Co spin valves

Accepted Manuscript Effect of the strong coupling on the exchange bias field in IrMn/Py/Ru/Co spin valves H.S. Tarazona, W. Alayo, C.V. Landauro, J. Quispe–Marcatoma PII: DOI: Reference:

S0304-8853(17)32216-3 http://dx.doi.org/10.1016/j.jmmm.2017.09.004 MAGMA 63133

To appear in:

Journal of Magnetism and Magnetic Materials

Please cite this article as: H.S. Tarazona, W. Alayo, C.V. Landauro, J. Quispe–Marcatoma, Effect of the strong coupling on the exchange bias field in IrMn/Py/Ru/Co spin valves, Journal of Magnetism and Magnetic Materials (2017), doi: http://dx.doi.org/10.1016/j.jmmm.2017.09.004

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Effect of the strong coupling on the exchange bias field in IrMn/Py/Ru/Co spin valves H. S. Tarazonaa , W. Alayob,∗, C. V. Landauroa,c , J. Quispe–Marcatomaa,c a

Facultad de Ciencias F´ısicas, Universidad Nacional Mayor de San Marcos, P. O. Box 14-0149, Lima, Peru b Departamento de F´ısica, IFM, Universidade Federal de Pelotas, 96160-900 Cap˜ ao do Le˜ ao, RS, Brazil. c Centro de Investigaciones Tecnol´ ogicas, Biom´edicas y Medioambientales, Calle Jos´e Santos Chocano 199, Bellavista, Callao - Peru

Abstract The IrMn/Py/Ru/Co (Py = Ni81 Fe19 ) spin valves have been produced by sputtering deposition and analyzed by magnetization measurements and a theoretical modelling of their exchange interactions, based on the macro-spin model. The Ru thickness was grown between 6 and 22 ˚ A, which is small enough to promote strong indirect coupling between Py and Co. Results of measurements showed a large and gradual change in the shape of hysteresis loops when the Ru thickness was varied. The theoretical analysis, using numerical calculations based on the gradient conjugate method, provides the exchange coupling constants (bilinear and biquadratic), the exchange anisotropy fields and the magnetic anisotropy fields (uniaxial and rotatable). The exchange bias fields of spin valves were compared to that of a IrMn/Py bilayer. We found that the difference between these fields oscillates with Ru thickness in the same manner as the bilinear coupling constants. Keywords: Spin valves, exchange coupling, magnetic anisotropy The spin valves structures, proposed by Dieny et al. [1], received a lot of attention due to their potential use in sensors and storage devices [2]. In general, these systems consist on two ferromagnetic (FM) layers, FM1 and FM2 , separated by a non-magnetic (NM) metal, one of them is in contact with an antiferromagnetic (AF) material, giving the AF/FM2 /NM/FM1 multilayer, as seen in Fig. 1. In many works, the NM layer is large enough for weakly coupled [3, 4, 13] or uncoupled FM layers. The FM1 layer has its magnetization free to rotate in response to the application of an external field, while, the FM2 layer is the fixed layer and its magnetization is pinned by the exchange coupling with the AF material. Here, we present an analysis of the IrMn/Py/Ru/Co structure with the FM layers strongly exchange coupled, considering both theoretical and experimental point of views. The theoretical study is based on the macro-spin model, using the phenomenological Helmholtz free energy. This model takes into account the Zeeman energy, the demagnetizing energy, uniaxial anisotropies for ∗

Corresponding author Email address: [email protected] (W. Alayo)

Preprint submitted to Journal of Magnetism and Magnetic Materials

September 6, 2017

both FM layers, the exchange bias coupling, the rotatable anisotropy, the bilinear and the biquadratic interlayer exchange coupling energy. The energy minima were calculated with a procedure briefly described below and the obtained equilibrium magnetization angular positions were used to calculate the magnetization curves. Moreover, we show that the indirect coupling across the Ru layer strongly affect the exchange bias field at the IrMn/Py interface. This is evidenced by exchange bias fields that increase (decrease) for a AF (FM) coupling, following an oscillatory behavior that reproduce the oscillations of the indirect exchange coupling.

Figure 1: Representative diagram of a AF/FM2 /NM/FM1 spin valve and the coordinate system for defining ~ i ) and applied magnetic field (H) ~ with respect to an anisotropy direction angles (ϕi ) of magnetizations (M (ˆ u), all lying in the x − y plane.

Considering the coordinates system shown in Fig. 1, the total free energy density, obtained within the Stoner-Wohlfarth formalism [5], for which, the magnetization vectors rotate coherently in response to an external field, can be expressed as:     Hu2 Hu1 2 2 cos ϕ1 + t2 M2 −H cos (ϕH − ϕ2 ) − cos ϕ2 E = t1 M1 −H cos (ϕH − ϕ1 ) − 2 2   HRA 2 +t2 M2 −HE cos(ϕ2 − ϕ3 ) − HW cos ϕ3 − cos (ϕ2 − ϕH ) + Hk cos ϕ2 2 −Jbl cos (ϕ1 − ϕ2 ) − Jbq cos2 (ϕ1 − ϕ2 ) (1) where ti , Mi and ϕi , being i = 1, 2, 3, are the thickness, saturation magnetization and the angles between magnetization vectors and an anisotropy in-plane axis uˆ, for the FM1 , ~ vector with respect to uˆ. The FM2 and AF layers, respectively. ϕH is the angle of the H magnetization of the AF layer refers to one of the antiferromagnetic sublattices at the AFM/FM2 interface and HW = σW /(t2 M2 ), where σW is the energy per unit surface of a 90◦ domain wall in the AFM layer [6]. The anisotropy fields for the FM layers are Hu1 = 2Ku1 /M1 and Hu2 = 2Ku2 /M2 , where Ku1 and Ku2 are the respective anisotropy constants. The exchange anisotropy field HE = JE /(t2 M2 ) is associated to the exchange bias energy JE . The term includind the HRA factor considers the existence of a rotatable anisotropy [7] KRA in the FM2 layer (HRA = 2KRA /M2 ), that indicates a tendency of 2

the magnetization to rotate through the external field. This term was considered because we use NiFe as the FM2 layer and it tends to rotate easily with the applied field [8]. The term including the Hk field (= 2Kk /M2 ) represents an additional contribution to the unidirectional anisotropy [9]. Jbl and Jbq are the bilinear an biquadratic coupling constants, respectively. We have developed a procedure for minimizing numerically the total free energy as a function of the ϕi angles. This procedure is based on the conjugate gradient method [10] and a brief description of this procedure is described below: 1. An initial set of angles, {ϕ}0 , are chosen to be fixed and then we calculate E0 . 2. The gradient, ∇E ({ϕ}0 ), of the total free energy and its magnitude is calculated. α∇E and 3. We move to a new position {ϕ}i+1 , following the rule: {ϕ}i+1 = {ϕ}i − ∇E({ϕ} i) then we calculate the corresponding energy, Ei+1 . 4. We evaluate whether Ei+1 < Ei . If this is true then we do {ϕ}i ← {ϕ}i+1 and {E}i ← {E}i+1 and return to step 2. Otherwise, we make α → α/2. 5. We evaluate whether α or ∇E ({ϕ}0 ) achieved a tolerance value. If this is satisfied, then the energy E0 and the set of angles {ϕ}0 are stored and we repeat the step 1 for a new value of the external magnetic field. Otherwise, we return to step 3. For simulations, we start in the saturated state. Thus, the equilibrium angles found in each step are used as input values for next step, with a new value of the magnetic field. After the minimization procedure, the normalized magnetization curves can be calculated ~ 1 and M ~ 2 along the field direction with the sum of projections of magnetization vectors M ˆ using [11, 12]: (h), M (H) = Ms

P2 ~ ˆ i=1 ti Mi · h P 2 i=1 ti Mi

(2)

For the experimental approach, the samples were grown at room temperature by magnetron sputtering onto single-crystalline Si(111) substrates. The base pressure was of the order of 2 × 10−8 Torr and the working pressure was set to 3 × 10−3 Torr in an argon atmosphere. Before the production of the spin valves, thick (∼ 1000˚ A) unique layers of each material were deposited under the same conditions in Si substrates. In this way we estimate the deposition rates; which were determined to be 1.0 ˚ A/s for Ru and Co and 1.6 ˚ A/s for Py and IrMn. Thus, the whole notation for the samples is written as Si(111)/Ru(70 ˚ A)/IrMn(60 ˚ A)/Py(40 ˚ A)/Ru(tRu )/Co(40 ˚ A)/Ru(50 ˚ A). The Ru buffer layers favours the antiferromagnetic phase of IrMn(111) [15] and all multilayers were capped with a 50 ˚ A thick Ru layer. The Ru intermediate layers were grown with different thicknesses, tRu , between 6 and 22 ˚ A. During the growth of all spin valves, a static magnetic field was applied along the plane of substrates in order to induce an unidirectional anisotropy. This field was established by fixing small permanent magnets with a field magnitude of ∼ 400 Oe. Magnetization measurements as a function of the applied magnetic field were carried out using a vibrating sample magnetometer (VSM) from Quantum Design, at room temperature. The external 3

Figure 2: (Color online) Magnetizations curves of the IrMn/Py/Ru(tRu )/Co spin valve system for diferents tRu . Circles represent the experimental data and blue lines are simulations peformed equations 1 and 2, using 4πM1 = 17.0 kOe, 4πM2 = 9.8 kOe, t1 = t2 = 40 ˚ A and parameters listed in Table 1.

field, during measurements, was always applied along the films plane and parallel to the orientation of the induced unidirectional anisotropy. Fig. 2 shows the experimental magnetization curves (open circles) for samples with different tRu . It is seen that the shape of the curves notably changes when tRu is varied. This is an indication of a strong exchange interaction between Py and Co magnetizations. For tRu = 6 and 8 ˚ A, the saturation field is higher than 1 kOe and the magnetization increases slowly for increasing applied field. This indicates an out phase rotation of magnetizations with the applied field and an antiparallel alignment at low field region, suggesting a strong AF coupling. However, it is possible to distinguish the presence of two loops that overlap to form the whole magnetization curve. These loops correspond to the Py and Co magnetic layers, and are shifted to the negative (Py) and positive side (Co) of the field axis. For tRu = 10 ˚ A, the hysteresis curve exhibits clearly the two loops. An AF coupling between Py and Co is also evidenced, but the saturation field is much lower than that for tRu = 6 and 8 ˚ A. For tRu = 14 ˚ A, the hysteresis cycle changes drastically and resembles the magnetization 4

curve of a AF/FM bilayer, for which, a single loop is shifted along the field axis. This indicates that the Py and Co magnetization vectors are strongly coupled and aligned parallel to each other. For tRu = 18 and 22 ˚ A, the loop of Py layer is shifted to negative side while the loop of Co layer is shifted to positive side along the field axis, indicating an AF coupling. Table 1: Exchange coupling and magnetic anisotropy constants of the IrMn/Py/Ru(tRu )/Co spin valves, obtained from fits of hystereis loops shown in Fig. 3.

tRu (˚ A)

Hu1 (Oe)

Hu2 (Oe)

HE (Oe)

HW (Oe)

HRA (Oe)

Hk (Oe)

Jbl (erg/cm2 )

Jbq (erg/cm2 )

χ2

6

50

4

410

130

-90

30

-0.192

-0.018

0.198

8

50

4

520

240

120

100

-0.242

-0.003

0.345

10

50

4

100

620

200

24

-0.022

-0.006

7.815

14

80

4

97

180

80

80

0.012

-0.007

1.620

18

55

4

200

800

230

110

-0.010

0

25.840

22

55

4

110

670

150

0

-0.001

0

57.88

The quantitative information was obtained by fitting equations 1 and 2 to the experimental data, using the saturation magnetization of 4πM1 = 17.0 kOe for Co and 4πM2 = 9.8 kOe for Py and layer thickness t1 = t2 = 40 ˚ A in all cases. The other parameters are listed in 2 Table 1, with the respective χ value; in Fig. 2 the solid lines are the calculated curves. In Fig. 3 we show the magnetization curves (left side) and their respective equilibrium angles (right side) for tRu = 6 ˚ A and tRu = 14 ˚ A corresponding to the strong AF and FM couplings, respectively. Red lines correspond to equilibrium angles of magnetization of the Co layer, ϕ1 , while blue lines, to the Py layer, ϕ2 . Moreover, the upper (lower) curve for ϕi (H) refers to the descending (ascending) branch of the hysteresis loops. We observe that for the case of strong AF coupling (Fig. 3(a)) the magnetization vectors of the Co (red arrow) and Py (blue arrow) layers rotate out of phase (ϕ1 6= ϕ2 ), whereas for strong FM coupling they rotate in phase (ϕ1 = ϕ2 ), for the descending branch, whereas, for the ascending branch, the magnetization vectors rotate out-of-phase, as deduced from the analysis made of their respective equilibrium angles. Moreover, in Fig. 3(a) we identify five magnetic phases which are separated by vertical dashed lines: (i) a saturated phase (H > 1150 Oe) where the Co and Py magnetizations are parallel to the applied field; (ii) a transition phase where reversal magnetization of Co layer takes place (70 Oe < H < 1150 Oe); (iii) an antiferromagnetic phase (−200 Oe < H < 70 Oe), where the Co and Py magnetization vectors are aligned antiparallely; (iv) a transition phase where reversal magnetization of Py layer takes place (−1300 Oe < H < −200 Oe); and (v) a second saturated phase (H < −1300 Oe). Likewise, for strong FM coupling (tRu = 14 ˚ A), from Fig. 3(b) we identified two first phase transitions at H1 ∼ −60 Oe and H2 ∼ 24 Oe where reversal magnetization of both Co and Py magnetization vectors take place. 5

Figure 3: (Color online) Experimental hysteresis loops (circles), with their respective fits (black lines), for the strongest (a) AF (tRu = 6 ˚ A) and (b) FM coupling (tRu = 14 ˚ A). The red (blue) arrows represent the direction of the Co (Py) magnetizations. The respective equilibrium angles ϕi (H) are shown at the right side and they were obtained by minimizing the free energy (Eq. 1).

It is important to note that for the lower values of tRu (6 and 8 ˚ A) it is commune the formation of island or defects instead continuous Ru spacer layers during the growth process. These defects would form bridges of direct FM exchange interaction between Co and Py (pinholes) and they may contributes to the total exchange interaction of the structure. However, the strength of the exchange interaction coming from pinholes depends on the size and number of holes and the distance between them. For a detailed description of this contribution these parameters must be considered in a micro-magnetic modelling of the exchange coupling of magnetic multilayers [16]. Depending on the holes density area, the direct FM coupling can be dominant and the hysteresis curve of the AF/FM2 /NM/FM1 must exhibit a single loop, as for a AF/FM bilayer. Here, for the two thinnest Ru layers, the magnetization curve could be adequately described considering only indirect exchange coupling. Other limitation of the used phenomenological model is the square shape of the fitting curves shown in figure 2 (tRu = 10, 14, 18 and 22 ˚ A) and in 3(b), which differs from the rounded shape of the experimental M-H curves. A more complex and polycrystalline model, considering a granular structure and multi-domain structure must improve the fit to 6

the experimental data [18]. Fitting results show oscillations of the bilinear exchange coupling, from negative (antiferromagnetic) to positive (ferromagnetic) values when tRu is varied. The Jbl values as a function of tRu are shown in Fig. 4. Red solid point are values obtained from fits. The type and strength of the bilinear coupling explain adequately the drastic change of the hysteresis curves of the spin valves, as described above. The strongest AF coupling occurs for tRu = 6 and 8 ˚ A, in which the curves present the highest saturation fields, whereas the strongest FM coupling has been observed for tRu = 14 ˚ A, which behaves as unique AF/FM bilayer, giving a good agreement between experimental data and theoretical calculations. The oscillatory behavior of Jbl with tRu has been observed in spin valves systems with Ru spacer in the weak coupling regime [13]. Moreover, a gradual decrease superposed to an oscillatory behavor of Jbl > 0 was also observed in spin valves with other non-magnetic spacers [15, 14]. Here, results for Jbl indicates a predominance of the RKKY-like exchange coupling mechanism over the magneto-static orange-peel coupling or N´eel’s mechanism. In this way, we performed a fit of the Jbl versus tRu curve using [17]: cos (q0 t + φ) (3) t2 where q0 is a parameter related to the size of the Fermi surface and t = tRu is the thickness of the non-magnetic layer. The solid line in Fig. 4 is a fit of Eq. 3 to the Jbl values. From this fit we obtain a period of tRu = 11˚ A. On the other hand, for tRu > 10˚ A, the shape of the calculated curves are quite square. This is because the macrospin model does not take into account the presence of several magnetic domains. In this sense, the rounded shape of the curves can be modeled considering a polycrystalline film with a distribution of uniaxial axis, uˆ in the FM1 layer and AF/FM2 interface [7, 18]. For tRu > 22 ˚ A the system would have weak interlayer coupling [13]. It is noteworthy that the inclusion of the rotatable anisotropy causes a widening of the hysteresis curve corresponding to the Py layer. This can be understood according to the polycrystalline model for exchange bias, which considers a granular AF/FM2 interface with unstable (rotatable) and stable (fixed) grains with uncompensated spins. The uniaxial anisotropy direction of unstable grains rotate irreversibly and produces an increment of coercivity of the hysteresis loop for Py layer. The exchange bias field of the Py layer varied according to the strong interlayer coupling between Py and Co; they were compared to that of a IrMn(60 ˚ A)/Py(40˚ A) bilayer, grown with the same procedure and under the same conditions of the spin valves. We found that the difference between the exchange bias field values of spin valves and the one of the bilayer, bilayer spin valves ∆Heb = Heb − Heb follows the same oscillatory behavior with tRu as the bilinear coupling constants. This is due to the interplay between the interlayer exchange interaction across Ru and the exchange bias effect. In the inset (a) of Fig. 4 are shown the ∆Heb values, obtained from experimental hysteresis loops, as a function of tRu . The same oscillatory behavior can be observed for Jbl and ∆Heb . The inset (b) displays the hysteresis cycle measured at room temperature of the IrMn(60 ˚ A)/Py(40˚ A) bilayer, for which the exchange bilayer bias field is Heb ≈ 135 Oe. Thus, the dominant RKKY-like coupling mechanism has also been observed directly from exchange bias fields in the spin valves. The biquadratic Jbl ∝

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Figure 4: (Color online) Bilinear exchange coupling constants, Jbl , as a function of the Ru layer thickness, tRu . Red poits were obtained from fits of hysteresis loops (see Fig.2) and the blue line is a fit of Eq. (3) to the data. Inset (a) shows the difference between the exchange bias fields of the spin valves and that of a IrMn(60˚ A)/Py(40˚ A) bilayer, whose hysteresis loop is shown in inset (b).

coupling constants are of the order of the bilinear ones. In calculations of hysteresis loops, for tRu = 20 and 22 ˚ A the Jbq parameters contributes for an additional uniaxial magnetic anisotropy for the Co layer. In summary, the IrMn(60˚ A)/Py(40˚ A)/Ru(tRu )/Co(40˚ A) spin valves has been studied by magnetization measurements. The thickness of Ru interlayer was in the range from 6 to 22 ˚ A to promote strong exchange coupling. A phenomenological description based on the macrospin model was used to interpret the experimental data. For this end, the total free energy was minimized employing the conjugate gradient method. For strong antiferromagnetic coupling, the system has an enhancement of its exchange bias field with respect to that of a IrMn(60˚ A)/Py(40˚ A) reference bilayer. Whereas, for strong ferromagnetic coupling, the spin valves behaves as an unique AF/FM bilayer, but with an exchange bias field lower than the reference bilayer. Theoretical hysteresis curves were obtained with the method proposed here and they were fitted to the experimental data. From these fits, we obtain a set of magnetic parameters, among them, it is remarkable the oscillatory behavior of the bilinear coupling constants as a function of tRu . Furthermore, the difference between the exchange 8

bias fields of spin valves and that of the reference bilayer reproduces the same oscillations as function of tRu observed for Jbl . Acknowledgements This work has been partially supported by the Brazilian agencies CNPq and CAPES. H.S.T. thanks to the Peruvian Doctoral Scholarship of CIENCIACTIVA (CONCYTEC) under Grant #218-2014-FONDECYT. C.V.L. and J.Q-M are grateful to CIENCIACTIVA (CONCYTEC) for financial support throught the Excellence Center Programs. We also acknowledge E.B. Saitovitch and CBPF for experimental facilities. [1] B. Dieny, V. S. Speriosu, S. Metin, S. S. P. Parkin, B. Gurney, P. Baumgart, and D. R. Wilhoit, J. Appl. Phys. 69 (1991) 4774. http://dx.doi.org/10.1063/1.348252. [2] Ching Tsang, Robert E. Fontana, Tsann Lin, D. E. Heim, Virgil S. Speriosu, Bruce A. Gurney, and Mason L. Williams, IEEE Trans. Mag. 30 (1994) 3801. https://doi.org/10.1109/20.333909. [3] L. Rodriguez–Su´ arez, S. M. Rezende, and A. Azevedo, Phys. Rev. B, 71 (2005) 224406-1–224406-6. https://doi.org/10.1103/PhysRevB.71.224406. [4] A. Layadi, J. Appl. Phys. 100 (2006) 083904-1–083904-8. http://dx.doi.org/10.1063/1.2358815. [5] E. C. Stoner, and E. P. Wohlfarth, Nature 160 (1947) 650. http://dx.doi.org/10.1038/160650a0. [6] D. Mauri, H. C. Siegmann, P. S. Bagus, and E. Kay, J. Appl. Phys. 62 (1987) 3047. http://dx.doi.org/10.1063/1.339367. [7] J. Geshev, L. G. Pereira, J. E. Schmidt, Phys. Rev. B, 66 (2002) 134432. https://doi.org/10.1103/PhysRevB.66.134432. [8] R. J. Prosen, J. O. Holmen, and B. E. Gran, J. Appl. Phys, 32 (1961) S91. https://doi.org/10.1063/1.2000512. [9] Marcos Antonio de Sousa, Fernando Pelegrini, Willian Alayo, Justiniano Quispe-Marcatoma, and Elisa Baggio-Saitovitch, Physica B 450 (2014) 167–172. http://dx.doi.org/10.1016/j.physb.2014.05.050. [10] William H. Press, Saul A. Teukolski, William T. Vetterling, and Brian P. Flannery, Numerical Recipes in C, The art of Scientific Computing, 2nd ed., Cambridge University Press, New York, 1998. [11] M. Czapkiewicz, T. Stobiecki, R. Rak, J. Wrona and C. G. Kim, Journal of Magnetics 9(2) (2004) 60–64. [12] S. M. Rezende, C. Chesman, M. A. Lucena, A. Azevedo, F. M. de Aguiar, and S. S. P. Parkin, J. Appl. Phys. 84 (1998) 958–972. http://dx.doi.org/10.1063/1.368161. [13] W. Alayo, Y. T. Xing, and E. Baggio-Saitovitch, J. Appl, Phys. 106 (2009) 113903-1–113903-6. http://dx.doi.org/10.1063/1.3257113. [14] J. L. Leal, and M. H. Kryder, J. Appl. Phys. 79 (1996) 2801–2803. http://dx.doi.org/10.1063/1.361115. [15] W. Alayo, M. A. Sousa, F. Pelegrini, and E. Baggio-Saitovitch, J. Appl. Phys. 109 (2011) 083917-1– 083917-5. http://dx.doi.org/10.1063/1.3569690. [16] J. F. Bobo, H. Kikuchi, O. Redon, E. Snoeck, M. Piecuch, R. L. White, Phys. Rev. B, 60 (1999) 4131–4141. https://doi.org/10.1103/PhysRevB.60.4131. [17] P. Bruno, J. Phys.: Condes. Matter 11 (1999) 9403–9419. https://doi.org/10.1088/09538984/11/48/305. [18] A. Harres, and J. Geshev, J.Phys.: Condens. Matter 24 (2012) 326004. https://doi.org/10.1088/09538984/24/32/326004.

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Highlights

Enhancement (reduction) of the exchange bias field for strong antiferromagnetic (ferromagnetic) coupling in spin valves.

Oscillatory behavior of the exchange bias field, modulated by the interlayer e coupling in spin valves.