# Consequences of Reduced Symmetry in Chiral Magnetic Thin Films

Over the last 15 years, material systems exhibiting the Dzyaloshinskii–Moriya interaction (DMI) have been extensively explored for their rich topological physics and promise as building blocks for a new kind of spintronics. To push the envelope of progress even further, I sought to understand the interplay between DMI and the consequences of reducing symmetry beyond that which is necessary for inducing DMI.

Firstly, I explored the impact of low crystal symmetry on DMI anisotropy in _{C2v} ferromagnet/heavy metal (FM/HM) films. To study the impact of DMI anisotropy on the topology of domain walls (DWs) and skyrmions in such systems I developed an augmented DW energy model that accounted for both Rashba and Dresselhaus DMI terms. Using this model in tandem with the ξ-vector approach to the Wulff construction, I computed the equilbrium shapes and magnetization profiles of bubble domains as a function of the DM vector, β, which parameterized the DM anistoropy. The results showed that the interplay between both forms of DMI and DW anisotropy results in largely elliptical skyrmions and antiskyrmions for various degrees of DMI anisotropy after accounting for faceting. These shapes were accompanied by anisotropic magnetization profiles for both skyrmions and antiskyrmions. Owing to the anisotropic *C*_{2v} unit cell, significant asymmetries in β-space also emerged. For skyrmions, the observed trends resembled the experimentally observed impact of in-plane uniaxial anisotropy in the absence of DMI anisotropy—thus highlighting the need to deconvolve the two effects which are nominally both present.

To experimentally realize such a material system, I attempted to fabricate all-FCC Pt/Co/Pt films on Si(110) substrates with an Ag growth seed using DC magnetron sputtering. While our XRD and SAED experiments confirmed that the Pt and Ag layers adopted the expected FCC(110) structure, they revealed that Co adopted a predominantly (10.0)- oriented HCP structure, which was attributed to the lower lattice mismatch of the Pt/Co interface compared to the FCC(110) case. Moreover, the measured M–H loops were characteristic of a clear in-plane easy axis whose strength decreases with thickness—possibly due to high stacking fault densities, Finally, Lorentz TEM imaging revealed sawtooth domains and crosstie DWs. These findings confirm the HCP-Co(10.0)/ FCC-Pt(110) epitaxial relationship between these films and provide valuable information for the design of future antiskyrmion hosts using *C*_{2v} films.

Motivated by experimentally observed unusual—and largely unexplained—domain wall behavior in the presence of* B*_{z} fields, I subsequently explored how applied fields induce symmetry-breaking effects on the dynamics of Dzyaloshinskii DWs in films. To address reports of significant Bloch chirality disparities in high-symmetry FM/HM films with perpendicular magnetic anisotropy, I showed that interfacial Rashba DMI (iDMI) can indeed give rise to a preferred Bloch chirality in the presence of an effective *B*_{z} field, despite the conventional wisdom that only Neel chirality is influenced by iDMI. Starting from the *q–φ* collective coordinates model and Slonczewski’s equations for the DW dynamics in the flow regime, I developed a 1-D analytical model of *B*_{z}-driven DW switching which describes a chirality-dependent DW susceptibility and DMI-dependent lability points; the latter are inflection points in the energy landscape where the magnetization of the DW can freely reorient. Ultimately, I generated a DW switching diagram—which I refer to as the *Dzyaloshinskii astroid*—that exhibits multichiral, monochiral, and precessional regimes; this astroid is analogous to the Slonczweski astroid of the Stoner–Wohlfarth model for single-domain switching. This diagram was corrobrated with 1-D and 2-D micromagnetic simulations. After demonstrating that this switching model can be extended to 2-D skyrmions, I outlined how asymmetric vertical Bloch line (VBL) nucleation and propagation could induce a preferred Bloch chirality even in the multichirality regime (i.e., at low fields), drawing from models of VBL statics and the discovery of such a mechanism for the precessional regime. Finally I revisited Slonczewski’s model of DW switching via the evolution of horizontal Bloch lines and discussed how his theory could be adapted for DMI systems.

Building on my understanding of* B*_{z}-induced chiral behavior, I demonstrated that dynamic symmetry breaking effects emerge naturally from a* transient flow *model of DW creep; I also explained the origins of perplexing experimental observations of highly asymmetric, dendritic domain growth in the creep regime. First of all, I asserted that the transient DW evolution between stationary states can be described by steady-state DW dynamics; as such, the dispersive DW stiffness can be computed based on the expected reorientation of DW moments to steady-state magnetization profiles in the presence of a net *B*_{z}* *field. My calculations revealed large modulations in the magnetization and DW stiffness profiles for an expanding domain. Beyond obtaining remarkable agreement with experimental results, this model also showed that the counter-intuitive growth angles coincided with itinerant DW segments where the inverse DW susceptibility was zero or near-zero, leading to discontinuities in the magnetization profile akin to VBLs. I explained this correlation by considering their vanishing effective mass; under a non-Markovian creep theory, the attempt creep velocity for these wall segments is damping-dominated (and therefore high)—but mass-dominated (and, thus, low) everywhere else. Furthermore, I showed that by modifying the Dzyaloshinskii astroid to account for in-plane fields and arbitrary orientations of the DW’s normal, both the DMI and Gilbert damping parameters can be extracted from the *B*_{x }dependence of the abrupt changes in the dominant domain growth angle. Finally, I discussed the universality of this* transient flow* model of DW stiffness in light of other observed features of asymmetric domain growth.

## History

## Date

2022-08-19## Degree Type

- Dissertation

## Department

- Materials Science and Engineering

## Degree Name

- Doctor of Philosophy (PhD)