Characterizing an Effective Magnetic Field during Asymmetric Creep Motion of Dzyaloshinskii Domain Walls
Creators: name: Jiang, Lai
Publisher: name: Carnegie Mellon University
Year: 2024
Subjects: Materials Engineering not elsewhere classified

description:  Recent findings have challenged traditional understanding of magnetic domain wall (DW)  creep motion in thin films under the influence of external magnetic field. While conventional belief held that domain growth directionality depends on the static magnetization  configuration of a domain wall, new observations of a highly unidirectional growth suggest  that is a result of dynamic reorientation of magnetization configuration. To expand our  understanding, I investigated the asymmetric creep motion of Dzyaloshinskii domain walls,  driven by external magnetic fields, and studied the relationship between domain growth  symmetry and intrinsic properties of the system.  
In this thesis, I investigated asymmetric magnetic domain wall motions in Pt/Co/Ni  thin films with a perpendicular magnetic anisotropy (PMA), and focused on the effects  of external magnetic fields. By using Magneto-Optical Kerr Effect (MOKE) Microscopy, I  observed that within the creep regime the Dzyaloshinskii domain wall exhibits directional  motion, which is influenced by the strength of out-of-plane (B<sub><em>z</em></sub>) and in-plane (B<sub><em>x</em></sub>) magnetic fields. As also seen previously, when B<sub>x</sub> was increased to a critical value, domain growth  direction have shown nearly 180◦ reversal. This critical value was referred to as the onset  f  ield, B<sub><em>onset</em></sub>, which can be used as a defining parameter of the measurements. It has been  suggested that, DW experiences a non-zero effective field during directional asymmetric  DWmotion, and this effective field should be notably smaller than applied field due to the  pinning effect and deviates DW magnetization away from its static equilibrium. Therefore, I  hypothesized that, the directional growth is directly influenced by B<sub>z</sub>, and the effective field  can be determined from studying the impact of applied perpendicular field B<sub>z</sub> on B<sub>onset</sub>.  
To test this hypothesis, I systematically varied the strength of the externally applied B<sub>z</sub>  to Pt/Co/Ni thin films, and compared the DW motion direction with a steady-state transient  model. This model determines steady-state DW magnetization based on dispersive stiffness model of Pellegren, Landau-Lifshitz-Gilbert (LLG) dynamics and Slonczewski’s equations for  the DW dynamics, such that the anisotropic DW motion velocities can be deduced from its  DWstiffness. I applied this transient model to study the directional asymmetric DW behavior,  and predicted the reversal of DW motion directionality (i.e. B<sub>onset</sub>). However, as I expected,  this transient model overwhelmingly predicts that the DW will be in a state of Walker  Breakdown if the value of the externally applied B<sub>z</sub> was used as the effective perpendicular  f  ield in the LLG equation. To rationalize this, I introduced the concept of B<sub>propagation</sub>, which  is the threshold arises from the pinning effects (B<sub>eff</sub> = 0 if B<sub>z </sub>&lt; B<sub>propagation</sub>). Based on the  negative correlation I found between onset field Bonset and Bz, which serves as an indirect  indicator of the static-to-dynamic deviation, I was able to extract the Bpropagation from the  discrepancy between the experimental and computational results and therefore determine  the effective field. Accordingly, the Gilbert damping coefficient α of the system could also  be deduced, which has reasonable agreement with experimental measurements. This study  further explores the directional domain growth within the creep regime, and expands the  understanding of impact of external fields on creep behaviors.  
To further understand the role of damping coefficient and DMI in asymmetric domain creep behavior, [Pt/[Co/Ni]×M]×N multi-layers were fabricated with same number of  Co/Ni interfaces and thickness, which should give comparable magnetostatic properties. As  the number of Pt/Co interfaces was increased, DMI and α coefficients were also increased.  The experimental observations of growth direction and onset fields of all samples have  shown good agreement with the transient steady-state model, including the increasing trend  in damping parameters with increased Pt/Co interface. This most notable result of the study  provides a strong support to my hypothesis that larger damping coefficient leads to smaller  dependence of onset fields on perpendicular field. It has been suggested that this transient  model could only be applied to thin films with highly asymmetric directional domain growth  where both DMI and α are low. However, my study has shown that this transient model  is valid to any thin film systems including moderately stronger DMI and larger damping  coefficients, and it predicts weaker directional growth in such systems.