This article is part of the series 11th Trends in NanoTechnology International Conference (TNT2010).

Open Access Nano Express

A compact model for magnetic tunnel junction (MTJ) switched by thermally assisted Spin transfer torque (TAS + STT)

Weisheng Zhao12*, Julien Duval12, Jacques-Olivier Klein12 and Claude Chappert12

Author Affiliations

1 IEF, Université Paris-Sud, 15 Rue Georges Clemenceau, Orsay, 91405, France

2 UMR8622, CNRS, Batiment 220, Campus d'Orsay, 91405, France

For all author emails, please log on.

Nanoscale Research Letters 2011, 6:368  doi:10.1186/1556-276X-6-368

The electronic version of this article is the complete one and can be found online at:

Received:2 November 2010
Accepted:28 April 2011
Published:28 April 2011

© 2011 Zhao et al; licensee Springer.

This is an Open Access article distributed under the terms of the Creative Commons Attribution License (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Thermally assisted spin transfer torque [TAS + STT] is a new switching approach for magnetic tunnel junction [MTJ] nanopillars that represents the best trade-off between data reliability, power efficiency and density. In this paper, we present a compact model for MTJ switched by this approach, which integrates a number of physical models such as temperature evaluation and STT dynamic switching models. Many experimental parameters are included directly to improve the simulation accuracy. It is programmed in the Verilog-A language and compatible with the standard IC CAD tools, providing an easy parameter configuration interface and allowing high-speed co-simulation of hybrid MTJ/CMOS circuits.


Spintronics is a very rapidly emerging area of R&D (Nobel Prize 2007) that has the potential to impact significantly on the future of all aspects of electronics beyond CMOS [1]. Magnetic tunnel junctions [MTJ] is one of the most promising spintronic devices for logic and memory applications, which combines magnetism and electronics and promises high write/read speed, non-volatility, infinite endurance etc. [2]. An MTJ is a nanopillar composed of two ferromagnetic [FM] layers and one oxide thin barrier. The Tunnel MagnetoResistance [TMR] phenomenon exists in MTJs [3], which describes the different resistance value RP and RAP corresponding to the parallel or anti-parallel configuration of the relative magnetization orientations of the two FM layers, respectively. For practical applications, the magnetization direction of one FM layer is pinned as reference and that of the other FM layer is free to store the binary state (see Figure 1a). Recently, TMR = RAP-RP/RP ratio was found to be more than 604% by using the MgO oxide barrier [4] and this allows MTJ to present excellent sensing performance.

thumbnailFigure 1. TAS + STT switching approach. (a) The MTJ nanopillar with two antiferromagnetic layers. (b) Bidirectional current switches the MTJ between the parallel and anti-parallel state

Today, most of the R&D efforts in MTJ are focused on its switching approaches, which are expected to be scalable, energy efficient, reliable and fast. A number of approaches have been investigated since 2002, such as thermally assisted switching [TAS] [5] and spin transfer torque [STT] [6,7]. However all of them suffer from either high power or stability issue and cannot meet the requirements for wide applications. Thermally assisted spin transfer torque [TAS + STT] is an emerging approach [8,9], which is based on the temperature dependence of exchange bias storage principle [10], as used in TAS [5]. This switching mechanism involves applying a low current through STT to raise the MTJ temperature above the blocking temperature (Tb) of the antiferromagnetic layer associated to the storage layer, resulting in a hysteresis loop centred about zero (see Figure 1). Tb depends mainly on the material composition (e.g. ~423K for IrMn and ~573K for PtMn). This method combines the advantages of both TAS and STT technologies, giving the best trade-off among data reliability, power efficiency, speed and density. Unlike other nanodevices [11], MTJ can be easily integrated with CMOS circuits [12]. Based on hybrid MTJ/CMOS [13], innovative memory and logic circuits are expected to provide high performance or new functionalities beyond CMOS. A Spice-compatible efficient compact model for MTJ is an essential requirement for the hybrid MTJ/CMOS design and simulation.

Physical model integration

This compact model is based on our previous STT MTJ model, which is composed of two sub-modules representing respectively the sensing and switching operations [14]. For sensing, the MTJ resistance and TMR ratio are calculated to obtain respectively RP and RAP [15]. For switching, the STT critical current, IC, calculation model was implemented to obtain the hysteresis loop margin of storage layer [5]. The present model offers an improvement over the previous work [14-17] as it integrates the temperature evaluation and STT dynamic switching models to describe the TAS + STT switching approach. In order to optimise the simulation speed, one of the most important performances for logic and memory designs, some physical phenomena like the oscillating effects during switching are omitted.

Temperature evaluation model

The temperature evaluation of MTJ depends on the form and duration of switching current according to Equations 1 and 2 [17,18]. As square current pulses are often used for logic and memory circuit design and simulation, Equation 1 can be then simplified to Equations 3 and 4 to describe respectively the heating and cooling operations driven by a current pulse. This model allows simulating the thermally assisted mechanism of TAS+STT approach. An equivalent electrical circuit corresponding to Equation 1 has been included to monitor the temperature evaluation of MTJ (see Figure 2a), which is based on a simple resistor/capacitor circuit. By adding a multiplier (M0) and an adder (A0), the temperature T can be observed in real time through the voltage node Vtemp (i.e. 1V = 1K). The values of R0 and C0 are set as constant to obtain τth calculated by Equation 2,



where V is the voltage across MTJ nanopillar, λ is thermal conductivity of the thermal barrier, CV is heat capacity per unit volume, j is current density, TR is room temperature, thick_b is the thickness of thermal barrier, thick_s is the total thickness of MTJ nanopillar and τth is the characteristic heating/cooling time. This leads to



where Dheat is the heating current pulse duration, Dcool is the cooling duration, and Theat and Tcool present respectively temperature of MTJ during heating/cooling operations.

thumbnailFigure 2. Circuit implementation for modelling and simulation. (a) Equivalent electrical RC circuit of temperature evaluation model. (b) MTJ switching circuit; either "Vg1" or "Vg2" is set to '1' to generate the current Iswitch. RC, resistor/capacitor

Spin Transfer Torque (STT) dynamic switching model

STT dynamic switching behaviours are described by Equations 5 and 6, which are crucial to simulate the power and speed performances of hybrid MTJ/CMOS circuits. Thermal fluctuations induce an initial angle Θ0 between the magnetization of the storage layer and its easy axis [19], which is approximated by Equation 6. High temperature increases Θ0 and then reduces the STT switching duration, Dswitch. STT state reversal depends on switching current value, Iswitch, which should be higher than the critical current, IC. Dswitch can be linearly reduced down to according to nanosecond range with high Iswitch [20]. This property is useful for the design and simulation of hybrid MTJ/CMOS circuits dedicated to logic applications, which require very high speed (e.g. approximately gigahertz).



where Hani is in-plane uniaxial magnetic anisotropy field, μ0Ms is saturation field in the storage layer, α is Gilbert damping coefficient, γ0 is the gyromagnetic constant, Vol is the volume of storage layer and kB is the Boltzmann constant.

Compact model simulation and validation

Co-simulation of Hybrid MTJ/CMOS circuit

This compact model has been developed in Verilog-A language and implemented on Cadence Virtuoso CAD platform [21]. Its default parameters correspond to a MTJ nanopillar BiFe(10)/IrMn(6)/CoFeB(1)/MgO(0.85)/CoFeB(3)/PtMn(6). Thanks to the graphical parameter configuration of Verilog-A, MTJ can be set easily with different material and process parameters. By using CMOS 65 nm design-kit, a simple hybrid circuit (see Figure 2b) [22] has been successfully simulated (see Figure 3), which validates the functionalities and behaviours of this model. The voltage pulse "Vg1" is activated at 40 ns and Iswitch begins to heat the MTJ from ambient temperature. As its temperature reaches up to Tb2 after ~11.22 ns, the model compares the Iswitch (approx 462.9 uA) with the STT critical current IC (~150 uA) and switches the state of MTJ from parallel [P] to anti-parallel [AP] state in about 6 ns according to the STT dynamic model. As "Vg1" is deactivated, MTJ begins to cool down to ambient temperature. The state can be reversed from AP to P by activating the control signal "Vg2", which generates Iswitch (approx-375.6uA). The Iswitch values are asymmetric as a constant voltage supply is used in the simulation (e.g. 1V) and the resistance of MTJ changes between two states (RP and RAP). It is important to note that the voltage pulse width should be longer than Dheat+Dswitch to ensure the reliable switching operation [5].

thumbnailFigure 3. Transient simulation of compact model. (a) and (b) Control signals activate the circuit to generate bidirectional currents. (c) MTJ is switched between the P and AP. (d) Temperature evaluation. (e) The state of MTJ. P, parallel; AP, anti-parallel.

Power and die area estimation

The silicon area of this hybrid circuit is ~9.8 um2 as the width of NMOS transistors is set to 1 μm to provide Iswitch much higher than IC and reduce the duration down to some nanoseconds. The whole switching operation of TAS + STT between the P and AP states dissipates ~2.7pJ of energy.


In this paper, we present the first compact model for MTJ nanopillar switching using the TAS+STT approach. Transient simulations of a hybrid MTJ/CMOS circuit validate its functionalities and demonstrate that it can be useful to calculate the critical circuit performances like speed, power and die area. The easy parameter interface of the Verilog-A language allows us to analyse the characteristics of MTJ with different materials, area and thin film thickness etc. By using this model, a number of hybrid MTJ/CMOS complex circuits are under investigation in our laboratory.

Competing interests

The authors declare that they have no competing interests.

Authors' contributions

ZWS, KJO and CC designed the modelling. DJ programmed the model. ZWS and DJ performed the simulation and wrote the manuscript.


The authors wish to acknowledge support from the French national projects CILOMAG, ANR-SPIN and NANO2012 project with STMicroelectronics.


  1. Chappert C, Fert A, Nguyen Van Dau F: "The emergence of spin electronics in data storage".

    Nat Mater 2007, 6:813-823. PubMed Abstract | Publisher Full Text OpenURL

  2. Zhao WS, Belhaire E, Chappert C, Mazoyer P: "Spin transfer torque (STT)-MRAM-based runtime reconfiguration FPGA circuit".

    ACM Trans Embedded Computing 2009., 9

    article 14


  3. Julliere M: "Tunnelling between ferromagnetic films".

    Phys Lett 1975, 54A:225-226. OpenURL

  4. Ikeda S, Hayakawa J, Ashizawa Y, Lee YM, Miura K, Hasegawa H, Tsunoda M, Matsukura F, Ohno H: "Tunnel magnetoresistance of 604% at 300 K by suppression of Ta diffusion in CoFeB/MgO/CoFeB pseudo-spin-valves annealed at high temperature".

    Appl Phys Lett 2008, 93:082508. Publisher Full Text OpenURL

  5. Prejbeanu IL, Kerekes M, Sousa RC, Sibuet H, Redon O, Dieny B, Nozière JP: "Thermally assisted MRAM".

    J Phys Condensed Matter 2007, 19:165218. Publisher Full Text OpenURL

  6. Slonczewski JC: "Current-drivern excitation of magnetic multilayers".

    J Magnetism Magnetic Mater 1996, 159:L1-L7. Publisher Full Text OpenURL

  7. Hayakawa J, Ikeda S, Lee YM, Sasaki R, Meguro T, Matsukara F, Takahashi H, Ohno H:

    Jpn J Appl Phys. 2005, 44:L1267-L1270. Publisher Full Text OpenURL

  8. Xi HW, Stricklin J, Li H, Chen YR, Wang XB, Zheng YK, Gao Z, Tang MX:

    IEEE Trans Magn. 2010, 46:860-866. OpenURL

  9. Dieny B, Sousa RC, Herault J, Papusoi C, Prenat G, Ebels U, Houssameddine D, Rodmacq B, Auffret S, Buda-Prejbeanu LD, Cyrille MC, Delaet B, Redon O, Ducruet C, Nozières JP: "Spin-transfer effect and its use in spintronic components".

    Int J Nanotechnol 2010, 7:591-614. Publisher Full Text OpenURL

  10. Chen YT: "The Effect of Interface Texture on Exchange Biasing in Ni(80)Fe(20)/Ir(20)Mn(80) System".

    Nanoscale Res Lett 2009, 4:90-93. PubMed Abstract | Publisher Full Text | PubMed Central Full Text OpenURL

  11. Navi K, Rashtian M, Khatir A, Keshavarzian P, Hashemipour O: "High Speed Capacitor-Inverter Based Carbon Nanotube Full Adder".

    Nanoscale Res Lett 2010, 5:859-862. PubMed Abstract | Publisher Full Text | PubMed Central Full Text OpenURL

  12. Matsunaga S, Hayakawa J, Ikeda S, Miura K, Hasegawa H, Endoh T, Ohno H, Hanyu T: "Fabrication of a Nonvolatile Full Adder Based on Logic-in-Memory Architecture Using Magnetic Tunnel Junctions".

    Appl Phys Exp 2008, 1:091301. OpenURL

  13. Zhao WS, Chappert C, Javerliac V, Nozière J-P: "High Speed, High Stability and Low Power Sensing Amplifier for MTJ/CMOS Hybrid Logic Circuits".

    IEEE Trans Magn 2009, 45:3784-3787. OpenURL

  14. Zhao WS, Belhaire E, Mistral Q, Chappert C, Javerliac V, Dieny B, Nicolle E: "Macro-model of Spin-Transfer Torque based Magnetic Tunnel Junction device for hybrid Magneti-CMOS design". In Procedings of the 2006 IEEE International Behavioral Modeling and simulation Workshop. San Jose CA; 2006:40-43. OpenURL

  15. Elbaraji M, Javerliac V, Guo W, Prenat G, Dieny B: "Dynamic compact model of thermally assisted switching magnetic tunnel junctions".

    J Appl Phys 2010, 106:123906. OpenURL

  16. Das B, Black WC Jr, Pohm AV: "Universal HSPICE macromodel for giant magnetoresistance memory bits".

    IEEE Trans Magn 2000, 36:2062-2072. Publisher Full Text OpenURL

  17. Roldan AM, Roldan JB, Reig C, Cubells-Beltran MD, Ramirez D, Cardoso S, Freitas PP: "A DC behavioral electical model for quasi-linear spin-valve devices including thermal effects for circuit simulation".

    Microelectron J 2011, 42:365-370. Publisher Full Text OpenURL

  18. Sousa RC, Prejbeanu IL, Stanescu D, Rodmacq B, Redon O, Dieny B, Wang JG, Freitas PP: "Tunneling hot spots and heating in magnetic tunnel junctions".

    J Appl Phys 2004, 95:6783-6785. Publisher Full Text OpenURL

  19. Koch RH, Katine JA, Sun JZ: "Time-Resolved Reversal of Spin-Transfer Switching in a Nanomagnet".

    Phys Rev Lett 2004, 92:088302. PubMed Abstract | Publisher Full Text OpenURL

  20. Devolder T, Hayakawa J, Ito K, Takahashi H, Ikeda S, Crozat P, Zerounian N, Kim JV, Chappert C, Ohno H: "Single-Shot Time-Resolved Measurements of Nanosecond-Scale Spin-Transfer Induced Switching: Stochastic Versus Deterministic Aspects".

    Phys Rev Lett 2008, 100:057206. PubMed Abstract | Publisher Full Text OpenURL

  21. Virtuoso Spectre Circuit Simulator User Guide


  22. Zhao WS, Belhaire E, Chappert C, Mazoyer P: "Power and Area Optimization for Run-Time Reconfiguration System On Programmable Chip Based on Magnetic Random Access memory".

    IEEE Trans Magn 2009, 45:776-780. OpenURL