THESIS
2018

xv, 119 pages : illustrations (chiefly color) ; 30 cm

**Abstract**
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...[

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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 10

^{5} A/cm

^{2} and 10

^{6} A/cm

^{2} in the new strategy far below 10

^{7}
A/cm

^{2} and 10

^{8} A/cm

^{2} in the conventional strategy. Furthermore, no external magnetic field is
needed for a deterministic switching in the new strategy.

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