Chirality-driven orbital magnetic moments as a new probe for topological magnetic structures

Abstract

When electrons are driven through unconventional magnetic structures, such as skyrmions, they experience emergent electromagnetic fields that originate several Hall effects. Independently, ground-state emergent magnetic fields can also lead to orbital magnetism, even without the spin–orbit interaction. The close parallel between the geometric theories of the Hall effects and of the orbital magnetization raises the question: does a skyrmion display topological orbital magnetism? Here we first address the smallest systems with nonvanishing emergent magnetic field, trimers, characterizing the orbital magnetic properties from first-principles. Armed with this understanding, we study the orbital magnetism of skyrmions and demonstrate that the contribution driven by the emergent magnetic field is topological. This means that the topological contribution to the orbital moment does not change under continuous deformations of the magnetic structure. Furthermore, we use it to propose a new experimental protocol for the identification of topological magnetic structures, by soft X-ray spectroscopy.

The chiral biquadratic pair interaction

“…Prominent examples are the antiferromagnetic uuddstate (a 2Q-state) [20,21] and the 3Q-state [22]. Interestingly, this 3Q-state (also magnetic skyrmions [23,24] and bobbers [25,26]) is a noncoplanar magnetic state that hosts interesting Berry-phase physics arising from its nonvanishing scalar spin chirality S S S i j ḱ · ( ), such as topological orbital ferromagnetism and Hall effects [27][28][29][30][31]. The concept of vector spin chirality is embodied by the antisymmetric bilinear Dzyaloshinskii-Moriya interaction (DMI), D S S ij i j · ( ) [3,4], which arises due to the combination of spin-orbit coupling and absence of spatial inversion symmetry.…”

Topological–chiral magnetic interactions driven by emergent orbital magnetism

“…The 3D magnetization textures of 2D skyrmions gives rise to a scalar spin chirality, a driving force behind a plethora of macroscopic phenomena. Examples are the topological Hall effect 18,19 or a finite topological orbital moment (TOM) [20][21][22][23][24][25] , which can both serve as experimental fingerprints of skyrmions. Texture-induced contributions to these macroscopic phenomena were also predicted in frustrated magnets 26,27 , where they originate from the non-trivial spin topology associated with the real-space configuration of magnetic moments S i as reflected by the scalar spin chirality χ ijk = S i · (S j × S k ).…”

Distinct magnetotransport and orbital fingerprints of chiral bobbers

“…The findings of our paper concerning transport properties are applicable to the orbital magnetism exhibited by the textures as well. In recent years, it was shown from model considerations, tight-binding and ab-initio studies, that the presence of non-zero scalar spin chirality in large skyrmions as well as in strongly frustrated spin systems is inevitably associated with pronounced contributions to the orbital magnetization (OM), which arises in response to the emergent field B em [31][32][33][34][35]. Indeed, our calculations indicate the nonvanishing topological contribution to the OM in STs, however, an intriguing finding is that the OM of chiral bobber systems is very closely correlated with the behavior of the HC, see for example Fig.…”