Thermal generation, manipulation and thermoelectric detection of skyrmions

Abstract

The efficient generation, manipulation and detection of magnetic skyrmions are important for the development of future spintronic devices. One approach is to use electric-current-induced spin torques. Recently, thermally induced skyrmion motion has also been observed, but wider experimental evidence and its capabilities remain limited. Here we report the thermal generation, manipulation and thermoelectric detection of nanoscale skyrmions in microstructured metallic multilayers integrated with on-chip heaters. The local application of heat can facilitate a domain morphological transition and the formation of skyrmions at the device edge, where a low energy barrier exists. We observe the unidirectional diffusion of skyrmions from hot regions to cold regions, which is due to the interplay among the repulsive forces between skyrmions, thermal spin–orbit torques, entropic forces and magnonic spin torques. The thermally generated skyrmions can also be electrically detected via the Nernst voltage.

Main

Magnetic skyrmions are particle-like spin textures that have been observed in chiral bulk magnets^1,2,3,4 and asymmetric magnetic multilayers^{5,6,7,8,9,10,11,12,13,14}. Electrical currents and current-induced spin–orbit torques (SOTs) can be used to manipulate skyrmions in various metallic systems^2,7,8,10,14, and such capabilities could be useful in the development of energy-efficient spintronic devices. Thermal effects can also be used to generate and manipulate skyrmions^15,16, which could lead to the development of unconventional computing¹⁷ and energy-harvesting¹⁸ applications. These thermal effects are, however, difficult to be observed in bulk samples and large-area films; therefore, microstructured devices need to be employed. Furthermore, the generation of skyrmions via a pure thermal effect^19,20,21 has not been experimentally demonstrated so far; moreover, whether the skyrmion motion driven by thermal gradients follows the direction of thermal diffusion or, oppositely, the direction of magnonic spin torque^15,20,22,23 remains an open question.

Here we show that nanoscale skyrmions in magnetic multilayers^2,8,10 can be thermally generated; we find that these skyrmions unidirectionally diffuse from hot regions to cold regions. Our microstructured devices are integrated with on-chip heaters that can elevate local temperatures and creating temperature gradients. The application of local heating facilitates the skyrmion generation out of other competing magnetic phases by overcoming the energy barriers^19,20. In our experiments, in particular, a local increase of temperature can overcome the low energy barrier that results in skyrmion generation at the device edge or through a domain morphological transition in the interior of the devices. A temperature-gradient-induced unidirectional diffusion from hot to cold regions is also experimentally observed and theoretically explained through the combined contribution from the repulsive forces between skyrmions, thermal SOTs, magnonic spin torques^15,20,22,23 and entropic forces²⁴. We further thermoelectrically detect these skyrmions by measuring the related anomalous Nernst voltages²⁵. Our results can be useful for studying skyrmions and their dynamics in magnetic metals and insulators^26,27 and may lead to various technologically relevant physics/device concepts to be investigated¹⁷.

Thermal generation of nanoscale skyrmions

We used asymmetric multilayers made of [Ta/Co₂₀Fe₆₀B₂₀/MgO]₁₅, [Pt/Co₆₀Fe₂₀B₂₀/MgO/Ta]₁₅ and [Pt/Co/Ta]₁₅, which are characterized by a monotonic increase in the interfacial Dzyaloshinskii–Moriya interaction (DMI) strengths^8,10,13,21 and damping parameters¹⁰. Magnetometry measurements reveal hysteresis loops that are similar to multilayers hosting either the Néel-type^10,11,13 or hybrid-type^28,29 skyrmions. Because the size of skyrmions in these multilayers is generally smaller than 200 nm, we employed a full-field, soft X-ray transmission microscope (XM-1 at the Advanced Light Source, Lawrence Berkeley National Laboratory¹⁰) with a spatial resolution down to 20 nm. The X-ray approach allows us to study the dynamics of skyrmions induced by a perpendicular magnetic field (μ₀H_⊥), electrical current (j_e), temperature (T) and temperature gradient (∇T(x)), with μ₀ being the vacuum permeability. The magnetic imaging was conducted at the Fe L₃ edge (708.5 eV) in the [Ta/Co₂₀Fe₆₀B₂₀/MgO]₁₅ multilayer and at the Co L₃ edge (778.5 eV) in the [Pt/Co₆₀Fe₂₀B₂₀/MgO/Ta]₁₅ and [Pt/Co/Ta]₁₅ multilayers. Note that the dominant features of the thermal generation of skyrmions in these three multilayers remain the same, indicating that the phenomenology revealed in our experiments is generic in skyrmion-hosting multilayers. We focus on the [Ta/Co₂₀Fe₆₀B₂₀/MgO]₁₅ multilayers, which exhibit the strongest X-ray magnetic circular dichroism contrast and a low-pinning effect^13,17, unless otherwise specified.

We fabricated devices by integrating magnetic multilayers with on-chip heaters and thermometers made of Ta (20 nm)/Pt (50 nm) for both in situ control/measurement of temperatures and anomalous Nernst measurements. These devices were prepared onto insulating Si₃N₄ (thickness, 100 nm) membranes to ensure X-ray transmission imaging. An optical image of the device is shown in Fig. 1a. By applying a pulse voltage (V_h) to the Ta/Pt heater, a local temperature gradient of ∇T(x) is created via heat dissipation in the insulating Si₃N₄ thin layer underneath. The dissipated heat arrives at the multilayer, which could generate skyrmions from different background orderings. Furthermore, the accompanied temperature gradient produces the diffusion of skyrmions and allows the electrical detection of thermally generated skyrmions by measuring the anomalous Nernst voltage (V_ANE) between two contacts. Additionally, symmetric heaters located on both sides of the multilayer enable the directional control of skyrmion generation. The calibrations of temperatures and temperature gradients, as discussed in Supplementary Information Part 8, suggest the existence of quasilinear temperature gradients in the multilayer. For the maximum voltage applied to the Ta/Pt heater, the Oersted field at the multilayer was calculated to be less than 0.22 mT; therefore, its influence on the skyrmion dynamics is negligible. The threshold depinning electrical current at room temperature (below which skyrmions do not move) is estimated to be of the order of J_th ≈ 10⁵ A cm^–2 by applying electrical currents to the multilayers, which is comparable to similar multilayers¹³.

Fig. 1: Thermal generation of skyrmions by using on-chip heaters.

a, Optical image of the integrated device with two identical Ta/Pt heaters on top of a 100-nm-thick Si₃N₄ membrane. The imaged area is marked as a blue circle in the centre of the [Ta/CoFeB/MgO]₁₅ multilayer channel. b, The computed temperature profile is shown in the top left, with a pulse voltage of amplitude V_h = 0.59 V and duration of 100 μs. A linescan of the temperature profile (cyan line) from which a linear temperature gradient in the multilayer can be determined is shown on the bottom left. Right: Temperatures of both the heaters (${T}_{{\mathrm{H}}1,2}^{\mathrm{S}}$) and those at the upper and lower edges of the multilayer channel were computed and labelled as ${T}_{{\mathrm{U}} - {\mathrm{E}}}^{\mathrm{S}}$ and ${T}_{{\mathrm{L}} - {\mathrm{E}}}^{\mathrm{S}}$, respectively. c,d, Transformation from the original stripe domains into densely packed skyrmions after applying a pulse voltage of duration 100 μs and V_h = 0.59 V to the upper heater (H1) under negative (μ₀H_⊥ = −25.6 mT) (c) and positive (μ₀H_⊥ = 25.4 mT) (d) magnetic fields. The white colour corresponds to downward magnetization, while the black colour denotes upward magnetization.

The temperature profile of the whole device on a 100-nm-thick Si₃N₄ membrane (500 × 500 μm²) was computed by the COMSOL Multiphysics software with material-specific parameters, as shown in Fig. 1b. Detailed descriptions are given in the Methods and Supplementary Information. A linescan of the device (cyan line) is shown in the lower side of Fig. 1b, which confirms a varying temperature profile along the x axis. For different voltages V_h applied to the upper heater (H1), the temperatures of both the heaters (${{{T}}_{{\mathrm{H}}1,2}^{\mathrm{S}}}$) and those at the upper/lower edges of the multilayer (${{{T}}_{{\mathrm{U}},{\mathrm{L}} - {\mathrm{E}}}^{\mathrm{S}}}$) were simulated, as shown in the right side of Fig. 1b. From the temperature difference between ${{T}}_{{\mathrm{U}} - {\mathrm{E}}}^{\mathrm{S}}$ and ${{T}}_{{\mathrm{L}} - {\mathrm{E}}}^{\mathrm{S}}$, the linear temperature gradient, ∇T(x), along the x axis in the multilayer can be found. The experimentally measured temperatures of both the heaters (H1,2) agree with the COMSOL simulations.

Representative images of the thermal generation of skyrmions in the [Ta/Co₂₀Fe₆₀B₂₀/MgO]₁₅ multilayers under positive and negative magnetic fields are shown in Fig. 1c,d, respectively. When a pulse voltage of duration 100 μs and amplitude V_h = 0.59 V is applied to the upper heater (H1), the original disordered stripe domains transform into densely packed skyrmions, as shown in Fig. 1c for μ₀H_⊥ = −25.6 mT and Fig. 1d for μ₀H_⊥ = 25.4 mT. Since the skyrmion topological charge ${\it{Q}} = 1/4\uppi {\int} {\bf{m} \cdot \left( {\partial _{\it{x}}{\bf{m}} \times \partial _{\it{y}}{\bf{m}}} \right)} {\mathrm{d}}x{\mathrm{d}}y$ is an odd function of the normalized magnetization m, it switches its sign under reversed external magnetic fields, as evidenced by the opposite colour contrasts shown in Fig. 1c,d. The temperatures at the upper/lower edges are ${{T}}_{{\mathrm{U}} - {\mathrm{E}}}^{\mathrm{S}} = 399.3\,{\mathrm {K}}$ and ${{T}}_{{\mathrm{L}} - {\mathrm{E}}}^{\mathrm{S}} = 392.5\,{\mathrm{K}}$, respectively, and the calculated temperature gradient in the multilayer is ∇T(x) = 1.6 K μm^–1. The diameter of the skyrmion is estimated to be around 140 nm by fitting the skyrmion profile (Supplementary Information Part 3), and the skyrmion density is 6.8 μm^–2. Note that the similar phenomena shown in Fig. 1c,d can also be repeated by using the lower heater (H2) located on the opposite side of the multilayer, as shown in Extended Data Fig. 1.

To resolve the detailed intermediate processes of skyrmion generation, a sequence of smaller pulse voltages was adopted to reduce the generation efficiency. At μ₀H_⊥ = −19.3 mT, stripe domains prevail in the multilayer. Following the increased number of pulses, three distinct behaviours can be identified, as shown in Fig. 2a: (1) nucleation of skyrmions from the hot edge, (2) transformation from the existing stripe domains into isolated skyrmions and (3) the unidirectional motion of thermally generated skyrmions from the hot region to the cold region. Intriguingly, under a saturated ferromagnetic (FM) background, coexisting stripe domains and isolated skyrmions can also be generated near the hot edge and from the interior of the multilayers (presumably around the structural defects with a low energy barrier³⁰), as shown in Fig. 2b. These characteristics can be clearly seen in Extended Data Figs. 1, 2 and 4 and in Supplementary Videos 1–4.

Fig. 2: Transformational dynamics and phase diagram in different multilayers.

a,b, Consecutive images acquired from the [Ta/CoFeB/MgO]₁₅ multilayer at μ₀H_⊥ = −19.3 mT (a) and μ₀H_⊥ = −27.6 mT (b) before and after applying the pulse voltages (duration fixed at 100 μs) to the upper heater (H1), where the computed temperatures at the hot side (${{T}}_{{\mathrm{U}} - {\mathrm{E}}}^{\mathrm{S}}$) can also be found. Images taken before and after applying the following pulse voltages to the heater are shown in a: V_h = 0.514 V (first), V_h = 0.517 V (second), V_h = 0.525 V (third) and V_h = 0.531 V (fourth) at μ₀H_⊥ = −19.3 mT. Images taken after applying the following pulse voltages to the heater are shown in b: V_h = 0.556 V (first), V_h = 0.560 V (second), V_h = 0.571 V (third) and V_h = 0.586 V (fourth) at μ₀H_⊥ = −27.6 mT. While the domains are absent from the original image, skyrmions and stripe domains can also be generated. c, In the [Pt/Co/Ta]₁₅ multilayer, skyrmions can be similarly generated from the hot edge ($436\,{\mathrm{K}} < {\it{T}}_{{\mathrm{U}} - {\mathrm{E}}}^{\mathrm{S}} < 464\,{\mathrm{K}}$), which then propagate from the hot side towards the cold side followed by the growing area of skyrmion lattices. The amplitude of voltages (100 μs) at the hot edges are V_h = 0.682 V (first), V_h = 0.701 V (second), V_h = 0.712 V (third) and V_h = 0.745 V (fourth). d, Dependence of the threshold skyrmion generation temperatures (${{T}}_{{\mathrm{U}} - {\mathrm{E}}}^{{\mathrm{th}}}$) on α at μ₀H_⊥ = 25.4 mT. e, Skyrmion generation rate as a function of ${{T}}_{{\mathrm{U}} - {\mathrm{E}}}^{\mathrm{S}}$ for the [Ta/CoFeB/MgO]₁₅ multilayer. f, Phase diagram summarizing the evolution of different magnetic phases as a function of ${{T}}_{{\mathrm{U}} - {\mathrm{E}}}^{\mathrm{S}}$ and μ₀H_⊥ for the [Ta/CoFeB/MgO]₁₅ multilayer.

Figure 2c shows the thermal generation of skyrmions in the [Pt/Co/Ta]₁₅ multilayer from a fully saturated FM background (μ₀H_⊥ = −47.8 mT). The diameter of skyrmions is around 95 nm in this multilayer owing to the elevated DMI strength. After applying a pulse voltage (duration of 100 μs, V_h = 0.68 V and ${{T}}_{{\mathrm{U}} - {\mathrm{E}}}^{\mathrm{S}} = 436\,{\mathrm{K}}$) across the upper heater (H1), skyrmions are solely generated from the hot edge, which then propagate towards the cold edge upon applying the next pulse voltage. Note that the pinning effect of skyrmions in the [Pt/Co/Ta]₁₅ multilayer is stronger compared with the [Ta/Co₂₀Fe₆₀B₂₀/MgO]₁₅ and [Pt/Co₆₀Fe₂₀B₂₀/MgO/Ta]₁₅ multilayers¹⁰. The representative thermal generation of skyrmions in the [Pt/Co₆₀Fe₂₀B₂₀/MgO/Ta]₁₅ multilayer is also shown in Extended Data Fig. 5. Since both the pinning effect and magnetic damping intimately correlate with structural inhomogeneities or defects, we empirically used the damping parameter (α) as an indicator to show the effect of pinning on skyrmion generation. As shown in Fig. 2d, a monotonic increase in the threshold temperatures $\left( {T_{{\mathrm{U}} - {\mathrm{E}}}^{{\mathrm{th}}}} \right)$ is required to produce densely packed skyrmion phases (μ₀H_⊥ = 24.6 mT). Since a large damping parameter reduces the thermal activation rate of skyrmion crossing the energy barrier, it increases ${{T}}_{{\mathrm{U}} - {\mathrm{E}}}^{{\mathrm{th}}}$. Other factors such as exchange interactions and boundary geometry are also important in determining ${{T}}_{{\mathrm{U}} - {\mathrm{E}}}^{{\mathrm{th}}}$, which requires further investigations.

To quantify the skyrmion generation rate as a function of pulse duration and amplitude, the total number of skyrmions was counted. When $375\,{\mathrm{K}} < {{T}}_{{\mathrm{U}} - {\mathrm{E}}}^{\mathrm{S}} < 385\,{\mathrm{K}}$ (intercept at the x axis), the increased ${{T}}_{{\mathrm{U}} - {\mathrm{E}}}^{\mathrm{S}}$ results in a linear increase in the skyrmion generation rate by 27 K^–1, as shown in Fig. 2e. The intercept at 375 K indicates the threshold temperature at which a substantial number of skyrmions are generated after applying a pulse voltage with a duration of 100 μs. A phase diagram summarizing the evolution of stripe domains, coexisting stripe domains and skyrmions, densely packed skyrmion lattice, and saturated FM states as a function of the magnetic field and temperature of the hot edge (${{T}}_{{\mathrm{U}} - {\mathrm{E}}}^{\mathrm{S}}$) for the [Ta/Co₂₀Fe₆₀B₂₀/MgO]₁₅ multilayer is shown in Fig. 2f. A similar phase diagram for the magnetic fields and pulse durations (fixed amplitude V_h = 0.53 V) is shown in Extended Data Fig. 6. In both phase diagrams, four different magnetic phases can be clearly distinguished. When the magnetic fields are small (|μ₀H_⊥| < 10 mT), an increase in ${{T}}_{{\mathrm{U}} - {\mathrm{E}}}^{\mathrm{S}}$ only results in a configurational change in the stripe domains. This is due to the fact that the skyrmion phase is locally unstable under weak magnetic fields. When |μ₀H_⊥| > 10 mT, thermal fluctuations in the range of $375\,{\mathrm{K}} < {{T}}_{{\mathrm{U}} - {\mathrm{E}}}^{\mathrm{S}} < 397\,{\mathrm{K}}$ produce a coexisting phase of the stripe domains and sparsely distributed skyrmions. This can be attributed to the stochastic nature of the thermally assisted skyrmion nucleation by overcoming the energy barrier separating the skyrmion and stripe phase. When ${{T}}_{{\mathrm{U}} - {\mathrm{E}}}^{\mathrm{S}} > 397\,{\mathrm{K}}$, thermal fluctuations further promote the nucleation of skyrmions and the system enters into a densely packed skyrmion lattice state. When |μ₀H_⊥| > 45 mT, the system remains in the FM state in the experimentally accessible temperature range, which indicates that the FM state is the globally stable state in this field region³¹.

Unidirectional diffusion of skyrmions

When skyrmion generation is efficient at the hot edge, there exists an increased repulsive force between the newly generated skyrmions and the existing skyrmions. This naturally results in the unidirectional motion of skyrmions from the hot region to the cold region. However, this unidirectional diffusion can also be attributed to the competition among the entropic forces²⁴, magnonic spin torques^{15,20,22,23,32} and thermal SOTs¹⁸. To quantify the contribution from these mechanisms, we designed a nanowire pointing to the heater. Skyrmion generation at the hot end is minimized due to the tip-like geometry, as shown in Fig. 3a. In fact, the implementation of this type of device may enable a single skyrmion to be generated in a controllable manner. Additionally, skyrmion generation can be suppressed if the temperature at the tip $\left( {{{T}}_{{\mathrm{U}} - {\mathrm{E}}}^{\mathrm{S}}} \right)$ can be made lower than the threshold temperature for skyrmion generation $\left( {{{T}}_{{\mathrm{U}} - {\mathrm{E}}}^{{\mathrm{th}}}} \right)$, as shown by the phase diagram in Fig. 2f. After applying pulse voltages of duration 500 ms and amplitudes in the range of 0.18–0.23 V (corresponding to $338\,{\mathrm{K}} < T_{{\mathrm{U}} - {\mathrm{E}}}^{\mathrm{S}} < 365\,{\mathrm{K}}$) to the heater, the thermal generation of skyrmion is completely suppressed. The resulting unidirectional diffusion driven by the temperature gradients along the nanowire is clearly observed, where ∇T(x) is in the range of 0.35–0.56 K μm^–1, as shown in Fig. 3a. Note that a few skyrmions annihilate when a larger ∇T(x) is applied. During the diffusion, sparsely distributed skyrmions align in the centre of the [Ta/Co₂₀Fe₆₀B₂₀/MgO]₁₅ nanowire, which can be clearly seen from the stochastic trajectory shown in Fig. 3a(8). This occurs as a result of the balanced skyrmion-edge interaction from both the edges³³. These results also suggest the presence of Brownian-like diffusion¹⁷. By taking the ratio between the displacements and pulse durations, the diffusion velocity can be calculated, as shown in Fig. 3a(9). The observed nonlinear velocity and absence of the skyrmion Hall effect^34,35 are consistent with the stochastic nature of skyrmion diffusion. Nevertheless, our experiments clearly show that the thermal diffusion of skyrmions is dominant over the opposite motion driven by magnonic currents^20,22,23,36.

Fig. 3: Experimental demonstration of thermally induced skyrmion diffusion and analytical understandings of skyrmion generation and diffusion.

a(1), Scanning electron microscopy image. (2)–(7), Following the increased temperature gradients (duration is fixed at 500 ms), unidirectional diffusion of skyrmions from the hot region to the cold region is observed in a device with a sharp tip made of the [Ta/CoFeB/MgO]₁₅ multilayer. (8),(9), Diffusion trajectory and velocity (v_D) of the selected skyrmions. Note that skyrmions with different dynamics are marked by squares, circles and a hexagon, where different colours are used to represent different skyrmions. The annihilated skyrmions in the larger temperature gradients are marked by squares. A pinned skyrmion is marked using a magenta hexagon. Those skyrmions diffusing from the hot region to the cold region are marked by circles. b, Micromagnetic simulation results. Following the increasing number of frames (p₀, p₆, p₂₃, p₅₃ and p₉₈), skyrmions are first nucleated at the hot edge, followed by directional motion from the hot region to the cold region. The time lapse between the consecutive frames is $\Delta {\it{t}} = 120{\it{J}}_{{\mathrm{ex}}}/\gamma {\it{D}}^2$. The coefficient of temperature gradient is k = 0.01J_ex/k_B. The film thickness is d = 0.1J_ex/D. The scale bar is 20J_ex/D. c,d, The integrated skyrmion probability ($P$) distributions as a function of the position (J_ex/D) at different times (t) obtained by solving the Fokker–Planck equation are shown for a drift velocity of F_m = 0.2 (c) and F_m = 0 (d). In the calculations, we use the absorbing boundary condition at x = 0 by setting $P\left( {x = 0} \right) = 0$ at the cold side and $\partial _x P\left( {{\it{x}} = {\it{L}}_x} \right) = 0$ at the hot side. The length (L_x) is in the unit of J_ex/D and time is in the unit of 4πd/γD.

Theory on skyrmion generation and diffusion

All the aforementioned experimental observations can be well addressed in a unified theoretical setting as follows. In our multilayer, competing metastable phases exist: stripe domains, mixture of stripe domains and skyrmions, skyrmion lattices, and saturated FM states. Near the (hot) edge, skyrmions can be generated without meeting any singularity. Together with the twisted edge spins induced by the unbalanced interfacial DMI^30,37, the energy barriers for skyrmion generation are relatively low. Local heating at the edge could, therefore, efficiently facilitate skyrmion generation from different magnetic phases. Our calculations based on the statistical rate theory³⁸ and Monte Carlo simulations given in the Supplementary Information confirm that the edge is the dominant source of skyrmion generation. Note that skyrmions can also be generated from the structural defects in the interior of the multilayers and by the coalescence of the stripe domains³⁹, which also exhibit low energy barriers.

Our experiments can be numerically reproduced by solving the stochastic Landau–Lifshitz–Gilbert equation in the presence of temperature gradients. In our micromagnetic simulations, other sources that could influence the dynamics of skyrmions, including the thermal spin Hall effect, magnonic spin torques arising from thermally excited magnons^20,22,23 and repulsive interaction between the skyrmions are taken into account. The system Hamiltonian reads as ${\cal{H}} = J_{\mathrm{ex}}/2\left( {\nabla S} \right)^2 + D\left[ {S_{\mathrm{z}}\left( {\nabla \cdot {\mathbf{S}}} \right) - \left( {{\mathbf{S}} \cdot \nabla } \right)S_{\mathrm{z}}} \right] - {\mathbf{H}}_{\mathrm{a}} \cdot {\mathbf{S}}$, where J_ex is the strength of the exchange interaction; D, the interfacial DMI parameter; and H_a, the perpendicular magnetic field. The equation of motion for spins (S) can be written as follows:

$$\partial _t{\mathbf{S}} = - \gamma {\mathbf{S}} \times \left( {{\mathbf{H}}_{{\mathrm{eff}}} + {\mathbf{h}}_{\mathrm{n}}} \right) + \alpha {\mathbf{S}} \times \partial _t{\mathbf{S}},$$

(1)

where γ is the gyromagnetic ratio, ${\mathbf{H}}_{{\mathrm{eff}}} = - \delta {\cal{H}}/\delta {\mathbf{S}}$ is the effective field and h_n is the random thermal fluctuating field at T(x) = kx. The choice of k is to ensure that the temperature at the hot edge (${{{T}}_{{\mathrm{U}} - {\mathrm{E}}}^{\mathrm{S}}}$) is comparable to the energy barrier U_B, such that appreciable numbers of skyrmions can be generated in the hot region in the timescale of the simulations. Using the saturated FM state as the initial state, the thermal generation of skyrmions from the hot edge of the devices can be seen, which is followed by unidirectional diffusion towards the cold region, as shown in Fig. 3b. If periodic stripe domains were used as the initial state instead, similar phenomena together with a morphological transition from the stripe domains to the isolated skyrmions were identified, as in Extended Data Fig. 7. In both cases, the multilayer is eventually filled with densely packed skyrmions. Once the temperature at the hot side is reduced, skyrmion nucleation is suppressed, and our simulation reproduces the thermal diffusion of skyrmions driven by the temperature gradient indicated in Fig. 3, as shown in Extended Data Fig. 8. Calculations performed by considering material-specific parameters and by taking into account the magnetostatic field added to the effective field of equation (1) show qualitatively similar results⁴⁰.

By assuming that skyrmion diffusion is much faster than the rate of skyrmion generation, the skyrmion–skyrmion repulsive interaction can be neglected. In this case, the thermal diffusion of a skyrmion driven by temperature gradients can be studied (as experimentally shown in Fig. 3a). After establishing the local thermal equilibrium with linear T(x), the thermal generation and subsequent diffusion of skyrmions can be described by the Fokker–Planck equation in dimensionless units as follows^20,23:

$$\partial _t P + \partial _x\left[ {F_{\mathrm{m}} P} \right] - G_{xx}\partial _x\left( {T\partial _x P} \right) = \omega _{\mathrm{s}}{\mathrm{exp}}\left[ { - \frac{{U_{\mathrm{B}}}}{{k_{\mathrm{B}}T}}} \right],$$

(2)

where P(x) is the probability of finding skyrmions at time t and position x. The second term on the left side describes the average drift velocity (F_m) of the skyrmion due to the magnonic spin torque and spin torque generated by thermoelectric currents, which competes with the pinning force due to defects. The third term on the left side describes the diffusion of skyrmions, where G_xx denotes the gyrotropic coupling component. The term on the right side of equation (2) corresponds to the thermal activation of skyrmions, where U_B denotes the energy barrier and ω_s denotes the attempt frequency. In the regime $k_{\mathrm{B}}T \ll U_{\mathrm{B}}$, skyrmion nucleation is greatly suppressed. Under a small temperature gradient, $F_{\mathrm{m}} P \gg G_{xx}T\partial _x P$. When the pinning is weak, free drift of the existing skyrmions can be enabled, and the direction of motion depends on the relative strength of the magnonic spin torque and SOT of thermoelectric currents.

When k_BT is comparable with U_B, the thermally assisted skyrmion generation becomes important. Subsequently, the dynamics is governed by the diffusion of skyrmions from the hot region to the cold region. As a clear demonstration, the time evolution of skyrmion densities for different amplitudes, namely, F_m = 0.2 and F_m = 0, is calculated and shown in Fig. 3c,d, respectively. It is evident that skyrmions can be thermally nucleated at the hot edge regardless of the choice of magnonic spin torque and spin torques from the thermoelectric current (F_m ≥ 0) and subsequently diffuse through the whole system with a gradient in the density, as indicated by the integrated probability for skyrmion distribution. Note that an intuitive picture of skyrmion diffusion driven by temperature gradients can be derived by treating skyrmions as rigid particles. The entropy of skyrmions in the hot region is larger than that in the cold region. The thermalization condition requires the balance of entropy, and therefore, skyrmions tend to move to the cold region to balance the entropy gradient. Effectively, skyrmions experience a force associated with the entropy gradient^24,41. This entropic force—together with the magnonic spin torque, repulsive force between skyrmions and pinning force—produces the skyrmion motion from the hot region to cold region.

Thermoelectric detection of skyrmions

The presence of skyrmions could affect the dynamics of conduction electrons^2,4. One well-known example is the anomalous Nernst effect (ANE)^18,42, where the Nernst voltage is expressed as $V_{\mathrm{ANE}} \propto M_{\mathrm{z}} \nabla T\left( x \right)$ and M_z represents the perpendicular magnetization which can be varied by the change in the total number of skyrmions. This motivates the electrical detection of thermally generated skyrmions using the same type of device shown in Fig. 1a. Note that skyrmions contribute to the Nernst voltage through both their magnetization and topology . The skyrmion diffusion could also produce a topological Nernst voltage, but it is expected to be much smaller^43,44. By referring to the resistance–current (R–I_heater) and resistance–temperature (R–T) curves of both the heaters (H1,2), the corresponding temperatures can be experimentally determined (labelled as ${{T}}_{1,2}^{\mathrm{M}}$), which are consistent with our COMSOL simulations. The temperature differences between ${{T}}_{{\mathrm{U}} - {\mathrm{E}}}^{\mathrm{S}}$ and ${{T}}_{{\mathrm{L}} - {\mathrm{E}}}^{\mathrm{S}}$, therefore, determine the temperature gradients ∇T(x) across the multilayer, as shown in Fig. 4a,b. For ∇T(x) = ±2.8 K μm^–1 generated by either the upper (H1) or lower (H2) heater, opposite signs of voltages can be observed, as shown in Fig. 4c. More ANE data are shown in Extended Data Fig. 9.

Fig. 4: Electrical detection of skyrmions via the ANE.

a,b, Combined with the COMSOL simulations and experimental measurements, the temperatures (a) and corresponding temperature gradients ∇T(x) (b) for the device are determined. The simulated (line)/measured (dot) temperatures of both the heaters are accordingly labelled as $T_{1,2}^{\mathrm{S}}/{{T}}_{1,2}^{\mathrm{M}}$. Error bars are determined from the standard deviation of five repetitive experiments. c, Opposite anomalous V_ANE measured with the opposite temperature gradients (∇T(x) = ±2.8 K μm^–1). d, At μ₀H_⊥ = 25 mT, after switching off I_heater = 6 mA, a smaller current I_heater = 3 mA that generates ∇T(x) = 0.9 K μm^–1 is applied to measure the time evolution of V_ANE, where several ‘quantized’ jumps with ΔV_ANE = 90 ± 10 nV can be found. After saturating the sample above μ₀H_⊥ = 500 mT and reducing the field back to μ₀H_⊥ = 25 mT, V_ANE falls back to the same value as before applying I_heater = 6 mA in which the ‘quantized’ jumps are absent. e, The corresponding I_Heater as a function of time used for the ANE measurement in d.

At fixed ∇T(x) and constant μ₀H_⊥, the change in V_ANE reflects the change in magnetization and hence the total skyrmion numbers. To demonstrate the electrical detection of a single skyrmion, we first applied a large current I_heater = 6 mA $\left( {{{T}}_{{\mathrm{U}} - {\mathrm{E}}}^{\mathrm{S}} = 428\,{\mathrm{K}} > {{T}}_{{\mathrm{U}} - {\mathrm{E}}}^{{\mathrm{th}}}} \right)$ to generate skyrmions and initiate their diffusion. Then, V_ANE was measured under a smaller current of I_heater = 3 mA to maintain ∇T(x) = 0.9 K μm^–1, where no new skyrmions were generated during the measurement $\left[ {\left( {{{T}}_{{\mathrm{U}} - {\mathrm{E}}}^{\mathrm{S}}\left( {325\,{\mathrm{K}}} \right) < {{T}}_{{\mathrm{U}} - {\mathrm{E}}}^{{\mathrm{th}}}\left( {375\,{\mathrm{K}}} \right)} \right)} \right]$. The time-dependent V_ANE measured at μ₀H_⊥ = 25 mT is shown in Fig. 4d and the corresponding current profile is shown in Fig. 4e. Right after switching to the current of I_heater = 3 mA, V_ANE decreases sharply, signifying the reduction in the total number of skyrmions and/or change in the magnetization configuration. Interestingly, we observed many discretized steps in the time evolution of V_ANE, where a change in V_ANE is discretized by ΔV_ANE = 90 ± 10 nV. Each discretized jump can be naturally explained by the annihilation of a single skyrmion in the multilayer, which results in a change in M_z as thermal equilibrium approaches⁴⁵. Compared with our micromagnetic simulations shown in Extended Data Fig. 8 and diffusion dynamics in Fig. 3a, we conclude that these discretized jumps, |V_ANE|, correspond to the disappearance of a single skyrmion, probably through sample edges or structural defects in the interior of the device. Our experiments, therefore, confirm that the ANE can be used for the thermoelectric detection of a single skyrmion in similar multilayers⁴⁶.

Conclusions

We have demonstrated the on-chip thermal generation, manipulation and thermoelectric detection of nanoscale skyrmions in metallic multilayers. By applying thermal gradients in devices with on-chip heaters, we observed the unidirectional diffusion of skyrmions from hot regions to cold regions. This effect can be attributed to a combination of repulsive forces between the skyrmions, entropic forces, magnonic spin torque and thermal SOTs. Further, single skyrmions could be thermoelectrically detected via the ANE, as shown by the discretized jumps in the Nernst voltages. Our approach could potentially be integrated with existing electrical manipulation schemes to study the different types of topological spin textures in various FM and ferroelectric materials^27,47,48,49. In particular, our approach could find applications in platforms based on insulating skyrmion-hosting materials, where electrical currents cannot be applied^26,27. Based on the Onsager reciprocal relation, the interacting thermal currents and skyrmion lattices could also be relevant to the topological phenomena, including the topological magnon Hall effect and thermally induced skyrmion Hall effect^4,25. Thus, the thermal generation, manipulation and thermoelectric detection of skyrmions could possibly trigger future discoveries in skyrmionics^3,4,12 and spin caloritronics¹⁸.

Methods

Interfacially asymmetric multilayers of [Ta (30 Å)/Co₂₀Fe₆₀B₂₀ (11 Å)/MgO (20 Å)]₁₅, [Pt (20 Å)/Co₆₀Fe₂₀B₂₀ (11 Å)/MgO (14 Å)/Ta (10 Å)]₁₅ and [Pt (15 Å)/Co (10 Å)/Ta (5 Å)]₁₅ were grown onto semi-insulating Si substrates covered with a 300-nm-thick thermally formed SiO₂ layer and onto 100-nm-thick insulating Si₃N₄ membranes on top of Si supporting frames. These films were made by using a d.c. magnetron sputtering system (AJA, Orion 8) at room temperature under Ar pressure of 3 mtorr with a base pressure of <2 × 10⁻⁸ torr. The Si₃N₄ membranes (electrical resistivity, ~10¹⁵–10¹⁶ Ω cm) used in this study were obtained from YW MEMS (Suzhou). Multilayer channels on the Si₃N₄ membranes were first patterned by using electron beam lithography and followed by a lift-off process, which were annealed in a vacuum for 30 min to induce the perpendicular magnetic anisotropy. Subsequently, Ta (20 nm)/Pt (50 nm) electrodes were deposited. A Quantum Design superconducting quantum interference device magnetometer was used to measure the magnetic properties. Damping parameters in the multilayers were determined from ferromagnetic resonance. To probe the dominant out-of-plane X-ray magnetic circular dichroism contrast, samples on the Si₃N₄ membrane for X-ray magnetic circular dichroism imaging were positioned with the plane normal to the incident circularly polarized X-ray beam. Note that the typical imaging acquisition time of a single frame is approximately 60 s, which is faster than the intrinsic domain dynamics; therefore, we probed the morphological changes in the domains before and after applying the pulse voltages to the heater. The best magnetic contrast is obtained at the Fe L₃ edge of 708.5 eV for the [Ta/Co₂₀Fe₆₀B₂₀/MgO]₁₅ multilayer. Due to the lower (absent) content of Fe and the corresponding weak signal, the magnetic contrasts for the [Pt/Co₆₀Fe₂₀B₂₀/MgO/Ta]₁₅ and [Pt(15Å)/Co(10Å)/Ta(5Å)]₁₅ multilayers were obtained at the Co L₃ edge of 778.5 eV. Voltage pulses supplied to the on-chip heaters were provided by an Agilent 81150A arbitrary waveform generator and monitored with a 50-Ω-terminated real-time oscilloscope, through which the current flowing in the heater could be calculated. Note that for the anomalous Nernst measurement, the length of the multilayer channel is 30 μm.

Temperature calibration for both the heaters was performed by first measuring the resistance change in the heaters as a function of the current/voltage; by comparing the temperature-dependent resistance changes, temperatures at both the heaters can be determined. The presence of constant temperature gradients is further confirmed through the anomalous Nernst measurement. The presence of quasilinear temperature gradients in the sample is also experimentally verified and discussed in Supplementary Information Part 8. Temperature profiles of the devices were simulated by using COMSOL Multiphysics software. We implemented a combined ‘Joule heating’ module, which includes the ‘AC/DC’ module to apply the pulse voltages and the ‘heat transfer’ module to describe the heat flow and temperature distribution. The simulation area was within the 500 µm × 500 µm Si₃N₄ (thickness, 100 nm) membrane window, with the boundary condition fixed at 293 K. For the heaters and electrodes, the following material parameters for Pt are used: thickness of 70 nm and electrical conductivity of 8.9 × 10⁶ S m^–1. The multilayer channels were simplified as follows: [Ta (15 nm)/Co₂₀Fe₆₀B₂₀ (5.5 nm)/MgO (10 nm)]₃, [Pt (10 nm)/Co₆₀Fe₂₀B₂₀ (5.5 nm)/MgO (9 nm)/Ta (5 nm)]₃ and [Pt (7.5 nm)/Co (5 nm)/Ta (2.5 nm)]₃ to save the simulation time. All the parameters including density ρ, specific heat capacity C_ρ, thermal conductivity κ and electrical conductivity σ used in the COMSOL simulations are shown in Supplementary Table 1 of Supplementary Information. Micromagnetic simulation studies were independently carried out using a home-built code and by using a state-of-the-art micromagnetic solver, PETASPIN: a complete description can be found in the Supplementary Information.

Extended data

Extended Data Fig. 1 Skyrmion generation and propagation in the [Ta/Co₂₀Fe₆₀B₂₀/MgO]₁₅ multilayer by using the lower heater.

At opposite magnetic fields, by applying pulse voltages (duration fixed at 100 μs) into the lower heater (H2), thermal generation of skyrmions, together with their subsequent propagation towards the cold side (upper side) are realized.

Extended Data Fig. 2 Skyrmion generation and propagation in the [Ta/Co₂₀Fe₆₀B₂₀/MgO]₁₅ multilayer at positive magnetic fields (+μ₀H_⊥) by using the upper heater.

At different positive magnetic fields, by applying pulse voltages (duration fixed at 100 μs) into the upper heater (H1), the thermal generation of skyrmions, together with the propagation towards the cold side are evident. The experimentally utilized parameters and the estimated temperatures at the upper edge (hot side) are also listed.

Extended Data Fig. 3 Domain morphological transition in the [Ta/Co₂₀Fe₆₀B₂₀/MgO]₁₅ multilayer at smaller magnetic fields by using the upper heater.

At smaller (positive/negative) magnetic fields and by applying pulse voltages (duration fixed at 100 μs) into the upper heater, thermally induced domain morphological transition is observed.

Extended Data Fig. 4 Skyrmion generation and propagation in the [Ta/Co₂₀Fe₆₀B₂₀/MgO]₁₅ multilayer by changing the pulse duration via the upper heater.

By increasing the duration of pulse voltages (amplitude is fixed at V_h= 0.526 V) in the upper heater, thermal generation of skyrmions and their propagation towards the cold side (lower edge) are observed.

Extended Data Fig. 5 Skyrmion generation and propagation in the [Pt/Co₆₀Fe₂₀B₂₀/MgO/Ta]₁₅ multilayer by using the upper heater.

At opposite magnetic fields, by applying increased amplitudes of pulse voltages (duration fixed at 300 μs) into the upper heater, thermal generation of skyrmions, together with their subsequent propagation towards the cold side are realized.

Extended Data Fig. 6 The phase diagram of skyrmion generation at different pulse durations in the [Ta/Co₂₀Fe₆₀B₂₀/MgO]₁₅ multilayer.

a, The response of competing magnetic phases to different pulse durations (with a fixed amplitude V_h = 0.526 V) and magnetic fields. b, The dependence of the maximum temperatures at the upper (hot) edge $\left( {T_{{\mathrm{U}} - {\mathrm{E}}}^{\mathrm{S}}} \right)$ on the pulse duration (t_pulse). The nonlinear increase of ${\mathrm{T}}_{{\mathrm{U}} - {\mathrm{E}}}^{\mathrm{S}}$ following the increase of pulse duration can be attributed to the fast dissipation of heat through substrate. c,d, Following the continuous increase of pulse duration above 4 ms, the system approaches thermal equilibrium with a constant temperature at the hot edge $\left( {{\mathrm{T}}_{{\mathrm{U}} - {\mathrm{E}}}^{\mathrm{S}} = 496K} \right)$ (c) and a constant temperature gradient in the multilayer ∇T(x) = 1.3 K μm^-1 (d).

Extended Data Fig. 7 Micromagnetic simulation results of transformation from stripe domains to densely packed skyrmion lattices driven by temperature gradients.

Following the increasing time, presented as the number of frames (1, 30, 100, 200, 300, 400), skyrmions are first nucleated at the hot edge, followed by the immediate thermal diffusion from the hot side towards the cold side. Meanwhile, skyrmions are also generated by breaking the stripe domains followed by relaxation in the hot side. The diffusion of skyrmions then pushes the stripe domains out of the simulation box. The time lapse between consecutive frames is $\Delta t = 60J_{{\mathrm{ex}}}/\gamma D^2$. The temperature gradient is $k = 0.01J_{{\mathrm{ex}}}/k_B$ and ${\it{H}}_a = 0.6{\it{D}}^2/{\it{J}}_{ex}$. Here we assume the film thickness is 0.1J_ex/D. The scale bar is 20J_ex/D. The open (periodic) boundary condition is used in the horizontal (vertical) direction.

Extended Data Fig. 8 Micromagnetic simulation results of the diffusion of skyrmions purely driven by temperature gradients.

The micromagnetic simulation of skyrmion diffusion in a nanowire geometry is performed by using the open boundary condition. First, skyrmions are thermally generated at high temperature side using a larger temperature gradient. Subsequently, the temperature gradient is reduced to avoid the nucleation of skyrmions at the hot side, which results in the diffusion of skyrmions towards the cold side. Some skyrmions exit the nanowire through the sample edge during the diffusion. The length and width of the nanowire are 120J_ex/D and 40J_ex/D, respectively. The thermal gradient for diffusion is k = 0.008J_ex/k_B. Disorders in spin anisotropy are introduced to suppress the magnonic spin torque by reducing the magnon mean free path. Here we assume the film thickness is 0.1J_ex/D. The scale bar is 10J_ex/D.

Extended Data Fig. 9 Anomalous Nernst effect measured under different temperature gradients in the [Ta/Co₂₀Fe₆₀B₂₀/MgO]₁₅ multilayer.

a, The evolution of anomalous Nernst voltages (V_ANE) measured with different currents supplied into the heater (I_Heater). b, Following the increase of I_Heater, a parabolic increase of saturated V_ANE(μ₀H_⊥ = 100mT) can be found. c, The evolution of V_ANE(μ₀H_⊥ = 100 mT) as a function of ∇T(x). d, The time evolution of V_ANE measured at a fixed I_Heater = 3 mA and μ₀H_⊥ = 25 mT, after switching off skyrmion generation currents (from 3.5 mA to 6 mA in 0.5 mA steps). Upon removing the increased DC currents used for generating skyrmions, discretized steps are gradually resolved. e, The corresponding I_Heater as a function of time used for the ANE measurement in d.