As previously mentioned, characterization of the material components is tantamount to developing competitive MRAM devices. In our lab, the workflow for researching material systems suitable for MRAM devices is as follows:
1. Materials Growth
• Sputtering
• Lithography
• Ion-beam Etching 2. Device Measurement
• Characterization of Magnetic Anisotropy
• Hall Measurements
• Current Switching Measurements
• Ferromagnetic Resonance Measurements 3. Data Analysis
• Cleaning Data
• Extracting Figures of Merit
• Compiling Results
Depending on the results of each step this process can be repeated any number of times,
generating a large amount of data from a wide range of measurements for any number of
materials systems. The key focus in this process is developing a material system to extract
several key figures of merit. This work focuses on the measurement and analysis steps and
creating a system that is both flexible enough to be quickly tailored to user specifications
while also providing a framework for quality measurements and data analysis. The
mea-surement and data analysis programs presented in this work were built to both increase the
speed and accuracy of measurements and data analysis while allowing the user to focus
on the research process instead of on back-end tasks.
Chapter 2
Theory
This section aims to provide a brief introduction of the underlying physics measurements
presented in this paper and the importance of the analysis of these measurements in regards
to MRAM devices.
2.1 Hall Effects
The Hall effect, also called the Ordinary Hall effect (OHE), was first discovered in 1879
by Edwin Hall, from which is derives its name [24]. The Hall effect is the difference in
voltage across a conductor when a current is applied in the presence of an applied magnetic
field (Fig. 2.1). The voltage change across the conductor is due to the Lorentz force acting
upon the charge carriers to be deflected to the edges of the material transverse to the current
flow direction. Since its discovery, several similar phenomenon that lead to accumulation
of electric charges or spin in material systems have come to share the Hall namesake.
Figure 2.1: Example of the Hall Effect
2.1.1 The Anomalous Hall Effect
Following his discovery of the OHE, Edwin Hall reported the discovery of an effect
sim-ilar to the OHE but of a much larger magnitude in ferromagnetic conductors which was
later named the Anomalous Hall effect (AHE) [25]. After over a century since it was
first discovered, it is now understood that the origins of the AHE can be understood as
a combination intrinsic and extrinsic effects (as shown in Fig. 2.2) [26]. The intrinsic
contribution to the AHE is related to the band structure and its interaction with electric
fields, which were more formally defined through Berry phase and Berry curvature. The
external contribution to the AHE comes from spin dependent scattering of carriers off of
impurities [2]. The combination of these effects gives rise to the relation:
ρxy = ROHz+ RAmz (2.1)
This equation shows the dependence of the transverse resistance ρxy, to the contribution
RO from the OHE with the application of an external field and also to RA, a material
specific parameter, and the magnetization in the z direction given by mz (Fig. 2.3) [2].
Generally the anomalous effect is larger than the ordinary Hall effect contribution.
Detec-tion of the AHE is possible in materials with populaDetec-tion differences in carriers or through
injection or excitation of non-equilibrium spin polarized currents [27]. This signal can
fur-ther be used to measure the magnetic orientation of samples with perpendicular magnetic
anisotropy (PMA).
Figure 2.2: The intrinsic and extrinsic mechanisms giving rise to the AHE [2]
2.1.2 The Spin Hall Effect
Originally proposed by in 1971 by Dyakonov and Perel and then again by Hirsch in 1999,
the Spin Hall effect (SHE) is in many ways analogous to the AHE, but instead of a charge
response, the SHE deals with the spin of the carriers as shown in as seen in Fig. 2.3
[28, 29]. The origins of the Spin Hall effect may come from extrinsic scattering effects as
originally postulated by Dyakonov and Perel or from the intrinsic interaction of spin orbit
coupling in the absence of scattering [3]. Since the first direct observation of the SHE in a
semiconductor by Kato et al. and the subsequent detection of an electrical signal through
the inverse Spin Hall effect (ISHE) by Saitoh et al. the Spin Hall effect has garnered
significant attention [30, 31].
Figure 2.3: Comparison of the AHE, SHE and ISHE [3]
The interest in the SHE and ISHE lead to a significant number of discoveries when
cou-pled with ferromagnetic samples [3]. Utilizing spin currents generated by spin pumping
allows for measurement of magnetization dynamics. Similarly generation of spin currents
through the SHE can induce spin torques, a key element in the creation of competitive
MRAM devices. The fundamentals of magnetization dynamics and spin torques along
with their importance to MRAM devices are explained in more detail in the next section.
The effects of the SHE are especially apparent in nonmagnetic materials with large
spin-orbit interactions. Application of a charge current through such a material will result
in a transverse spin current which can be described by:
Js= ¯h
2eΘSH(σ× Je) (2.2)
where Je is the charge current density, σ is the spin polarization unit vector, ΘSH is
the spin hall angle and Jsis the spin current density [32].