Amazing stuff!
"In the past few years, physicists have created long-predicted quasiparticles called hopfions—3D, localized, knot-like arrangements of a magnetic material’s spin texture.
A hopfion can be described in terms of its Hopf number H, which counts how many loops of spins are interlinked in the knot.
Researchers have proposed using hopfions in spintronic computers, where H would encode information. This is because a hopfion is a topologically protected state, meaning H stays the same under many deformation conditions.
In new computational work ... have developed a method for splitting high-H hopfions into multiple lower-H hopfions, an operation that would be useful for such spintronic information-storage devices.
The team modeled a two-layer structure in which hopfions were hosted by a magnetic material adjacent to a heavy metal.
An electric current flowing along the heavy-metal layer generated a perpendicular spin-polarized current via the spin Hall effect. This spin-polarized current leaked into the magnetic layer and exerted a torque on the magnetic moments, pulling different parts of the magnetic texture in opposite directions and thereby stretching the hopfions. The researchers found that, once the torque exceeded a threshold, it could overcome a hopfion’s topological protection and tear a higher-H hopfion into multiple lower-H hopfions. An H = 4 hopfion, for example, could split into four H = 1 hopfions or two H = 2 hopfions depending on the strength of the spin-orbit torque. ..."
From the abstract:
"Knots formed by the intertwining of strings have attracted broad interest across various scientific disciplines owing to their rich topology. This concept has recently gained increasing importance in condensed matter physics, as exemplified by a magnetic hopfion labeled by a topological invariant called the Hopf number 𝐻.
Here, we show that spin-orbit torque (SOT) enables dynamic manipulation of the Hopf number of magnetic hopfions. We investigate the SOT-driven evolution of hopfions, revealing the splitting of a high-𝐻 hopfion into multiple lower-𝐻 ones, a process that can be quantified by an effective tension picture.
Comparative analysis across different 𝐻 uncovers a hierarchy of instabilities that dictates these dynamical topological transitions.
These findings not only indicate potential applications of hopfions in SOT-driven multilevel memory devices, but also provide a paradigm for the dynamical control of knot topology."
Fig. 1
(a) Schematic illustrations of magnetic hopfions with 𝐻=1,2, and 4, shown by the isosurfaces of 𝑆𝑧=0, along with their corresponding preimages that satisfy 𝑆𝑥=1 (blue) and 𝑆𝑥=−1 (red). The color code in the inset is used throughout this Letter to depict spin orientations.
(b) A typical setup for this study. A spin current injected from the lower heavy metal layer works on magnetic moments as a SOT, thereby inducing hopfion dynamics in the upper magnetic layer. Snapshots of the 𝐻=2
(c) and 𝐻=4
(d) hopfions under (𝐵,𝜁)=(0.003,0.002) and (𝐵,𝜁)=(0.003,0.0021), respectively. The lower panels show their preimages to support the observation of changes in the knot topology.
