barcelona, Cerdanyola del Vallès, E-08193 Barcelona, Spain Federal University of Techonology – Paraná, Campus Dois Vizinhos, Estrada para Boa Esperança, km 04, PR, 85660-000 Dois Vizinhos, Brazil c Institució Catalana de Recerca i Estudis Avançats (ICREA), Pg. Lluís Companys 23, E-08010 Barcelona, Spain b
A R T I C LE I N FO
A B S T R A C T
Keywords: Magnetic properties of interfaces Magnetic anisotropy Micromagnetic simulations Exchange interactions: magnetically ordered materials Hysteresis in magnetism
Training is a common effect in exchange bias systems and accounts for the decrease of the exchange bias loop shift and coercivity with consecutively measured hysteresis loops until steady values. This is an ageing-like phenomenon that is related to the metastable state of the ferromagnetic/antiferromagnetic interface after field cooling. However, its origin still remains intriguing and not univoquely established. Here, by micromagnetic simulations considering discrete non-interacting antiferromagnetic grains embedded in a ferromagnetic matrix, it is demonstrated that the origin of training in granular Co-CoO exchange bias systems prepared by O ion implantation into Co thin films is linked to the perpendicular anisotropy of rotatable interface uncompensated spins. The simulations are compared to experimental data as reported in Physical Review B 89 (2014) 144407. The out-of-plane nature of the rotatable anisotropy of the system is also responsible for the magnetic reversal asymmetry between the first and the second magnetic reversals, evidencing the interconnection between training and magnetization reversal, suggesting that training effect and magnetization reversal asymmetry are ultimately interconnected through perpendicular anisotropy.
1. Introduction The magnetic interaction between a ferromagnet (FM) and the interfacial uncompensated spins (UCS) of an antiferromagnetic (AFM) material is the leading mechanism of exchange bias (EB) phenomenon [1–4]. The typical manifestations of EB are the horizontal displacement of hysteresis loops by a quantity called exchange bias field (HEB ) and an increase of coercive field (HC ) of the FM/UCS system. This effect is commonly established by cooling the system below the Néel temperature of the AFM under an applied magnetic field down to the working temperature. In general, EB systems also exhibit training effect which results in a decrease of HC and HEB upon successive magnetic cycles [5]. This effect depends on both the intrinsic properties of the AFM constituent, such as magnetic anisotropy, and the interactions between the FM and interfacial UCSs [6]. Training is commonly divided in athermal and thermal according the behavior of the UCSs during hysteresis loop measurements. Athermal training accounts for the abrupt reduction of HC and HEB between the first and the second consecutively measured hysteresis loops, whereas thermal training refers to the slight decreases in HC and HEB for the subsequent measurements, ultimately reaching steady values [7,8]. Regarding the latter type of training, Binek et al.
⁎
has derived an equation that describes it as a thermodynamically-governed spin relaxation at the interface towards the equilibrium configuration [9]. In polycrystalline heterosystems, finite temperature activates a fraction of the uncompensated spins which reorient when magnetic field is applied. These spins can find local or global minima and become compensated, i.e., not adding to bias anymore [7]. More recently, numerical simulations on Co/CoO bilayers demonstrated that training effect is not only governed by magnetic compensation but by the spread of easy axes distribution of highly anisotropic UCSs due to their coupling to the AFM matrix [10], relaxation of rotatable spins is the mechanism of thermal training in Fe3O2 thin films as well [11]. Conversely, athermal training occurs only during the first magnetization reversal and it is essentially temperature independent. Hoffman argued symmetry issues in the AFM (i.e., AFMs with multiple easy anisotropy axes) as its origin [12]. That is, upon field-cooling, a noncollinear configuration of the AFM is achieved which relaxes to an antiparallel arrangement after the first magnetization reversal. Brems et al. considered a single FM domain that interacts with UCSs with cubic anisotropy and found that the reorientation of the magnetization towards AFM easy axes different from the one closest to the induced by the field-cooling is responsible for training [13]. The authors also
Corresponding authors. E-mail addresses: [email protected] (E. Menéndez), [email protected] (T. Dias).
https://doi.org/10.1016/j.jmmm.2019.01.104 Received 30 November 2018; Received in revised form 21 January 2019; Accepted 29 January 2019 Available online 31 January 2019 0304-8853/ © 2019 Published by Elsevier B.V.
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the FM/AFM interface is considered granular, but the whole AFM and the FM counterparts. Our model considers UCSs which can interact laterally with FM grains and not only horizontally as it happens in bilayers. The results of the simulations were compared to the experimental results reported in Physical Review B 89 (2014) 144407 (Ref. [24]) on granular Co-CoO EB systems prepared by O ion implantation into Co thin films.
showed that the untrained state can be restored by applying a strong inplane magnetic field perpendicular to the direction in which EB was set. In the framework of a polycrystalline model for exchange bias, Harres and Geshev have demonstrated that athermal training arises from interactions between UCSs, regardless of their anisotropy [14]. Several models have been proposed to explain EB. However, a unified theory that, for example, not only explains the loop shift but also training is still lacking. Taking into account FM/AFM bilayers, for instance, Fulcomer and Charap considered that the AFM material is composed by an assembly of grains with distributed sizes and shapes coupled to a single FM [15]. This model properly describes the temperature dependence of HEB and HC , training effects, and blocking temperature (temperature above which EB vanishes). Stiles and McMichael have proposed that single-domain AFM grains can interact with the FM by both direct interfacial and spin-flop interactions [16]. They considered a rotatable anisotropy term, − MFM·HRA , in the total magnetic anisotropy in order to be able to explain the frequently observed isotropic resonance field shift in ferromagnetic resonance measurements, where HRA is the rotatable anisotropy field, which is practically parallel to the applied field Happlied , and MFM the saturation magnetization of the FM. Later on, another rotatable anisotropy term, proportional to − (MFM·Happlied)2 , was included in order to explain the HC enhancement [17]. This is ascribed to the additional uniaxial anisotropy sensed by the FM. Other attempts, such as the domain state model, mainly attribute EB phenomena to defect concentration in the AFM [18]. With the aim to go beyond systems with single FM layers and properly describe granular systems, Harres and Geshev,[19] based on the Fulcomer and Charap model, considered that a strong FM/AFM exchange interaction can break the FM into small-sized grains which interact with two types of UCSs. The first type corresponds to spins that virtually do not modify their magnetization during FM reversals (from now on referred as set). The exchange interaction between a set UCS and the adjacent ferromagnetic grain (Jset ) results in a torque that originates the shift. The second type of UCSs are the so-called rotatable (rot) spins, which contribute to HC by accompanying the FM magnetization reversal. This polycrystalline model has proved to be able to reproduce the coercivity of the loop taken in a direction perpendicular to the field applied during the cooling. It has also predicted that both anisotropy and exchange coupling magnitudes are needed in order to classify an UCS as set or rot spin. Highly anisotropic UCS enhances HC if the coupling with the FM grain is strong enough, while low-anisotropy spins pin the FM if the respective coupling is weak. However, as can be seen in Ref. [10], rot spins may play also a role in determining bias while thermal training. Even though EB was discovered in partially oxidized Co fine particles [1], the majority of EB investigations are based on thin films, such as bilayers or multilayers, due to the essential role of this effect in spintronics [20]. Recently, ion implantation has been shown as an alternative approach to form AFM oxides embedded in a FM matrix by, for instance, O ion implantation into Co thin films, resulting in multiple FM-AFM interfaces [21,22]. This overcomes conventional approaches such as surface oxidation by exposing the sample to air or to a controlled oxygen atmosphere, which result in ultra-thin AFM layers, due to the self-limiting nature of surface oxidation, and a single FM/AFM interface. Moreover, it has been demonstrated that the interplay between the intrinsic properties of the investigated materials and ion implantation allows for engineering systems with enhanced exchange bias properties and tunable magnetization reversal mechanisms. However, a suitable theoretical framework to model granular EB systems with discrete and buried AFM constituents, which is for instance crucial to understand systems such as those prepared by ion implantation, is still lacking [23,24]. In this work, we present a micromagnetic approach to numerically simulate the exchange bias properties of non-layered FM/AFM systems with multiple interfaces and buried AFM constituents. Namely, not only
2. Model Micromagnetic numerical simulations were carried out in a mesh composed by 256 × 256 × 5 (327,680) cells with an individual cell volume of 6 × 6 × 6 nm3 . From the total number of cells, approximately 2.4 × 105 form the AFM constituent. Limited size effects were avoided by repeating the system 10 times in both x and y directions. The total energy of the system is minimized when the normalized magnetization mj of the jth cell points towards a direction parallel to the effective field H eff, j acting on the cell. Ferromagnetic cells are affected by an effective field that takes into account the Zeeman term, magnetic anisotropy (in our case, uniaxial), and FM exchange interactions described by the exchange stiffness Aex . The AFM cells are not influenced by the Zeeman term. The demagnetizing field is not directly computed to the UCSs, but it is reflected in the uniaxial UCS anisotropy. The assumption of uniaxial anisotropy for the UCSs is in accordance with phenomenological computations that have demonstrated that a competition between magnetocrystalline and shape anisotropy is induced in non-interacting single-domain AFM grains [27]. The interfacial exchange fields added to H eff , due to FM/set and/or FM/rot coupling, are given by:
H exc,FM =
H exc,AFM =
2Ji (mFM − mAFM); μ0 δMFM
2Ji (mAFM − mFM). μ0 δMAFM
(1)
(2)
Eq. (1) accounts for the exchange interaction field acting on a FM cell, and Eq. (2) for an AFM cell. In both equations, Ji represents the exchange coupling constant (subscript i denotes either rot or set-type UCSs), MFM and MAFM are the FM and AFM saturation magnetizations, respectively, and μ0 is the vacuum permeability. The parameter δ is the range where Hexc,FM(AFM) acts, which is twice the cell size along the direction of contact. Eqs. (1) and (2) are applicable to any FM/AFM system regardless microstructure. To validate our granular model, we simulate the experimental results reported in Physical Review B 89 (2014) 144407 (Ref. [24]) on granular Co-CoO systems prepared by O ion implantation into Co thin films. We focus on the experimental conditions of the employed fluences and, specifically, on the sample implanted to a fluence of 5 × 1016 ions/cm2, which contains 8 at.% of O. In O-implanted Co thin films, the incorporation of O takes place mainly at the grain boundaries of the Co. Nonetheless, for this regime of fluences, AFM Co oxides are likely to grow in a discontinuous way, being rather isolated from each other [22,24]. In order to take into account that the AFM is discrete and its constituents might not interact among each other, the total simulation mesh has been divided into grains with a lateral size of approximately 12 nm using a 2D Voronoi tessellation. A fraction of these grains are considered either set or rot UCSs. It is important to note that the micromagnetic premise of continuous variation of magnetization is not satisfied at the vicinity of set UCSs. Thus, the validity of our model is achieved by taking the cosine between nearest-neighbors’ magnetization instead of ∇m2 , as the theory of magnetism proposes to describe the exchange energy between neighboring magnetic cells [28]. In contrast to most reported simulations on exchange-biased systems, our results do not emerge from interacting FM and AFM layers, but from discrete AFM constituents buried in a FM matrix. This is schematically depicted in Fig. 1, which shows the division of the sample into small-sized grains and the distribution of AFM grains inside a 171
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The ratio of rotatable and stable UCSs during the simulations has been fixed to 1:1, since it properly reproduces the experimental results. The number of set UCSs is related to the loop shift, whereas rot-type spins affects the drop in both HC and HEB between the first and the second loops.
3. Results and discussion We have checked the validity of our model by comparing the obtained micromagnetic simulations to previous reported experimental results corresponding to granular Co-CoO systems prepared by the implantation of O ions into 30 nm-thick Co thin films as presented in Ref. [24]. Specifically, we have focused on a sample implanted to a fluence of 5 × 1010 ions/cm2, which results in 8 at.% O. This sample shows rich EB phenomena, such as a large HEB , strong training effects and asymmetry between the first the and second magnetization reversals. During the simulations, the cobalt from FM cells is described with typical parameters found in the literature: exchange stiffness Aex = 13 pJ/m and MFM = 1.4 MA/m. Inside the AFM grains, the exchange stiffness was chosen to be 9 pJ/m, which is in accordance to values to CoO found in literature [29], and the interface UCSs are considered non-interacting. In order to equally divide the interfacial exchange energy between AFM and FM adjacent cells, MAFM = MFM has been taken for the uncompensated AFM spins. The saturation magnetization of the UCS (i.e. MAFM ) does not influence our results, since no Zeeman term was considered for the AFM counterpart. The uniaxial anisotropy constants as well as the easy-axes directions are free parameters used to fit the experimental data. The experimental curves were obtained by superconducting quantum interference device (SQUID) magnetometry at a temperature of 10 K upon field-cooling the sample from room temperature in an inplane magnetic field of 400 mT. As can be seen in Fig. 2, the experimental hysteresis loops evidence a pronounced training effect between the first (untrained) and the second (trained) cycles. The experimental data are compared to the average x component of the magnetization
Fig. 1. Schematic top view of the constituent distribution of the system used for the micromagnetic simulations. Uncompensated spins are represented by colorfilled areas in dark grey, while blank zones correspond to FM grains. Black lines are the grain boundaries. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
particulate FM film, modeling in first approximation the finite size and non-interacting nature of the experimental system. In contrast to CoCoO bilayers, which exhibit a single FM/AFM interface, each UCS of ion-implanted Co-CoO systems interacts with more than one FM grain via multiple FM/AFM interfaces. In Fig. 1, about 8% of the grains are considered either rot or set uncompensated spins since the data which are simulated correspond to an O-implanted sample with 8 at.% of O.
Fig. 2. First and second hysteresis loops obtained from the simulated x (black and blue lines) and y (red and green lines) components of magnetization together with the low-temperature experimental results (circles and squares correspond to the first and second loops, respectively) presented in Ref. [24] considering (a) Krot = 50 kJ/m3 , φrot = 0°; and (b) Krot = 21 kJ/m3 , φrot = 90°. Other parameters were fixed during simulations: KFM = 6.5 kJ/m3 , Kset = 1.8 MJ/m3 , φFM = φset = 90°, MFM = MAFM = 1.4 MA/m , Jrot = 1.20 mJ/m2 , and Jset = 0.80 mJ/m2 . The cartoons in each panel represent FM, set, and rot anisotropy directions. 172
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(〈m x 〉) as a function of the magnetic applied field Happlied (applied along x direction) resulting from our numerical simulations. In order to investigate the magnetization reversal mechanisms, the simulated inplane perpendicular average magnetization (〈m y 〉) is also shown in Fig. 2. The uniaxial anisotropy constants as well as their directions with respect to the polar angle (denoted by φ ) were varied in order to achieve the best agreement between the experimental and the numerically simulated results. While φ = 0° corresponds to the direction perpendicular to the plane of the film, φ = 90° corresponds to in-plane directions. The best fitting magnetization curves simulated through our model were obtained for in-plane FM and set anisotropies with KFM = 6.5 × 103 J/m3 and Kset = 1.8 × 106 J/m3, respectively. We have compared out-of-plane and in-plane rot spins’ anisotropy directions φrot = 0°, Krot = 5 × 10 4 J/m3; with (i) and (ii) φrot = 90°, Krot = 2.1 × 10 4 J/m3. In our model, KFM is kept non-refinable. The use of a lower Krot value when considering in-plane rather than out-of-plane allows for properly simulating the coercivities. That is, taking into consideration in-plane anisotropy and keeping Krot = 5 × 10 4 J/m3 rather than 2.1 × 10 4 J/m3 would result in much broader hysteresis loops. This is why, during the simulations, not only the anisotropy direction of rot UCSs was modified but also Krot value. As can be seen in Fig. 2(a), out-of-plane rotatable anisotropy (φrot = 0°) is required to satisfactory simulate the athermal training between the first and the second measured hysteresis loops. μ0 HC decays from 48 to about 35 mT (around 27% of its original value), while |μ0 HEB | drops from 65 to 49 mT (about 25% of its original value). This is in agreement with the already envisaged out-of-plane anisotropy of CoCoO granular and clustered systems [24,25]. The perpendicular anisotropy of rot UCSs can be partly linked to the O ion implantation since it tends to hybridize Co perpendicularly [30,31]. As a consequence of the field-cooling, most of the FM and the UCSs are metastably forced to be oriented in the direction of the applied magnetic field (i.e., in-plane). During the first reversal, the magnetic moments of rot UCSs reorient according to their anisotropy (perpendicular) and the closest FM moments follow this orientation due to their strong exchange interaction with rot spins, not contributing to the longitudinal magnetization (along x) and, thus, giving rise to training. Conversely, in Fig. 2(b) it is shown that, when in-plane rotatable anisotropy is considered during the simulation, no differences between 〈m x 〉1 and 〈m x 〉2 are observed and thus no training effect takes place for in-plane rot UCS anisotropy. In certain parallelism, perpendicular anisotropy has already been observed to rule exchange bias properties in other systems, such as Pt/Co/ Cu/IrMn and Pd/Co/IrMn [32,33]. The uniaxial anisotropy constants used are about two orders of magnitude lower than those reported in literature. The reduced value of KFM can be ascribed to both the presence of stacking faults in thin Co films and the coexistence of fcc and hcp phases of Co [10,24]. The reduced values of Kset and Krot are a consequence of the way we have described the system, since there is no antiferromagnetic matrix to build-up UCS anisotropies. The obtained effective coupling between CoO spins and the adjacent FM grains were Jset = 0.80 mJ/m2 and Jrot = 1.20 mJ/m2, which are in concordance with values reported in the literature [3,10]. Due to the morphology of the system, each UCS can interact with more than one FM grain, which increases the effective contact area when compared to FM/AFM bilayers. In our micromagnetic simulations, this is reflected in a larger amount of magnetic cells under the influence of exchange anisotropy. This results in low anisotropic UCSs adding to both bias and HC . Co-CoO exchange-biased systems prepared by low fluence O ion implantation exhibit magnetization reversal asymmetry between the first and the second magnetic reversals as it happens in Co/CoO films [24,26,36]. The first reversal is governed by domain wall nucleation and motion, whereas coherent rotation is the dominant mechanism in the subsequent reversals. Fig. 2 also shows the orthogonal in-plane component of the magnetic moment 〈m y 〉 of the first two hysteresis loops since it accounts for magnetization reversal mechanisms which
involve spin rotation. As it happens with training, the experimentally observed asymmetry between the first and the second reversals is only observed if perpendicular rot anisotropy is taken into account. That is, during the first reversal 〈m y 〉 is negligible, whereas for subsequent reversals this orthogonal contribution becomes significant in agreement with the fact that coherent rotation becomes enabled from the second reversal on. In order to investigate the influence of large magnetic fields on the system [34,35], we have performed simulations after applying an external field of 4 T along x , y and z directions were carried out to simulate the trained state. No significant differences have been observed between the hysteresis loops of the trained state simulated with maximum applied magnetic fields of 500 mT and 4 T. Out-of-plane contributions to the sample magnetization naturally arise in our simulations in agreement with the experimental results from Ref. [24]. Specifically, the polarized neutron reflectometry results indicate a loss of in-plane magnetization which scales with the number of measured loops, suggesting an increase of out-of-plane contributions which cannot be probed by this technique. Hence, we also simulate the evolution of the perpendicular component z for the first two hysteresis loops (Fig. 3). Upon field-cooling, magnetization remains in the plane of the sample. Thus, when initiating the first magnetic reversal, there is virtually no 〈mz 〉. However, when the applied field reaches a value of μ0 Happlied ≈ −80 mT, the magnetization of FM grains that interact with rot UCSs partially rotate towards the out-of-plane direction. After the first reversal, the z contribution remains and reinforces with consecutive reversals, in agreement with the loss of in-plane contributions with reversals envisaged by polarized neutron reflectometry in Ref. [24]. The field-cooling results in a metastable state with its magnetization frozen in the plane of the sample. With reversals, configurations with out-of-plane components arise because they are energetically favorable. As one can see in Fig. 3, the hysteretic behavior of 〈mz 〉 shows a vertical shift. This is due to the fact that FM moments that interact with rot UCSs rotate towards + z and, during the first reversal and from second reversal on, a fraction of these magnetic moments become frustrated, probably due to the interaction with other UCSs. It is worth mentioning that perpendicular magnetization goes to zero for |μ0 Happlied | > 500 mT as expected from fully saturated in-plane hysteresis. It should be noted that the noise of hysteresis loops of Fig. 3 is ascribed to the reduced quantity of FM cells which are influenced by the perpendicular anisotropy of the rot UCSs, since it is considered that the exchange interaction extends only to the first-neighbors. Perpendicular contribution to the effective field are small when compared to the inplane ones, as a consequence fluctuation of 〈mz 〉 can occur without
Fig. 3. Evolution of the out-of-plane magnetization during the untrained (black solid line) and first trained (dashed red line) magnetic cycles for simulations considering perpendicular rot anisotropy with Krot = 5 × 10 4 J/m3 . 173
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affecting significantly the effective field and, thus, the global energy.
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4. Summary and conclusions In summary, we have theoretically investigated using micromagnetic simulations the athermal training effect in granular Co-CoO exchange-biased systems prepared by ion implantation in Co thin films by comparing the simulations to the experimental results obtained in Physical Review B 89 (2014) 144407. Instead of a bilayer system, we have considered non-interacting and discrete AFM grains buried inside a FM thin film, successfully reproducing training and magnetization reversal asymmetry, whose origin and interdependence is linked to the perpendicular anisotropy of rotatable spins. Acknowledgements This work was supported by the Brazilian Foundation CNPq under Project Nos. 402013/2016-6 and 104289/2018-0, the Generalitat de Catalunya (2017-SGR-292) and the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 665919. T.D and G.J. thank the facilities of Laboratório de Pesquisa em Computação Aplicada (LPCA-UTFPR). Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, athttps://doi.org/10.1016/j.jmmm.2019.01.104. References [1] [2] [3] [4] [5] [6] [7] [8] [9]
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