Fig 1. Panel a: sketch of the multilayer stacks, b: magnetizations of a target skyrmion (TSk) and an hopfion. c: calculated dichroic images from X-PEEM and MTXM. The direction of the photon angular momentum is indicated for X-PEEM (in-plane and out-of-plane) and MTXM (only out-of-plane). The yellow shaded areas in the upper part of the structures of panel b represent approximately the probing depth of PEEM. In the case of MTXM the X-rays transverse the whole sample thickness.
Cerdanyola del Vallès, 26th March 2021. One of the active fields on computer technology in the spintronics area is the search for novel magnetic entities to efficiently transport magnetic information through a magnetic circuit. Magnetic singularities in ferromagnetic or antiferromagnetic materials have emerged as potential candidates since often they exhibit a “topologically protection” which means that they are stable against perturbations. Among the most famous singularities are skyrmions which are characterized by a continuous magnetization distribution that experiences a full rotation of the magnetization from up to down when crossing the structure. Depending on whether the rotation is along or orthogonal to the radial direction, they are referred to as Néel or Bloch-type skyrmions. So far, skyrmions have been treated as two dimensional singularities assuming that in one direction (usually defined as z direction for a magnetization in the x-y plane) the magnetization does not change. Target skyrmions belong to a subgroup of the skyrmion family where the perpendicular magnetization rotates several times along the radial direction, as for example ↓↑ ↓↑ from center to the edge. Theoretical work indicates that target skyrmions can be transformed into Hopfions which are three dimensional magnetic distributions constituted from skyrmion strings that form a closed loop. Hopfion (named after Heinz Hopf, a German mathematician) quasiparticles have been known to exist in liquid crystals but not yet been found in magnetic thin films or heterostructures. In magnetic systems, their stability is due to the proper balance of the exchange interaction favoring parallel or antiparallel orientations and the Dzyaloshinksi–Moriya interaction favoring magnetization canting.
A collaboration between US scientists from Lawrence Berkeley National Laboratory and MISTRAL associated scientists, has recently published an article providing a strong indication of the existence of magnetic Hopfions in magnetic heterostructures. The work is based on four pillars: 1) magnetic simulations allowed to predict the magnetization textures, 2) fabrication of the appropriate magnetic stacks specially designed for hosting target skyrmions or Hopfions, 3) the measurements with X-PEEM at ALS and 4) magnetic X-ray transmission microscopy (MTXM) at ALBA. X-PEEM dichroic images mapped the full three-dimensional surface magnetization whereas MTXM provided information from the whole multilayers. Combining both sets of measurements from the same samples provided evidence of magnetic textures as those expected for Hopfions.
Figure 1a shows the stacking of the multilayers fabricated with DC sputtering. The top one was made to host a target skyrmion and the bottom one to host a Hopfion. Panel b illustrates the corresponding the corresponding magnetization textures of a target skyrmion from the seven repeats of a three-layer stack with a 1.5nm Co layer and of an Hopfion from a stack where the top and bottom ten repeats had Co layer of only 1.0nm. Note that the target skyrmion has a radial perpendicular magnetization as ↑ ↓↑ (black, white, black arrows). The Hopfion has also the same sequence of perpendicular magnetization but it displays a twist of the skyrmion magnetization. Panel c in the figure simulates the dichroicimages from PEEM and magnetic TXM showing a striking discrepancy between the X-PEEM images for the target skyrmion and the Hopfion.
Figure 2 shows representative results of the measurements confirming the simulated experimental data in Fig 1c.
As seen in the figure, PEEM images show different contrast at both sides of the structure which corresponds to two opposite in-plane magnetizations as expected from the simulations (fig 1c, lower panel) whereas TXM exhibits a circular symmetry which is due to the sum of the individual contributions of the different Co layers across the stack.
Even though the presented combination of X-PEEM and MTXM is not a direct and full 3D reconstruction of the spin texture with nanometer spatial resolution, the obtained results provide strong indications that magnetic Hopfions have been stabilized in the magnetic multilayers as predicted from theory. Based on current developments of topographic methods, in particular those that exploit the spatial coherence of the X-rays, as it's the case in fourth generation sources, allow to anticipate that nm resolution is within reach. The results presented here open the door to exploiting novel phenomena in magnetic Hopfions, including hopfion dynamics that could lead to new applications in three dimensional spintronics. For example, the vanishing gyrovector in Hopfions would enable racetrack devices, which are not impacted by undesirable Hall effects that seems to limit such devices based on skyrmions.
Fig 2. Panel a: PEEM dichroic images at the Co L3 absorption energy for two different directions of the incoming X-ray beam (red arrows). The samples are nominally identical cylinders of 3x10 stacks as depicted in Fig 1a and have 400 nm diameter. Panel b: X-ray dichroic transmission images at normal incidence. Scale bars 500 nm.
