Complex Chiral Modulations in FeGe Close to Magnetic Ordering

We report on detailed polarized small-angle neutron scattering on cubic FeGe in magnetic fields applied either along (transverse) the scattering vector or parallel (longitudinal) to the neutron beam. The ($H$, $T$) phase diagrams for all principal axes contain a segmented $A$-phase region just below the onset of magnetic order. Hexagonal Bragg-spot patterns were observed across the entire $A$-phase region for the longitudinal geometry. Scattering intensity was observed in parts of the $A$ phase for both scattering configurations. Only in a distinct pocket ($A_1$) was vanishing scattering intensity found in the transverse geometry.

Figure 1

(a) SANS map for the transverse geometry with the polarization ${\mathbf{P}}_0\perp \mathbf{k}$, i.e., perpendicular to the incoming neutron beam, but parallel to $\mathbf{H}$ and the $⟨100⟩$ direction. (b)–(d) Representative scattering maps for the longitudinal geometry (${\mathbf{P}}_0\parallel \mathbf{k}$). Hexagonal Bragg-spot pattern with ${\mathbf{Q}}_h={\mathbf{Q}}_s$ are found in a well defined ($H$, $T$) range for all principal axes.

Figure 2

Integrated intensity vs $H$ at various temperatures after zero $H$ cooling. (a)–(c) Transverse geometry. Lower ($H_{c1}$) and upper critical field ($H_{c2}$) as well as the lower and upper boundaries of the $A$ phase, $H_{A_L}$, and $H_{A_U}$, are defined for each $T$ as indicated in (a). (d)–(f) Longitudinal geometry. $H_{A_L}$ and $H_{A_U}$ are the same for all the temperatures and $H$ directions. The integrated intensity of the sixfold Bragg pattern shows an almost constant, plateaulike $H$ dependence, followed by a pronounced maximum above $H_{A^{*}}$, which changes with $T$ and $H$ direction. The scattering intensity of each of the six Bragg spots has a count rate very similar to that of the single Bragg spot in the transverse geometry.

Figure 3

Intensity maps for transverse (left) and longitudinal (right) scattering geometry. The symbol size represents the intensity and dots indicate vanishing intensity. (a)–(c) Strong intensity in the major part of the phase diagram confirms the magnetic structure reported in Ref. 34. (d)–(f) The $H$-induced intensity variation indicates a segmentation of the $A$-phase region. The shaded regions correspond to the sixfold scattering in the longitudinal geometry. Field-cooled data (symbols connected by a horizontal solid line) give an idea about the $T$ width of the precursor region. The intensity at $H=0$ for $⟨100⟩$ is indicative for the occurrence of the helical spin structure.

Figure 4

Magnetic phase diagram of FeGe based on integrated SANS intensities (colored symbols) and magnetic susceptibility data (dotted lines) [27] for $H\parallel [100]$. The two pockets, $A_1$ and $A_2$, of the $A$-phase region and the phase lines are based on the magnetic-susceptibility data. Solid lines represent the lower ($H_{A_L}^{Lg}$ and $H_{A_L}^{Tr}$) and upper ($H_{A_U}^{Lg}$ and $H_{A_U}^{Tr}$) boundaries of the $A$ phase in the longitudinal and transverse geometry, respectively.