Ab initio modelling of the spin Hall effect in doped and alloyed systems

: With applications in magnetoresistive RAM.

Abstract

Spin Hall effect (SHE) based magnetoresistive technology (MRAM) [1–4] has promise in
nonvolatile, low power memory applications. To capitalise on this promise, it is of crucial
importance that the most suitable materials are chosen for the purposes of design. To
this end, it has been shown that alloying and doping materials can lead to the enhancement
of important parameters relating to the SHE, such as the spin Hall angle (SHA) and spin Hall
conductivity (SHC) in systems such as β-W [5–16] and binary Pt based alloys [17–37]. In this
work, ab initio techniques, based around the spin polarised Korringa-Kohn-Rostoker (SPR-KKR)
[38–40] implementation of density functional theory (DFT) [41, 42] are used to model the SHE
of these promising doped and alloyed materials, with a view to understanding the underlying
theory. This will help to inform future material design considerations for SHE-MRAM.
The material, β-W was chosen as the first point of investigation, due to its large experimentally
observed SHA of around 0.3 [5–14]. As the presence of O and N impurities are required to stabilise
the formation of the A15 structure of this material, it was unknown whether this large SHA
was due to scattering from these impurities or intrinsic effects. Analysis of the SHC and spin
diffusion length of β-W and bcc W, as well as analysis of the SHC of O and N doped β-W and
bcc W show that the SHC within β-W is driven by intrinsic effects and that scattering plays a
small role in the overall SHC. To explain the observations, this work provides a suggestion that
uniformly dispersed O and N atoms are not how the β-W doped crystals are arranged and they
preferentially migrate to the grain boundaries of the film. This grain boundary migration may
help to stabilise the β-W grains, which themselves have a large SHA. This work opens up the
possibility of grain boundary engineering of high SOC low symmetry crystals like β-W to be a
potential method for enhancing the SHE.
Pt-based alloys are also analysed using the SPR-KKR exploiting the coherent potential approximation (CPA), as they have vast potential in SHE-MRAM [17–37]. A model of the longitudinal
charge conductivity (CC) and SHC is presented as a function of Pt concentration for these alloys.
This model explains why there is a direct linear relationship between the intrinsic SHC of the
chosen alloy partner element to Pt and the position of the peak in SHA. This work shows that
the magnitude of the maximum longitudinal resistivity for the alloy is a very good indicator as to
the maximum SHA for the alloy, with a linear relationship between those two parameters. The
work extends the theory of the SHE within binary alloys and provide means to estimating the
strength and magnitude of the SHA within such materials, without having to resort to lengthy
calculations or experiments.
Finally, the CrPt binary alloy system is investigated for both the case where magnetism is
switched on and where it is not, as this is a particularly promising candidate for SHE-MRAM
[36, 37] and is unique in the materials investigated thus far due to its magnetism. In this work
it is shown that the presence of weak magnetism for such an alloy leads to an enhancement of
the SHC, and the CC, but leads to an overall reduction in the SHA. It is also shown that for a
i
chemically disordered fcc CrPt lattice, the Pt concentration at which the magnetism is observed
depends strongly on the lattice parameter used in the calculation. A shift in lattice parameter of
around 2% is enough to totally change the magnetic character of the material and therefore its
spin dynamics, leading to an increase in the calculated SHA from 0.073 to 0.077 and a shift from
the position of the maximum from 70% Pt concentration to 80% Pt concentration. It is shown
that a small amount of lattice strain is desirable for enhancing the SHA of CrPt. Therefore, the
choice of substrate may be a vitally important design consideration for SHE-MRAM devices that
involve CrPt. These results widen the potential of lattice strain engineering as a fruitful avenue
of exploration for optimisation of the SHE-MRAM in CrPt and similar systems.

Date of Award	18 Jun 2024
Original language	English
Awarding Institution	University of Bristol
Supervisor	Martin Gradhand (Supervisor) & Stephen B Dugdale (Supervisor)