Conical Magnetic Structure and Atomic Displacements in Chiral Helimagnet Yb(Ni,Cu)$_3$Al$_9$ in Magnetic Fields along the Helical $c$ Axis

TL;DR

This work probes the conical magnetic state in the uniaxial chiral helimagnet Yb(Ni$_{1-x}$Cu$_x$)$_3$Al$_9$ under magnetic fields along the helix axis using resonant X-ray diffraction. A simple $q=(0,0,1)$ 120$^{\circ}$ mean-field framework links the Néel temperature $T_N$ and the critical field $H_c^z$ to strong intralayer exchanges, while the field-induced, weaker interlayer couplings govern $H_c^x$; concomitant atomic displacements with the same modulation as the conical order reveal a strong spin-lattice coupling via field-induced quadrupole moments. The experiments show critical fields of $H_c^z = 4$ T for $x=0$ and $H_c^z = 7$ T for $x=0.05$, with lattice distortions evidenced by nonresonant Thomson scattering and the appearance of quadrupole moments $O_{zx}$ and $O_{yz}$. The zero-field $E2$ contribution, arising from a magnetic octupole, must be included to explain observed fundamental-peak intensities, highlighting subtle multipole effects at play in this $f$-electron system. Overall, the results clarify how intralayer versus interlayer exchange, together with spin-lattice coupling, shapes field-induced noncollinear spin textures in chiral magnets, and demonstrate a clear link between magnetic order and lattice distortions in Yb-based materials.

Abstract

We investigated the conical magnetic state of a uniaxial chiral helimagnet Yb(Ni$_{1-x}$Cu$_x$)$_3$Al$_9$ induced in magnetic fields applied along the $c$ axis, which coincides with the helical axis at zero field. Using resonant X-ray diffraction, we clearly observed the disappearance of magnetic satellite peaks, corresponding to the transition from the conical to the field-induced ferromagnetic state. The critical fields were determined to be 4 T for $x=0$ and 7 T for $x= 0.05$, which were hardly discernible in the magnetization curves. We also found that atomic displacements with the same propagation vector emerge simultaneously with the onset of the conical order. The transition temperature $T_{\text{N}}$ and the critical fields for $H \parallel c$ ($H_{\text{c}}^{z}$) and $H\perp c$ ($H_{\text{c}}^{x}$) are discussed on the basis of a mean-field calculation for a simple $q=1$ model of the magnetic structure. We propose that $T_{\text{N}}$ and $H_{\text{c}}^{z}$ primarily reflect the dominant intralayer exchange interactions within the honeycomb Yb-layer, whereas $H_{\text{c}}^{x}$ is governed by the much weaker interlayer coupling.

Figures (10)

• Figure 1: (Color online) (a) Magnetic structure of YbNi$_3$Al$_9$ for the right-handed crystal. The magnetic moments of Yb-a and Yb-b are indicated by different colors. The magnetic moments rotate clockwise when propagating along the $c$ axis. (b) Absorption coefficient of YbNi$_3$Al$_9$ deduced from the fluorescence spectrum. (c) X-ray energy dependence of the intensity of the (6, 0, $-0.83$) resonant magnetic Bragg diffraction. Triangles represent the background intensities.
• Figure 2: (Color online) (a) Reciprocal-space scans along (6, 0, $L$) at several magnetic fields applied along the helical $c$ axis. The incident X-ray polarization is RCP. (b) Magnetic-field dependence of the wave number $q$.
• Figure 3: (Color online) (a--c) Incident-polarization ($\Delta\theta_{\text{PR}}$) dependence of the peak intensity in magnetic fields of 0, 0.4, and 1.6 T applied along the $c$ axis, without polarization analysis. The background has been subtracted. The vertical dashed lines indicate the positions of the RCP and LCP states. The solid lines represent fits obtained by convolving Eq. (\ref{['eq:CrossSec2']}) with a Gaussian resolution function.
• Figure 4: (Color online) (a) Reciprocal-space scan along $(6, 0, L)$ in magnetic fields applied along the $c$ axis. The incident X-rays are $\pi$ polarized ($P_3 = -1$). (b) Magnetic-field dependence of the wavenumber $q$.
• Figure 5: (Color online) (a) X-ray energy dependence of the peak intensity in magnetic fields applied along the $c$ axis. (b) Magnetic-field dependence of the nonresonant intensity at 8.920 keV.