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Thermodynamic insights into the intricate magnetic phase diagram of EuAl 4

The tetragonal intermetallic compound EuAl 4 hosts an exciting variety of low-temperature phases. In addition to a charge density wave below 140 K, four ordered magnetic phases are observed below 15.4 K. Recently, a skyrmion phase was proposed based on Hall effect measurements under a c-axis magnetic field. Here, we present a detailed investigation of the phase transitions in EuAl 4 under c-axis magnetic field. Our dilatometry, heat-capacity, DC magnetometry, AC magnetic susceptibility, and resonant ultrasound spectroscopy measurements reveal three magnetic phase transitions not previously reported. The first key result is a detailed H ∥ [001] magnetic phase diagram mapping the seven phases we observe. Second, we identify a high-field phase, phase VII, which directly corresponds to the region were skyrmions have been previously suggested. Our results provide guidance for future studies exploring the complex magnetic interactions and spin structures in EuAl 4 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Anisotropic magnetism and electronic structure of trigonal EuAl 2 Ge 2 single crystals

Understanding the interplay between magnetic and electronic degrees of freedom is of profound recent interest in different Eu-based magnetic topological materials. Here, we studied the magnetic and electronic properties of the layered Zintl-phase compound EuAl 2 Ge 2 crystallizing in the trigonal CaAl 2 Si 2 -type structure. We report zero-field neutron diffraction, temperature T - and magnetic-field H-dependent magnetic susceptibility χ(T, H), isothermal magnetization M(T, H), heat capacity C p (T, H), and electrical resistivity ρ(T, H) measurements, together with T-dependent angle-resolved photoemission spectroscopy (ARPES) measurements complemented with first-principle calculations. EuAl 2 Ge 2 undergoes second-order A-type antiferromagnetic (AFM) ordering below T N = 27.5(5) K, with the Eu moments (Eu 2+ , S = 7/2) aligned ferromagnetically in the ab plane while these layers are stacked antiferromagnetically along the c axis. The critical fields at which all moments become parallel to the field are 37.5(5) and 52.5(5) kOe for H ∥ ab and H ∥ c, respectively. The H = 0 magnetic structure consists of trigonal AFM domains associated with ab-plane magnetic anisotropy and a field-induced reorientation of the Eu spins in the domains is also evident at T = 2 K below the critical field H c1 = 2.5(1) kOe. The ρ(T) measurements reveal metallic behavior transforming into a slight resistivity increase on cooling towards T N . A pronounced loss of spin-disorder scattering is observed below T N . The ARPES results show that EuAl 2 Ge 2 is metallic both above and below T N , and the Fermi surface is anisotropic with two hole pockets at the zone center and one small electron pocket at each M point. In the AFM phase, we directly observe folded bands in ARPES due to the doubling of the magnetic unit cell along the c axis with an enhancement of quasiparticle weight due to the complex change in the coupling between the magnetic moments and itinerant electrons on cooling below T N . The observed electronic structure is well reproduced by first-principle calculations, which also predict the presence of nontrivial electronic states near the Fermi level in the AFM phase with Z 2 topological numbers 1;(000)

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Origin of charge density wave in topological semimetals SrAl 4 and EuAl 4

Topological semimetals in BaAl 4 -type structure show many interesting behaviors, such as charge density wave (CDW) in SrAl 4 and EuAl 4 , but not the isostructural and isovalent BaAl 4 , SrGa 4 , and BaGa 4 . Here using Wannier functions based on density functional theory, we calculate the susceptibility functions with millions of k-points to reach the small q-vector and study the origin and driving force behind the CDW. Our comparative study reveals that the origin of the CDW in SrAl 4 and EuAl 4 is the strong electron-phonon coupling interaction for the transverse acoustic mode at small q-vector along the Γ-Z direction besides the maximum of the real part of the susceptibility function from the nested Fermi surfaces of the Dirac-like bands, which explains well the absence of CDW in the other closely related compounds in a good agreement with experiment. We also connect the different CDW behaviors in the Al compounds to the macroscopic elastic properties.

36 MATERIALS SCIENCE↗

Band Structure and Charge Ordering of Dirac Semimetal EuAl 4 at Low Temperatures

In this article, EuAl 4 is proposed to host a topological Hall state. This material also undergoes four consecutive antiferromagnetic (AFM) transitions upon cooling below T N1 = 15.4 K in the presence of charge density wave (CDW) order that sets in below T CDW = 140 K. We use angle-resolved photoemission spectroscopy and density-functional-theory calculations to study how magnetic ordering affects the electronic properties in EuAl 4 . Here, we found changes in the band structure upon each of the four consecutive AFM transitions including band splitting, renormalizations, and appearance of new bands forming additional Fermi sheets. In addition we also found significant enhancement of the quasiparticles’ lifetime due to suppression of spin flip scattering, similar to what was previously reported for ferromagnetic EuCd 2 As 2 . Surprisingly, we observe that most significant changes in electronic properties occur not at T N1 , but instead at the AFM3 to AFM4 transition, which coincides with the largest drop in resistivity.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Materials Data on EuAl by Materials Project

EuAl is delta Molybdenum Boride-like structured and crystallizes in the orthorhombic Pnma space group. The structure is three-dimensional. Eu is bonded in a 7-coordinate geometry to seven equivalent Al atoms. There are a spread of Eu–Al bond distances ranging from 3.33–3.64 Å. Al is bonded in a 9-coordinate geometry to seven equivalent Eu and two equivalent Al atoms. Both Al–Al bond lengths are 2.79 Å.

36 MATERIALS SCIENCE↗

Incommensurate Transverse Peierls Transition and Signature of Chiral Charge Density Wave in EuAl 4

In one-dimensional quantum materials, electrons and lattices can undergo a Peierls transition, a translational symmetry-breaking instability traditionally understood through electron coupling to longitudinal acoustic phonons. Recently, this paradigm has been revised in topological semimetals, where transverse acoustic phonons couple to p-orbital electrons, giving rise to a transverse Peierls transition. Importantly, transverse Peierls transition-induced distortions can further break mirror or inversion symmetries, producing nematic or chiral charge density waves. Here, we report the experimental identification of an incommensurate transverse Peierls transition in EuAl 4 . Using meV-resolution inelastic x-ray scattering, we observe complete softening of a transverse acoustic phonon upon cooling, while the longitudinal acoustic mode remains unaffected. First-principles calculations reveal that the transverse Peierls transition wavevector coincides with a charge susceptibility peak connecting nested Dirac bands. Second harmonic generation confirms mirror symmetry breaking, supporting a chiral charge density wave stabilized by the transverse Peierls transition.

36 MATERIALS SCIENCE↗

Complex magnetic ordering in EuAl 4 –A 151 Eu Mössbauer study

151 Eu Mössbauer spectroscopy has been used to investigate the behaviour of EuAl 4 through the four magnetic transitions that occur below 16 K. We find clear evidence for the first transition (T N1 , the onset of order) where an incommensurate modulated magnetic structure appears, and the third (T N3 ) where the modulation disappears at the tetragonal → orthorhombic structural transition. We see no changes at the lowest transition (T N4 ) but find that the modulation amplitude passes through a maximum at T N2 . Data on the isostructural but magnetically simpler EuGa 4 are also presented for comparison.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Spontaneous Chirality Flipping in an Orthogonal Spin-Charge Ordered Topological Magnet

The asymmetric distribution of chiral objects with opposite chirality is of great fundamental interest ranging from molecular biology to particle physics. In quantum materials, chiral states can build on inversion-symmetry-breaking lattice structures or emerge from spontaneous magnetic ordering induced by competing interactions. Although the handedness of a chiral state can be changed through external fields, a spontaneous chirality flipping has yet to be discovered. We present experimental evidence of chirality flipping via changing temperature in a topological magnet EuAl 4 , which features orthogonal spin density waves (SDW) and charge density waves (CDW). Using circular dichroism of Bragg peaks in the resonant magnetic x-ray scattering, we find that the chirality of the helical SDW flips through a first-order phase transition with modified SDW wavelength. Intriguingly, we observe that the CDW couples strongly with the SDW and displays a rare commensurate-to-incommensurate transition at the chirality flipping temperature. Combining with first-principles calculations and angle-resolved photoemission spectroscopy, our results support a Fermi surface origin of the helical SDW with intertwined spin, charge, and lattice degrees of freedom in EuAl 4 . Our results reveal an unprecedented spontaneous chirality flipping and lay the groundwork for a new functional manipulation of chirality through momentum-dependent spin-charge-lattice interactions. Published by the American Physical Society 2024

3-dimensional systems↗

LaueMatching: an approach for rapid and robust indexing of Laue diffraction patterns

Traditional Laue diffraction pattern indexing often struggles with noisy data, weak signals, peak overlap and missing reflections, particularly from complex or deformed microstructures. Here, we introduce LaueMatching, a high-throughput indexing algorithm designed to overcome these limitations. LaueMatching utilizes a fundamentally different approach based on direct pattern correlation: experimentally pre-processed images are compared against a comprehensive pre-computed library of simulated diffraction patterns corresponding to a dense grid of possible orientations. This approach bypasses the need for explicit peak identification and fitting, steps that are often a failure point for traditional methods. The algorithm rapidly and robustly indexes multiple crystallographic orientations and crystal systems simultaneously, even from challenging patterns. LaueMatching's effectiveness and accuracy have been rigorously tested and validated on diverse experimental (Ni, Al, EuAl 2 O 4 ) and simulated diffraction patterns, demonstrating high-fidelity orientation refinement. Code to implement this approach on both CPU and GPU resources can be downloaded from https://github.com/AdvancedPhotonSource/LaueMatching.

36 MATERIALS SCIENCE↗