The quantum origins of skyrmions and half-skyrmions in Cu2OSeO3

Abstract: The Skyrme-particle, the $skyrmion$, was introduced over half a century ago and used to construct field theories for dense nuclear matter. But with skyrmions being mathematical objects - special types of topological solitons - they can emerge in much broader contexts. Recently skyrmions were observed in helimagnets, forming nanoscale spin-textures that hold promise as information carriers. Extending over length-scales much larger than the inter-atomic spacing, these skyrmions behave as large, classical objects, yet deep inside they are of quantum origin. Penetrating into their microscopic roots requires a multi-scale approach, spanning the full quantum to classical domain. By exploiting a natural separation of exchange energy scales, we achieve this for the first time in the skyrmionic Mott insulator Cu$_2$OSeO$_3$. Atomistic ab initio calculations reveal that its magnetic building blocks are strongly fluctuating Cu$_4$ tetrahedra. These spawn a continuum theory with a skyrmionic texture that agrees well with reported experiments. It also brings to light a decay of skyrmions into half-skyrmions in a specific temperature and magnetic field range. The theoretical multiscale approach explains the strong renormalization of the local moments and predicts further fingerprints of the quantum origin of magnetic skyrmions that can be observed in Cu$_2$OSeO$_3$, like weakly dispersive high-energy excitations associated with the Cu$_4$ tetrahedra, a weak antiferromagnetic modulation of the primary ferrimagnetic order, and a fractionalized skyrmion phase.

• The paper reveals that a multi-scale quantum-classical analysis explains how Cu₄ tetrahedra in Cu2OSeO3 drive the emergence of skyrmions and half-skyrmions.
• It employs density functional theory and Quantum Monte Carlo simulations to quantitatively assess key magnetic interactions such as -8 K ferromagnetic exchange and Dzyaloshinskii-Moriya couplings.
• Findings predict temperature and magnetic field–dependent transitions between skyrmion states, highlighting potential pathways for advanced spintronic applications.

An Examination of the Quantum Origins of Skyrmions and Half-Skyrmions in Cu$_2$OSeO$_3$

The paper focuses on investigating the quantum mechanical aspects behind the formation of skyrmions and half-skyrmions in the skyrmionic Mott insulator, Cu$_2$OSeO$_3$. Skyrmions, as magnetic topological solitons, have been identified in various helimagnets and are proposed as potential nanoscale information carriers.

Key Findings

The authors employ a multi-scale approach integrating quantum and classical domain analysis to elucidate the origins and dynamics of skyrmions in Cu$_2$OSeO$_3$. The analysis begins with atomistic {\it ab initio} calculations pinpointing strongly fluctuating Cu$_4$ tetrahedra as the significant building blocks of the magnetic structure. This complex interaction forms the foundation for a continuum theory, aligning well with experimental observations.

Among the prominent findings:

• The emergence of skyrmions transitioning into half-skyrmions at specific temperature and magnetic field conditions.
• A thorough quantification of exchange couplings revealed that nanometer-scale skyrmions arise as classical structures rooted in quantum mechanics.
• The work explicates the decay of skyrmions into half-skyrmions, with theoretical predictions for further behaviors such as weakly dispersive high-energy excitations, attributed to Cu$_4$ tetrahedra.

Numerical Insights

The calculations demonstrate that the magnetic Cu$^{2+}$ ions in Cu$_2$OSeO$_3$ form a distinct 3D network, affirming a hierarchy of magnetic energy scales. Couplings within Cu$_4$ tetrahedra are divided into strong and weak, influencing the quantum fluctuations and renormalizing local moments in the system.

• The exchange interactions ($-8$ K effective ferromagnetic interactions) and Dzyaloshinskii-Moriya interactions are quantified using density functional theory, corroborated by Quantum Monte Carlo simulations.
• The helix period aligns closely with observed experimental values, asserting the model's validity.

Implications

The research offers significant implications in both theoretical understanding and practical applications. The methodology demonstrates capability in unveiling the deep quantum origins of skyrmion structures, greatly influencing future studies on skyrmionic materials. The fractionalized skyrmion phases present a novel avenue for exploration in topological matter studies. Experimentally, observing these emergent magnetic phases and their transitions could drive developments in spintronics, particularly in designing more efficient data storage and processing mechanisms.

Future Directions

Future work could explore the broader effects of quantum fluctuation elements on skyrmion stability and dynamics in other materials. Through detailed experimentation, such as neutron scattering, the predictions surrounding weakly antiferromagnetic modulations and high-energy excitation characteristics can be further probed. These endeavors may uncover additional subtleties of skyrmionic phases, honing the potential energy efficiency in electronic applications via control over magnetic textures.

In conclusion, this research provides a detailed and comprehensive framework for understanding the quantum underpinnings of skyrmions in Cu$_2$OSeO$_3$, offering a model that not only aligns with experimental data but also extends our grasp of topological magnetic phenomena in quantum materials.