On the magnetic contribution of itinerant electrons to neutron diffraction in the topological antiferromagnet CeAlGe

Abstract

We report a neutron diffraction study of the magnetic structure of CeAlGe, a candidate topological semimetal that hosts a non-collinear, multi-$\mathbf{k}$ magnetic phase. By measuring both low- and high-momentum-transfer magnetic Bragg peaks within a single experimental setup, we refine a magnetic structure model based solely on localized Ce moments. This model, which differs from that obtained using only high-$Q$ data, quantitatively reproduces the observed intensities, including the $(000)$ zeroth-order magnetic satellites that are especially sensitive to subtle components of the modulation. While a contribution from itinerant electrons to the zeroth satellite cannot be definitively excluded, our analysis reveals no unambiguous evidence for such effects within experimental uncertainty. The refined magnetic structures exhibit topologically nontrivial winding patterns, derived from the fitted magnetic parameters, that support localized, particle-like spin textures with half-integer topological charges. These features provide a natural microscopic origin for the observed topological Hall effect, establishing CeAlGe as a model system where magnetism and topology are intimately linked.

Figures (15)

• Figure 1: Magnetic structure of CeAlGe corresponding to the experimentally refined Model C (see Table \ref{['mag_table']}). The $x$- and $y$-axes are given in units of the crystallographic unit cell. The magnetic modulation has a period of approximately 15 unit cells; the figure displays one full magnetic period (15 $\times$ 15 cells) projected onto the $xy$-plane. Ce1 and Ce2 sites are represented by small filled and large open black circles, respectively. The out-of-plane ($z$) component of the magnetic moments is indicated by color. The moments form ferromagnetic chains along the $z$-axis at each $(x,y)$ position.
• Figure 2: The Rietveld refinement pattern and the calculated profile of the neutron diffraction data for ${\rm CeAlGe}$ at T=10 K measured with the wavelength $\lambda=2.45$ Å at HRPT diffractometer. The rows of tics show the Bragg peak positions. The difference between observed and calculated intensities is shown by the dotted blue line.
• Figure 3: The Rietveld refinement pattern and the calculated profile of the neutron diffraction data for ${\rm CeAlGe}$ at T=10 K measured at CNCS/SNS with the wavelength $\lambda=4.96$ Å. The rows of tics show the Bragg peak positions. The difference between observed and calculated intensities is shown by the dotted blue line.
• Figure 4: Raw neutron diffraction difference patterns ("1.7 K - 10 K") as a function of the scattering vector $Q$, containing purely magnetic contributions, measured at DMC/SINQ (black line and open symbols) and CNCS/SNS (blue dotted line and closed symbols) with wavelengths $\lambda = 4.506$ and 4.96 Å, respectively. The patterns were rescaled to match the integral intensity of the diffraction peak at $Q \simeq 0.85$ Å$^{-1}$.
• Figure 5: The difference pattern containing purely magnetic contribution, measured at CNCS/SNS with the wavelength (a) $\lambda=12.31$ Å and (b) $\lambda=4.96$ Å. The tics show the Bragg peak positions. The calculated intensities based on model A, B and C are shown by green, red and blue dashed lines, respectively.