Switching Phase Diagrams and Backhopping in Magnetic Tunnel Junctions (MTJs)

A spin-polarized current flowing through a ferromagnet can exert a torque on the local magnetization [1,2]. This phenomenon is currently intensively investigated due to its potential application in magnetic random access memory (MRAM) or in telecommunication devices. Presently, the structure of choice for spin-torque devices includes a magnetic tunnel junction (MTJ) with an MgO barrier, due to their large magnetoresistance signals. However, a key step towards the practical implementation as MRAM elements is the reduction of the critical voltages, in order to keep the size of the selection transistor down and compete with existing technologies [3]. A second issue (but equally important) is the thermal stability of the devices, as data retention for over ten years is required for industrial applications.

The thermal stability of the MgO-MTJs is currently evaluated based on the formalism developed for metallic nanopillars [4]. However, it has been pointed out that based on this formalism, the thermal stability coefficients evaluated for switching starting from different states (parallel or antiparallel) have different values in MgO-MTJs [5]. In addition, magnetic tunnel junctions also exhibit a somewhat obscure behaviour referred to as ‘back-hopping’, whereby reliable switching to the desired state is achieved for applied voltages of the order of the critical voltage, but a larger applied bias induces a telegraph-noise behaviour [6, 7]. Back-hopping is characteristic for MTJs, as it has not been observed in metallic multilayers, and poses serious concerns for designing industrially-competitive MRAM devices.

We evaluate the switching voltages and their temperature dependence by analytically and numerically solving the modified Landau-Lifshitz-Gilbert equation which includes both Slonczewski-like (in-plane) and field-like (out-of-plane) torque terms (equation 1). Here, γ is the gyromagnetic ratio, Heff the effective field (including the anisotropy, demagnetization field and applied field), α the Gilbert damping coefficient, Ms the saturation magnetization and V¬mag the volume of the free layer. and are the coefficients for in-plane and out-of-plane spin-transfer torques, respectively, which can be determined from spin-torque bias dependence measurements [8, 9, 10], and is the vector of the spin polarization (parallel to the pinned layer magnetization).

In metallic spin-valves, the out-of-plane torque has been demonstrated to be about two orders of magnitude lower than the in-plane spin-torque, and can generally be neglected [11], yielding a linear dependence of the switching current on the applied field. In MgO-MTJs, the field-like torque can be of the order of 25% of the in-plane torque [7], and needs to be taken into account. Its quadratic dependence on the applied voltage [9,12] translates into a more complex correlation between the critical bias and the external field, altering the shape of the phase diagram, as demonstrated experimentally [5]. It also offers a potential explanation for the occurrence of back-hopping at a large bias. In addition, it alters the temperature dependence of the critical voltages, which needs to be taken into account when evaluating the thermal stability of such devices.

References:

[1] J. C. Slonczewski, Journal of Magnetism and Magnetic Material 159, L1 (1996)
[2] L. Berger, Physical Review B 54, 9359 (1996)
[3] Z. Diao et al., Journal of Physics: Condensed Matter 19, 165209 (2007)
[4] S. Ikeda et al., Nature Materials 9, 721 (2010)
[5] S.-C. Oh et al., Nature Physics 5, 898 (2009)
[6] J. Z. Sun, J. Appl. Phys. 105, 07D109 (2009)
[7] T. Min et al., J. Appl. Phys. 105, 07D126 (2009)
[8] H. Kubota et al., Nature Phys. 4, 37 (2008)
[9] J. C. Sankey et al., Nature Phys. 4, 67 (2008)
[10] A. Deac et al., Nature Physics 4, 803 (2008)
[11] M. A. Zimmler et al., Phys. Rev. B 70, 184438 (2004)
[12] I. Theodonis et al., Phys. Rev. Lett, 97, 237205 (2006)