Backhopping in magnetic tunnel junctions: Micromagnetic approach and experiment

Journal of Magnetism and Magnetic Materials 374 (2015) 451–454

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Journal of Magnetism and Magnetic Materials journal homepage: www.elsevier.com/locate/jmmm

Backhopping in magnetic tunnel junctions: Micromagnetic approach and experiment Marek Frankowski n, Witold Skowroń ski, Maciej Czapkiewicz, Tomasz Stobiecki AGH University of Science and Technology, Department of Electronics, al. Mickiewicza 30, 30-059 Kraków, Poland

art ic l e i nf o

a b s t r a c t

Article history: Received 2 June 2014 Received in revised form 14 August 2014 Available online 26 August 2014

Micromagnetic simulations of Current Induced Magnetization Switching (CIMS) loops in CoFeB/MgO/ CoFeB exchange-biased Magnetic Tunnel Junctions (MTJ) are discussed. Our model uses the Landau– Lifshitz–Gilbert equation with the Slonczewski's Spin-Transfer-Torque (STT) component. The current density for STT is calculated from the applied bias voltage and tunnel magnetoresistance which depends on the local magnetization vectors arrangement. We take into account the change in the anti-parallel state resistance with increasing bias voltage. Using such model we investigate influence of the interlayer exchange coupling, between free and reference layers across the barrier, on the backhopping effect in anti-parallel to parallel switching. We compare our simulated CIMS loops with the experimental data obtained from MTJs with different MgO barrier thicknesses. & 2014 Elsevier B.V. All rights reserved.

Keywords: Spintronic Simulation OOMMF STT MTJ IEC Switching Backhopping Micromagnetic

1. Introduction Magnetic Tunnel Junctions (MTJs) are currently one of the most universal spintronic devices. The possibility of controlling the resistance of the MTJ, consisting of two thin ferromagnetic layers, separated by insulating barrier, by means of spin polarized current enables numerous possible applications, such as microwave oscillators [1–3] and novel magnetic random access memories [6,7]. In these cases spin-polarized current that flows through the MTJ interacts with the magnetization of ferromagnetic layer, called the Free Layer (FL) due to the Spin-Transfer-Torque (STT) [4,5], which brings the magnetization of the FL into precession. If the current value is sufficiently high, it can flip the FL magnetization between Anti-Parallel (AP) and Parallel (P) alignment with respect to the Reference Layer (RL). This phenomenon is called the Current Induced Magnetization Switching (CIMS) [8,9]. However, experimental data show that in MgO based MTJs random back-and-forth switching caused by high magnitude magnetization oscillations can occur. The effect was reported during switching from AP to P state and is called the backhopping [10]. It originates from the competition between in-plane and out-of-plane STT components, as for certain bias voltage range they have similar magnitudes and opposite signs [11]. When such bias voltage range is

n

Corresponding author. E-mail addresses: [email protected], [email protected] (M. Frankowski).

http://dx.doi.org/10.1016/j.jmmm.2014.08.056 0304-8853/& 2014 Elsevier B.V. All rights reserved.

located within the regime of switching voltage, there is a possibility of backhopping occurrence. The switching process itself was analyzed theoretically using macrospin [12,13] and micromagnetic models [14–16]. However, to reproduce the whole CIMS hysteresis loop and investigate backhopping we introduce a model that includes calculations of local current densities [18,20] from Tunnel Magnetoresistance (TMR) effect [21], as well as changes of AP state resistance due to applied bias voltage [22–24]. Recently, backhopping phenomenon has been investigated experimentally and analyzed by means of macrospin model [11]. It has been shown that the probability of the backhopping phenomenon can be controlled by adjusting interlayer exchange coupling (IEC) between FL and RL through MgO barrier and, therefore, changing a constant component of out-of-plane torque [11] is given by the formula: τoop ¼ b0 þ b1 J þ b2 J 2 , where J is the current density. Only linear b1 and quadratic b2 coefficients of outof-plane torque can be fitted to experimental torque data, because the calculated torque values are integrals of measured torkances [3] and the constant coefficient is unknown. Therefore, in this work, we use micromagnetic simulation approach with effective coupling (being a sum of IEC and demagnetization energy calculated dynamically for real MTJ geometry) instead of implementing constant component b0 of out-of-plane torque. We solve the Landau–Lifshitz–Gilbert equation with the Slonczewski's STT component to investigate the magnetization dynamics. Experimentally

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M. Frankowski et al. / Journal of Magnetism and Magnetic Materials 374 (2015) 451–454

evidenced dependence of backhopping occurrence on effective coupling varying with MgO thickness is well reproduced.

2. MTJ structure and experiment Our exchange biased spin valve MTJ was deposited with the following layer structure (thicknesses in nm) Ta(5)/CuN(50)/Ta(3)/ CuN(50)/Ta(3)/PtMn(16)/Co70Fe30(2)/Ru(0.9)/Co40Fe40B20(2.3)/ wedge MgO(0.7–1.1)/Co40Fe40B20(2.3)/Ta(10)/CuN(30)/Ru(7). The deposition and nanofabrication processes were similar to the one used in our previous studies [9]. In this case MTJs were nano-patterned to pillars with an elliptical cross-section of 150  250 nm with three different MgO barrier thicknesses: 0.76 nm, 0.95 nm and 1.01 nm. TMR measurements show different field shifts (Hs) in resistance vs. magnetic field hysteresis loops, which originate from effective IEC dependency on MgO thickness. The Hs fields were for 0.76 nm H s ¼  21:7 Oe (effective anti-ferromagnetic coupling), 0.95 nm H s ¼  3:7 Oe (effective anti-ferromagnetic coupling) and 1.01 nm H s ¼ 47 Oe (effective ferromagnetic coupling). CIMS measurements were conducted by applying 10 ms-long voltage pulses of increasing amplitude and probing the resistance state both after and during the pulse which is depicted in Fig. 1 (a) and (b), respectively. Note that the applied bias voltage affects the resistance of the AP state [22–24]. In addition, since the in-plane torque value depends on the current density it is also important to take into account the actual MTJ resistance during switching at high bias voltage for the purpose of theoretical calculation of the switching voltage values.

Fig. 1. Experimental CIMS loops for 0.95 nm MgO thickness: (a) resistance measured after voltage pulse and (b) during the pulse. Arrows shows time evolution of the experiment. Note the changes in resistance of the AP state on picture (b).

valve MTJ by Lacour et al. [25] and Liebing et al. [26]: R ¼ RP þ

3. Micromagnetic model and simulations In order to micromagnetically simulate the CIMS hysteresis loops in the MTJs, we have used Object Oriented Micromagnetic Framework OOMMF [17] with our extension for the STT and local current densities [18,19]. In our simulations we solve the Landau–Lifshitz–Gilbert equation with the STT components: ! ! dm ! ! ! ∂m ¼  γ 0 m  H eff þ αm  dt ∂t ! ! ! ! ! þ γ 0 aJ m  ðm  p Þ þ γ 0 bJ m  p ;

ð1Þ

where the first term corresponds to the magnetization precession, second corresponds to damping, third and forth correspond to in! plane and out-of-plane torques, respectively. m is the normalized magnetization vector of the FL, γ 0 ¼ 2:21  105 m=A s is the ! gyromagnetic factor, H eff is the effective field derived by mini! mizing the local energy densities, α is the damping factor, and p is the normalized RL magnetization vector. The in-plane torque factor is written as follows: aJ ¼

ℏ ηJ; 2eμ0 M s t

ð2Þ

where t is the FL thickness, η is the effective polarization, J is the current density. The perpendicular torque is implemented as bJ ¼ b1 J þ b2 J 2 , where b1 ¼ 2:7  10  9 m and b2 ¼ 2:8  10  19 m3 =A are the quadratic function components, taken from the experimental data [3]. The current density is calculated using Ohm's law from applied voltage and resistance, where resistance is given locally in the discretized junction surface by the phenomenological formula for cosine dependence as has also been reported for exchange biased spin

RAP  RP ð1  cos θÞ; 2

ð3Þ

where θ is an angle between magnetization vectors of FL and RL, RP (for θ ¼ 0) and RAP (for θ¼ 1801) are resistances of the P and AP states, respectively. Resistances of P and AP for different bias voltages are taken from phenomenological fit to the experimental data. Since our model introduces bias voltage as a time-dependent parameter, the calculated current also changes with time and its local density depends on the TMR values via local magnetization orientation [18]. It is even more important for the backhopping effect, as at the same bias voltage the magnetization is switching between P and AP, the junction current density fluctuations get rapid and vastly non-uniform, which makes competition between current-dependent torques very complicated. Snapshots from simulation of switching process in during backhopping are depicted in Fig. 2. For the purpose of our model the fabricated MTJs were parametrized as follows: the space discretization cell size of 2  2  1 nm, the FL with the uniaxial anisotropy constant of K FL ¼ 1 kJ=m3 , the saturation magnetization of M FL ¼ 1150 kA=m and the damping constant equals α¼0.01, coupled to RL with the coupling energy depending on the MgO thickness shown later, RL uniaxial anisotropy constant has K RL ¼ 32 kJ=m3 and the saturation magnetization of M RL ¼ 1400 kA=m. The RL was coupled to the CoFe Pinned Layer (PL) with the interlayer surface energy of J Ru ¼  0:015 mJ=m2 through the Ru layer. PL uniaxial anisotropy constant of K PL ¼ 60 kJ=m3 , saturation magnetization of M PL ¼ 1400 kA=m. Exchange bias field was set to H EB ¼ 80 mT and applied with random orientation in 30 nm diameter circular areas. This represents the poly-crystalline PtMn and randomly oriented PtMn grains which couple to CoFe grains of the PL (Fig. 3a) as was described by Tsunoda [27].

M. Frankowski et al. / Journal of Magnetism and Magnetic Materials 374 (2015) 451–454

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Fig. 2. Simulation snapshots during backhopping for sample with 0.95 nm MgO barrier thickness for selected voltages. Rows correspond to time moments selected from subsequent simulation stages. Columns present: (a) magnetization distribution in FL – the arrows show direction of local magnetization vectors. (b) Current density profile – saturation of color corresponds to local value (darker areas represents higher local current density and lower local resistance). (c) Out-of-plane torque distribution in FL – arrows show the direction of local torque vectors.

Fig. 3. Example of randomized exchange bias field distribution (a) and resulting magnetization distribution in PL (b). Arrows indicate the field direction. Note slight deviations from uniform distribution of magnetization in PL.

The dispersion of the local magnetization vectors in the PL (Fig. 3b) affects Hs field, as such disorder disturbs closing the demagnetization field lines between PL and RL. That disturbance makes the synthetic anti-ferromagnet non-ideal, therefore greater part of the demagnetization field from RL affects the FL, enhancing anit-ferromagnetic coupling by a few Oe, depending on the randomized case. The IEC energy through MgO was set to adjust simulated Hs, in which demagentization field contribution calculated dynamically during simulation is included, to experimental data. Obtained values are for 0.76 nm J MgO ¼ 7:1 μJ=m2 , 0.95 nm J MgO ¼ 2 μJ=m2 and 1.01 nm J MgO ¼ 0:1 μJ=m2 .

4. Results and discussion Using our model we have performed simulations of CIMS hysteresis loops for IEC values listed above. Calculated loops are depicted and compared with experimental data in Fig. 4. Simulation results are with a good agreement with the experiment and show that for an effective anti-ferromagnetic coupling

there is a backhopping in the regime of switching voltage while for the effective ferromagnetic coupling there is no backhopping and the state after the switching is stable. Realistic micro-spin calculations taking into account complicated dynamics determined by rapidly changing local current densities and non-uniform coupling including dynamically calculated demagnetization field confirm previous report [11] on coupling dependency of backhopping probability. Critical voltage is higher in simulation than in experiment because our model does not include thermal activation process which decreases switching voltage. The OOMMF extension code was developed as an open source software, which, together with short user manual and sample simulation configuration files, can be found on one of the authors homepage [19]. It allows for using some common curves as phenomenological models of the AP state resistance voltage dependence.

5. Summary In summary, we have investigate CIMS hysteresis loop in MgO based MTJ both experimentally and by means of micromagnetic simulations. We have observed AP state resistance changes and developed a model that incorporates these changes to the Landau– Lifshitz–Gilbert equation with STT components. Our model allows for simulations of CIMS hysteresis loops by setting a voltage sweep. We have investigated backhopping occurrence as a function of effective IEC through MgO barrier confirming previous macrospin calculations which show that for ferromagnetic coupling there can be no backhopping near switching voltage. Our model reproduces experimental data in qualitative agreement.

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Fig. 4. Experimental CIMS hysteresis loops for MgO thicknesses 1.01 nm (a), 0.95 nm (b), 0.76 nm (c) and simulation results for those thicknesses, respectively (d), (e), (f). For thickest MgO resulting in anti-ferromagnetic effective coupling backhopping occurs for switching voltage: (a) and (d). For intermediate effective coupling there is backhopping near switching voltage regime: (b) and (e). For thinnest barrier there is no hazard of backhopping: (c) and (f).

Acknowledgments This work was supported partially by statutory activity 11.11.230.016. M.F. acknowledges the Polish Ministry of Science and Higher Education Diamond Grant DI2011001541. W.S. acknowledges the Foundation for Polish Science (FNP) scholarship under START Programme. M.C. and T.S. acknowledge the NANOSPIN Grant no. PSPB-045/2010 from Switzerland through the Swiss Contribution. Numerical calculations were supported in part by PL-GRID infrastructure. References [1] A.M. Deac, A. Fukushima, H. Kubota, H. Maehara, Y. Suzuki, S. Yuasa, Y. Nagamine, K. Tsunekawa, D.D. Djayaprawira, N. Watanabe, Nat. Phys. 4 (2008) 803. [2] W. Skowroń ski, T. Stobiecki, J. Wrona, G. Reiss, S. van Dijken, Appl. Phys. Express 5 (2012) 063005. [3] W. Skowroń ski, M. Czapkiewicz, M. Frankowski, J. Wrona, T. Stobiecki, G. Reiss, K. Chalapat, G.S. Paraoanu, S. van Dijken, Phys. Rev. B 87 (2013) 094419. [4] J.C. Slonczewski, J. Magn. Magn. Mater. 159 (1996) L1. [5] L. Berger, Phys. Rev. B 54 (1996) 9353. [6] Y. Huai, F. Albert, P. Nguyen, M. Pakala, T. Valet, Appl. Phys. Lett. 84 (2004) 3118. [7] R. Takemura, T. Kawahara, K. Miura, H. Yamamoto, J. Hayakawa, N. Matsuzaki, K. Ono, M. Yamanouchi, K. Ito, H. Takahashi, S. Ikeda, H. Hasegawa, H. Matsuoka, H. Ohno, IEEE J. Solid-State Circuits 45 (2010) 869. [8] Y.W. Liu, Z.Z. Zhang, P.P. Freitas, J.L. Martins, Appl. Phys. Lett. 82 (17) (2003) 2871–2873.

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