Researchers have demonstrated a superconducting diode effect within ferromagnetic superconductors by manipulating magnetic domain walls. The work, led by Dong Hui Han of the Korea Advanced Institute of Science and Technology, reveals that current-driven movement of these domain walls under an external field leads to two distinct, direction-dependent critical currents. This “nonreciprocal Walker breakdown” causes phase slips and dissipation, effectively creating the superconducting diode effect within a single material. The team’s findings suggest a path toward nanoscale superconducting devices that bypass the need for complex engineered structures.
Domain-Wall Dynamics Drive Superconducting Diode Effect
Current-driven magnetic domain wall motion within a specific external field generates two distinct critical currents, a surprising asymmetry revealed in recent work on ferromagnetic superconductors. These direction-dependent thresholds define the onset of a unique breakdown in the domain wall’s behavior, termed a nonreciprocal Walker breakdown, and are important for understanding the observed superconducting diode effect. The constant rotation of this domain wall, once initiated, directly leads to phase slips within the ferromagnetic superconductor, effectively creating dissipation channels.
This connection between domain wall precession and phase slips is the key mechanism by which the nonreciprocal Walker breakdown manifests as a superconducting diode effect, where current flows more easily in one direction than the other. Researchers analytically examined the dependence of this breakdown on both the applied magnetic field and the Gilbert damping, verifying their theoretical predictions through detailed micromagnetic simulations.
These simulations allowed for a precise mapping of the domain wall dynamics and the resulting dissipation, confirming the theoretical framework. Further analysis considered the impact of pinning on these dynamics, revealing that introducing pinning generates an effective inertia, potentially enhancing the diode effect. In the absence of pinning, the domain wall’s motion is governed by an overdamped regime, where inertia is negligible and the effective potential dictates its behavior.
However, pinning introduces an inertial component, creating a dependence on initial conditions and providing an additional pathway to achieve a finite diode efficiency, denoted as η. The team suggests that manipulating both the magnetic field conditions and the geometry of the pinning notch offers a route to control η, potentially opening avenues for future applications. The study extends the analysis to ferromagnetic superconductors by using a hydrodynamic theory previously developed for these materials.
This framework establishes that the supercurrent-driven magnetization dynamics in ferromagnetic superconductors closely mirrors that of conventional ferromagnets, allowing the superconducting diode effect to arise from the same nonreciprocal Walker breakdown observed in simpler systems. The researchers note that the DMI, or Dzyaloshinskii-Moriya interaction, which breaks inversion symmetry, may play a role analogous to an external magnetic field in maximizing the diode efficiency. “Therefore, in noncentrosymmetric FMSCs such as UIr, the condition for maximizing the diode efficiency η may deviate from = ,” the authors write.
Micromagnetic simulations, performed with specific magnetic field and magnetization values, = = 226 Oe and M = 40 kA/m, demonstrated the effect of demagnetization on the precessional dynamics of a domain wall pinned at a notch. These simulations provide further validation of the theoretical model and highlight the importance of carefully controlling the material parameters to optimize the superconducting diode effect.
Nonreciprocal Walker Breakdown in Ferromagnetic Systems
Specifically, the work details how a quasi-one-dimensional domain wall behaves within a ferromagnetic thin film, described by a Hamiltonian density incorporating exchange interactions, anisotropy and external magnetic fields. The dynamics of magnetization are then governed by the Landau-Lifshitz-Gilbert equation, a fundamental equation describing the precession of magnetization vectors. This equation, when combined with the spin-transfer torque, provides a complete picture of how the domain wall responds to applied currents and magnetic fields.
The inclusion of both adiabatic and nonadiabatic spin-transfer torque is essential for accurately modeling the domain wall’s behavior. The analysis of the nonreciprocal Walker breakdown considers both unpinned and notch-pinned domain walls, with the latter representing a more realistic scenario where the wall’s motion is constrained by geometric features within the material. These notches, characterized by parameters nx and ny, introduce localized pinning that influences the critical currents at which the breakdown occurs.
The researchers demonstrate that the voltage generated across the domain wall, and thus the magnitude of the diode effect, is directly related to the emergent electric fields described by equations 13 and 34 in the paper. The hydrodynamic theory applied to FMSCs highlights the incompressible limit, where the supercurrent-driven magnetization dynamics closely resemble those in ferromagnets. This allows the researchers to use existing knowledge of domain wall behavior in ferromagnets to predict and understand the superconducting diode effect in FMSCs.
The team’s approach provides a pathway to realizing the SDE by exploiting the nonreciprocal dynamics of magnetic textures within these superconducting materials. The theoretical results are further supported by detailed micromagnetic simulations, solidifying the understanding of this complex phenomenon and clearing the way for future exploration of novel superconducting devices.
Current-Driven Domain Walls Generate Nonreciprocal Behavior
These notches, the researchers suggest, offer a means of controlling the domain wall’s behavior and fine-tuning the magnitude of the diode effect. The team extended their analysis to ferromagnetic superconductors, accounting for the additional effects of superconductivity to identify specific experimental conditions needed to observe the predicted effect. Their work proposes that topological defects, such as domain walls, within these materials is an intrinsic nanoscale platform for nonlinear nonreciprocal superconducting functionalities.
This approach circumvents the need for complicated engineered heterostructures, potentially enabling the miniaturization of superconducting devices down to the nanometer scale, a challenge for conventional Josephson junctions. The researchers used the established understanding of domain wall behavior in conventional ferromagnets to predict the dynamics within ferromagnetic superconductors.
Phase Slips Map Walker Breakdown to Diode Effect
This control is important because the constant rotation of the domain wall, induced by the nonreciprocal Walker breakdown, directly generates phase slips, events that open dissipation channels and ultimately manifest as the superconducting diode effect. Specifically, the maximum diode efficiency reaches 1/3 when external magnetic fields are applied simultaneously along two directions with equal intensity, a finding that parallels the thermodynamic diode effect observed in twisted nodal superconductors.
The researchers note that breaking both time-reversal symmetry and mirror symmetries is essential for inducing this effect, with the applied magnetic fields playing distinct roles in disrupting these symmetries. “To induce the diode effect, both TRS and mirror symmetries must be broken,” the researchers write, explaining the fundamental requirements for realizing the phenomenon. The team’s approach relies on the nonreciprocal Walker breakdown of a magnetic domain wall, where the precession of the wall induces phase slips within the ferromagnetic superconductor.
They first established theoretical frameworks to describe this breakdown in both pinned and unpinned cases, deriving analytical expressions for critical current densities and diode efficiency. The analysis considered how the azimuthal angle of the domain wall on the y-z plane interacts with mirror operations, which are broken by the applied magnetic fields. This detailed examination of symmetry breaking provides a pathway for optimizing the diode effect’s performance and tailoring it to specific material properties.
Emergent Electric Fields and Spin-Motive Force in Superconductors
The emergence of electric fields directly linked to spin dynamics provides a novel dissipation mechanism within ferromagnetic superconductors, a phenomenon previously unseen in materials where Joule heating is absent. These emergent fields, arising from the constant rotation of magnetic domain walls, manifest as a spin-motive force, the superconducting counterpart to current-driven magnetization observed in spintronics. This connection establishes a pathway for understanding how the observed superconducting diode effect originates at a fundamental level, bypassing traditional dissipation channels.
The magnetic fields employed in these experiments achieve this, but play distinct roles beyond simply breaking symmetry. This detailed interplay between symmetry and field orientation is important for optimizing the efficiency of the effect, as the emergent electric fields are directly tied to these broken symmetries.
This is not a single threshold beyond which the wall moves, but two, differing based on the direction of the driving current. The work identifies specific criteria for realizing the predicted superconducting diode effect in experimental conditions.
This allows for a precise understanding of how the diode effect arises and how it can be optimized. The researchers note that the emergent electric field has an identical form to the adiabatic spin-motive force, resulting in the same voltage.
👉 More information
🗞 Superconducting diode effect in magnetic superconductors realized by nonreciprocal domain-wall dynamics
✍️ Dong Hui Han, Suk Bum Chung and Se Kwon Kim
🧠 DOI: http://link.aps.org/doi/10.1103/k96f-s31s
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