TY  - JOUR
AU  - Rybakov, Filipp N.
AU  - Kiselev, Nikolai S.
AU  - Borisov, Aleksandr B.
AU  - Döring, Lukas
AU  - Melcher, Christof
AU  - Blügel, Stefan
TI  - Magnetic hopfions in solids
JO  - APL materials
VL  - 10
IS  - 11
SN  - 2166-532X
CY  - Melville, NY
PB  - AIP Publ.
M1  - FZJ-2022-04612
SP  - 111113 -
PY  - 2022
AB  - Hopfions are an intriguing class of string-like solitons, named according to a classical topological concept classifying three-dimensional direction fields. The search for hopfions in real physical systems has been ongoing for nearly half a century, starting with the seminal work of Faddeev. However, so far, realizations in bulk solids are missing. Here, we show that hopfions appear as emergent particles of the classical Heisenberg model with competing exchange interactions. This requires going beyond the model approach used in prior work and deriving a general micromagnetic energy functional directly from a spin-lattice Hamiltonian. We present a definite parameter space in which the existence of hopfions is possible. This opens a concrete vista to combine computational approaches such as density functional theory with material informatics to find magnetic crystals that can host hopfions. As proof of principle, we show how zero-field hopfions can be visualized by the means of off-axis electron holography in a transmission electron microscope.
LB  - PUB:(DE-HGF)16
UR  - <Go to ISI:>//WOS:000884993000001
DO  - DOI:10.1063/5.0099942
UR  - https://juser.fz-juelich.de/record/911320
ER  -