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At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Experimental confirmation of the magnetic ordering transition induced by an electronic structure change in the metallic triangular antiferromagnet Co 1/3⁢ TaS 2

We report angle-resolved photoemission spectroscopy (ARPES) studies combined with DFT+DMFT calculations to confirm that the magnetic ordering vector transition from Q=(1/2,0,0) to Q=(1/3,0,0) in the metallic triangular antiferromagnets Co 1/3±𝜀⁢ TaS 2 (𝜀 ≈ 0.007) is induced by the electronic structure change in the system. The ARPES-measured Fermi surface (FS) maps of Co 0.325 ⁢TaS 2 show two hexagonal and one circular holelike FSs around Γ, which matches well with the triple- Q state by taking into account the contribution of nesting vectors occurring between Co 3⁢𝑑 and Ta 5⁢𝑑 orbitals. In the case of Co 0.340 ⁢TaS 2 , a new electron pocket around K appears, and the FS geometry changes as a result of the correlation effect of Co 4 ⁢S 18 tripods forming in the system. The magnetic susceptibility calculations based on the charge-self-consistent DFT+DMFT band structures and the random phase approximation indicate that the most stable magnetic ordering vector (1/2,0,0) split into (1/6,0,0) and (1/2,0,0), which is consistent with the magnetic phase transition around 𝑥=1/3 in Co 𝑥 ⁢TaS 2 .

Fermi surface↗
DOE OSTI2024

Two-step electronic response to magnetic ordering in a van der Waals ferromagnet

The two-dimensional material Cr 2 ⁢Ge 2 ⁢Te 6 is a member of the class of insulating van der Waals (vdW) magnets. Here, using high resolution angle-resolved photoemission spectroscopy in a detailed temperature dependence study, we identify a clear response of the electronic structure to a dimensional crossover in the form of two distinct temperature scales marking onsets of modifications in the electronic structure. Specifically, we observe Te 𝑝-orbital-dominated bands to undergo changes at the Curie transition temperature 𝑇 𝐶 while the Cr 𝑑-orbital-dominated bands begin evolving at a higher temperature scale. Combined with neutron scattering, density functional theory calculations, and Monte Carlo simulations, we find that the electronic system can be consistently understood to respond sequentially to the distinct temperatures at which in-plane and out-of-plane spin correlations exceed a characteristic length scale. Finally, our findings reveal the sensitivity of the orbital-selective electronic structure for probing the dynamical evolution of local moment correlations in vdW insulating magnets.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Stripe magnetic order and field-induced quantum criticality in the perfect triangular-lattice antiferromagnet CsCeSe 2

The two-dimensional triangular-lattice antiferromagnet (TLAF) is a textbook example of frustrated magnetic systems. Despite its simplicity, the TLAF model exhibits a highly rich and complex magnetic phase diagram, featuring numerous distinct ground states that can be stabilized through frustrated next-nearest-neighbor couplings or anisotropy. In this paper, we report low-temperature magnetic properties of the TLAF material CsCeSe 2 . The inelastic neutron scattering (INS) together with specific heat measurements and density functional theory calculations of crystalline electric field suggest that the ground state of Ce ions is a Kramers doublet with strong easy-plane anisotropy. Elastic neutron scattering measurements demonstrate the presence of stripe-yz magnetic order that develops below T N = 0.35K, with the zero-field ordered moment of m Ce ≈ 0.65μ B . Application of magnetic field first increases the ordering temperature by about 20% at the intermediate field region and eventually suppresses the stripe order in favor of the field-polarized ferromagnetic state via a continuous quantum phase transition (QPT). The field-induced response demonstrates sizable anisotropy for different in-plane directions, B ∥ a and B ⊥ ⁢a, which indicates the presence of bond-dependent coupling in the spin Hamiltonian. As a result, we further show theoretically that the presence of anisotropic bond-dependent interactions can change the universality class of QPT for B ∥ a and B ⊥ ⁢a.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Absence of Long-Range Magnetic Ordering in a Trirutile High-Entropy Oxide (Mn 0.2 Fe 0.2 Co 0.2 Ni 0.2 Cu 0.2 )Ta 1.92 O 6–δ

Functionalities of solid-state materials are usually considered to be dependent on their crystal structures. The limited structural types observed in the emerging high-entropy oxides put constraints on the exploration of their physical properties and potential applications. Herein, we synthesized the first high-entropy oxide in a trirutile structure, (Mn 0.2 Fe 0.2 Co 0.2 Ni 0.2 Cu 0.2 )Ta 1.92 O 6–δ , and investigated its magnetism. The phase purity and high-entropy nature were confirmed by powder Xray diffraction and energy-dispersive spectroscopy, respectively. X-ray photoelectron spectroscopy indicated divalent Mn, Co, Ni, and Cu along with trivalent Fe. Magnetic property measurements showed antiferromagnetic coupling and potential short-range magnetic ordering below ~4 K. The temperature-dependent heat capacity data measured under zero and high magnetic fields confirmed the lack of long-range magnetic ordering and a possible low-temperature phonon excitation. The discovery of the first trirutile high-entropy oxide opens a new pathway for studying the relationship between the highly disordered atomic arrangement and magnetic interaction. Furthermore, it provides a new direction for exploring the functionalities of highentropy oxides.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Long-range magnetic order with disordered spin orientations in a high-entropy antiferromagnet

Disorder in magnetic systems typically suppresses long-range order, promoting short-range states such as spin glasses and magnetic clusters. This is particularly prominent in high-entropy materials, characterized by the random distributions of local magnetic entities and exchange interactions. However, in rare exceptions, long-range magnetic order can persist in high-entropy systems, while the microscopic characters and underlying mechanisms remain elusive, especially the magnetic behaviors of individual elements. Here, combining neutron diffraction and resonant soft x-ray scattering, we have conducted an element-specific investigation into the magnetic order of a high-entropy honeycomb-lattice van der Waals material (Mn 1/4 Fe 1/4 Co 1/4 Ni 1/4 )PS 3 . Despite significant atomic disorder, long-range zigzag antiferromagnetic order is observed below 72 K, with all four transition-metal elements participating in a unified phase transition. However, the spin orientations of various elements are distinct, attributed to the competition between single-ion anisotropies and exchange interactions. Our findings showcase a novel form of long-range magnetic order with disordered spin orientations, which is synergically stabilized by distinct magnetic elements in a high entropy magnet, offering a new paradigm for understanding complex magnetic systems.

Shen, Yao [Chinese Academy of Sciences (CAS), Beij↗
DOE OSTI2021

Strong Magnetocrystalline Anisotropy Arising from Metal–Ligand Covalency in a Metal–Organic Candidate for 2D Magnetic Order

Layered metal–organic frameworks are promising candidates for new two-dimensional magnets, as their synthetic programmability of these materials can provide a route to diverse structural and electronic properties. However, such framework materials typically lack the heavy elements that engender magnetocrystalline anisotropy in the monolayer ferromagnets reported to date. Alternative sources of magnetic anisotropy are therefore needed in these materials. Here, we report the synthesis of single crystals of the framework material (NMe 4 ) 2 [Fe 2 L 3 ] (H 2 L = 3,6-dichloro-2,5-dihydroxybenzoquinone) and evaluate the angular dependence of its magnetic properties. Oriented-crystal magnetization measurements reveal strong uniaxial anisotropy, where the easy axis is aligned with the crystallographic c axis. While the spin carriers of this structure are isotropic $S = ^5/_2$ Fe III metal centers and $S = ^1/_2$ organic linkers, the anisotropy energy of the framework material is comparable to that of reported 2D ferromagnets. Density functional theory calculations indicate that the observed magnetocrystalline anisotropy arises from ligand-to-metal charge transfer that enhances the magnetic anisotropy of the otherwise isotropic Fe centers, suggesting that metal–ligand covalency can be utilized as a general additive for the development of 2D magnets. These results in this study show the possibility for (NMe 4 ) 2 [Fe 2 L 3 ] to retain magnetic order down to the 2D monolayer limit. In addition, the combination of large magnetic anisotropy and semiconducting character in (NMe 4 ) 2 [Fe 2 L 3 ] highlights its potential as a new 2D magnetic semiconductor.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

First-principles investigation of uranium mononitride (UN): Effect of magnetic ordering, spin-orbit interactions and exchange correlation functional

Uranium mononitride (UN) is a promising nuclear fuel that combines the advantageous properties of readily used UO 2 and uranium alloys. Various properties of UN have been previously studied using different density functional theory (DFT) methodologies; however, there are still inconsistencies when it comes to the dynamical stability and defect properties of UN. We address these inconsistencies by studying the UN phonons and defect properties using DFT calculations employing two generalized gradient approximation (GGA) exchange-correlation functionals: PBE and AM05, with and without an added on-site Coulomb repulsion term (+U). Furthermore, we investigate the importance of spin-orbit coupling (SOC) when calculating the properties of UN. We use the different methodologies to determine the preference of UN to have antiferromagnetic (AFM) ordering, as seen in experiments, or ferromagnetic (FM) ordering of the uranium spins. We compare the crystallographic properties, density of states, the DFT X-ray photoelectron spectra and phonon dispersions calculated using the different methodologies. We demonstrate that GGA + U reproduces the AFM ordering in UN, but the crystal structure is dynamically unstable. We also show that magnetic ordering is important in finding the lowest energy defective structure, and that SOC has a distinct influence on the energy of the different uranium interstitial defects. Lastly, we discuss the point defect formation energies under U-rich and N-rich conditions, and the stoichiometric formation energies calculated with the different methodologies, providing insight into the observed tendency for forming hypostoichiometric UN.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Magnetic order and spin liquid behavior in [Mo 3 ] 11+ molecular magnets

Molecular magnets based on [Mo 3 ] 11+ units with one unpaired electron per trimer have attracted recent interest due to the identification of quantum spin liquid candidacy in some family members. Here, we present comprehensive measurements on polycrystalline samples of ZnScMo 3 O 8 , MgScMo 3 O 8 , and Na 3 Sc 2 Mo 5 O 16 with the same Mo 3 O 13 magnetic building blocks. In this work, the crystal structures are characterized with x-ray or neutron powder diffraction and the magnetic ground states are determined by performing ac and dc susceptibility, specific heat, neutron powder diffraction, and muon spin relaxation measurements. Our work indicates that ZnScMo 3 O 8 and MgScMo 3 O 8 have ferromagnetic Curie-Weiss temperatures of 18.5 and 11.9 K, ordered ground states with net moments (low-moment ferromagnetism or canted antiferromagnetism), and zero field ordering temperatures of $T_c$ = 6 K and $T_c$ < 2 K, respectively. On the other hand, Na 3 Sc 2 Mo 5 O 16 hosts a dynamical magnetic ground state with no evidence for magnetic ordering or spin freezing down to 20 mK despite an antiferromagnetic Curie-Weiss temperature of –36.2 K, and therefore is a candidate for quantum spin liquid behavior. By comparing the present results to past work on the same family of materials, we construct a phase diagram which illustrates that the magnetic ground states of these Mo-based molecular magnets are very sensitive to small changes in the nearest-neighbor Mo-Mo distance.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Magnetic order and physical properties of the kagome metal UNb 6 ⁢Sn 6

The 𝑅⁢𝑀 6 ⁢𝑋 6 family of materials (𝑅 = rare-earth, 𝑀 = transition metal, 𝑋 = Ga, Si, Ge, Sn) produces an array of emergent phenomena, such as charge density waves, intrinsic Hall effects, and complex magnetic order, due to its kagome net of transition metal atoms, its local-moment magnetic anisotropies, and its extensive chemical tunability. Here, in this study, we report UNb 6⁢ Sn 6 , a new “166” material containing both an actinide and a 4⁢𝑑 transition metal, along with its nonmagnetic analog ThNb6⁢Sn6, to investigate the properties of a 5⁢𝑓−4⁢𝑑 electron 166 system. UNb 6 ⁢Sn 6 crystallizes in the hexagonal 𝑃⁢6/𝑚⁢𝑚⁢𝑚 space group with a small degree of disorder due to shifts in the size of the CoSn-like cages along the 𝑐 axis. Upon cooling at zero magnetic field, the material undergoes two magnetic phase transitions at 𝑇 2 = 46K and 𝑇 N = 43K. The low-temperature, zero-field phase is an antiferromagnet with ordered uranium moments and a k = (0,0,1/2) propagation vector determined by neutron diffraction. Remarkably, with a magnetic field applied along the 𝑐 axis, five additional magnetic transitions occur, evidenced by magnetization and resistivity data, before the moment saturates at 2.62 𝜇 B /U at 2 K and ≥ 13.6T. In two magnetic phase regions, the Hall resistivity of UNb 6⁢ Sn 6 significantly deviates from the magnetization, suggesting that the phases have a large Berry curvature or a change in the Fermi surface. The unknown magnetic ordering of the field-dependent phases of UNb 6⁢ Sn 6 demonstrates the complexity of the 5⁢𝑓−4⁢𝑑 166 system and encourages further study of its properties.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Superstructures and magnetic order in heavily Cu-substituted ( Fe 1 – x Cu x ) 1 + y Te

Most iron-based superconductors exhibit stripe-type magnetism, characterized by the ordering vector Q = ($\frac{1}{2},\frac{1}{2}$). In contrast, Fe 1+y Te, the parent compound of the Fe 1+y Te 1–x Se x superconductors, exhibits double-stripe magnetic order associated with the ordering vector Q = ($\frac{1}{2},0$). Here, we use elastic neutron scattering to investigate heavily Cu-substituted (Fe 1–x Cu x ) 1+y Te compounds and reveal that (1) for x ≳ 0.4, short-range magnetic order emerges around the stripe-type vector at Q = ($\frac{1}{2}$ ± δ, $\frac{1}{2}$ ± δ, $\frac{1}{2}$) with δ ≈ 0.05; (2) the short-range magnetic order is associated with a superstructure modulation at Q = ($\frac{1}{3},\frac{1}{3},\frac{1}{2}$), with the magnetic correlation length shorter than that for the superstructure; and (3) for x ≳ 0.55, we observe an additional intergrown phase with higher Cu content, characterized by a superstructure modulation vector Q = ($\frac{1}{3},\frac{1}{3},0$) and magnetic peaks at Q = ($\frac{2}{3},\frac{1}{3},\frac{1}{2}$)/($\frac{1}{3},\frac{2}{3},\frac{1}{2}$). The positions of superstructure peaks suggest that relative to the tetragonal unit cell of Fe 1+y Te, heavy Cu substitution leads to Fe-Cu orderings that expand the unit cell by $\sqrt{2}$ × 3$\sqrt{2}$ times in the ab plane, corroborated by first-principles calculations that suggest the formation of spin chains and spin ladders. Finally, our findings show that stripe-type magnetism is common in magnetically diluted iron pnictides and chalcogenides, despite the varying associated atomic orderings

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Absence of long-range magnetic order in Fe 1–δ Te 2 (δ ≈ 0.1) crystals

Transition metal dichalcogenides attract considerable attention due to variety of interesting properties, including long range magnetism in nanocrystals. Here we have investigated magnetic, thermal and electrical properties of FeTe 2 single crystal with iron vacancy defects. Magnetic measurements shows paramagnetic state and the absence of magnetic order with small anisotropy in magnetic susceptibility. Fe 3d orbitals are well hybridized, contributing to bad metal electrical resistivity. Observed thermal conductivity values below room temperature are rather low and comparable to high performance thermoelectric materials. Furthermore, our results indicate that FeTe 2 can form in highly defective marcasite crystal structure which can be exploited in future materials design.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Origin of magnetic ordering in half-Heusler RuMnGa

The half-Heusler alloy RuMnGa having valence electron count (VEC) 18 has recently been theoretically proposed to exhibit compensated ferrimagnetic (CFiM) character instead of the expected nonmagnetic ground state. On the other hand, a preliminary experimental study proposed ferromagnetic (FM) ordering. As no half-Heusler system with VEC 18 is known to exhibit magnetic ordering, we have investigated the details of crystal structure and magnetic properties of RuMnGa using a combination of experimental tools, viz., x-ray and neutron diffraction techniques, dc and ac susceptibility, isothermal magnetization, heat capacity, resistivity and neutron depolarisation measurements. Rietveld refinements of x-ray and neutron diffraction data suggest single phase nature of the compound with elemental composition RuMn 0.86 Ga 1.14 . We have shown that the system exhibits FM-type ordering owing to the inherent presence of this minor off-stoichiometry, showing very low magnetic moment. Further, the system also exhibits reentrant canonical spin-glass behavior, which is rarely observed in half-Heusler alloys. The temperature coefficient of resistivity changes its sign from negative to positive and further to negative as the temperature decreases.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Direct observation of magnetic ordering induced via systematic lattice disorder in artificial rhombus spin ices

It is critical to understand the effect of lattice geometry on the order parameter of a condensed matter system, as it controls phase transitions in such systems. Artificial spin ices (ASIs) are two-dimensional lattices of Ising-like nanomagnets that provide an opportunity to explore such phenomena by lithographically controlling the lattice geometry to observe its influence on magnetic ordering and frustration effects. Here we report a systematic approach to studying the effects of disorder in rhombus ASIs generated from combinations of five vertex motifs. We investigate four geometries characterized by a geometric order parameter, with symmetries ranging from periodic to quasiperiodic to random. Lorentz transmission electron microscopy data indicates magnetic domain behavior depends on chains of strongly-coupled islands in the periodic and sixfold-twinned lattices, while the behavior of the disordered lattice is dominated by vertex motifs with large configurational degeneracy. Utilizing micromagnetic simulations, a quantitative analysis of the lattice energetics showed that the experimental rotationally-demagnetized state of the disordered ASI was closer in energy to the idealized ground state compared to other periodic and twinned ASIs. Finally, our work provides a unique pathway for using degeneracy, magnetic frustration, and order to control the magnetization behavior of designer disordered systems.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Magnetic Ordering in a High‐Spin Donor–Acceptor Conjugated Polymer

Abstract The development of open‐shell organic molecules that magnetically order at room temperature,which can be practically applied, remains a grand challenge in chemistry, physics, and materials science. Despite the exploration of vast chemical space, design paradigms for organic paramagnetic centers generally result in unpaired electron spins that are unstable or isotropic. Here, a high‐spin conjugated polymer is demonstrated, which is composed of alternating cyclopentadithiophene and benzo[1,2‐ c ;4,5‐ c ′]bis[1,2,5]thiadiazole heterocycles, in which macromolecular structure and topology coalesce to promote the spin center generation and intermolecular exchange coupling. Electron paramagnetic resonance (EPR) spectroscopy is consistent with spatially localized spins, while magnetic susceptibility measurements show clear anisotropic spin ordering and exchange interactions that persist at room temperature. The application of long‐range π‐correlations for spin center generation promotes remarkable stability. This work offers a fundamentally new approach to the implementation of this long‐sought‐after physical phenomenon within organic materials and the integration of manifold properties within emerging technologies.

Steelman, Michael E.↗
DOE OSTI2022

Magnetic ordering in GdAuAl 4 Ge 2 and TbAuAl 4 Ge 2 : Layered compounds with triangular lanthanide nets

In this work, we report the synthesis and magnetic properties of GdAuAl 4 Ge 2 and TbAuAl 4 Ge 2 , where temperature and magnetic field dependent magnetization, heat capacity, and electrical resistivity measurements reveal that both compounds exhibit several magnetically ordered states at low temperatures, with evidence for magnetic fluctuations extending into the paramagnetic temperature region. For magnetic fields applied in the ab-plane there is particularly rich behavior, with several ordered state regions that are separated by metamagnetic phase transitions. Despite Gd being an isotropic S-state ion and Tb having an anisotropic J-state, there are similarities in the phase diagrams for the two compounds, suggesting that factors such as the symmetry of the crystalline lattice, which features well separated triangular planes of lanthanide ions, or the Ruderman–Kittel–Kasuya– Yosida interaction control the magnetism. We also point out similarities to other centrosymmetric compounds that host skyrmion lattices such as Gd 2 PdSi 3 , and propose that the LnAuAl 4 Ge 2 family of compounds are of interest as reservoirs for complex magnetism and electronic behaviors.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Cleavable quaternary oxychlorides with high magnetic ordering temperatures

Quaternary oxychlorides derived from Ruddlesden–Popper 3d transition metal oxides offer a route to cleavable crystals with bulk antiferromagnetic ordering temperatures reaching at least 550 K. Here, we study the magnetic, optical, and mechanical behavior of Sr 2 FeO 3 Cl, Ca 2 FeO 3 Cl, Ca 3 Fe 2 O 5 Cl 2 , and Sr 3 Fe 2 O 5 Cl 2 . Through optical absorption measurements, we show that these antiferromagnetic semiconductors have optical band gaps of ≈2.1(1) eV. The magnetic ordering symmetries and temperatures were probed by neutron powder diffraction and Mössbauer spectroscopy on polycrystalline samples, demonstrating Néel temperatures (T N ) near room temperature in the single layer Sr 2 FeO 3 Cl (T N ≈ 311 K) and Ca 2 FeO 3 Cl (T N ≈ 360 K), and the double-layer compound Sr 3 Fe 2 O 5 Cl 2 has T N ≈ 545 K. The high-spin moments of Fe 3+ lie within the basal plane and the magnetic structures are compensated within each magnetic layer and characterized by magnetic propagation vectors k = ($\frac{1}{2}$ $\frac{1}{2}$ 0). Magnetization results demonstrate the quasi-2D nature of the magnetism, with a broad maximum in the susceptibility near 2T N for Sr 2 FeO 3 Cl. Scotch tape tests and mechanical exfoliation onto SiO 2 confirm the micaceous nature of these crystals with cleavage down to a single unit cell (two magnetic layers) achieved for Sr 3 Fe 2 O 5 Cl 2 . In conclusion, this paper highlights strong antiferromagnetic interactions, semiconducting band gaps, and cleavability of quaternary Fe-based oxychlorides and motivates future work on crystals and exfoliated flakes of these and related oxyhalide systems.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Magnetic ordering in Eu 2 In and Eu 2 Sn

Eu 2 In and Eu 2 Sn crystallize in the orthorhombic Co 2 Si-type structure (oP12, Pnma, No. 62) with In and Sn atoms occupying one 4c site and the Eu atoms filling two other 4c sites. Eu 2 In has a nearly ideal first-order magnetostructural transition (FOMT) at 55 K with a hysteresis of less than 0.1 K, a large entropy change and an adiabatic temperature change of 5.0 K in a field of 2 T. The anhysteretic nature of the FOMT is likely due to there being no change in cell symmetry and relatively small changes in the lattice parameters. There is no magnetostructural transition in Eu2Sn. In this work we present the results of powder neutron diffraction, magnetization, and Eu Mössbauer spectroscopy aimed to investigate the nature of magnetic order for both Eu 2 In and Eu 2 Sn. The Eu Mössbauer spectrum of Eu 2 In at 5 K shows two equal area components, consistent with Eu occupying two equal multiplicity crystallographic sites. However, the different hyperfine fields (B) of 27 T and 17 T suggest that the magnetic environments of the Eu moments on the two 4c sites are different. Neutron diffraction data at 2.5 K show that in Eu 2 In the order is ferromagnetic, with Eu moments on both Eu sites oriented parallel to the a-axis; moment values of 6.8 μB and 6.5 μB were found. For Eu 2 Sn measurements find two antiferromagnetic transitions, which are corroborated by neutron diffraction. Analysis of density-functional theory calculations shows negligible energy difference between differing magnetic configurations, indirectly supporting stability of multiple magnetic structures observed experimentally. While the transition at T N1 = 30 K corresponds to the formation of a simple k 1 = 0 antiferromagnetic structure with Eu-moments pointing along the b-axis, at T N2 = 13 K a coexisting second magnetic order with k 2 = [0, ½, ½] appears.

36 MATERIALS SCIENCE↗