Ripple state in the frustrated honeycomb-lattice Heisenberg - - PowerPoint PPT Presentation

Ripple state in the frustrated honeycomb-lattice Heisenberg antiferromagnet

Tokuro Shimokawa (OIST), Hikaru Kawamura (Osaka Univ.)

• T. S. and H. Kawamura, arXiv:1810.02951 (accepted in PRL 2019)

Introduction

Triple-q skyrmion-lattice state

• S. Mühlbauer, et al, Science 323, 915 (2009).

Chiral magnet MnSi Multiple-q states organizing complex magnetic structures are exotic states of matter in magnetic solids.

• N. Nagaosa and Y. Tokura, Nat. Nano. 8, 899-911 (2013).

Image by Lorentz transmission electron microscopy

Antisymmetric interaction plays important roles for stabilizing the skyrmion-lattice state

Introduction

J1-J3 classical triangular-lattice Heisenberg model

・Anti-Skyrmion state can also appear. ・A mixed state of skyrmion and antiskyrmion domains appears.

• T. Okubo, S. Chung, and H. Kawamura, PRL 108, 017206 (2012).

・Skyrmion state can appear without the DM interaction.

MC phase diagram Spin structure factors Snapshot of spin and chirality config. in the triple-q state and Z state

Purpose, model and method in our study

We mainly focus the J2/J1=0.18 case under magnetic fields at moderate temperature.

Search for more exotic frustration-induced multiple-q states!

J1 J2 J1-J2 classical honeycomb-lattice Heisenberg model Monte Carlo (MC) simulation Heat-bath, over-relaxation, temperature-exchange methods Open/Periodic boundary conditions Maximum system size N=115200 (L=240)

• T. S., T. Okubo and H. Kawamura, arXiv:1902.01582

For other J2/J1 cases

Ring-like degeneracy

Ground state phase diagram under H=0

• S. Katsura, et al., J. Stat. Phys. 42, 381 (1986).

J1 J2 J1-J2 classical honeycomb-lattice Heisenberg model Ring-like degeneracy

Ring-like degeneracy could be a source for exotic states

Finite-temperature phase diagram under H=0

Pancake liquid Ring liquid

Sublattice static spin structure factors in each state

Single-q Single-q

• S. Okumura, et al., JPSJ 79, 114705 (2010).

Para

Ring-degeneracy in J2/J1=0.18

T-H phase diagram at J2/J1=0.18

Para.

Single-q (INT)

Single-q ,ring-liquid, pancake-liquid states

Ring-liquid Pancake-liquid

Ripple state under open B.C.

Ripple state (open B.C.)

Single-q (INT) Ring-liquid Spiral is running along every direction from a core Ring-like pattern still remains in the static spin structure factor

Phase transition between ring-liquid and ripple states

Ring-liquid Ripple

Sublattice local scalar chirality Sublattice spin texture

Z2 symmetry is broken spontaneously in the ripple state.

Si・(Sj×Sk)

Definition of the sublattice local scalar chirality

Ripple state under periodic B.C.

Sublattice xy spin texture in the ripple state (L=180, periodic) Incompatibility against the periodic B.C. produces an interference effect and vortex/antivortex textures. Vortex Antivortex L=240, periodic The ripple state does not form a crystal although the translational symmetry is broken in algebraic manner.

Candidate material?

S=3/2 bilayer honeycomb-lattice antiferromagnet

Interlayer coupling is not negligible..., but the nature of its ordering might be understandable within a single-layer honeycomb-lattice classical Heisenberg model.

• S. Okumura, et al., JPSJ 79, 114705 (2010).
• M. Matsuda et al, PRL 105, 187201 (2010).
• O. Smirnova et al, JACS 131, 8313 (2009).

Quantum spin liquid candidate Field-induced phase transition accompanied with AF LRO in the xy plane Magnetization curve

Field-induced AF region

Ripple state might appear in the single crystal of the Bi3Mn4O12(NO3)?

AF SRO is enhanced by the field in our theoretical model (by Okumura et al)

Ripple state can induce a giant-electric polarization vortex

• H. Katsura, et al, PRL 95, 057205 (2005).

Spin Single-q Polarization texture

• A. K. Yadev, et al, Nature 530, 198

(2016).

Ripple state

Summary

We have found a new type of multiple-q state, ripple state, in the J1-J2 classical honeycomb-lattice Heisenberg antiferromagnet, discussing its possible realization in S=3/2 honeycomb-lattice antiferromagnet Bi3Mn4O12(NO3). Ripple Ring

• T. S. and H. Kawamura, arXiv:1810.02951

(Related work is, T. S., T. Okubo and H. Kawamura, arXiv:1902.01582)