Spin phases of the helimagnetic insulator ${\mathrm{Cu}}_2{\mathrm{OSeO}}_3$ probed by magnon heat conduction

We report studies of thermal conductivity as functions of magnetic field and temperature in the helimagnetic insulator ${\mathrm{Cu}}_2{\mathrm{OSeO}}_3$ that reveal novel features of the spin-phase transitions as probed by magnon heat conduction. The tilted conical spiral and low-temperature skyrmion phases, recently identified in small-angle neutron scattering studies, are clearly identified by sharp signatures in the magnon thermal conductivity. Magnon scattering associated with the presence of domain boundaries in the tilted conical phase and regions of skyrmion and conical-phase coexistence are identified.

Figure 1

(a)–(d): $\kappa , T_{avg}$ and $dM/dH$ vs field (corrected for demagnetization) at $T\simeq 2.30$ K for four configurations of the applied field and heat flow. $H\perp J_q$ for (a) and (c), $H\left|\right|J_q$ for (b) and (d). Specimens were cooled in zero field and hysteresis loops traversed sequentially from (arrows, upper panel): ${\mu }_{0}H=0\to 200$ mT, 200 mT $\to -200$ mT, $-200$ mT $\to 0$. The spin phases are distinguished by different background shading and labels: helical ($H$), conical ($C$), tilted conical ($\mathit{TC}$), low-temperature skyrmion (LTS), and fully polarized ($\mathit{FP}$).

Figure 2

Low-$T$ phase diagrams for (a) $H\left|\right|\left[110\right]$ and (b) $H\left|\right|\left[001\right]$. Filled (open) points are from features in $dM/dH$ ($\kappa$). Dashed lines are guides. (c) Upper panels: the $H>0$ portion of $\kappa \left(H\right)$ scans from Figs. 1 and 1. Middle panel: SANS intensities for increasing (“up”) and decreasing (“down”) fields (from Ref. [26]) for the $\mathit{TC}$ (solid curves) and LTS (dashed curves) phases. Field values for the SANS data were shifted upward by 5 mT to align the onset of the $\mathit{TC}$-phase intensity with the leading edge of the sharp peak in $dM/dH$, consistent with the calibration established in Ref. [26]. Lower panel: $dM/dH$ from Fig. 1.

Figure 3

(a) Skyrmion spin textures in the LTS phase, (b) an idealized planar boundary between tilted conical domains of the $\mathit{TC}$ phase (the planes represent layers of atomic spins oriented in the direction dictated by the adjacent conical spirals), (c) $\kappa \left(H\right)$ at $T=3.09$ K for a second specimen with the same configuration as in Fig. 1 but at higher field in the fully polarized state where $\kappa \to {\kappa }_L$ due to the field-induced spin gap. Low-field data at additional temperatures for this specimen are presented in Fig. S3 [24]. (d) Change with field in the specific heat (from Ref. [26]) extended to higher field (dashed lines) and magnon mean-free path computed from kinetic theory as described in the text from data in Fig. 2. The horizontal dashed line indicates the specimen transverse dimension ${\ell }_0$. (e) Zero-field $\kappa \left(T\right)$ for heat flow along different crystallographic directions. Also shown ($+,\times$ and solid curves as guides) are the maximum magnon contributions, ${\kappa }_m^{max}$, inferred for two [110] specimens as described in the text, and for two [111] specimens from Ref. [3] (open squares and triangles).