Magnetic Blue Phase in the Chiral Itinerant Magnet MnSi

Chiral nematic liquid crystals sometimes form blue phases characterized by spirals twisting in different directions. By combining model calculations with neutron-scattering experiments, we show that the magnetic analogue of blue phases does form in the chiral itinerant magnet MnSi in a large part of the phase diagram. The properties of this blue phase explain a number of previously reported puzzling features of MnSi such as partial magnetic order and a two-component specific-heat and thermal-expansion anomaly at the magnetic transition.

Figure 1

Calculations for clusters of spins interacting via Eq. (1). Real-space $6\times 6\times 6$ unit-cell clusters: (a) helix locked in the cubic 111 direction (as in the low-$T$ phase) and (b) the optimized structure. Parallel spins have the same color. (c),(d) Calculated magnetic SANS intensity of (a) and (b), respectively. The 20% variation along the ring in (d) is most likely due to the finite size, the cubic shape, and the small number of clusters averaged over. (e) Average energies $E$ (arbitrary units) per pair of nearest-neighbor spins interacting via Eq. (1) for FM order (green), a locked helix (red), and optimized configurations (blue) vs the number of sites $N$. Zero is $E$ of a pair of spins in a fully optimized (unfrustrated) 1D chain. (f) Optimized $12\times 12\times 12$ unit-cell cluster.

Figure 2

Scans across (a) and along (b) the ring of magnetic scattering at $E=0$. Schematic insets show the scan trajectories in the $[110/001]$ scattering plane. Black dots depict positions of magnetic Bragg peaks below $T_c$. Lines are guides to the eye. (a) Inset on the right: High-resolution scan revealing magnetic satellite peaks around the nuclear (110) Bragg peak. Main frame: Scans measured with relaxed resolution allowing us to trace the satellites up to 100 K (data do not change above 200 K, and thus 200 K is taken as background). Small peaks around 0.94 and 1.06 are nuclear artifacts equally present at all $T$ and hence not affecting the magnetic signal. (b) High-resolution scans along the ring from [111] to [11-1].

Figure 3

$T$ dependence of neutron scattering intensity at [111] and [110] satellite positions (a) compared to the specific-heat data (b) from Ref. 18.

Figure 4

Intrinsic $E$ width of the magnetic signal at $\mathbf{Q}=(1.018,1.018,0)$ at different $T$ with a linear fit. It scales inversely with the correlation lifetime. Values were extracted from fitting the convolution of a Gaussian (measured experimental resolution) and a Lorentzian (intrinsic signal) to $E$ scans.