Anomalous Temperature Behavior of the Chiral Spin Helix in ${\mathrm{CrNb}}_3{\mathrm{S}}_6$ Thin Lamellae

Using Lorentz transmission electron microscopy and small-angle electron scattering techniques, we investigate the temperature-dependent evolution of a magnetic stripe pattern period in thin-film lamellae of the prototype monoaxial chiral helimagnet ${\mathrm{CrNb}}_3{\mathrm{S}}_6$. The sinusoidal stripe pattern appears due to formation of a chiral helimagnetic order (CHM) in this material. We found that as the temperature increases, the CHM period is initially independent of temperature and then starts to shrink above the temperature of about 90 K, which is far below the magnetic phase transition temperature for the bulk material $T_c$ (123 K). The stripe order disappears at around 140 K, far above $T_c$. We argue that this cascade of transitions reflects a three-stage hierarchical behavior of melting in two dimensions.

Figure 1

(a) Schematic of the chiral helimagnetic order (CHM) with a period $L$. (b) Magnetization curves of the bulk ${\mathrm{CrNb}}_3{\mathrm{S}}_6$ single crystal as a function of $T$ with a small $H$ applied perpendicular to the helical axis. (c) Temperature dependence of $L$ expected from 3D mean-field theory.

Figure 2

Stripe pattern in a thin lamella of ${\mathrm{CrNb}}_3{\mathrm{S}}_6$ crystal at various temperatures. Lorentz Fresnel images and SAES data are given in (a)–(e) and (f)–(j), respectively. The insets in (a)–(c) present harmonic intensity profiles of the CHM. A pair of fundamental satellite peaks is indicated by arrows in (f)–(i). Intensity line trace along dotted arrows in the $c^{*}$ direction is shown below (i), indicating the presence of spots associated with the magnetic stripe pattern at 137 K.

Figure 3

The CHM period (a) and wave number (b) as a function of $T$ in a thin lamella of ${\mathrm{CrNb}}_3{\mathrm{S}}_6$ crystal. Blue squares represent the data obtained by the Lorentz Fresnel and DPC methods. Green circle and red triangles correspond to the SAES data taken with increasing and decreasing $T$, respectively. The inset in (a) shows the curve derived from the 3D mean-field theory together with the experimental data and $T_c$ for the bulk crystal. Three regions which show different kinds of $T$ dependence are clearly seen. Regions I, II, and III correspond to the solid phase (the CHM with the constant period), the floating solid phase (the shrinkage of the CHM period), and the isotropic fluid phase (the paramagnetic regime), respectively.