Quintuplet condensation in the skyrmionic insulator Cu2OSeO3 at ultrahigh magnetic fields

TL;DR

The paper investigates magnon Bose-Einstein condensation in the insulating skyrmion-host Cu$_2$OSeO$_3$ under ultrahigh magnetic fields, focusing on the regime between the $\frac{1}{2}$ plateau and full saturation. By mapping the Cu$_4$ tetrahedral units to a pseudospin-$\tfrac{1}{2}$ XXZ model and applying tetrahedral mean-field theory, complemented by QMC, the authors describe an intermediate canted XY ferrimagnetic phase that emerges from the closing of the triplet-quintuplet gap and condenses at $Q=0$. Experimentally, ultrahigh-field Faraday rotation up to $500$ T reveals a dome-like polarization signal driven by linear magnetoelectric coupling, enabling observation of long-range transverse order via EFIF even when $M_\perp$ vanishes. They show that Dzyaloshinskii–Moriya interactions are negligible at high fields, so the observed magnon BEC is captured by exchange terms alone, linking strong electron correlations, magnetoelectric coupling, and extreme-field magnetism in a Mott insulator with skyrmion physics.

Abstract

We report ultrahigh magnetic field Faraday rotation results on the chiral helimagnet Cu2OSeO3, the first Mott insulator showing skyrmion lattice phases and a linear magnetoelectric effect. Between 180 and 300 T, we find signatures of a Bose-Einstein condensation (BEC) of magnons, which can be described as a canted XY ferrimagnet. Due to the magnetoelectric coupling, the transverse magnetic order of the indivual Cu2+ spins is accompanied by a characteristic dome-like electric polarization which is crucial for the observation of the condensate via the Faraday rotation effect.

Figures (10)

• Figure 1: (a) Inset: Network of Cu$^{2+}$ ions in Cu$_2$OSeO$_3$. Cu(1) and Cu(2) represented by blue and brown spheres, respectively. The intra-tetrahedral couplings $J_\text{s}^{\text{AF}}$ and $J_\text{s}^{\text{FM}}$ and the inter-tetrahedral couplings $J_\text{w}^{\text{AF}}$ and $J_\text{w}^{\text{FM}}$ are shown by bold and thin lines (the longer-range Cu(1)-Cu(2) coupling $J_\text{O$\cdots$\!{O}}^{\text{AF}}$ is not shown) Janson2014. The subscripts 's' and 'w' stand for 'strong' and 'weak' couplings, respectively. Main: Field-dependence of the energy diagram (energies measured from the zero-field ground state triplet) of an isolated Cu$_4$ cluster for the exchange parameters of Ref. Ozerov2014. (b) Temperature-field phase diagram, showing the low-field conical, helical, skyrmionic phases (schematic), and the high-field magnon condensate presented in this study (see text).
• Figure 1: Magnetic-field waveforms by the single-turn coil (STC) and electromagnetic flux compression (EMFC).
• Figure 2: Faraday rotation angle of Cu$_2$OSeO$_3$ normalized by the sample thickness, (a) $\theta_\mathrm{F}/d$ and (b) $\theta_\mathrm{F}'/d$ [Eq. (\ref{['eq:theta2']})] as a function of a magnetic field at 5 K. The inset in (a) shows the transmission intensity. Contributions from the natural and magnetic optical activities ($\theta_\mathrm{NOA}$, $\theta_\mathrm{MOA}$) and the linear background ($\theta_\mathrm{BG}$) are indicated by the dashed lines. $B_\mathrm{c}$ and $B_\mathrm{s}$ indicate the end of the $\frac{1}{2}$ plateau and the saturation magnetic field, respectively.
• Figure 2: Magnetic-field waveforms by the single-turn coil (blue, inset) and the dual-pulse magnet (black).
• Figure 3: Comparison between the TMF theory (solid lines), effective $\tau$ model (dashed lines) and QMC calculations (open symbols), using the exchange parameters of Ref. Ozerov2014. Results are shown for the $x$- and $z$-components of the Cu(1) and Cu(2) spins, as well as for the total $S^x$ and $S^z$.