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  <front>
    <journal-meta>
      <journal-id journal-id-type="nlm-ta">Microstructures</journal-id>
      <journal-id journal-id-type="publisher-id">microstructures</journal-id>
      <journal-title-group>
        <journal-title>Microstructures</journal-title>
      </journal-title-group>
      <issn pub-type="epub">2770-2995</issn>
      <publisher>
        <publisher-name>OAE Publishing Inc.</publisher-name>
      </publisher>
    </journal-meta>
    <article-meta>
      <article-id pub-id-type="doi">10.20517/microstructures.2026.24</article-id>
      <article-id pub-id-type="publisher-id">MICROSTRUCTURES-2026-24</article-id>
      <article-categories>
        <subj-group>
          <subject>Research Article</subject>
        </subj-group>
      </article-categories>
      <title-group>
        <article-title>Magnetic anisotropic pinning and symmetry breaking in ruthenate superlattices</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <name>
            <surname>Jiang</surname>
            <given-names>Zhongyuan</given-names>
          </name>
          <xref ref-type="aff" rid="I1">
            <sup>1</sup>
          </xref>
          <xref ref-type="aff" rid="I1035">
            <sup>#</sup>
          </xref>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Zhang</surname>
            <given-names>Zhiwei</given-names>
          </name>
          <xref ref-type="aff" rid="I2">
            <sup>2</sup>
          </xref>
          <xref ref-type="aff" rid="I1035">
            <sup>#</sup>
          </xref>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Zhao</surname>
            <given-names>Kesen</given-names>
          </name>
          <xref ref-type="aff" rid="I3">
            <sup>3</sup>
          </xref>
          <xref ref-type="aff" rid="I1035">
            <sup>#</sup>
          </xref>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Meng</surname>
            <given-names>Wenjie</given-names>
          </name>
          <xref ref-type="aff" rid="I3">
            <sup>3</sup>
          </xref>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Zhao</surname>
            <given-names>Yuanyuan</given-names>
          </name>
          <xref ref-type="aff" rid="I2">
            <sup>2</sup>
          </xref>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Hou</surname>
            <given-names>Yubin</given-names>
          </name>
          <xref ref-type="aff" rid="I3">
            <sup>3</sup>
          </xref>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Cui</surname>
            <given-names>Zhangzhang</given-names>
          </name>
          <xref ref-type="aff" rid="I1">
            <sup>1</sup>
          </xref>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Zhang</surname>
            <given-names>Jian</given-names>
          </name>
          <xref ref-type="aff" rid="I1">
            <sup>1</sup>
          </xref>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Shan</surname>
            <given-names>Zheling</given-names>
          </name>
          <xref ref-type="aff" rid="I1">
            <sup>1</sup>
          </xref>
        </contrib>
        <contrib contrib-type="author" corresp="yes">
          <contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-5686-5519</contrib-id>
          <name>
            <surname>Huang</surname>
            <given-names>Haoliang</given-names>
          </name>
          <xref ref-type="aff" rid="I2">
            <sup>2</sup>
          </xref>
          <xref ref-type="corresp" rid="cor1">*</xref>
        </contrib>
        <contrib contrib-type="author" corresp="yes">
          <contrib-id contrib-id-type="orcid">https://orcid.org/0000-0003-1934-8165</contrib-id>
          <name>
            <surname>Lu</surname>
            <given-names>Qingyou</given-names>
          </name>
          <xref ref-type="aff" rid="I1">
            <sup>1</sup>
          </xref>
          <xref ref-type="aff" rid="I3">
            <sup>3</sup>
          </xref>
          <xref ref-type="corresp" rid="cor1">*</xref>
        </contrib>
        <contrib contrib-type="author" corresp="yes">
		<contrib-id contrib-id-type="orcid">https://orcid.org/0000-0001-8240-5404</contrib-id>
          <name>
            <surname>Lu</surname>
            <given-names>Yalin</given-names>
          </name>
          <xref ref-type="aff" rid="I1">
            <sup>1</sup>
          </xref>
          <xref ref-type="corresp" rid="cor1">*</xref>
        </contrib>
      </contrib-group>
      <aff id="I1"><sup>1</sup>Hefei National Laboratory, Anhui Laboratory of Advanced Photon Science and Technology, Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei 230026, Anhui, China.</aff>
      <aff id="I2"><sup>2</sup>Quantum Science Center of Guangdong-Hong Kong-Macao Greater Bay Area, Shenzhen 518045, Guangdong, China.</aff>
      <aff id="I3"><sup>3</sup>Anhui Province Key Laboratory of Condensed Matter Physics at Extreme Conditions, High Magnetic Field Laboratory, Chinese Academy of Sciences, Hefei 230031, Anhui, China.</aff>
      <aff id="I1035"><sup>#</sup>These authors contributed equally to this work.</aff>
      <author-notes>
        <corresp id="cor1">Correspondence to: Dr. Haoliang Huang, Quantum Science Center of Guangdong-Hong Kong-Macao Greater Bay Area, Shenzhen 518045, Guangdong, China. E-mail: <email>huanghaoliang@quantumsc.cn</email>; Pro. Qingyou Lu, Anhui Province Key Laboratory of Condensed Matter Physics at Extreme Conditions, High Magnetic Field Laboratory, Chinese Academy of Sciences, Hefei 230031, Anhui, China. E-mail: <email>qxl@ustc.edu.cn</email>; Prof. Yalin Lu, Hefei National Laboratory, Anhui Laboratory of Advanced Photon Science and Technology, Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei 230026, Anhui, China. E-mail: <email>yllu@ustc.edu.cn</email></corresp>
        <fn fn-type="other">
          <p><bold>Received:</bold> 15 Feb 2026 | <bold>First Decision:</bold> 16 Apr 2026 | <bold>Revised:</bold> 7 May 2026 | <bold>Accepted:</bold> 12 Jun 2026 | <bold>Published:</bold> 21 Jul 2026</p>
        </fn>
        <fn fn-type="other">
          <p><bold>Academic Editor:</bold> Jun Chen | <bold>Copy Editor:</bold> Shu-Yuan Duan | <bold>Production Editor:</bold> Shu-Yuan Duan</p>
        </fn>
      </author-notes>
      <pub-date pub-type="ppub">
        <year>2026</year>
      </pub-date>
      <pub-date pub-type="epub">
        <day>21</day>
        <month>7</month>
        <year>2026</year>
      </pub-date>
      <volume>6</volume>
	  <issue>4</issue>
      <elocation-id>2026098</elocation-id>
      <permissions>
        <copyright-statement>© The Author(s) 2026.</copyright-statement>
        <license xlink:href="https://creativecommons.org/licenses/by/4.0/">
          <license-p>© The Author(s) 2026.<bold>Open Access</bold>This article is licensed under a Creative Commons Attribution 4.0 International License (<uri xlink:href="https://creativecommons.org/licenses/by/4.0/">https://creativecommons.org/licenses/by/4.0/</uri>), which permits unrestricted use, sharing, adaptation, distribution and reproduction in any medium or format, for any purpose, even commercially, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.</license-p>
        </license>
      </permissions>
      <abstract>
        <p>Interfacial engineering enables various emergent effects such as spin reorientations and transport anisotropy. Noncollinear spin textures are essential for realizing many emergent quantum transport phenomena. However, driving such spin structures requires precise control of the interfacial magnetic coupling in complex oxide heterostructures. Here, by utilizing competing exchange interactions at the interface between ferromagnetic metal SrRuO<sub>3</sub> and ferromagnetic insulator LaCoO<sub>3</sub>, we investigated a noncollinear spin configuration in SrRuO<sub>3</sub> sublayers. Stripe-like domains were induced by out-of-plane rather than in-plane magnetic fields, indicating strong anisotropy pinning in our superlattices. The observed magneto-transport anisotropy can be well explained by our proposed spin reorientation configurations. No magnetic skymionic textures were observed in our superlattice samples. The interfacial exchange interaction may compete with the Dzyaloshinskii-Moriya interaction (DMI) that stabilizes skyrmions, featuring a higher exchange coupling energy than that for the topological spin textures according to our micromagnetic simulations. Our work highlights the potential of interfacial engineering in tuning the spintronic properties by designing proper interfacial interactions.</p>
      </abstract>
      <kwd-group>
        <kwd>Interfacial coupling</kwd>
        <kwd>magnetic microstructures</kwd>
        <kwd>magnetic anisotropic pinning</kwd>
        <kwd>spin reorientation</kwd>
        <kwd>superlattice</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec id="sec1">
      <title>INTRODUCTION</title>
      <p>Interfacial engineering in complex correlated oxide heterostructures has emerged as a powerful paradigm for designing novel quantum states of matter. At atomic-layer-thick interfaces, lattice strain<sup>[<xref ref-type="bibr" rid="B1">1</xref>-<xref ref-type="bibr" rid="B4">4</xref>]</sup>, electronic reconstruction<sup>[<xref ref-type="bibr" rid="B5">5</xref>,<xref ref-type="bibr" rid="B6">6</xref>]</sup>, superconducting pairing<sup>[<xref ref-type="bibr" rid="B7">7</xref>-<xref ref-type="bibr" rid="B9">9</xref>]</sup> and spin reorientation<sup>[<xref ref-type="bibr" rid="B10">10</xref>]</sup> can give rise to various emergent phenomena not found in the constituent bulk materials. These engineered quantum phases hold significant potential for next-generation electronic and quantum information technologies. For example, customized interface exchange coupling can be achieved by delicately regulating the selection of the bulk materials, growth conditions as well as the design of the inter-layers, thereby obtaining spintronic functions designed on demand<sup>[<xref ref-type="bibr" rid="B1">1</xref>,<xref ref-type="bibr" rid="B4">4</xref>,<xref ref-type="bibr" rid="B11">11</xref>]</sup>. In particular, when two materials with distinct magnetic orders form an interface, the mismatch of spin configurations at the interface will induce significant magnetic proximity effects and lead to abnormal electronic transport characteristics<sup>[<xref ref-type="bibr" rid="B12">12</xref>-<xref ref-type="bibr" rid="B14">14</xref>]</sup>, providing an ideal platform for exploring novel quantum phenomena.</p>
      <p>SrRuO<sub>3</sub> (SRO), for instance, is a well-known itinerant ferromagnet (<italic>T</italic><sub>C</sub> ~ 120 K) with unique transport and magnetic properties. SRO-based interfaces can host multiple interesting effects, such as interfacial oxygen distortion, strain-induced anisotropy, anomalous Hall effect (AHE), and skyrmionic spin textures, offering potential routes to design switches of various spintronic behaviors<sup>[<xref ref-type="bibr" rid="B2">2</xref>,<xref ref-type="bibr" rid="B15">15</xref>-<xref ref-type="bibr" rid="B24">24</xref>]</sup>. In magnetic thin films and heterostructures, the competition among Heisenberg exchange, magnetic anisotropy, dipolar interaction, and long-range magnetic order commonly gives rise to spatially modulated magnetic order, including stripe-like or labyrinthine domain patterns<sup>[<xref ref-type="bibr" rid="B25">25</xref>,<xref ref-type="bibr" rid="B26">26</xref>]</sup>. Magnetic skyrmions, in contrast, represent a more specific class of topological spin textures that usually require suitable symmetry breaking, Dzyaloshinskii-Moriya interaction (DMI), magnetic anisotropy, and appropriate magnetic-field and temperature conditions<sup>[<xref ref-type="bibr" rid="B10">10</xref>,<xref ref-type="bibr" rid="B16">16</xref>,<xref ref-type="bibr" rid="B17">17</xref>,<xref ref-type="bibr" rid="B24">24</xref>]</sup>. It is worth noting that the specifically designed SRO heterostructures exhibit hump-shaped Hall resistivity arising at particular field strengths and temperatures, which is sometimes alternatively attributed to the topological Hall effect (THE) associated with magnetic skyrmions<sup>[<xref ref-type="bibr" rid="B27">27</xref>-<xref ref-type="bibr" rid="B29">29</xref>]</sup>, although its origin remains highly debated<sup>[<xref ref-type="bibr" rid="B30">30</xref>-<xref ref-type="bibr" rid="B33">33</xref>]</sup>. Therefore, direct magnetic-domain imaging is important for distinguishing skyrmion-like textures from stripe-like magnetic domains.</p>
      <p>Furthermore, SRO can exhibit perpendicular magnetic anisotropy (PMA) under compressive strain with the spin orientation preferring the film-normal direction<sup>[<xref ref-type="bibr" rid="B34">34</xref>-<xref ref-type="bibr" rid="B36">36</xref>]</sup>. In contrast, while a non-magnetic insulator ground state in bulk, tensile-strained LaCoO<sub>3</sub> (LCO) thin films can stabilize a ferromagnetic (FM) insulating phase with a lower Curie temperature (75 ~ 85 K) and exhibit in-plane magnetic anisotropy (IMA)<sup>[<xref ref-type="bibr" rid="B37">37</xref>]</sup>. This stark contrast, i.e., a strained FM metal with PMA (SRO) adjacent to a strained FM insulator with IMA (LCO), creates an ideal interface for generating profound magnetic frustration and symmetry breaking. The direct exchange coupling at such an interface is expected to compete with the intrinsic anisotropy of each layer, providing a possible route to noncollinear spin reorientation, exotic domain structures, and manipulation of topological defects.</p>
      <p>In this study, high-quality LCO/SRO superlattices were prepared to investigate the interfacial spin reorientation and magnetic anisotropy in oxide heterostructures. We observe stripe-like magnetic domains with pronounced anisotropy in the LCO/SRO superlattices. No skyrmion-like circular spin textures are observed in our magnetic force microscopy (MFM) measurements within the explored temperature and magnetic-field range. Based on the MFM, angular magneto-resistance, Hall transport, and micromagnetic simulation results, we propose that noncollinear ferromagnetic spin reorientation may occur at the LCO/SRO interfaces. The observed stripe-like magnetic domains and magneto-transport anisotropy are consistent with this interpretation, providing experimental support and a useful perspective for understanding and tuning anisotropic magnetic textures in oxide superlattices with competing interfacial magnetic interactions. </p>
    </sec>
<sec id="sec2">
      <title>MATERIALS AND METHODS</title>
      <sec id="sec2-1">
        <title>Thin film deposition and superlattice preparation</title>
        <p>The superlattices (LCO<sub>M</sub>/SRO<sub>N</sub>)<sub>12</sub> (denoted by L<sub>M</sub>S<sub>N</sub>, where M and N denote the number of unit cells of LCO and SRO, respectively, in each bilayer period, and the subscript 12 indicates 12 repetitions of the LCO/SRO bilayer) were grown on TiO<sub>2</sub>-terminated SrTiO<sub>3</sub> (STO) substrates (from MTI Corporation Inc., China) by pulsed laser deposition (PLD, PASCAL Co., Ltd. Japan) assisted with reflection high energy electron diffraction (RHEED). We have successfully designed and prepared various superlattices, among which L<sub>9</sub>S<sub>6</sub>, L<sub>7</sub>S<sub>6</sub>, and L<sub>5</sub>S<sub>5</sub> were particularly investigated. During the growth of the superlattices, the substrate temperature, oxygen partial pressure, and repetition rate of the laser pulse were 750°C, 100 mTorr, and 2 Hz, respectively. The laser fluence set at ~ 2 J cm<sup>-2</sup> for the SRO layer and 1.2 J cm<sup>-2</sup> for the LCO layer.</p>
      </sec>
      <sec id="sec2-2">
        <title>X-ray characterizations and scanning transmission electron microscopy</title>
        <p>X-ray characterizations, including X-ray diffraction (XRD), X-ray reflectivity (XRR), and reciprocal space mapping (RSM), of the superlattices were performed using a four-circle diffractometer (Cu Kα, SmartLab, Rigaku, Japan). Scanning transmission electron microscopy (STEM) was performed using an FEI Titan Themis G2 (FEI, USA), equipped with a double spherical-aberration corrector and a high brightness field-emission gun. The cross-section of the specimens was prepared using a FEI Helios 600i dual-beam FIB/SEM machine. Pt electron-beam deposition and C ion-beam deposition were conducted in order to protect the sample surface from beam damage. Both X-ray characterization and STEM experiments were conducted at room temperature.</p>
      </sec>
      <sec id="sec2-3">
        <title>Magnetic force microscopy</title>
        <p>MFM measurements were performed on the top surface of the superlattice films in a 12 T superconducting magnet placed in ultrahigh vacuum at the High Magnetic Field Laboratory in Hefei, China. The spatial resolution of the microscope is 10 nm. A rotation sample plate is mounted on the axis, allowing for an <italic>in-situ</italic> field angle ranging from 0° to 180°. For signal detection, we utilized custom piezoresistive cantilevers (SCL-Sensor Tech., PRSA-L300-F50-STD) characterized by a hollow beam structure and a resonance frequency of ~ 37 kHz. The tips were magnetically coated with a Ti (5 nm)/Co (30 nm)/Au (5 nm) film using electron beam evaporation and pre-magnetized perpendicular to the cantilever beam. The readout electronics consisted of a home-made active Wheatstone bridge preamplifier (gain 1,000×) interfaced with a commercial RHK R9 controller. Topographic images were acquired in tapping mode, while MFM images were acquired in constant-height mode approximately 100 nm above the sample surface. The resulting MFM contrast maps the resonant frequency shift caused by the out-of-plane stray field gradient, where dark and light regions represent attractive and repulsive magnetic forces, respectively. Post-processing of the SPM data was conducted using WSxM. All MFM images presented in this work were measured on the top surface of the as-grown superlattice films. Cross-sectional MFM was not performed in this study. The superlattice terminates with an SRO layer (topmost surface). The MFM probe detects magnetic stray fields emanating from this top SRO layer. The signal primarily reflects the magnetization state of the SRO layer because: SRO is metallic and ferromagnetic with strong stray-field contrast, while LCO is insulating with weak magnetic contrast at the measurement temperatures (5-300 K), and the 6uc (~ 2.4 nm) top SRO thickness is within the typical MFM detection depth.</p>
      </sec>
      <sec id="sec2-4">
        <title>Magnetic-field-angle-dependent resistivity</title>
        <p>All transport measurements were performed using a physical property measurement system (PPMS, Quantum Design, USA) equipped with a sample rotator. The magnetic-field-angle-dependent resistivity (MAR) is defined as MAR = [<italic>ρ</italic>(<italic>θ</italic>) - <italic>ρ</italic>(0˚)]/<italic>ρ</italic>(0˚), where <italic>θ</italic> is the angle of the magnetic field with respect to the film normal (e.g. 0˚ for field pointing out-of-plane). For the transport measurements, Hall electrodes were fabricated using the evaporation method. The current was applied in the plane of the film along the [100] direction of the STO substrate, and the magnetic field was rotated in the plane perpendicular to the current direction (the <italic>ac</italic> plane), with <italic>θ</italic> = 0° corresponding to the field applied perpendicular to the film plane.</p>
      </sec>
      <sec id="sec2-5">
        <title>Static micromagnetic simulation</title>
        <p>An all-Python-based micromagnetic framework were employed that computes the magnetostatic field via 3D fast Fourier transform (FFT) convolution and the magnetization is relaxed toward a steady state through an energy-minimization alignment scheme. At each iteration the local moment is rotated toward the direction of the effective field with a damping-like coefficient serving purely as a convergence parameter until the system reaches a local energy minimum. The micromagnetic simulations were performed under two regimes: (A) a DMI-dominated regime and (B) an interfacial-exchange-dominated regime. The total energy functional includes exchange, uniaxial anisotropy (PMA for SRO, IMA for LCO), demagnetizing (computed via FFT-based convolution), interfacial DMI, Zeeman, and an effective interfacial exchange interaction term at the LCO/SRO boundary. The 2D model simulation and its comparison with the standard GPU-based solver mumax3 are provided in <inline-supplementary-material content-type="local-data" mimetype="application/pdf" xlink:href="microstructures6024-SupplementaryMaterials.pdf">Supplementary Table 1</inline-supplementary-material>. The parameters used for SRO and LCO layers are summarized in <inline-supplementary-material content-type="local-data" mimetype="application/pdf" xlink:href="microstructures6024-SupplementaryMaterials.pdf">Supplementary Table 2</inline-supplementary-material>, while the parameters used for Case A and Case B are listed in <inline-supplementary-material content-type="local-data" mimetype="application/pdf" xlink:href="microstructures6024-SupplementaryMaterials.pdf">Supplementary Table 3</inline-supplementary-material>.</p>
      </sec>
      <sec id="sec2-6">
        <title>Anomalous hall effect analysis</title>
        <p>The Hall resistivity was analyzed using a two-channel AHE model, which is expressed as <italic>ρ</italic><sub>xy</sub> = R<sub>1</sub>M<sub>1</sub> + R<sub>2</sub>M<sub>2</sub> + <italic>ρ</italic><sub>xy</sub><sup>OHE</sup>, where R<sub>1</sub> and R<sub>2</sub> are the anomalous Hall coefficients of two distinct magnetic channels, M<sub>1</sub> and M<sub>2</sub> are their respective magnetizations, and <italic>ρ</italic><sub>xy</sub><sup>OHE</sup> is the ordinary Hall resistivity. The two channels are assigned to represent the bulk-like SRO ferromagnetic component (weakly coercive S-loop) and the interfacial ferromagnetic coupling component (highly coercive L-loop), respectively. The model parameters were determined by least-squares fitting to the experimental Hall data. We note that this phenomenological model assumes isotropic magnetic properties and does not account for possible contributions from noncollinear spin textures or inhomogeneous magnetization distributions.</p>
      </sec>
    </sec>
    <sec id="sec3">
      <title>RESULTS AND DISCUSSION</title>
      <sec id="sec3-1">
        <title>Atomically layer-by-layer growth</title>
        <p>LCO/SRO superlattices were prepared by alternating growth of LCO and SRO on top of TiO<sub>2</sub>-terminated STO substrates. <xref ref-type="fig" rid="fig1">Figure 1A</xref> shows the conceptual stacking of the LCO and the SRO layers on STO. The STEM image identifies each atomic layer with no ambiguity. RHEED images during sample preparation were captured for the three sets of samples [<xref ref-type="fig" rid="fig1">Figure 1B</xref>-<xref ref-type="fig" rid="fig1">D</xref>], which present the layer-by-layer nature of the growth. XRD measurements [<xref ref-type="fig" rid="fig1">Figure 1E</xref>] show rigid epitaxy of the superlattice to the substrate according to the result of the (002) substrate peak and the superlattice satellite peaks (SL0, ±1, ±2), including beating patterns due to the whole film thickness and the satellite peaks (SLx) due to each LCO/SRO layer pair. The XRR patterns were in good agreement with the theoretical fit for L<sub>9</sub>S<sub>6</sub>, L<sub>7</sub>S<sub>6</sub> and L<sub>5</sub>S<sub>5</sub> structures, respectively [<xref ref-type="fig" rid="fig1">Figure 1F</xref>]. The combination of RHEED, STEM, XRD and XRR shows the high atomic layer-by-layer quality for all of our superlattice samples.</p>
        <fig id="fig1" position="float">
          <label>Figure 1</label>
          <caption>
            <p>Structural characterization of LCO/SRO superlattices. (A) Schematic illustration of the superlattice structure (left) and cross-sectional STEM image of the L<sub>9</sub>S<sub>6</sub> sample (right), showing atomically sharp interfaces between LCO (blue) and SRO (yellow) layers grown on STO substrate (gray). The scale bar represents 20 nm; (B-D) RHEED patterns along the [100] azimuth for L<sub>9</sub>S<sub>6</sub>, L<sub>7</sub>S<sub>6</sub>, and L<sub>5</sub>S<sub>5</sub>, respectively; (E) XRD <italic>θ</italic>-2<italic>θ</italic> scans around the (002) reflection, showing the substrate peak (STO), the superlattice zero-order peak (SL0), and satellite peaks (±1, ±2) arising from the artificial periodicity; (F) XRR data (symbols) and theoretical fits (solid lines) for the three superlattice samples. Well-defined Kiessig oscillations demonstrate an agreement between experimental data and fits for the designed layer thicknesses. LCO: LaCoO<sub>3</sub>; SRO: SrRuO<sub>3</sub>; STEM: scanning transmission electron microscopy; XRD: X-ray diffraction; XRR: X-ray reflectivity; STO: SrTiO<sub>3</sub>.</p>
          </caption>
          <graphic xlink:href="microstructures6024.fig.1.jpg"/>
        </fig>
        <p>The lattice constants of bulk STO, LCO, and SRO are approximately 3.905 Å, 3.837 Å, and 3.923 Å, respectively. Reciprocal space mapping (RSM) around the (103) reflection was performed to determine the in-plane lattice parameters of the superlattices [<inline-supplementary-material content-type="local-data" mimetype="application/pdf" xlink:href="microstructures6024-SupplementaryMaterials.pdf">Supplementary Figure 1</inline-supplementary-material>]. The RSM results confirm that the superlattices are coherently strained to the STO substrate. The SRO and LCO suffer from compressive and tensile strain, respectively. This corresponds to a tensile strain of +1.8% for LCO and a compressive strain of -0.5% for SRO. The out-of-plane lattice parameters were determined from the XRD data, showing elongation consistent with the Poisson effect under biaxial compressive strain. The strain state is an important factor influencing the magnetic anisotropy of both LCO and SRO layers, as compressive strain in SRO is known to favor perpendicular magnetic anisotropy, while tensile strain in LCO can stabilize ferromagnetic order with in-plane magnetic anisotropy.</p>
      </sec>
      <sec id="sec3-2">
        <title>Magnetic anisotropic pinning</title>
        <p>We performed the cryogenic MFM measurements to directly image the magnetic domain evolution for our superlattice samples. Here, we focus on the L<sub>9</sub>S<sub>6</sub> samples. <xref ref-type="fig" rid="fig2">Figure 2A</xref> shows a series of the MFM images at 75 K with the field applied perpendicular to the film plane and swept in a complete loop. Stripe-like domains emerge at ~ 1 T, become saturated at higher field strengths, and reappear as the field strength decreases back to 1 T in both positive and negative field-scanning directions. <xref ref-type="fig" rid="fig2">Figure 2B</xref> shows corresponding MFM images at 25 K. A notable difference is that at lower temperature, stripe-like domains appear at smaller field strength (denoted from cyan brackets) and persist to higher fields, indicating enhanced magnetic anisotropy pinning. Complete sets of MFM loop measurements with out-of-plane fields can be found in <inline-supplementary-material content-type="local-data" mimetype="application/pdf" xlink:href="microstructures6024-SupplementaryMaterials.pdf">Supplementary Figures 2</inline-supplementary-material>-<inline-supplementary-material content-type="local-data" mimetype="application/pdf" xlink:href="microstructures6024-SupplementaryMaterials.pdf">5</inline-supplementary-material>. The stripe-like domains are stabilized at intermediate fields (~ 1 T), but disperse at both low fields (&lt; 0.5 T, near demagnetized state) and high fields (> 7 T, field-polarized state). By contrast, when the field is applied in-plane, no magnetic stripe is observed even at 10 T [<inline-supplementary-material content-type="local-data" mimetype="application/pdf" xlink:href="microstructures6024-SupplementaryMaterials.pdf">Supplementary Figure 6</inline-supplementary-material> and <inline-supplementary-material content-type="local-data" mimetype="application/pdf" xlink:href="microstructures6024-SupplementaryMaterials.pdf">7</inline-supplementary-material>], demonstrating that the stripe formation is highly anisotropic and favored by out-of-plane magnetic fields. While magnetic anisotropy has been reported in similar materials<sup>[<xref ref-type="bibr" rid="B38">38</xref>-<xref ref-type="bibr" rid="B40">40</xref>]</sup>, the particular stripe morphology observed here appears to be characteristic of this superlattice architecture. </p>
        <fig id="fig2" position="float">
          <label>Figure 2</label>
          <caption>
            <p>Magnetic-field-dependent top-surface MFM images of L<sub>9</sub>S<sub>6</sub> super lattice under out-of-plane magnetic fields. (A)MFM images acquired at 75 K during a magnetic field loop applied along the out-of-plane direction. The magnetic field sequence is: -0.00 T → -0.06 T → -1.00T  → -11.80 T → -5.00 T → -1.00 T → -0.00T → 0.30 T → 1.00 T → 5.00 T → 10.00 T → 5.00 T → 1.00 T → 0.00 T. The blue box high lights the field region (-1.00T) where stripe-like domains exhibit optimal contrast; (B) Corresponding MFM images at 25 K with the field sequence: -0.00 T → -0.05 T → -1.00 T → -10.00 T → -5.00 T → -1.00 T → -0.00 T → 0.30 T → 1.00 T → 5.00 T → 11.80 T → 5.00 T → 1.00 T → 0.00 T. Arrows indicate the field sweep directions. No circular skyrmion-like features are observed even at fields up to 11.8 T. The colour scales for images in A (in arrow order) are 0.18, 0.65, 0.55, 0.35, 0.55, 0.7, 0.16, 0.65, 0.55, 0.55, 0.5, 0.4, 0.65, and 0.16 Hz, respectively. The colour scales for images in B (in arrow order) are 0.2, 1.5, 0.8, 0.65, 1.0, 1.1, 0.16, 1.3, 0.8, 0.9, 0.8, 1.0, 0.9, and 0.2 Hz, respectively. MFM: Magnetic force microscopy.</p>
          </caption>
          <graphic xlink:href="microstructures6024.fig.2.jpg"/>
        </fig>
      </sec>
      <sec id="sec3-3">
        <title>Symmetry analysis and phase diagram of MAR evolution</title>
        <p>To further investigate the magnetic anisotropy, we conducted the MAR measurements as a function of temperature and magnetic field. MAR plots for different experimental conditions are presented in <xref ref-type="fig" rid="fig3">Figure 3</xref> for the L<sub>9</sub>S<sub>6</sub> samples. Forward and backward field-angle scans are shown in <inline-supplementary-material content-type="local-data" mimetype="application/pdf" xlink:href="microstructures6024-SupplementaryMaterials.pdf">Supplementary Figure 8</inline-supplementary-material>. Hysteretic behavior of magneto-resistivity, indicative of coercive ferromagnetism, is observed but diminishes as higher temperature elevates the thermal fluctuations and higher field enhances the magnetization alignment. More importantly, a purely two-fold symmetric MAR signal would be expected if the SRO magnetization maintains a single, fixed orientation. Therefore, the emergence of any higher-order symmetry component may imply intrinsic spin reorientations within the SRO layers.</p>
        <fig id="fig3" position="float">
          <label>Figure 3</label>
          <caption>
            <p>Harmonic decomposition of MAR results for L<sub>9</sub>S<sub>6</sub>, based on “2 + 4 + 8” model consisting of a two-fold, a four-fold and an eight-fold component. The original data are in grey circles. Fit curves are red solid lines. The two-fold, four-fold and eight-fold curves are blue, green and orange dashed lines, respectively. The inset brackets present the fitting results for each measurement condition. MAR: Magnetic-field-angle-dependent resistivity.</p>
          </caption>
          <graphic xlink:href="microstructures6024.fig.3.jpg"/>
        </fig>
        <p>To quantitatively characterize the evolution of the MAR symmetry, we developed a harmonic decomposition model to assess the magneto-transport anisotropy. The MAR signal was fitted with three components, one two-fold and one four-fold and one eight-fold, capturing the dominant symmetries: MAR(<italic>θ</italic>) = A<sub>0</sub> + A<sub>2</sub>cos(2<italic>θ</italic> + <italic>φ</italic><sub>2</sub>) + A<sub>4</sub>cos(4<italic>θ</italic> + <italic>φ</italic><sub>4</sub>) + A<sub>8</sub>cos(8<italic>θ</italic> + <italic>φ</italic><sub>8</sub>), where A<sub>2</sub>, A<sub>4</sub>, and A<sub>8</sub> are the amplitudes, and <italic>φ</italic><sub>2</sub>, <italic>φ</italic><sub>4</sub>, <italic>φ</italic><sub>8</sub> are the remnant phases of the two-fold, four-fold and eight-fold components, respectively. The results were plotted in <xref ref-type="fig" rid="fig3">Figure 3</xref>. It is noted that a two-component decomposition with one two-fold and one four-fold underfits the MAR signal though A<sub>4</sub>/A<sub>2</sub> still appears to be a good order parameter for the symmetry and its evolution with field and temperature (see <inline-supplementary-material content-type="local-data" mimetype="application/pdf" xlink:href="microstructures6024-SupplementaryMaterials.pdf">Supplementary Figures 9</inline-supplementary-material> and <inline-supplementary-material content-type="local-data" mimetype="application/pdf" xlink:href="microstructures6024-SupplementaryMaterials.pdf">10</inline-supplementary-material>), assuring the necessity of the eight-fold component. The two-fold component originates from the uniaxial anisotropy of the SRO layer with its spin canted by interfacial exchange coupling. The four-fold component arises from the superposition of contributions from multiple SRO sublayers with different spin orientations. The eight-fold component captures higher-order angular anisotropy from crystal symmetry breaking and spin-orbit coupling, consistent with eight-fold symmetry reported in other SRO superlattice systems<sup>[<xref ref-type="bibr" rid="B41">41</xref>]</sup>.</p>
        <p>The fitting results reveal several important features. The systematic evolution of the three-component (2-fold, 4-fold and 8-fold) amplitudes with field and temperature is summarized in <inline-supplementary-material content-type="local-data" mimetype="application/pdf" xlink:href="microstructures6024-SupplementaryMaterials.pdf">Supplementary Figure 11</inline-supplementary-material>. The phase diagrams provide crucial quantitative support for the presence of spin reorientation. First, the amplitude A<sub>2</sub> of the dominant component increases monotonically with field strength at all temperatures, reflecting the progressive alignment of the bulk-like SRO spins toward the field direction. The secondary amplitudes A<sub>4</sub> and A<sub>8</sub> exhibit more complex field dependence, with non-monotonic evolution that reflects the competing effects of field-induced alignment, interfacial exchange pinning, and higher-order crystal symmetry. At 25 K, the two-fold amplitude A<sub>2</sub> show systematic field-dependent evolution, where the interfacial coupling is strongest. At 75 K, the 3 T and 5 T data show anomalous four-fold dominance due to proximity to the LCO Curie temperature, while the 7 T and 9 T data exhibit significantly reduced amplitudes as spins are highly aligned by strong fields. </p>
      </sec>
      <sec id="sec3-4">
        <title>Vertically varying noncollinear spin reorientation</title>
        <p>To provide additional support of the competition between interfacial exchange coupling and DMI in the LCO/SRO superlattice, we performed 2D magnetostatic energy minimization simulations. <xref ref-type="fig" rid="fig4">Figure 4</xref> shows the M<sub>z</sub> spatial distribution maps and depth-dependent magnetization profiles. The simulation of the SRO magnetization at different magnetic fields is summarized in <inline-supplementary-material content-type="local-data" mimetype="application/pdf" xlink:href="microstructures6024-SupplementaryMaterials.pdf">Supplementary Table 4</inline-supplementary-material>. The magnetic stripe domains are saturated by field ≲ 7 T for the DMI-dominated regime (Case A) and field ≲ 9 T for the interfacial-exchange-dominated regime (Case B), indicating that the interfacial exchange interaction competes with the Zeeman energy. The depth-resolved magnetization profiles reveal a field-driven spin reorientation: at zero field, the average spin tilt angle <italic>θ</italic> ≈ 5.5° for Case A and <italic>θ</italic> ≈ 3.8° for Case B (with respect to out-of-plane direction), consistent with stripe-domain formation; with increasing field, <italic>θ</italic> increases to maximum at 5 T and decreases back to 0° at 9 T, reflecting the competition between the applied Zeeman energy and the interfacial exchange coupling. The average tilt angle of SRO spins at 5 T is ~ 15° for Case A and ~ 8° for Case B, consistent with the effect of DMI in stabilizing chiral or stripe-spiral textures. Since the thickness of each SRO layer (2.4 nm) is comparable to the exchange length, the entire layer responds coherently to interfacial coupling rather than maintaining a bulk-like out-of-plane orientation. This systematic canting favors the formation of anisotropic stripe domains.</p>
        <fig id="fig4" position="float">
          <label>Figure 4</label>
          <caption>
            <p>Micromagnetic simulation results for L<sub>9</sub>S<sub>6</sub> structure under two regimes, Case A: the DMI-dominated regime and Case B: interfacial-exchange-dominated regime. The upper panel: M<sub>z</sub> spatial distribution maps with different field strength from 0 to 9 T applied in the out-of-plane direction. The color bar denoted the magnetization ratio. The lower panel: depth-dependent magnetization profiles. Field dependence of SRO magnetization and average spin tilt angle is also provided. DMI: Dzyaloshinskii-Moriya interaction; SRO: SrRuO<sub>3</sub>.</p>
          </caption>
          <graphic xlink:href="microstructures6024.fig.4.jpg"/>
        </fig>
        <p>With the MAR analysis and the simulation results, we therefore propose a vertically evolving spin texture within the SRO layers, driven by interfacial exchange coupling between the PMA-SRO and the IMA-LCO [<xref ref-type="fig" rid="fig5">Figure 5A</xref>]. The coupling may cant SRO spins adjacent to the interface toward the in-plane direction (inheriting the IMA of LCO), while SRO spins in the layer interior retain a stronger tendency toward the out-of-plane orientation (reflecting the PMA of bulk SRO). The phase evolution of the harmonic components directly demonstrates the proposed field-driven spin reorientation: as the magnetic field increases, the spin orientations in different SRO sublayers rotate at different rates, changing the relative phases of their transport contributions (See <inline-supplementary-material content-type="local-data" mimetype="application/pdf" xlink:href="microstructures6024-SupplementaryMaterials.pdf">Supplementary Figure 12</inline-supplementary-material>). The phase difference <italic>φ</italic><sub>4</sub> - <italic>φ</italic><sub>2</sub> ≈ -48° at 25 K, 3 T and -10° at 25 K, 5 T, directly demonstrating the field-driven spin reorientation.</p>
        <fig id="fig5" position="float">
          <label>Figure 5</label>
          <caption>
            <p>Field-driven evolution of spin configuration and its correlation with magnetoresistance anisotropy. (A) Schematic illustration of the proposed noncollinear spin configuration in the SRO layer. The spin orientation evolves from PMA (bulk-like, orange region) to canted (interface region, yellow) to IMA (LCO bulk, blue arrows); (B) MAR <italic>vs.</italic> <italic>θ</italic> at 25 K for various magnetic fields (-3 T to -9 T). Left panel: MFM images acquired at <italic>θ</italic> = 0° (H ⊥ <italic>ab</italic>). Right panel: MFM images acquired at <italic>θ</italic> = 90° (H ∥ <italic>ab</italic>). MFM: Magnetic force microscopy; IMA: in-plane magnetic anisotropy; SRO: SrRuO<sub>3</sub>; PMA: perpendicular magnetic anisotropy; MAR: magnetic-field-angle-dependent resistivity.</p>
          </caption>
          <graphic xlink:href="microstructures6024.fig.5.jpg"/>
        </fig>
        <p>This proposed noncollinear spin-reorientation model also suggests a correlation of the magneto-transport properties to the magnetic anisotropic stripe pinning. <xref ref-type="fig" rid="fig5">Figure 5B</xref> shows the MAR vs. <italic>θ</italic> plot for various fields at 25 K. The minimal resistivity occurs at <italic>θ</italic> = 90° (in-plane field), where no magnetic stripe is formed. The stripe-like domain formation introduces localized exchange interaction and enhanced scattering, thereby suppression of conductivity. Nevertheless, direct verification of the proposed vertically varying spin configuration would benefit from techniques such as polarized neutron reflectometry.</p>
      </sec>
      <sec id="sec3-5">
        <title>AHE and topological properties</title>
        <p>Our MFM results found no signature of the skyrmion structure, which is nanoscale chiral magnetic spot and is often regarded as topological Hall features. The absence of skyrmion-like features in our samples might be the result of the competition between interface exchange interactions and DMI<sup>[<xref ref-type="bibr" rid="B40">40</xref>-<xref ref-type="bibr" rid="B44">44</xref>]</sup>. <xref ref-type="fig" rid="fig6">Figure 6</xref> shows field-dependent Hall resistivity (after subtracting the ordinary Hall contribution) at 25 K with vertical magnetic fields, overlaid with MFM images at corresponding fields. Green symbols represent experimental data, and the red curve shows a fit using the conventional two-channel AHE model also conducted in earlier works<sup>[<xref ref-type="bibr" rid="B31">31</xref>,<xref ref-type="bibr" rid="B32">32</xref>,<xref ref-type="bibr" rid="B45">45</xref>]</sup>. The fitting quality is reasonable except near the peak and valley regions (~ ±1.2 T), where significant deviations occur (See <inline-supplementary-material content-type="local-data" mimetype="application/pdf" xlink:href="microstructures6024-SupplementaryMaterials.pdf">Supplementary Figure 10</inline-supplementary-material>).</p>
        <fig id="fig6" position="float" width="450">
          <label>Figure 6</label>
          <caption>
            <p>Hall resistivity and magnetic domain evolution under vertical magnetic fields. Field-dependent Hall resistivity (after subtracting the ordinary Hall contribution, <italic>ρ</italic><sub>xy</sub> - <italic>ρ</italic><sub>xy</sub><sup>OHE</sup>) measured at 25 K with the magnetic field applied perpendicular to the film plane (H ⊥ <italic>ab</italic>). Green symbols represent experimental data, while the thick red curve shows the fit using a two-channel AHE model. The arrows indicate the magnetic field sweep direction. MFM images acquired at representative magnetic fields (-10.00 T, -5.00 T, -2.50 T, -1.20 T, -1.00 T, and -0.05 T) are overlaid, with yellow circles marking the corresponding positions on the Hall curve. OHE: ordinary Hall effect; AHE: anomalous Hall effect; MFM: magnetic force microscopy.</p>
          </caption>
          <graphic xlink:href="microstructures6024.fig.6.jpg"/>
        </fig>
        <p>The MFM images reveal an anticorrelation between stripe-domain visibility and the Hall resistivity anomaly: stripe-like domains are pronounced at low fields (-0.05 T, -1.0 T) and high fields (> -5 T), but become significantly suppressed near -1.2 T - precisely where the Hall resistivity exhibits its peak feature. This anticorrelation suggests that the Hall anomaly may include contribution from spin-reorientation-induced transport anisotropy, possibly reflected by the peak structure: near -1.2 T, the competing interfacial and bulk anisotropies drive a transition from the noncollinear, stripe-domain state toward a more uniformly canted spin configuration, producing enhanced spin-chirality-dependent scattering that is not captured by the two-channel AHE model.</p>
        <p>The two-channel AHE model assumes isotropic magnetic properties and thus provides no information about the detailed spin configuration in our samples. The systematic underfitting of peak and valley regions may indicate residual contributions from the proposed noncollinear spin texture, which could reflect complex interplay between spin-orbit coupling and vertically varying spin reorientation in our superlattices. The observed anticorrelation between stripe-domain evolution and Hall resistivity anomaly is suggestive of a topological contribution, though we cannot fully exclude inhomogeneous magnetization dynamics or domain-reconfiguration effects as alternative origins. Our combined MFM, MAR measurements and micromagnetic simulations thus provide critical constraints on the spin configuration, revealing how interfacial engineering can stabilize novel magnetic textures that suppress topological skyrmions while generating distinctive magneto-transport signatures through noncollinear spin arrangements. Although our observational results cannot quantitatively determine the relative energy scales of interfacial exchange interaction and DMI, the idea that interfacial exchange competes with or inhibits DMI is still a physically reasonable assumption that is consistent with the observed magnetic microstructure. Future work that combines element-specific spectroscopic analysis with first-principles calculations might be able to obtain the microscopic parameters needed to directly verify this assumption.</p>
      </sec>
      <sec id="sec3-6">
        <title>Thickness-dependent transport properties</title>
        <p>To assess the generality of our observations, we systematically compared the transport properties across the three superlattice structures: L<sub>9</sub>S<sub>6</sub>, L<sub>7</sub>S<sub>6</sub>, and L<sub>5</sub>S<sub>5</sub>. As shown in <inline-supplementary-material content-type="local-data" mimetype="application/pdf" xlink:href="microstructures6024-SupplementaryMaterials.pdf">Supplementary Figures 13</inline-supplementary-material>-<inline-supplementary-material content-type="local-data" mimetype="application/pdf" xlink:href="microstructures6024-SupplementaryMaterials.pdf">16</inline-supplementary-material>, all three samples exhibit qualitatively similar Hall resistivity anomalies and temperature-dependent resistivity and magnetization behavior, indicating that the observed magnetic phenomena are robust features of the LCO/SRO superlattice architecture. Notably, the two-channel AHE model fits reveal that the interfacial L-loop component exhibits prominent dependence on LCO layer thickness [<inline-supplementary-material content-type="local-data" mimetype="application/pdf" xlink:href="microstructures6024-SupplementaryMaterials.pdf">Supplementary Figure 13</inline-supplementary-material>]. The temperature-dependent resistivity shows a slope change at approximately 75 ~ 85 K for all samples [<inline-supplementary-material content-type="local-data" mimetype="application/pdf" xlink:href="microstructures6024-SupplementaryMaterials.pdf">Supplementary Figure 15A</inline-supplementary-material> and <inline-supplementary-material content-type="local-data" mimetype="application/pdf" xlink:href="microstructures6024-SupplementaryMaterials.pdf">B</inline-supplementary-material>], which we attribute to the Curie temperature of the LCO layers. The negative magneto-resistivity increases with decreasing temperature for all samples except peaked at respective critical temperatures as labeled by arrows with different colors [<inline-supplementary-material content-type="local-data" mimetype="application/pdf" xlink:href="microstructures6024-SupplementaryMaterials.pdf">Supplementary Figure 15C</inline-supplementary-material>]. The field-dependence of the magneto-resistivity is more significant for L<sub>5</sub>S<sub>5</sub> [<inline-supplementary-material content-type="local-data" mimetype="application/pdf" xlink:href="microstructures6024-SupplementaryMaterials.pdf">Supplementary Figure 15D</inline-supplementary-material>], suggesting that the thickness of LCO layers has a complex correlation to the spin-dependent scattering. These thickness-dependent trends support our interpretation that the observed anisotropic stripe pinning and multi-fold MAR symmetry originate from interfacial exchange coupling. While these thickness-dependent trends are consistent with the proposed interfacial coupling picture, a more comprehensive study with additional samples - particularly structures with sub-unit-cell SRO thicknesses and variable LCO/SRO periodicities - would be needed to fully establish the quantitative relationship between layer thickness, strain state, and magnetic properties, and to rule out alternative explanations such as disorder-induced localization effects.</p>
      </sec>
    </sec>
    <sec id="sec4">
      <title>CONCLUSIONS</title>
      <p>We synthesized LCO/SRO superlattices on STO substrates with various combinations of layer thicknesses using PLD. One-dimensional magnetic stripe-like domains are induced by out-of-plane magnetic field at intermediate strengths (~ 1 T) rather than in-plane field, indicating a strong magnetic anisotropic pinning in these superlattice samples. Field- and temperature-dependent magneto-transport measurements show that these stripe-like domains are associated with elimination of conductivity and exhibits complex combinations of rotation-symmetric components that evolve systematically with experimental conditions. We propose a model of vertically varying noncollinear spin configuration within the SRO layers, where spins reorient from out-of-plane in the bulk interior to in-plane near the interfaces due to strong exchange coupling with LCO. This proposed spin texture provides a consistent explanation for the observed MAR results and micromagnetic simulation results. No skyrmion structures are observed even at 10 T, suggesting that interfacial exchange interaction along with DMI may be insufficient for the appearance of skyrmionic features. Instead, stripe-like domains are stabilized in these superlattice samples. Our results demonstrate that superlattice design can influence emergent magnetic effects, including magneto-transport anomalies and magnetic anisotropy, providing experimental guidance for potential spintronic applications.</p>
    </sec>
  </body>
  <back>
    <sec>
      <title>DECLARATIONS</title>
      <sec>
        <title>Acknowledgement</title>
        <p>We thank the staff members of the SMA System (<uri xlink:href="https://cstr.cn/31125.02.SHMFF.SM2.SMA">https://cstr.cn/31125.02.SHMFF.SM2.SMA</uri>) at the Steady High Magnetic Field Facility, CAS (<uri xlink:href="https://cstr.cn/31125.02.SHMFF">https://cstr.cn/31125.02.SHMFF</uri>), for providing technical support and assistance in data collection and analysis. </p>
      </sec>
      <sec>
        <title>Authors’ contributions</title>
        <p>Experimental design: Huang, H.; Lu, Y.</p>
        <p>Experiments and data collection: Jiang, Z.; Zhao, K.; Meng, W.; Hou, Y.; Cui, Z.; Zhang, J.; Shan, Z.; Lu, Q.</p>
        <p>Theoretical modelling and simulations: Zhang, Z.; Zhao, Y.</p>
        <p>Data analysis: Jiang, Z.; Zhao, K.; Meng, W.; Zhang, Z.; Zhao, Y.</p>
        <p>Manuscript writing and revision: Zhang, Z.; Huang, H.; Lu, Y.</p>
        <p>Supervision: Lu, Y.</p>
      </sec>
      <sec>
        <title>Availability of data and materials </title>
        <p>The data supporting the findings of this study are available within this Article and its <inline-supplementary-material content-type="local-data" mimetype="application/pdf" xlink:href="microstructures6024-SupplementaryMaterials.pdf">Supplementary Materials</inline-supplementary-material>. Further data are available from the corresponding authors upon request.</p>
      </sec>
      <sec>
        <title>AI and AI-assisted tools statement</title>
        <p>During the preparation of this manuscript, the AI tool Kimi (version K2.5, released 2026-01-27) was used solely for language editing. The tool did not influence the study design, data collection, analysis, interpretation, or the scientific content of the work. All authors take full responsibility for the accuracy, integrity, and final content of the manuscript.</p>
      </sec>
      <sec>
        <title>Financial support and sponsorship</title>
        <p>This work was supported by Guangdong Major Project of Basic Research (2025B0303000004), the Natural Science Foundation of Anhui Province (2208085ME113), Hefei National Lab (ZB2025020100), Guangdong Provincial Quantum Science Strategic Initiative (GDZX2501001, GDZX2401003 and GDZX2401004), National Key R&amp;D Program of China (2023YFA1607701, 2024YFA1408101), National Natural Science Foundation of China (51627901 and 12527803) and the support from Station of Quantum Materials. </p>
      </sec>
      <sec>
        <title>Conflicts of interest</title>
        <p>All authors declared that there are no conflicts of interest.</p>
      </sec>
      <sec>
        <title>Ethical approval and consent to participate</title>
        <p>Not applicable.</p>
      </sec>
      <sec>
        <title>Consent for publication</title>
        <p>Not applicable.</p>
      </sec>
      <sec>
        <title>Copyright</title>
<p>&#x00A9; The Author(s) 2026.</p>
</sec>
<sec sec-type="supplementary-material">
      <title>Supplementary Materials</title>
	  <supplementary-material content-type="local-data">
		<media xlink:href="microstructures6024-SupplementaryMaterials.pdf" mimetype="application/pdf">
			<caption>
				<p>Supplementary Materials</p>
			</caption>
		</media>
	  </supplementary-material>

	  </sec>
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