Collinear Magnetic Structure in the Diamond Network Magnet EuTi$_2$Al$_{20}$

TL;DR

EuTi2Al20 hosts Eu2+ spins on a diamond network and exhibits antiferromagnetic order with propagation vector $q_m=(1,0,0)$ in zero field. The authors combine neutron powder diffraction and resonant X-ray diffraction with symmetry analysis to identify a collinear AFM state described by $mX_2$ and compatible with magnetic space groups $P_Inna$ or $P_Inn2$, revealing twelve magnetic domains. They argue that stabilizing X-point order requires longer-range exchange, such as $J_4$, consistent with RKKY interactions in this metal, and that simple $J_1$-$J_2$ models are insufficient. The work provides a concrete experimental reference for frustration on the diamond network and motivates future field-dependent studies to explore interaction-driven quantum states and possible field-induced spin textures.

Abstract

The magnetic structure of EuTi$_2$Al$_{20}$, in which magnetic Eu$^{2+}$ ions form a diamond network, was investigated using neutron and resonant X-ray diffraction on powder and single-crystal samples. The propagation vector was determined to be $\textbf{\textit{q}}_{\rm m}=(1,0,0)$~r.l.u. from these diffraction measurements. All possible magnetic structures in the space group $Fd\bar{3}m$ with this propagation vector were examined using the irreducible representation method and magnetic space group analysis. This magnetic structure was identified as a collinear antiferromagnetic structure with the magnetic space group $P_Inna$ (\#52.320) or $P_Inn2$ (\#34.164) under zero magnetic field. In these magnetic structure, frustration arises from competing magnetic interactions on the diamond network. These findings provide a concrete experimental reference for assessing the role of competing interactions in diamond-network magnets and motivate further studies of interaction-driven quantum states.

Figures (5)

• Figure 1: (a) The diamond network composed of Eu sites of EuTi$_2$Al$_{20}$. The first-, second-, third-, and fourth-neighbor exchange interaction terms are denoted by $J_1$, $J_2$, $J_3$, and $J_4$. (b) Crystal structure of EuTi$_2$Al$_{20}$ showing the network of the Eu-Al/Ti-Al cages. Note that it is translated by $(-1/8,-1/8,-1/8)$ relative to (a). (c) Configuration of resonant X-ray diffraction (RXD) experiment.
• Figure 2: (a) Neutron powder diffraction (NPD) patterns at 1.7 K and 20 K. The reflection angles for each basis vectors (BVs) are indicated by black bars. The star marker indicates an unknown reflection. Inset: difference pattern (1.7 K - 20 K) with the expected positions of magnetic reflections from $\psi_1-\psi_6$.(b-e) Resonant X-ray diffraction (RXD) results. (b) Rocking curve (RC) of the fundamental reflection $(8,0,0)$ at 1.8 K and 0 T. (c) RC of the magnetic reflection $(10,1,0)$ at 1.5 K and 0 T. (d) Energy and (e) temperature dependence of the magnetic reflection $(10,1,0)$.
• Figure 3: (a) Position of the observed magnetic reflection at 1.5 K and 0 T. (b) Relation between the fundamental Bragg reflection and the magnetic reflection. (c), (e), (g) $2\theta$ dependence of the magnetic reflection, and (d), (f), (h) corresponding polarization analysis of the magnetic reflection, respectively.
• Figure 4: (a) Magnetic subgroup corresponding to the irreducible representation mX$_2$. (b) Magnetic structure of $P_Inn2$ (#34.164). Left: $(m_1,m_2)=(\alpha,\beta)$, Right: $(m_1,m_2)=(\beta,-\alpha)$ with $\textbf{q}_{\rm A}=(1,0,0)$ r.l.u. The red and blue dashed lines trace the tetrahedral units on each sublattice of the diamond network. The red and blue arrows represent the magnetic moments at the Eu sites #1 and #2, respectively.
• Figure 5: Order-parameter space of $(m_1,m_2)$ in two dimentional irrep ${\rm mX}_2$ with $\textbf{q}_{\rm A}=(1,0,0)$ r.l.u. Blue solid and green dashed lines denote the $P_Inna$ and $P_I\bar{4}n2$, respectively. The red-shaded region represents $P_Inn2$. Symmetry operations are indicated by arrows: spatial inversion $\mathcal{P}$ with black solid arrows, time-reversal $\mathcal{T}$ with black dotted arrows, and $C_{4x} +\textbf{t}$ ($\textbf{t}=(-1/4,-1/4,-1/4)$) around Eu atom #1 denoted in Table \ref{['t1']} of the X-point subgroup of $Fd\bar{3}m$ with black dash-dotted arrow.