This thesis investigates the dynamic magnetic susceptibility and spin-orbit-torque magnetic random access memory (SOT-MRAM) in two aspects: (1) the general expressions of the dynamic magnetic susceptibility matrix and anatomy of electric signals and dc-voltage lineshape in both ferromagnetic resonance (FMR) and spin torque ferromagnetic resonance (st-FMR), and (2) a new strategy of SOT-MRAM that breaks the current density threshold.

The electrical detection of FMR is a popular tool to probe material parameters like the spin-Hall angle of heavy metals. However, the experimentally extracted material parameters show a large discrepancy for the same materials with different experiments of various setups and various sensible analysis, which indicates some missing ingredients in our cu...[ Read more ]

This thesis investigates the dynamic magnetic susceptibility and spin-orbit-torque magnetic random access memory (SOT-MRAM) in two aspects: (1) the general expressions of the dynamic magnetic susceptibility matrix and anatomy of electric signals and dc-voltage lineshape in both ferromagnetic resonance (FMR) and spin torque ferromagnetic resonance (st-FMR), and (2) a new strategy of SOT-MRAM that breaks the current density threshold.

The electrical detection of FMR is a popular tool to probe material parameters like the spin-Hall angle of heavy metals. However, the experimentally extracted material parameters show a large discrepancy for the same materials with different experiments of various setups and various sensible analysis, which indicates some missing ingredients in our current understanding of FMR. Since the dynamic magnetic susceptibility is a central quantity of FMR, we firstly obtain the general form of the dynamic magnetic susceptibility matrix of an arbitrary ferromagnet based on the causality principle and the fact that the microwave absorption near FMR is a Lorentzian function of microwave frequency for a fixed static magnetic field. With the knowledge of the dynamic magnetic susceptibility matrix, the general form of the corresponding dc-voltage lineshape from electrical detection of FMR is also obtained. Our main findings are as follows. The dynamic magnetic susceptibility is not a Polder tensor for a material with an arbitrary magnetic anisotropy. The two off-diagonal matrix elements of the tensor near FMR are not, in general, opposite to each other. The frequency-dependence of dynamic magnetic susceptibility near FMR is fully characterized by six real numbers, while its field-dependence is fully characterized by seven real numbers. A recipe of how to determine these numbers by standard microwave absorption measurements for a sample with an arbitrary magnetic anisotropy is also proposed. With these results, one can unambiguously separate the contributions of the anisotropic magnetoresistance (AMR) and the anomalous Hall effect (AHE) to the dc voltage signals from the inverse spin-Hall effect (ISHE), and determine the spin-Hall angle.

In recent years, st-FMR is becoming another popular method for measuring the spin-Hall angle where an rf current is directly applied in the sample, however, the spin-Hall angle was often over-estimated from st-FMR experiments. Thus, a careful analysis of st-FMR in a heavy-metal/ ferromagnet bilayer system is also carried out. The magnetization in ferromagnet is driven by both radio-frequency (rf) Oersted field generated by the rf electric current in the system and so called rf spin-orbit torque from the spin current flowing perpendicularly from the heavy-metal to the ferromagnet due to the spin-Hall effect. The magnetization motion can resonate with two rf driving forces. By using the universal form of the dynamic magnetic susceptibility matrix near FMR, the electric signals originated from the AMR, AHE and ISHE are analyzed and dc-voltage lineshape near the st-FMR are obtained. A recipe for extracting the spin-Hall angle of the heavy-metal from the experiments is proposed.

Besides the probing of material parameters by FMR and st-FMR, the manipulation of magnetization is also an essential issue in the designs of new devices. The SOT-MRAM is a promising technology for the next generation of data storage devices because writing charge current does not pass through the memory cells so that the cells do not suffer from the Joule heating and associated device damaging. However, high reversal current density threshold is a challenging issue in this technology. This outstanding problem is now solved by a new strategy with a fixed magnitude of the driven current density and time varying current direction. The theoretical limit of minimal reversal current density of this new strategy is only a fraction (the Gilbert damping coefficient) of the threshold current density of the conventional strategy. The Euler-Lagrange equation for the fastest magnetization reversal path and the optimal current pulse is derived for an arbitrary magnetic cell and arbitrary spin-orbit torque. For CoFeB/Ta SOT-MRAMs, the theoretical limit of minimal reversal current density and current density for a GHz switching rate are respectively of the order of 10⁵ A/cm² and 10⁶ A/cm² in the new strategy far below 10⁷ A/cm² and 10⁸ A/cm² in the conventional strategy. Furthermore, no external magnetic field is needed for a deterministic switching in the new strategy.