Skyrmion magnets and topological spin textures

5 problems

• What stabilizes skyrmion lattices in centrosymmetric magnets like $\mathrm{Gd_2PdSi_3}$?

  Contested

  Most skyrmions appear in crystals lacking mirror symmetry, where a twisting interaction favors them. $\mathrm{Gd_2PdSi_3}$ and $\mathrm{GdRu_2Si_2}$ have that symmetry yet host very small skyrmions, and the competing explanations involve geometric frustration or interactions carried by conduction electrons.

• Stable free-standing hopfions in bulk chiral magnets

  Open

  A hopfion is a three-dimensional knotted twist of spins in which the lines of equal spin direction form linked loops. In bulk crystals hopfions have so far been seen only attached to skyrmion strings, and a free one has not been observed.

• How does a two-dimensional skyrmion lattice melt?

  Partially resolved

  A sheet of skyrmions can melt like a 2D crystal, possibly through an intermediate hexatic phase that keeps orientation order but loses positional order. Whether this two-step melting is generic, and how pinning changes it, is open.

• Can quantum skyrmions be observed in a real magnet?

  Open

  When a skyrmion is only a few atoms wide and made of small spins, quantum mechanics should matter, letting it tunnel or form superpositions. No experiment has yet shown a skyrmion behaving quantum mechanically.

• Are topological Hall signals in thin films evidence of skyrmions?

  Contested

  Skyrmions should deflect electrons and add a bump to the Hall voltage, called the topological Hall effect. Many reported bumps in thin films can also come from two magnetic layers or regions with opposite ordinary anomalous Hall signals, so they may not prove skyrmions exist.