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Topological spin structures have been a topic of considerable research interest since the discovery of magnetic skyrmions1,2. In magnetic thin films with sufficient perpendicular magnetic anisotropy and Dzyaloshinskii–Moriya interaction (DMI), such skyrmions can be stabilized and used as current-driven information carriers. The magnetic meron is another type of topological spin structure3, which is generally in pairs of merons and antimerons, and can be viewed as a skyrmion analogue for in-plane magnetized films4. In-plane magnetized systems are more common than perpendicular magnetized systems, and provide greater material and design flexibility. Thus, there is a growing interest in merons and their potential applications are steadily increasing5,6,7,8. However, methods to construct large-scale and long-range ordered meron lattices remain limited due to their intrinsically complex spin structure. Current techniques require stabilization under low temperature8,9 and/or an external magnetic field10,11 to suppress the detrimental effects of thermal fluctuations.

Recent work has explored the use of spin currents and/or light to control topological spin structures5,12,13,14,15,16. However, the reverse phenomenon—using such topological structures and lattices to control light—is largely unexplored. The first step in such an exploration is understanding how the chirality of topologically protected magnetic quasiparticles transfers to both electrons and photons. This could, in turn, lead to novel applications in fields such as photonics, spintronics and information science.

In this Article, we report the construction of large-scale topological meron lattices that are stable at room temperature and under zero magnetic field. The system is based on a Pd/Fe/MgO trilayer structure fabricated using a high-magnetic-field (HMF)-assisted molecular-beam epitaxy (MBE) approach. The lattices can be used for chirality transfer from magnetic quasiparticles to electrons and then to photons, and we use the meron lattices as spin injectors in nitride-based light-emitting diodes (LEDs). The resulting photoemission of the LEDs is circularly polarized by as much as 22.5%.

Material growth and structural characterization

The stabilization of large-scale meron lattices at room temperature and without a magnetic field requires a strong DMI (that is, an antisymmetric spin-exchange interaction arising from relativistic spin–orbit coupling6) and a highly ordered spin structure. In magnetic thin films, interfacial DMI typically dominates and emerges from the interfaces of heavy metal/ferromagnet or ferromagnet/oxide layers17,18. To obtain a high DMI, we designed a trilayer consisting of a thin Fe film sandwiched by Pd and MgO layers (Pd/Fe/MgO) on an approximately 6 mm × 6 mm gallium nitride (GaN) wafer. Meanwhile, we introduced an HMF during the growth of the Fe film to further break the spatial inversion symmetry and to control the orbital alignment for higher ordering in crystallization and spin (Methods and Extended Data Fig. 1). Thin-film growth under the HMF of up to 9 T was realized by custom-designed MBE equipment (Fig. 1a and Extended Data Fig. 2). In the growth process, vertical magnetic fields with four different magnitudes (0, 2, 6 and 9 T) were exerted at room temperature to take advantage of the exchange interaction between HMF and Fe magnetic moment below the Curie temperature. The morphology of the trilayer was measured using atomic force microscopy (AFM; Extended Data Fig. 3a), and the surface roughness showed an apparent decrease (from 2.21 to 1.85 nm) under an increased-growth magnetic field (Fig. 1b). Two diffraction peaks referring to the {110} and {200} planes of body-centred cubic Fe were detected by grazing-incidence X-ray diffraction (GIXRD; Extended Data Fig. 3b), and the average grain sizes of the Fe films showed a rising trend from 17.03 to 35.68 nm (Fig. 1b), as extracted from the Debye–Scherrer formula. The larger grain size mainly indicated a quality improvement in crystalline Fe (ref. 19), which was also believed to be the reason for the decreased surface roughness of the trilayer. Meanwhile, the intensities of these two peaks were compared with each other, and a raised ratio of IFe{110}/IFe{200} was found with the increasing magnitude of the magnetic field (Fig. 1b). This indicated that the HMF promoted Fe crystallization on an energetically favourable plane.

Fig. 1: Designed equipment and properties of Pd/Fe/MgO samples grown under different magnetic fields.
figure 1

a, Schematic of the designed MBE with in situ HMF. The sample stage was placed at the centre of the tube bore with a maximum magnetic field of 9 T. b, Surface roughness values, GIXRD full-width at half-maximum (FWHM) of Fe{110} and Fe{200}, grain sizes and ratio of IFe{110}/IFe{200}, where IFe{110} and IFe{200} are the intensities of Fe{110} and Fe{200} diffraction peaks, respectively. c,d, Bright-field high-resolution TEM images (top) of samples of 0 T (c) and 9 T (d). Inverse FFT images (middle) and FFT diffraction patterns (bottom) of the Fe films, showing crystallinity in different zones, as marked by the red and blue boxes.

Source data

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The interfacial structures and chemical distributions of the trilayers were observed using transmission electron microscopy (TEM). We focused on the samples constructed under 0 and 9 T fields to gain insights into any structural difference caused by the HMF (Fig. 1c,d). Compared with the 0 T sample, clear interfaces could be seen from the 9 T sample in the high-angle annular dark-field image (Extended Data Fig. 4 shows the measured elemental distributions). The compactness and uniformity of each layer were increased by the HMF owing to the suppressed diffusion of Fe atoms. Moreover, the lattice fringes of the Fe film could be clearly recognized by high-resolution TEM in the 9 T sample but not in the 0 T sample. At the same time, better crystalline quality was found in the 9 T sample, as the fast Fourier transform (FFT) patterns evolved from scatters into grouped spots. From both macro- and micro-observations above, one might infer that a higher ordering in crystallization was achieved within the trilayer by the HMF growth method.

Magnetism characterization

After the structural analyses, the samples were subsequently profiled for their magnetism characterizations. The magnetic hysteresis loops were measured by a vibrating sample magnetometer at room temperature. To ease the illustration, the in-plane and out-of-plane magnetic hysteresis loops were merely displayed for the 0 and 9 T as-grown samples. The saturation magnetizations of the samples (Ms; Fig. 2a,b) were dramatically increased by the HMF during growth, indicating an improvement in the crystalline and spin ordering from a magnetic point of view. Simultaneously, a stronger dominance of in-plane magnetic anisotropy was found from the higher squareness of the in-plane loop. Additionally, the magnetic domains were further characterized by magnetic force microscopy (MFM) at room temperature without an external magnetic field. The configurations of the magnetic domains were clearly impacted by the magnitudes of the magnetic field at sample growth (Fig. 2c). For instance, the domains were shapeless in the 0 T sample. The stripe domains with an apparent periodicity (a period consisting of the coexistence of spin-up and spin-down domains20) started to emerge in the 2 T sample. For the 6 and 9 T samples, the magnetic domains displayed circular textures in pairs (especially, the polarities of the adjacent domains were opposite) (Fig. 2c, white boxes). Moreover, the magnetic moments (S(ri) and S(rj)) located on neighbouring atomic sites ri and rj were non-collinear (that is, the existence of S(ri) × S(rj)). Furthermore, this spin rotation also depended on the strength of the DMI vector Dind following the interaction Hamiltonian21, namely, HDMI = −Dind • (S(ri) × S(rj)). Here Dind was estimated from the frequency shift of the counterpropagating Damon–Eshbach spin waves in the Brillouin light scattering (BLS) measurement (Methods and Extended Data Fig. 5). The magnitude of Dind gradually changed from −0.0731 to −0.4266 mJ m–2 (Fig. 2d) with the enhanced-growth magnetic field. The negative values indicated a left-handed spin chirality22, which was determined by the interaction of the spin–orbit coupling, Hund’s first rule and d orbital23. The increased absolute value of Dind was, thus, attributable to the crystalline ordering improvement of the Pd/Fe/MgO trilayer23 and the enlarged proximity-induced magnetization within the Pd and MgO layers24,25. The observed DMI in the 6 and 9 T samples were strong enough to stabilize topological spin structures because an interfacial DMI value of 0.22 mJ m–2 was able to stabilize skyrmions26. Based on the comprehensive analyses of the strong DMI, the dominant in-plane magnetic anisotropy and the circular magnetic domains in pairs, we confirmed the construction of meron lattices in both 6 and 9 T samples. Encouragingly, this meron lattice was truly large scale, as it could be observed in the majority of areas on the 6 mm × 6 mm wafer (Fig. 2e shows five examples), and it was stable in the condition of room temperature and without an external magnetic field. In addition, the constructed meron lattice was further tested for its time-dependent stability. After 530 days, the meron lattice could still be clearly observed (Fig. 2f).

Fig. 2: Magnetic properties of samples measured at room temperature.
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a,b, Out-of-plane (OP) (a) and in-plane (IP) (b) magnetic hysteresis loops of the samples grown under 0 and 9 T magnetic fields. c, Out-of-plane MFM images at room temperature, where the blue and red colours represent regions with negative and positive out-of-plane components of magnetization, respectively. The white boxes highlighted for the 6 and 9 T samples were the suspected meron pair. d, Relationship between the magnitude of Dind and growth magnetic field. e, Demonstration for the constructed large-scale meron lattice. f, Out-of-plane MFM images of the 9 T sample measured 530 days after the trilayer construction.

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Topology identification and chirality transfer analysis

To further understand the characteristics of the constructed meron lattice, a direct topology identification was conducted by the Lorentz TEM determining the swirling manner of in-plane spin components (Methods). The alternated dark and white contrast indicated the existence of meron pairs27. Periodically arranged meron pairs are observed in Fig. 3a. The in-plane magnetization distribution was reconstructed from the transport-of-intensity equation analysis (Fig. 3b). The topological spin structure in each meron pair consisted of two arrangements with polarities in an opposite way (that is, core-up and core-down for meron and antimeron, respectively), which was in line with the typical Bloch-type meron pair7,27,28. Both Néel and Bloch types are able to exist in magnetic thin films with strong interfacial DMI29, and the dominance of the Néel or Bloch type is dependent on the competition between the interfacial DMI and demagnetization field30. The Lorentz TEM uses the electrons travelling vertically through the whole sample and presents the overall dominated spin texture as the result. The observed result of dominant Bloch-type meron pairs was also confirmed by the micromagnetic simulations based on the experimental parameters of the 9 T sample (Extended Data Fig. 6). The in-plane component of the spin structure in a meron pair and its potential for electron spin modulation were further analysed (Fig. 3c). Two situations were considered when electrons were passing through the topological meron structure. One was the electrons being injected in the in-plane directions (x–y plane), and the transport would theoretically follow the topological Hall effect13,28,31. The other was the injection from the z axis, and the electrons would be deflected by an additional Lorentz force induced by the topological meron without an external magnetic field (Fmeron) following the equations deduced from another work32.

$${{{F}}}_{{{{meron}}}_{{{x}}}}=-\frac{{{\hslash }}}{{{2}}}{v}_{{{\rm{e}}}_{z}}{\bf{S}}({\bf{r}}){{\cdot}}\left[\frac{{{\partial }}{\bf{S}}({\bf{r}})}{{{\partial }}{{y}}}\times \frac{{{\partial }}{\bf{S}}({\bf{r}})}{{{\partial }}{{z}}}\right],$$
(1)
$${{{F}}}_{{{{meron}}}_{{{y}}}}=-\frac{{{\hslash }}}{{{2}}}{v}_{{{\rm{e}}}_{z}}{\bf{S}}({\bf{r}}){{\cdot}}\left[\frac{{{\partial }}{\bf{S}}({\bf{r}})}{{{\partial }}{{z}}}\times \frac{{{\partial }}{\bf{S}}({\bf{r}})}{{{\partial }}{{x}}}\right],$$
(2)

where \({v}_{{{\rm{e}}}_{z}}\) is the electron velocity along the z axis and \({\hslash}\) is the reduced Planck constant. The Fmeron is correlated to the Berry curvature that is inversely proportional to the size of the meron core. It is because the core size of the constructed meron was particularly small, and thus, Fmeron should be sufficient to change the positions of electrons on the x–y plane; the moving trajectories were different in the meron and antimeron areas (Fig. 3d). Also, Fmeron was perpendicular to the direction of the topological spin at all times. In the meron area, Fmeron converged the electrons into the core region, and therefore, these electrons were polarized along the core spin. In the antimeron area, the injected electrons would move along different directions (diverged and converged), and the diverged-direction force would theoretically drive half of the injected electrons of this area to the adjacent meron area. The number of output electrons from these two areas would, thus, be different. Simultaneously, the spin directions of electrons would be differentiated following the S(r) of areas according to Hund’s coupling23. Therefore, the constructed meron lattices could potentially modulate the electron spins with a theoretical spin polarization of up to 50% (Methods provides the calculation details). Meanwhile, the injected electrons would exert a reciprocal Magnus force33 on the meron pairs, which were centrosymmetric within both meron and antimeron areas. The cores of these two areas could still remain static as long as the current density is not too large, and thus, the modulation could be continuous and stable. This modulation capacity could be applied in various scenarios by taking advantage of the non-volatility and resistance against thermal and magnetic fluctuations5.

Fig. 3: Topology identification of spin textures and the trajectory of electrons injecting through the meron lattice.
figure 3

a, Overfocused Lorentz TEM images of meron pairs with alternated dark and white contrast measured under zero magnetic field and at 300 K. Scale bar, 200 nm. b, Schematic of the meron pair and in-plane spin component distributions were deduced from the selected domain region at 300 K by using the transport-of-intensity equation. The colour wheel for the direction of in-plane magnetization is shown in the inset. c, Observed spin structure of a meron pair with two arrangements (antimeron and meron) on the x–y plane, and analysis of Fmeron for electrons injected along the −z direction. The blue and red arrows represented negative and positive out-of-plane components of magnetization. d, Trajectory of electrons injecting through a meron pair. The purple balls with letter ‘e’ were electrons, and the directions of electron spins after injection are illustrated by the purple arrows. The magnetic moment arrangement was consistent along the z axis since the thickness of Fe was less than its exchange interaction length.

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Topology-induced spin LED creation

To verify the electron spin modulation and explore its potential for novel applications, the meron lattice was applied in a photoelectronic scenario. The use of the topological spin structure would be a new route to control the chirality of photon emission, and would differ from existing technologies/materials34,35,36,37. The verification was conducted on a nitride-based LED using the meron lattice in Pd/Fe/MgO trilayer as a spin injector (Methods), and we named the resulting device a topology-induced spin LED (T-LED). The working principle of the T-LED included two physical stages: electron spin polarization induced by the meron lattice and the subsequent radiative transition of spin electrons. The first stage is shown in Fig. 3d, and the second stage is shown in Fig. 4a.

Fig. 4: T-LED at room temperature and without external magnetic field.
figure 4

a, Schematic of the T-LED structure and circularly polarized electroluminescence measurement, the principle of chirality transfer from injected electrons to emitted photons and the optical microscopy image of surface-emitting light. MQWs, CBM and VBM stand for multiple quantum well structures, conduction band minimum and valence band maximum, respectively. b, Circularly polarized electroluminescence spectra of LEDs grown under 0 and 9 T magnetic fields. c, The P values of different LEDs fabricated under four grown magnetic fields. d, Comparison between T-LED and nitride-based spin LEDs from the literature. The T-LED was a surface-emitting geometry, having substantially higher luminous efficiency than that of the edge-emitting geometry due to the anisotropic carrier transition.

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According to the selection rules of electronic transitions, spin-up and spin-down electrons would result in light with the right (σ+)-circular and left (σ−)-circular polarization, respectively, when injected into the LEDs with a quantum well structure38,39,40. Under practical LED working conditions (RT and zero magnetic field) and an applied current of 1 mA, the fabricated T-LEDs emitted a blue light and the circular polarization of electroluminescence was measured. A comparison between LEDs fabricated under 0 and 9 T magnetic fields is displayed in Fig. 4b, where the degrees of electroluminescence circular polarization (P) were calculated from the integrated intensities of the σ+ and σ− emissions35. Owing to the HMF during T-LED fabrication, P was dramatically improved from 0.9% (0 T sample) to 22.5% (9 T sample) (Fig. 4c). The low P value in the 0 T sample was due to the non-topological spontaneous magnetization of Fe. Hence, the observed improvements in T-LEDs made under high-growth magnetic fields were attributed to the modulation of electron spin from the meron lattices. This contribution was confirmed via the negligible out-of-plane magnetic remanence and a comparative trial between LEDs with and without the trilayer (Extended Data Fig. 7).

Meanwhile, the reduced electroluminescence circular polarization in the forced ferromagnetic state further illustrated the dominated contribution from the meron lattice (Extended Data Fig. 8). In addition, a notable improvement in electroluminescence circular polarization was also found between 6 and 9 T, indicating that the performance of T-LED was strongly correlated with the area and order of the meron lattice. The P value of 22.5% is higher than previous reports35,36,37,41,42,43,44 (Fig. 4d) and also corroborates the earlier observation that the constructed meron lattice is large scale in the T-LED. Therefore, the involvement of large-scale topological meron lattices can directly control the chirality of the emitted light and consequently overcome the current limitations of spin LEDs (that is, the weak polarization in practical LED working conditions).

Our T-LED with high circular polarization illustrates the possibility of chirality transfer from topological magnetic quasiparticles to fermions with mass and further to massless bosons. Furthermore, the T-LED has an advanced external quantum efficiency of 16.24% under a working current density of 0.156 A cm–2 (Extended Data Fig. 9). It is ready to be used in three-dimensional displays for device miniaturization and energy conservation, and could potentially be applied in bioimaging and quantum technology.

Conclusions

We have reported the construction of millimetre-scale topological meron lattices that are stable at room temperature and under zero magnetic field. The system is based on a Pd/Fe/MgO trilayer structure that is fabricated using an HMF-assisted MBE technique. The lattices can be used for chirality transfer from topologically protected quasiparticles to electrons and then photons, and we used the lattices to develop topology-induced spin LEDs that can provide 22.5% circularly polarized electroluminescence at room temperature and under zero magnetic field. Our work highlights the practical potential of topological meron lattices, as well as their ability to control spins, electronics and light.

Methods

Theoretical support (first-principles calculations) for using HMF in growth

A previous study reported that the FeNi thin film grown under HMF had fewer surface defects and higher magnetic moment45. Accordingly, the Fe magnetic moments were increased in our calculations to emulate the influences of the growth magnetic field. The Kohn–Sham density functional theory using the Vienna ab initio simulation package46 was applied to study the electronic structures of the Fe film. Also, 1 × 1 × 2 cells of body-centred cubic Fe were adopted for investigation. The generalized gradient approximation parameterized by Perdew–Burke–Ernzerhof47 was utilized to describe the exchange–correlation functional. The Brillouin zone was sampled with an 8 × 8 × 8 Monkhorst–Pack k-point grid centred at the Γ point. The energy and force convergence criteria on each atom were less than 10−6 eV and 0.01 eV Å−1, respectively. The results showed that the increased Fe magnetic moments led to a higher spin polarization on the d orbital (Extended Data Fig. 1a). Meanwhile, the spin charges diffused more widely with the increase in Fe magnetic moment (Extended Data Fig. 1b), which indicated an increasing spin coupling among the Fe atoms. Hence, we aimed to take advantage of the exchange interaction between HMF and d orbital below the Curie temperature to align the ordering of spin structures within the Fe film. The crystalline quality of Fe would be subsequently improved as the s and p orbitals were ordered due to their strong hybridization with the d orbital.

Designed MBE with an in situ HMF and sample growth protocol

A cryogen-free superconducting magnet (Cryomagnetics custom-model 9 Tesla) surrounding a tube bore with a diameter of 100 mm was used to produce the HMF. A controllable shutter and a compact sample stage with 0° to 180° rotatable, heating and variable cooling functions were designed and integrated inside the narrow cylindrical water-cooled chamber. Three Knudsen cells and one plasma source were set at a 600 mm distance below the sample stage to overcome the beam-source angle limitation. The heating wires were alternately winded parallel and antiparallel to the direction of the magnetic field, avoiding the strong Lorentz force of the HMF. The sample stage was thermally isolated from the cryocooling of the superconducting magnet and placed at the centre of the tube bore, with the maximum magnetic intensity of 9 T (Fig. 1a and Extended Data Fig. 2). In addition, a vacuum space was created between the tube bore and superconducting magnet to simultaneously avoid thermal conduction. Ultrathin MgO layers were grown at 473 K with the assistance of an oxygen plasma working at 2.5 × 10−2 Pa. The Fe films were grown under out-of-plane magnetic fields of 0, 2, 6 and 9 T at room temperature to prevent interlayer diffusion. Pd capping layers were deposited under zero magnetic field to prevent oxidation. The thicknesses of the 2, 6 and 9 T samples were similar (1.5, 5.0 and 4.2 nm for the MgO, Fe and Pd layers, respectively). The existence of the meron lattice was influenced by the thickness of the Fe layer, as we tested four thicknesses (2.5, 5.0, 20.0 and 70.0 nm). As shown in Extended Data Fig. 10, the meron lattice could stably exist within the trilayers having an ~5–20-nm-thick Fe layer.

Structural and crystalline characterizations

Surface morphologies of the Pd/Fe/MgO trilayers were scanned using an AFM system (SPA400 NanoNavi). The crystalline structures of ultrathin Fe films were measured by a GIXRD system (Rigaku IV) with Cu Kα radiation (wavelength, λ = 1.5405 Å) and 1° grazing angle. According to the Debye–Scherrer formula (D = k1λ/Bcosθ, where k1 is the Scherrer constant (0.89), θ is the diffraction angle and B is the full-width at half-maximum of the diffraction peaks), the average crystallite size (D) of Fe layers monotonously increased with the HMF. The cross-sectional images of the trilayers were observed by a scanning TEM instrument (Talos F200X) with energy-dispersive spectroscopy analysis. All the FFT and inverse FFT results of the high-resolution TEM micrographs used in this work were calculated by the DigitalMicrograph software (v. 3.7.4).

Magnetic characterization

The magnetic properties of the thin films were measured at room temperature by a vibrating sample magnetometer (MicroSense EZ9) equipped with a 360° rotational stage. Magnetic-domain imaging was performed via MFM using a high-performance cobalt–chromium reflective coating probe in a scanning probe microscope (Bruker Dimension Icon).

The BLS experiments were performed to study the DMI by measuring the frequency shift of the counterpropagating Damon–Eshbach spin waves48. The BLS setup included a single-mode diode pump solid-state laser (wavelength of 532 nm and power of 200 mW) and an external in-plane magnetic field. A six-pass Fabry–Pérot interferometer was employed to analyse the collected backscattered light. The spectra were obtained through the accumulation of photons after several hours, which ensured the accuracy of fitted Stokes (anti-Stokes) peak values. A free spectral range (FSR) of 50 GHz and a 29 multichannel analyser were selected, where the frequency resolution estimated by FSR/29 was less than 0.1 GHz. According to the photon–magnon momentum conservation law in the scattering process, the amplitude of the in-plane wavevector was linked to the incidence light angle (θ) by k = (4π/λ)sin(θ). In this work, k was varied from 0 to 21.4 μm–1. The wavevector dependence of the frequency shift for Stokes and anti-Stokes peaks were measured, and the strength of DMI could be calculated by \(\Delta f=\frac{2\gamma {D}_{{{\rm{ind}}}}}{\uppi {M}_{{\rm{s}}}}k\), where ∆f is the frequency difference in the Stokes (fS) and anti-Stokes (fAS) peaks and γ is the gyromagnetic ratio. The frequency shift, namely, ∆f = | fAS| − | fS|, is determined by fitting the BLS peaks with the Lorentzian function.

Lorentz TEM observations were studied by using a JEOL-2100F instrument, and zero magnetic field was applied during the observation. The magnetic-domain-wall contrast was imaged under the convergent or divergent electron beam, and the under- and overfocused images were recorded by a charge-coupled device camera. Besides, the quantitative in-plane magnetization components were further analysed according to the transport-of-intensity equation49 by the QPt software (HREM Research v.3.1). A substrate selection was conducted in our preliminary experiment, and Si, GaN, Si3N4 and sapphire substrates for Lorentz TEM sample preparation were evaluated. Except for Si3N4, ion thinning of the substrate was required for the observation. It was because the constructed trilayer was very thin, and thus, the preservation of the trilayer could not be guaranteed in the thinned region for TEM after ion thinning. Therefore, a 20 nm Si3N4 membrane was finally selected as the substrate for the trilayer growth and Lorentz TEM observation. The Fe layer within the trilayer was similarly grown under a 9 T magnetic field.

Micromagnetic simulations

Micromagnetic simulations were performed using the GPU-accelerated MuMax3 software50. The simulation model was a square film with 3 µm × 3 µm area under the 5 × 5 × 1 periodic boundary condition. The uniaxial anisotropy constant Ku1 (−0.5 × 105 J m–3), Ms (1.8 × 106 A m–1) and interfacial DMI vector Dind (−0.4266 mJ m–2) were used. These material parameters were acquired from the experimental results. The exchange stiffness Aex was set as 1.0 × 10−11 J m–1. The magnetization was initially set to be randomly distributed and then adequately relaxed by minimizing the total energy of the simulated system.

Hund’s coupling in the meron pair

The Hamiltonian \({\bf{H}}={{h}_{e}}\sum _{ < {\bf{i}},{\bf{j}} > }{{\bf{c}}}_{{\bf{i}}}^{+}{{\bf{c}}}_{{\bf{j}}}+{J}\sum _{{\bf{i}}}{{\bf{S}}}({\bf{r}}_{{\bf{i}}}){\rm{\cdot}}({{\bf{c}}}_{{\bf{i}}}^{+}{\bf{\sigma }}{{\bf{c}}}_{{\bf{i}}})\), where \({{\bf{c}}}_{{\bf{i}}}^{+}\) and ci are the creation and annihilation operators of electrons on site ri, respectively; σ is the vector of Pauli matrices. In addition to the nearest-neighbour electron hopping with amplitude he, the interaction between the electrons and the local spin structure is primarily contributed to Hund’s coupling of electron spins to the magnetization with interaction strength J. In systems having a large positive coupling (J > 0), the electron spin follows the topologically non-trivial spin texture S(ri).

Theoretical limit of spin polarization

The magnitude of spin polarization depends on the velocity and position of the injected electrons and the thickness of the meron lattice. The theoretical limit was assumed, where non-spin-polarized electrons (amount of N) were evenly injected into the meron and antimeron areas, the amounts of spin electrons passing through the meron (core-up) and antimeron (core-down) regions were Nmeron = N/2 + N/4 = 3N/4 and Nantimeron = N/4, respectively. Therefore, the theoretical limit of spin polarization was 50%, as shown in the following formula: \({\rm{Theoretical}}\,{\rm{limit}}=\frac{{N}_{{{\rm{meron}}}}-{N}_{{{\rm{antimeron}}}}}{{N}_{{{\rm{meron}}}}+{N}_{{{\rm{antimeron}}}}}=\frac{\frac{3}{4}N-\frac{1}{4}N}{\frac{3}{4}N+\frac{1}{4}N}=\frac{\frac{1}{2}N}{N}=\frac{1}{2}=50 \%\).

T-LED fabrication and characterization

The LEDs were fabricated via the metal–organic chemical vapour deposition process (Veeco, K465i), laser lift-off and metallic bonding techniques according to our previous work41. Eight periods of InGaN quantum wells were designed for lifting the degeneracy of the heavy-hole and light-hole bands at the Γ point (the thickness of QWs was comparable with the excitonic Bohr radius), which was aimed to suppress the cancellation of optical polarization caused by the overlap of heavy-hole and light-hole transitions with opposite circular polarization signs. The Pd/Fe/MgO trilayer was constructed by the designed MBE above the n-GaN layer of LEDs (Fig. 4a). In the T-LED operation, electrons first passed through the meron lattice and then the n-GaN transport layer before injecting into the multiple quantum wells to emit light. The electron spin diffusion length of n-GaN was generally around 200 nm, and thus, the thickness of the n-GaN transport layer was controlled at 100 nm to suppress spin relaxation51. The circularly polarized electroluminescence spectra were collected with a surface-emitting geometry under a current density of 0.156 A cm–2. The circular polarization of the emitted σ+ and σ− lights was distinguished through a linear analyser placed after a quarter-wave plate. The degrees of electroluminescence circular polarization (P) were determined by the integrated intensities (I) of the emission peaks with σ+- and σ−-circular polarizations, that is, P = \(\frac{{I}_{{{\sigma }}+}-{I}_{{{\sigma }}-}}{{I}_{{{\sigma }}+}+{I}_{{{\sigma }}-}}\).

The electroluminescence efficiency was calculated and presented as external quantum efficiency as per the following equation52: \({{\rm{EQE}}}=\frac{{P}_{{{\rm{free}}}}/hv}{I/e}\), where Pfree is the optical power emitted into free space, I is the injection current, h is the Planck constant, v is the velocity of light and e is the elemental charge. The Pfree value was measured using an integrating sphere by Spectro 320 optical scanning spectrometer (model ISP500-220) with LED-850 TEC temperature control system.