Mapping Metastable Magnetic Textures in (Fe0.5Co0.5)5GeTe2 with in-situ Lorentz Transmission Electron Microscopy

Technical Summary: Mapping Metastable Magnetic Textures in (Fe0.5Co0.5)5GeTe2

Problem Statement
Topologically protected magnetic textures, such as skyrmions, offer a promising route for low-energy control of magnetism via electric currents, fields, and strain. However, these states are typically studied under non-ambient conditions (low temperatures, high magnetic fields) where they are thermodynamically stable. A significant gap exists in understanding how to generate and stabilize these textures at zero magnetic field and near room temperature. In many materials, removing the stabilizing magnetic field causes skyrmions to relax immediately into lower-energy cycloidal or helical states due to a lack of thermodynamic energy barriers. Furthermore, existing characterization techniques like neutron diffraction and transport measurements often struggle to distinguish between complex, aperiodic, or mixed spin states (e.g., parallel vs. labyrinthine cycloids) in real space.

Methodology
The authors investigate the metastability of magnetic textures in the van der Waals layered material (Fe0.5Co0.5)5GeTe2 (FCGT). The study employs in-situ Lorentz transmission electron microscopy (LTEM) with precise control over temperature and magnetic fields.

• Imaging: LTEM is used to visualize domain walls (Néel type) by defocusing the electron beam (+600 µm) and tilting the sample (+18°). The objective lens is turned off to prevent magnetic saturation, with fine control applied via adjacent condenser lenses and calibrated Hall sensors.
• Thermal/Magnetic Protocol: The researchers utilize field-cooling cycles. Samples are heated above the Curie temperature ($T_c \approx 390$ K) to reset the magnetic state to paramagnetic. They are then cooled to a specific base temperature ($T_i$) under a specific cooling magnetic field ($B_{cool}$). Finally, the field is removed to observe the resulting zero-field state.
• Phase Mapping: By systematically varying $T_i$ (ranging from 203 K to 323 K) and $B_{cool}$, the authors construct a phase diagram of the resulting metastable zero-field spin structures.
• Analysis: Magnetic induction maps are reconstructed using single-image transport of intensity equation (TIE) methods via the PyLorentz package to quantitatively compare spin textures.

Key Results
The study reveals that the magnetic ground state of FCGT is not solely determined by the instantaneous temperature and field, but is highly dependent on the thermal and magnetic field history (path dependence).

1. Field-Cooling Selection of States:

   • Zero-Field Cooling: Results in a highly parallel cycloidal state (the equilibrium state at room temperature).
   • Low Field Cooling ($< 210$ Oe): Yields a labyrinthine cycloidal state.
   • Intermediate Field Cooling (210–265 Oe): Produces a mixed state where skyrmions and labyrinthine cycloidal domains coexist.
   • High Field Cooling (210 Oe to Saturation): Generates a metastable, zero-field skyrmion state. These skyrmions are tightly packed and extend across the sample but lack long-range hexagonal order.

2. Temperature Dependence:

   • Room Temperature to ~313 K: Metastable zero-field skyrmions are robust. The system remains trapped in the skyrmion state even after the field is removed because the energy barrier prevents relaxation to the cycloidal state.
   • High Temperatures (~323 K): Skyrmions are only stable under an applied magnetic field. Upon field removal, the system relaxes to the cycloidal state, indicating the energy barrier is insufficient for metastability near $T_c$.
   • Low Temperatures ($\le 203$ K): The helimagnetic ordering (driven by Dzyaloshinskii–Moriya interaction, DMI) weakens. Field cooling results in large, irregular circular domains rather than uniform skyrmions. While topologically similar to skyrmions, these "circle domains" lack the continuous spin canting characteristic of DMI-stabilized skyrmions, suggesting the exchange interaction dominates over DMI at these temperatures.

3. Magnetic Saturation Effects:
   Applying a magnetic field greater than the saturation field ($B_{sat}$) erases the previous path history. Whether the sample was previously in a cycloidal or skyrmion state, saturating the material and then removing the field consistently results in a labyrinthine cycloidal state.

4. Phase Diagram Construction:
   The authors map the temperature-magnetic field phase space, defining specific regions where parallel cycloids, labyrinthine cycloids, mixed states, and metastable skyrmions can be selected. This map serves as a "roadmap" for processing FCGT to achieve a desired spin state.

Significance and Claims
The paper claims to provide the first systematic mapping of the thermal and magnetic field history required to generate metastable zero-field skyrmions in FCGT.

• Path Dependence: The work demonstrates that in FCGT, the spin state is uniquely determined by the processing path through temperature-field space, unlike in many other skyrmionic materials where the state is determined by the instantaneous field.
• Metastability Mechanism: The authors argue that the stability of zero-field skyrmions in FCGT arises from a thermodynamic energy barrier that prevents the system from overcoming the topological constraint (180° spin flips) required to relax to the cycloidal state.
• Methodological Advantage: The study highlights LTEM as a superior tool for identifying complex, aperiodic, and mixed magnetic states that are often invisible or indistinguishable using neutron diffraction or transport measurements.
• Broader Applicability: The mapping technique and insights into spin state metastability are presented as broadly applicable to the discovery and manipulation of exotic spin textures in other magnetic materials, emphasizing the necessity of understanding processing conditions to create and sustain specific topological states.