A fluctuation-free pathway for a topological magnetic phase transition

Abstract

Topological magnetic textures are particle-like spin configurations stabilized by competing interactions. Their formation is commonly attributed to fluctuation-driven, first-order nucleation processes requiring activation over a topological energy barrier. Here, we demonstrate an alternative barrier- and fluctuation-free pathway for nucleating topological magnetic textures, triggered in our experiments by an excitation-induced spin reorientation transition. By combining x-ray imaging, scattering and micromagnetic simulations, we show that the system follows a deterministic cascade of symmetry-breaking phase transitions after excitation. First, the system undergoes a second-order phase transition from a homogeneous state to weak stripe domains, then a first-order transition to topologically trivial bubbles, and finally a topological switching event into skyrmionic textures. Through simulations, we generalize our findings and demonstrate that this pathway is active in a vast range of low-anisotropy materials. This previously unrecognized, spontaneous transition pathway suggests strategies for rapid, low-energy generation of topological spin textures and points to a general role of intrinsic modulational instabilities in phase transitions beyond magnetism.

Figures (19)

• Figure 1: Evidence of spin-reorientation-transition-mediated topological switching.a-c, Scanning transmission x-ray microscopy images of magnetic states in a double-gradient magnetic multilayer before (a), during (b), and after (c) quasi-static heating of the material. Insets: SAXS patterns of the cocoon-hosting single-gradient section of the material during the same process. The SAXS signal in (b) has been multiplied by a factor 10 to improve visibility. d, Temperature-dependence of the interfacial magnetic anisotropy $K_\mathrm{s}$ and saturation magnetization $M_\mathrm{s}$ of our materials. The pink arrows are a guide to the eye, exemplifying the change of the micromagnetic parameters during a thermal excitation pulse to a transient pseudo-temperature $\Theta_\mathrm{p}$. See \ref{['sec:Methods']} for details. e-g, Micromagnetic simulation of the thermal excitation process from room temperature to a maximum transient pseudo-temperature $\Theta_\mathrm{p}$, akin to the one displayed in (a-c). Isosurfaces display the normalized out-of-plane magnetization $m_z={M_z}/{M_\mathrm{s}}$. Blue: $m_z=+0.5$, white: $m_z=0$, red: $m_z=-0.5$. The plot on the side displays the layer-dependent quality factor $Q$ of a typical double-gradient magnetic multilayer at room temperature.
• Figure 1: Spontaneous cocoon nucleation during field cycling Out-of-plane hysteresis loop of a double-gradient multilayer, acquired with FTH. Skyrmions (darker spots) nucleate in a few sparse centers, likely associated with material defects. Cocoons (lighter spots) nucleate in dense lattices. The labels report the current applied to the electromagnet, proportional to the out-of-plane field applied to the sample. An exact calibration of the externally applied field is not available for this measurement. The sample structure is $d_0=1.6\nm$, $N_\text{SG}=13$ layers, $S=0.1\nm$, $N_\text{ML}=15$, $d_\text{ML}=1.5\nm$.
• Figure 2: Micromagnetic simulations match the experimentally observed topological transitions.a-d, Scanning transmission x-ray microscopy (STXM) images of representative topological transitions in a double-gradient multilayer track, here induced by 40-long current pulses. The signal corresponds to the thickness-integrated x-ray magnetic circular dichroism. Full black or white contrast corresponds to 3D worms, reduced contrast to cocoons. e, Field-current density ($B$,$j$) phase diagram of the magnetic states produced after the current pulse (obtained from over 200 measurements). The density of cocoons and 3D worms is represented by magenta or yellow colours, respectively, as shown in the inset. Dashed lines mark approximate phase boundaries. Symbols mark the points where the transitions in (a-d) were observed. The $j$ axis is on a quadratic scale. f-i, Simulated magnetic states before and after cycling of the pseudo-temperature $\Theta$ (see \ref{['sec:Methods']}). Images display the net out-of-plane magnetization averaged along the material thickness ${\langle m_z \rangle}_z$. j, Field-temperature ($B$,$\Theta_\mathrm{p}$) phase diagram of simulated transitions, analogous to the one displayed in (e), but for micromagnetic simulation results.
• Figure 2: Topological switching induced by a variety of excitations.a-d, X-ray microscopy images of magnetic states before and after excitation, produced via (a,b) 40 current pulses, (c) direct current heating and (d) femtosecond infrared laser pulses. All images show the thickness-averaged x-ray magnetic circular dichroism contrast in double-gradient magnetic multilayers. Sample structures are (a-c) $N_\text{SG}=13$, $d_0=1.6\nm$, $N_\text{ML}=15$, $d_\text{ML}=1.0\nm$ and (d) $N_\text{SG}=13$, $d_0=1.6\nm$, $N_\text{ML}=15$, $d_\text{ML}=0.9\nm$. (a-c) are STXM images, (d) are FTH reconstructions. The inhomogeneous magnetic contrast in (d) is due to artifacts of the FTH microscopy technique. White scalebars are 1µm.
• Figure 3: The three-step process of fluctuation-free topological switching.a-f, Snapshots of the cocoon lattice formation process (micromagnetic simulations) upon adiabatic reduction of the pseudo-temperature $\Theta$ at $B=140\mT$ in a single-gradient multilayer. Colour represents isosurfaces of the normalized out-of-plane magnetization. Blue: $m_z=+0.5$, white: $m_z=0$, red: $m_z=-0.5$. g, Sketches of surface magnetic charges during weak stripe formation. h, Sketch of the energy diagram for the weak stripe transition. i, Mode dispersion $\omega(\boldsymbol{q})$ of magnons propagating along the $x$ axis for two exemplary pseudo-temperatures above the first critical temperature ($\Theta >\Theta_\mathrm{1}$) and dependence of the band gap $\Delta$ as a function of $\Theta$. The dashed line is a linear fit. j, Sketches of surface magnetic charges during the weak stripe to bubble transition. k, Sketch of the energy diagram for the bubble formation transition. l, Mode dispersion of magnons propagating along the pre-existing weak stripe pattern displayed in (c) for two exemplary pseudo-temperatures above the second critical temperature ($\Theta >\Theta_\mathrm{2}$) and dependence of the band gap $\Delta$ as a function of $\Theta$. The dashed line is a fit to $\Delta \propto \sqrt{\Theta-\Theta_\mathrm{2}}$. The points at $\Theta \approx \Theta_\mathrm{2}$ displaying an apparent $\Delta=0$ are an artifact of the method used for computing the magnon bandgap (see \ref{['sec:Methods']}). m, Sketch of the dipolar stray fields acting on a cocoon in (e,f). n, Sketch of the energy diagram for the topological transition. o, 3D representation of a single cocoon during a topological switching process. Contour: $m_z=0$ isosurface of the out-of-plane magnetization. Colour: local topological charge density $n$ on a log scale. The 2D images below the 3D contours show the spin configuration of the domain wall that surrounds the cocoon in the second layer from the bottom, along with the local topological charge density. $N$ represents the total topological charge of each layer.