[Paper Review] Néel-type Skyrmion Lattice with Confined Orientation in the Polar Magnetic Semiconductor GaV$_4$S$_8$

I. Kézsmárki, S. Bordács+12 more|arXiv (Cornell University)|Feb 27, 2015

Magnetic properties of thin films4 citations

TL;DR

This study reports the first experimental realization of a Néel-type skyrmion lattice (SkL) in the polar magnetic semiconductor GaV₄S₈ with rhombohedral (C₃v) symmetry, where the skyrmion vortices are confined to the magnetic easy axis rather than being field-controlled. The SkL forms over a broad temperature range and arises from a non-chiral spin texture driven by Dzyaloshinskii-Moriya interactions in a breathing pyrochlore lattice, confirmed by SANS, AFM, and magnetization measurements, establishing a new archetype of skyrmion formation in non-centrosymmetric, non-chiral systems.

ABSTRACT

Following the early prediction of the skyrmion lattice (SkL) - a periodic array of spin vortices - it has been observed recently in various magnetic crystals mostly with chiral structure. Although non-chiral but polar crystals with C$_{nv}$ symmetry were identifed as ideal SkL hosts in pioneering theoretical studies this archetype of SkL has remained experimentally unexplored. Here, we report the discovery of a SkL in the polar magnetic semiconductor GaV$_4$S$_8$ with rhombohedral (C$_{3v}$) symmetry and easy axis anisotropy. The SkL exists over an unusually broad temperature range compared with other bulk crystals and the orientation of the vortices is not controlled by the external magnetic feld but instead confned to the magnetic easy axis. Supporting theory attributes these unique features to a new non-chiral or Néel-type of SkL describable as a superposition of spin cycloids in contrast to the Bloch-type SkL in chiral magnets described in terms of spin helices.

Motivation & Objective

• To identify and characterize a skyrmion lattice in a non-chiral, polar magnetic semiconductor with C₃v symmetry, specifically GaV₄S₈.
• To investigate the origin of skyrmion formation in the absence of chiral crystal structures, challenging the conventional view that chiral symmetry is required for skyrmion stability.
• To determine whether the skyrmion lattice in GaV₄S₈ exhibits field-independent orientation, as predicted by non-chiral skyrmion theory.
• To establish the role of the breathing pyrochlore lattice and orbital ordering in stabilizing the skyrmion phase via Dzyaloshinskii-Moriya interactions.
• To validate theoretical models of non-chiral skyrmion lattices through experimental measurements of magnetic structure and phase transitions.

Proposed method

• Small-angle neutron scattering (SANS) was used to probe long-wavelength magnetic order in a 25.5 mg single crystal of GaV₄S₈, with neutron beam alignment parallel to the applied magnetic field and sample rotation to map magnetic diffraction peaks across the Ewald sphere.
• Atomic force microscopy (AFM) in the magnetic force microscopy (MFM) mode was employed to image magnetic domains at low temperatures (below 10 K), with magnetic contrast arising from dissipative tip-sample interactions.
• Magnetic susceptibility and magnetization measurements were performed on single crystals at various field orientations ([100], [110], [111]) to map the magnetic phase diagram and identify field-induced transitions.
• Monte Carlo simulations were conducted on two-dimensional and three-dimensional spin models with XXZ anisotropy and Dzyaloshinskii-Moriya (DM) interactions, using periodic boundary conditions and a lattice with 144×144 and 72×72×8 sites, respectively.
• The Dzyaloshinskii-Moriya interaction was modeled as a vector coupling term in the Hamiltonian: $\mathcal{H}_{\rm DM} = -D\sum_{i} \left[\hat{\bm{y}}\cdot(\bm{m}_{i}\times\bm{m}_{i+\hat{x}}) - \hat{\bm{x}}\cdot(\bm{m}_{i}\times\bm{m}_{i+\hat{y}})\right]$, with parameters derived from low-temperature magnetization and cycloidal pitch data.
• Theoretical phase diagrams were constructed by analyzing temperature-dependent specific heat and net magnetization, identifying transitions between paramagnetic, ferromagnetic, cycloidal, and skyrmion lattice phases.

Experimental results

Research questions

• RQ1 Can a skyrmion lattice form in a non-chiral, polar magnetic semiconductor with C₃v symmetry, such as GaV₄S₈, despite the absence of structural chirality?
• RQ2 What is the origin of the skyrmion lattice's field-independent orientation in GaV₄S₈, and how does it differ from field-controlled skyrmion phases in chiral magnets?
• RQ3 How does the breathing pyrochlore lattice structure of GaV₄S₈ influence the formation of skyrmion textures through spin-orbit coupling and orbital ordering?
• RQ4 What is the role of the Dzyaloshinskii-Moriya interaction in stabilizing a non-chiral (Néel-type) skyrmion lattice in the absence of inversion symmetry breaking from chiral lattice structure?
• RQ5 Can theoretical models of non-chiral skyrmion lattices accurately predict the observed magnetic phase transitions and spin textures in GaV₄S₈?

Key findings

• A Néel-type skyrmion lattice was experimentally observed in GaV₄S₈, a polar magnetic semiconductor with rhombohedral (C₃v) symmetry, marking the first realization of a non-chiral skyrmion phase in a bulk crystal.
• The skyrmion lattice forms over a broad temperature range (from ~10 K up to ~42 K, the structural transition temperature), indicating high thermal stability.
• The orientation of the skyrmion vortices is confined to the magnetic easy axis (along the [111] direction) and is not controlled by the external magnetic field, distinguishing it from field-tuned skyrmions in chiral materials.
• Small-angle neutron scattering (SANS) revealed a well-defined, hexagonal magnetic diffraction pattern consistent with a skyrmion lattice, with Bragg peaks shifting upon field application and sample rotation.
• Atomic force microscopy (AFM) imaging at 8.9 K revealed alternating structural domains with different rhombohedral axes, and magnetic contrast was observed only below 10 K, indicating low spin density and strong spin fluctuations.
• Theoretical Monte Carlo simulations confirmed that the skyrmion lattice state is stabilized by Dzyaloshinskii-Moriya interactions in a system with XXZ anisotropy and orbital ordering, with the Néel-type skyrmion texture arising from spin rotations in planes perpendicular to the domain boundaries.