[Paper Review] Meron-antimeron crystals in noncentrosymmetric itinerant magnets on a triangular lattice

Satoru Hayami, Ryota Yambe|arXiv (Cornell University)|Jul 7, 2021

Magnetic properties of thin filmsPhysics and Astronomy90 references44 citations

TL;DR

This paper proposes that meron-antimeron crystals (MAX) can be stabilized in noncentrosymmetric itinerant magnets on a triangular lattice through the interplay of biquadratic interactions (from spin-charge coupling) and Dzyaloshinskii-Moriya (DM) interactions (from spin-orbit coupling). Using simulated annealing on an effective spin model, the authors identify both rectangular and triangular MAX phases, with the triangular MAX exhibiting highly anisotropic field responses, transforming into skyrmion crystals under certain field orientations.

ABSTRACT

Multiple-$Q$ magnetic states often induce nontrivial topological spin textures, such as a skyrmion and a hedgehog. We theoretically investigate yet another multiple-$Q$ state with topological defects, a meron-antimeron crystal (MAX), represented by a periodic array of the meron and antimeron with a half-integer skyrmion number. Performing simulated annealing for an effective spin model of noncentrosymmetric itinerant magnets on a triangular lattice, we show that rectangular-shaped and triangular-shaped MAXs are stabilized by the interplay between the biquadratic interaction arising from the spin-charge coupling and the Dzyaloshinskii-Moriya interaction arising from the spin-orbit coupling. We also discuss the effect of a magnetic field on the triangular MAX, where highly anisotropic responses against a field direction are found. In particular, we show that the triangular MAX turns into the skyrmion crystal for the fields along the $y$ and $z$ directions, while it is replaced by another chiral state for the field along the $x$ direction. These results would inspire further experimental investigation of the MAXs in itinerant magnets.

Motivation & Objective

• To investigate the stability of meron-antimeron crystals (MAX) in noncentrosymmetric itinerant magnets on a triangular lattice.
• To identify the microscopic mechanisms enabling the formation of triangular MAX phases.
• To explore the response of triangular MAX to external magnetic fields and determine field-direction-dependent phase transitions.
• To clarify the role of biquadratic and Dzyaloshinskii-Moriya interactions in stabilizing exotic multiple-Q states.

Proposed method

• Develops an effective spin model derived from a Kondo lattice Hamiltonian with relativistic spin-orbit coupling on a C6v-symmetric triangular lattice.
• Includes symmetric anisotropic RKKY, Dzyaloshinskii-Moriya (DM), biquadratic, and single-ion anisotropy interactions in momentum space.
• Performs simulated annealing to explore ground states across parameter space, identifying stable MAX and SkX phases.
• Analyzes spin textures via skyrmion number and spin density wave superposition to classify multiple-Q states.
• Applies external magnetic fields in different directions to probe field-induced phase transitions in the triangular MAX.
• Uses Fourier analysis and spin texture visualization to characterize the 3Q state nature of the triangular MAX.

Experimental results

Research questions

• RQ1 Can meron-antimeron crystals (MAX) be stabilized in noncentrosymmetric itinerant magnets on a triangular lattice?
• RQ2 What is the role of biquadratic and Dzyaloshinskii-Moriya interactions in stabilizing the triangular MAX phase?
• RQ3 How does an external magnetic field influence the stability and topology of the triangular MAX?
• RQ4 What are the field-direction-dependent phase transitions from the triangular MAX to other chiral magnetic states?

Key findings

• The triangular MAX is stabilized by the interplay between biquadratic interactions (from spin-charge coupling) and Dzyaloshinskii-Moriya interactions (from spin-orbit coupling).
• The triangular MAX is characterized as a 3Q state formed by three cycloidal spin density waves with different intensities.
• Increasing the DM interaction transforms the triangular MAX into a triangular skyrmion crystal (SkX) with skyrmion numbers ±1.
• Decreasing the biquadratic interaction leads to a rectangular MAX phase composed of two equal-intensity cycloidal waves.
• Under a magnetic field along the y or z direction, the triangular MAX transforms into a skyrmion crystal with nsk = ±1.
• Along the x direction, the field induces a distinct chiral magnetic ordering different from SkX, indicating highly anisotropic field responses.