Current-induced dynamics in hybrid geometry MgO-based spin-torque nano-oscillators

Spin-torque nano-oscillators (STNOs) are prospective successors of transistor-based emitters and receivers of radio-frequency signals in commonly used remote communication systems. In comparison to the conventional electronic oscillators, STNOs offer the advantage of being tunable over a wide range of frequencies simply by adjusting the applied current, the smaller lateral size (up to 50 times) and the lower power consumption as the lateral size of the device is reduced. It has already been demonstrated that the output signal characteristics of STNOs are compatible with the requirements for applications: they can provide output powers in the µW range, frequencies of the order of GHz, quality factors Q (equal to df/f, where f is the frequency, and df is the linewidth) up to several thousands (e.g., 3 200), and can be integrated into Phase-Locked Loop (PLL) circuits. The most promising type of spin-torque oscillators is the hybrid geometry STNOs utilizing an in-plane magnetized fixed layer, an out-of-plane magnetized free layer and the MgO tunnel barrier as a spacer. This geometry maximizes the output power, since the full parallel-to-antiparallel resistance variation can be exploited in the limit of large magnetization precession angle (i.e., when the magnetization oscillates fully within the plane of the STNO stack). Moreover, the considered hybrid geometry allows for the reduction of the critical currents, enables functionality regardless of the applied magnetic or current history and requires a simplified fabrication process in comparison to the opposite hybrid geometry, consisting of an in-plane magnetized free layer and an out-of-plane reference layer, which requires an additional read-out layer. Simultaneously, the choice of the spacer material in considered STNOs is motivated by the increase of both the output power (via large magnetoresistance ratios) and the power conversion rate ('output power to input power' ratio), compared to their fully metallic counterparts. Despite the many advantages of MgO-based hybrid geometry STNOs, unexplained issues related to the physics behind their principle of operation remained. In this thesis, the main focus is put on the two key aspects related to the out-of-plane steady-state precession in hybrid STNOs: the precession mechanism (combined with the analysis of the influence of the bias dependence of the tunnel magnetoresistance) and the zero-field oscillations stabilized by an in-plane shape anisotropy. State-of-the-art theoretical studies demonstrated that stable precession in hybrid geometry STNOs can only be sustained if the in-plane component of the spin-transfer torque (STT) exhibits an asymmetric dependence on the angle between the free and the polarizing layer (which is true for fully metallic devices, but not for the MgO-based magnetic tunnel junctions (MTJs)). Nevertheless, recent experimental reports showed that spin-transfer driven dynamics can also be sustained in MgO-based STNOs with this particular configuration. In this thesis, a phenomenological and straightforward mechanism responsible for sustaining the dynamics in considered system is suggested. The mechanism is based on the fact that, in MgO-based MTJs, the strong cosine-type angular dependence of the tunnel magnetoresistance, at constant applied current, translates into an angle-dependent voltage component, which results in an angle-dependent spin-transfer torque giving a rise to the angular asymmetry of the in-plane STT and, thus, enabling steady-state precession to be sustained. Subsequently, the bias dependence of the tunnel magnetoresistance (TMR), which has been so far neglected in similar calculations, is taken into account. According to the results of analytical and numerical studies, the TMR bias dependence brings about a gradual quenching of the dynamics at large applied currents. The theoretical model yields trends confirming our experimental results. The most important conclusion regarding to this part of the thesis is that, while the angular dependence of the tunnel magnetoresistance introduces an angular asymmetry for the in-plane spin transfer torque parameter (which helps maintain steady-state precession), the bias dependence of the resistance works to reduce this asymmetry. Thus, these two mechanisms allow us to tune the asymmetry of the in-plane STT as function of current and to control the dynamical response of the actual device. Except for the precession mechanism, the thesis is also focused on the issue of zero-field oscillations, which would be especially desirable from the point of view of potential applications. According to the state-of-the-art theoretical studies, for hybrid geometry devices with circular cross-section (i.e., exhibiting no other anisotropy terms), current-driven dynamics cannot be excited at zero applied field. Indeed, zero-field oscillations have only been experimentally observed for systems having the free layer magnetization slightly tilted from the normal to the plane, which has usually been achieved by introducing an in-plane shape anisotropy. In the thesis, the influence of the in-plane shape anisotropy of the MTJ on zero-field dynamics in the hybrid geometry MgO-based STNOs is analytically and numerically investigated. In agreement with the previous reports, no zero-field dynamics for circular nano-pillars is observed; however, according to the numerical data, an additional in-plane anisotropy smaller than the effective out-of-plane anisotropy of the free layer enables zero-field steady-state precession. Accordingly, the lack of an in-plane anisotropy component (e.g., for circular cross-section nano-pillars), or the presence of an in-plane shape anisotropy equal or greater than the out-of-plane effective anisotropy, inhibits the stabilization of dynamics in the free layer at zero field. The results of analytical and numerical studies and the general trends identified in the corresponding experimental data are found to be in excellent qualitative agreement.:1. Introduction 1.1. Short history of magnetotransport applications 1.2. Spin-transfer torque induced effects and devices 1.3. Goals of the thesis 2. Fundamentals 2.1. Electronic transport in single transition metal layers 2.2. Tunnel magnetoresistance (TMR) 2.2.1. Electronic transport in magnetic tunnel junctions 2.2.2. Tunnel magnetoresistance versus structural properties of the multilayer 2.2.3. Bias voltage and temperature dependence of tunnel magnetoresistance 2.2.4. Angular dependence of tunnel magnetoresistance 2.3. Spin-transfer torque in GMR/TMR structures 2.3.1. Spin-transfer torque 2.3.2. Landau-Lifshitz-Gilbert (LLG) equation 2.3.3. LLG equation and spin-transfer torques 2.3.4. Bias voltage dependence of spin-transfer torques in MTJs 2.3.5. Angular dependence of spin-transfer torque 2.4. Spin-torque-based phenomena 2.4.1. Current-induced switching 2.4.2. Current-induced dynamics 3. Experimental 3.1. General characteristics of MgO-based magnetic tunnel junctions 3.2. STNO samples 3.2.1. Samples by AIST (Tsukuba, Japan) 3.2.2. Samples by HZDR / SINGULUS (Dresden / Kahl am Main, Germany) 3.3. Magnetotransport measurements 3.3.1. Experimental setup and data analysis 3.3.2. Experimental results 3.4. Aspects to be explained 4 Numerical and analytical calculations 4.1 Out-of-plane steady-state precession in hybrid geometry STNO 4.1.1 Angular dependence of tunnel magnetoresistance as a mechanism of stable precession 4.1.2. Influence of the bias dependence of tunnel magnetoresistance 4.1.3. Comparison with the experimental data 4.1.4. Comparison with the GMR-type counterpart 4.1.5. Summary 4.2. Zero-field dynamics in hybrid geometry STNO stabilized by in-plane shape anisotropy 4.2.1. Effect of the in-plane shape anisotropy 4.2.2. Zero-field dynamics 4.2.3. Summary 5. Conclusions 6. Outlook Appendix Bibliography