[Paper Review] Direct control of the skyrmion phase stability by electric field in a magnetoelectric insulator

Alexander Kruchkov, J. S. White+4 more|arXiv (Cornell University)|Mar 17, 2017

Advanced Condensed Matter Physics3 citations

TL;DR

This study demonstrates direct electrical control of the skyrmion phase stability in the magnetoelectric insulator Cu2OSeO3 using moderate electric fields (kV/mm). By combining small-angle neutron scattering (SANS) experiments with an expanded mean-field theory including fluctuations, the authors show that the skyrmion lattice phase can be reversibly expanded or contracted by tuning the polarity of the applied electric field, offering a pathway for electrically driven skyrmionic devices with enhanced phase stability.

ABSTRACT

Magnetic skyrmions are topologically protected spin-whirl quasiparticles currently considered as promising components for ultra-dense memory devices. In the bulk they form lattices that are stable over just a few Kelvin below the ordering temperature. This narrow stability range presents a key challenge for applications, and finding ways to tune the SkL stability over a wider phase space is a pressing issue. Here we show experimentally that the skyrmion phase in the magnetoelectric insulator ${ ext{Cu}_2 ext{O} ext{Se} ext{O}_3}$ can either expand or shrink substantially depending on the polarity of a moderate applied electric field. The data are well-described by an expanded mean-field model with fluctuations that show how the electric field provides a direct control of the free energy difference between the skyrmion and the surrounding conical phase. Our finding of the direct electric field control of the skyrmion phase stability offers enormous potential for skyrmionic applications based on a magnetoelectric coupling.

Motivation & Objective

• To address the narrow stability range of the skyrmion lattice (SkL) phase in bulk materials, which limits practical applications.
• To investigate whether electric fields can directly tune the free energy difference between the skyrmion and conical phases in a magnetoelectric insulator.
• To experimentally verify electric field-induced expansion or contraction of the SkL phase space in Cu2OSeO3 using direct microscopic probing.
• To develop a theoretical framework that includes both mean-field effects and fluctuation corrections to accurately describe phase stability under electric fields.

Proposed method

• Small-angle neutron scattering (SANS) was used to directly observe the skyrmion lattice diffraction pattern and monitor changes in phase stability under applied electric fields.
• Theoretical analysis employed first-order perturbation theory on the mean-field free energy to model the electric field's effect on the skyrmion lattice.
• A new approach to fluctuation-induced free energy was developed, incorporating Gaussian fluctuations near T_C to capture critical mode contributions.
• The effective model included parameters such as Dzyaloshinskii-Moriya interaction (D), Heisenberg exchange (J), and magnetoelectric coupling (λ), with experimental values derived from SANS and susceptibility measurements.
• Phase diagrams were calculated by varying the electric field polarity, and the results were compared with experimental SANS data to validate the model.
• The electric field was applied along the [111] direction to maximize coupling with the chiral spin structure, aligning E and H fields for optimal control.

Experimental results

Research questions

• RQ1 Can an electric field directly tune the stability of the skyrmion lattice phase in a magnetoelectric insulator?
• RQ2 How does the electric field modify the free energy difference between the skyrmion and conical phases?
• RQ3 To what extent can the skyrmion phase space be expanded or contracted via electric field control?
• RQ4 What is the role of thermal fluctuations in stabilizing or destabilizing the skyrmion phase under electric fields?
• RQ5 Can the theoretical prediction of electric field-induced phase tuning be experimentally verified using direct microscopic imaging?

Key findings

• The skyrmion phase in Cu2OSeO3 expanded or contracted significantly depending on the polarity of the applied electric field, with changes observed in both temperature and magnetic field ranges.
• SANS measurements confirmed a reversible shift in the skyrmion phase boundary, with the phase pocket shifting by up to 10% of the original width under ±5×10⁶ V/m fields.
• Theoretical modeling showed that the electric field induces a first-order shift in the skyrmion lattice free energy comparable in magnitude to the energy difference between the skyrmion and conical phases.
• Fluctuation corrections were found to be essential for accurately describing the phase stability, with the dominant contribution to free energy difference arising from short-wavelength (ferromagnetic-like) modes.
• The magnetoelectric coupling parameter λ was extracted as 9.23×10⁻⁹ m/V, consistent with the observed field response and enabling quantitative prediction of phase tuning.
• The results demonstrate that electric fields can reversibly control skyrmion phase stability over a wide range of T and H, offering a viable route for electrically driven skyrmionic devices.