Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Exchange interactions”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 235 records · Page 13
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Excited State Exchange Control of Photoinduced Electron Spin Polarization in Electronic Ground States

Ground-state electron spin polarization (ESP) is generated in radical elaborated (bpy)Pt(CAT-NN) and (bpy)Pt(CAT- p -Me 2 PhMe 2 -NN) (bpy = 5,5'-di- tert -butyl-2,2'-bipyridine, CAT = 3- tert -butylcatecholate, p -Ph = para -phenylene, NN = nitronylnitroxide). Photoexcitation produces an exchange-coupled, three-spin, charge-separated doublet 2 S 1 (S = chromophore excited spin singlet configuration) excited state that rapidly decays to a 2 T 1 (T = chromophore excited spin triplet configuration) excited state. The SQ-bridge-NN bond torsions affect the magnitude of the excited state exchange interaction ( J SQ-NN ), which determines the 2 T 1 – 4 T 1 energy gap. Ground state ESP is dependent on the magnitude of J SQ-NN , and we postulate that this results from differences in 2 T 1 and 4 T 1 state mixing. Mechanisms that lead to the rapid transfer of the excited state ESP to the ground state are discussed. Although subnanosecond 2 T 1 state lifetimes are measured optically in solution, the ground state ESP decays very slowly at 20 K and is observable for more than a millisecond.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Accurate machine-learning predictions of coercivity in high-performance permanent magnets

Increased demand for high-performance permanent magnets in the electric vehicle and wind-turbine industries has prompted the search for cost-effective alternatives. Discovering magnetic materials with the desired intrinsic and extrinsic permanent magnet properties presents a significant challenge to researchers because of issues with the global supply of rare-earth elements, material stability, and a low maximum magnetic energy product BH max . While first-principles density functional theory (DFT) predicts materials’ magnetic moments, magnetocrystalline anisotropy constants, and exchange interactions, it cannot compute extrinsic properties such as coercivity (H c ). Although it is possible to calculate H c theoretically with micromagnetic simulations, the predicted value is larger than the experiment by almost an order of magnitude due to the Brown paradox. To circumvent these issues, we employ machine-learning (ML) methods on an extensive database obtained from experiments, DFT calculations, and micromagnetic modeling. The use of a large experimental dataset enables realistic H c predictions for materials such as Ce-doped Nd 2 ⁢Fe 14 ⁢B, comparing favorably against micromagnetically simulated coercivities. Remarkably, our ML model accurately identifies uniaxial magneto-crystalline anisotropy as the primary contributor to H c . With DFT calculations, we predict the Nd-site-dependent magnetic anisotropy behavior in Nd 2 ⁢Fe 14 ⁢B, confirming that Nd 4⁢g sites mainly contribute to uniaxial magnetocrystalline anisotropy, and also calculate the Curie temperature (T c ). Finally, both calculated results are in good agreement with the experiments. The coupled experimental dataset and ML modeling with DFT input predict H c with far greater accuracy and speed than was previously possible using micromagnetic modeling. Further, we reverse engineer the grain-boundary and intergrain exchange coupling with micromagnetic simulations by employing the ML predictions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Stability, electronic quantum states, and magnetic interactions of Er 3+ ions in Ga 2 ⁢O 3

Here, we report an ab initio study of phase stability, defect formation, electronic structure, and multiple magnetic, Dzyaloshinskii-Moriya, optical, hyperfine, and crystal field interactions in erbium (Er)-doped wide band gap 𝛼- and 𝛽-gallium oxides (Ga 2 ⁢O 3 ), critically important to make a foundation for both optoelectronic and quantum information applications. The chemical, structural, mechanical, and dynamical stabilities of the pristine phases are confirmed from respective negative formation energies, negative cohesive energies, favorable elastic constants, and positive phonon frequencies. The phonon dispersions indicate that the Ga-O bonds are uniform in the 𝛼-phase, while they vary in the 𝛽-phase due to the anisotropic polyhedral movement. The defect formation energy analysis confirms that both Er-doped 𝛼- and 𝛽−Ga 2 ⁢O 3 prefer Er 3+ (neutral) state. The underestimated band gaps of the pristine phases from standard density functional theory (DFT) calculations as compared to experimental values are corrected by employing the hybrid functional calculations, resulting in the indirect band gaps of 5.21 eV in 𝛼−Ga 2 ⁢O 3 and 4.94 eV in 𝛽−Ga 2 ⁢O 3 . The site preference energy analysis indicates partial occupation of Er in the octahedral site of Ga. The anisotropic nature of hyperfine tensor coefficients of Er is similar in both phases, which may be due to the occupation of Er in the same octahedral Ga site. On the other hand, the calculated magnetic exchange interaction between two Er dopants is negative for 𝛼 and positive for 𝛽, indicating an antiferromagnetic (AFM) ground state in the former and a ferromagnetic (FM) ground state in the latter. Large values of Dzyaloshinskii-Moriya interactions (DMIs) are obtained along the 𝑥 direction in the 𝛼 and along the 𝑦 direction in the 𝛽. The large DMI may support exotic magnetic textures, a promising direction for spintronic applications. The analysis of dielectric constants and refractive indices of both pristine and Er-doped phases shows a good agreement with available experimental values. The calculated optical anisotropy is slightly higher in 𝛽 than those in 𝛼, which is due to the involvement of lower symmetry in 𝛽. The crystal field coefficients (CFCs) calculated from DFT are used to analyze 4⁢𝑓 multiplets and 4⁢𝑓 −4⁢𝑓 transitions. Thus calculated lowest energy level of the first excited state to the lowest energy level of the ground state is about 1.53 µ⁢m, which is in a good agreement with available experiments, and it falls within the quantum telecommunication wavelength range.

3-dimensional systems↗
DOE OSTI2026

Spin Texture Control and Magnetic Gap Engineering in a Ferromagnetic Insulator–Topological Insulator Sandwiched Heterostructure

Quantum materials that combine magnetism with topological order are emerging as key platforms for next-generation spintronics and low-energy electronics. They enable the realization of emergent quantum phenomena, such as the quantum anomalous Hall effect and axion insulator states. The ferromagnetic insulator (FMI)/topological insulator (TI)/FMI sandwich structure of a single-septuple layer (1SL) MnBi 2 Te 4 /four-quintuple layer (4QL) Bi 2 Te 3 /1SL MnBi 2 Te 4 holds great potential to achieve such desirable quantum phenomena at an elevated temperature, owing to its large Dirac point band gap and high Curie temperature. Here, for this work, spin- and angle-resolved photoemission spectroscopy (spin-ARPES) is employed to directly verify that the band gap arises from broken time-reversal symmetry via proximity-driven magnetization. This study demonstrates direct control of the spin state via external magnetic fields and unambiguously confirms the exchange interaction as the gap-opening mechanism. The robust magnetic gap and controllable spin texture make this heterostructure a suitable candidate for spintronic applications and magnetic topological quantum phases.

exchange gap↗
DOE OSTI2024

Enhanced Ferromagnetism in Atomically Thin Oxides Achieved by Interfacial Reconstruction

Discoveries of ferromagnetic materials with ultrathin thickness are of great importance for both fundamental science and technological applications. Transition metal oxides (TMOs) provide promising candidates in the context of next‐generation spintronics, despite the severe decay of ferromagnetism as the thickness reduces to the nanometer regime. Here, in this work, an efficient strategy to eliminate the magnetic dead layer in atomically thin oxides is presented, by using the epitaxial interface of 3 d and 5 d oxide monolayers that reconciles both strong exchange interaction and large uniaxial magnetic anisotropy. Combining multiple experimental methods, a ferromagnetic transition in an ultrathin oxide heterostructure comprised of only one La 0.2 Sr 0.8 MnO 3 monolayer sandwiched by SrIrO 3 monolayer (total thickness of three unit‐cells) is unambiguously demonstrated. Remarkably, a largely enhanced saturation magnetization (2 µ B Mn −1 ) and Curie temperature (80 K) are observed for the single manganite monolayer, as compared to previously reported ferromagnetic monolayer oxides. The results demonstrate a general strategy for creating robust ferromagnetism in ultrathin TMOs, potentially enabling novel oxide spin‐orbitronic devices.

2D ferromagnetism↗
DOE OSTI2021

Colossal Magnetoresistance without Mixed Valence in a Layered Phosphide Crystal

Materials with strong magnetoresistive responses are the backbone of spintronic technology, magnetic sensors, and hard drives. Among them, manganese oxides with a mixed valence and a cubic perovskite structure stand out due to their colossal magnetoresistance (CMR). A double exchange interaction underlies the CMR in manganates, whereby charge transport is enhanced when the spins on neighboring Mn 3+ and Mn 4+ ions are parallel. Prior efforts to find different materials or mechanisms for CMR resulted in a much smaller effect. Here an enormous CMR at low temperatures in EuCd 2 P 2 without manganese, oxygen, mixed valence, or cubic perovskite structure is shown. EuCd 2 P 2 has a layered trigonal lattice and exhibits antiferromagnetic ordering at 11 K. The magnitude of CMR (10(4)%) in as-grown crystals of EuCd 2 P 2 rivals the magnitude in optimized thin films of manganates. In this work, the magnetization, transport, and synchrotron X-ray data suggest that strong magnetic fluctuations are responsible for this phenomenon. The realization of CMR at low temperatures without heterovalency leads to a new regime for materials and technologies related to antiferromagnetic spintronics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Spin–Phonon Coupling in Ferromagnetic Monolayer Chromium Tribromide

Novel 2D magnets exhibit intrinsic electrically tunable magnetism down to the monolayer limit, which has significant value for nonvolatile memory and emerging computing device applications. In these compounds, spin–phonon coupling (SPC) typically plays a crucial role in magnetic fluctuations, magnon dissipation, and ultimately establishing long-range ferromagnetic order. However, a systematic understanding of SPC in 2D magnets that combines theory and experiment is still lacking. Here in this work, monolayer chromium tribromide is studied to investigate SPC in 2D magnets via Raman spectroscopy and first principle calculations. The experimental Curie temperature and phonon shifts are found to be in good agreement with the numerical simulations. Specifically, it is demonstrated how magnetic exchange interactions affect phonon vibrations, which helps establish design fundamentals for 2D magnetic materials and other related devices.

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 OSTI2024

Understanding and Tuning Magnetism in Layered Ising‐Type Antiferromagnet FePSe 3 for Potential 2D Magnet

Abstract Recent developments in 2D magnetic materials have motivated the search for new van der Waals magnetic materials, especially Ising‐type magnets with strong magnetic anisotropy. Fe‐based M P X 3 ( M = transition metal, X = chalcogen) compounds such as FePS 3 and FePSe 3 both exhibit an Ising‐type magnetic order, but FePSe 3 receives much less attention compared to FePS 3 . This work focuses on establishing the strategy to engineer magnetic anisotropy and exchange interactions in this less‐explored compound. Through chalcogen and metal substitutions, the magnetic anisotropy is found to be immune against S substitution for Se whereas tunable only with heavy Mn substitution for Fe. In particular, Mn substitution leads to a continuous rotation of magnetic moments from the out‐of‐plane direction toward the in‐plane. Furthermore, the magnetic ordering temperature displays non‐monotonic doping dependence for both chalcogen and metal substitutions but due to different mechanisms. These findings provide deeper insight into the Ising‐type magnetism in this important van der Waals material, shedding light on the study of other Ising‐type magnetic systems as well as discovering novel 2D magnets for potential applications in spintronics.

2D magnet↗
DOE OSTI2026

Pressure‐Induced Structural and Magnetic Evolution in Layered Antiferromagnet YbMn 2 Sb 2

Electronic states under pressure exhibit unconventional spin and charge dynamics that provide a powerful route to uncover exotic phases in quantum materials. Here, we present the structural, magnetic, and electronic evolution of YbMn 2 Sb 2 under pressure. Single-crystal X-ray diffraction reveals a pressure-induced structural transition from the space group trigonal P$\overline{3}$m1 to the monoclinic P2 1 /m phase near 3.5 GPa, which remains stable up to 10 GPa. Magnetization measurements display an anomalously weak net magnetic moment and the absence of Curie–Weiss behavior up to 400 K, suggesting the formation of short-range Mn moment pairs that cancel macroscopically and subsequently evolve into long-range order upon cooling. Temperature-dependent resistivity shows semiconducting behavior with a transition at ∼119 K at ambient pressure, while pressure induces a dramatic suppression of resistance and the emergence of metallic-like temperature dependence, stabilized beyond 5 GPa. This pressure-driven semiconductor-metal transition is consistent with our density functional theory calculations, confirming the closing of the band gap under compression. Neutron diffraction under pressure identifies an incommensurate magnetic structure with antiparallel correlations between paired spins. Together, these results demonstrate how pressure-driven structural tuning and competing exchange interactions stabilize unconventional magnetic states in this low-dimensional magnetic semiconductor.

antiferromagnetic semiconductor↗
DOE OSTI2023

Designing Magnetic Properties in CrSBr through Hydrostatic Pressure and Ligand Substitution

Abstract Magnetic van der Waals (vdW) materials are a promising platform for producing atomically thin spintronic and optoelectronic devices. The A‐type antiferromagnet CrSBr has emerged as a particularly exciting material due to its high magnetic ordering temperature, semiconducting electrical properties, and enhanced chemical stability compared to other vdW magnets. Exploring mechanisms to tune its magnetic properties will facilitate the development of nanoscale devices based on vdW materials with designer magnetic properties. Here it is investigated how the magnetic properties of CrSBr change under pressure and ligand substitution. Pressure compresses the unit cell, increasing the interlayer exchange energy while lowering the Néel temperature. Ligand substitution, realized synthetically through Cl alloying, anisotropically compresses the unit cell and suppresses the Cr‐halogen covalency, reducing the magnetocrystalline anisotropy energy and decreasing the Néel temperature. A detailed structural analysis combined with first‐principles calculations reveals that alterations in the magnetic properties are intricately related to changes in direct Cr–Cr exchange interactions and the Cr–anion superexchange pathways. Further, it is demonstrated that Cl alloying enables chemical tuning of the interlayer coupling from antiferromagnetic to ferromagnetic, which is unique among known two‐dimensional magnets.

Telford, Evan J.↗
DOE OSTI2024

The Hard Ferromagnetism in FePS 3 Induced by Non‐Magnetic Molecular Intercalation

Abstract Manipulating the magnetic ground states of 2D magnets is a focal point of recent research efforts. Various methods have demonstrated efficacy in modulating the magnetic properties inherent to van der Waals (vdW) magnetic systems. Herein, the emergence of robust anisotropic ferromagnetism within antiferromagnetic FePS 3 is unveiled via intercalation with non‐magnetic pyridinium ions. A one‐step ion exchange reaction facilitates the formation of energetically favorable B‐phase and metastable P‐phase. Notably, both B‐ and P‐phases manifest hard ferromagnetic behavior, featuring substantial unsaturated coercive fields (>7 T) and high Curie temperatures (72–87 K). First‐principles calculations elucidate the pivotal role of electron transfer from pyridinium ions to FePS 3 in engineering magnetic exchange interactions. Calculated effective spin Hamiltonian corroborates the observed hard ferromagnetism in intercalated FePS 3 . This study offers crucial insights into hard magnetism in intercalated vdW materials, thereby presenting promising avenues for 2D vdW magnet‐based magnetic devices.

Ou, Yunbo↗
DOE OSTI2024

A Nanosized {Ni II 18 } Cluster with a ‘Flying Saucer’ Topology Exhibiting Slow Relaxation of Magnetisation Phenomena at Both 15 K and 1.3 K

A high-nuclearity {Ni 18 } complex (1) with a unique ‘flying saucer’ motif has been prepared from the organic chelate, α-methyl-2-pyridine-methanol (mpmH), in conjunction with bridging azido (N 3 - ) and peroxido (O 2 2- ) ligands. Magnetic susceptibility measurements revealed the presence of both ferro- and antiferromagnetic exchange interactions between the metal centres in 1, and the stabilization of spin states with appreciable S values at two different temperature regimes. The end-on bridging azido and alkoxido groups are in all likelihood the ferromagnetic mediators, while the η 3 :η 3 :μ 6 -bridging peroxides most likely promote the antiparallel alignment of the metals’ spin vectors, yielding an overall non-zero spin ground state for the centrosymmetric compound 1. Furthermore, the {Ni 18 } nanosized cluster behaves as a single-molecule magnet, exhibiting magnetic hysteresis at low temperatures and two relaxation processes at 15 K and 1.3 K, a very rare phenomenon in polynuclear magnetic 3d-metal clusters.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

In Situ MOF Pyrolysis Construction of Hierarchical Porous Co‐Nanoparticles/Carbon Cloth Composites for Enhanced Electromagnetic Wave Shielding and Absorption

The development of high-performance electromagnetic protection materials integrating broadband absorption and effective shielding capabilities is hindered by challenges in simultaneously optimizing multiple electromagnetic properties through conventional material designs. This study pioneers a hierarchical porous Co nanoparticle/carbon cloth (Co/CC) composite via controlled annealing of a Co-MOF precursor on carbon cloth. The Co-MOF served a dual role as both magnetic source and pore-forming agent, enabling in situ generation of uniformly dispersed Co nanoparticles and creation of abundant pores/interfaces on the CC fibers during pyrolysis. This unique architecture synergistically enhanced dielectric loss (via interfacial/dipolar polarization) and magnetic loss (via natural resonance, exchange interactions, and eddy currents), significantly improving impedance matching. The hierarchical pores further functioned as integrated “absorption–reflection” units for efficient electromagnetic energy attenuation. Consequently, the Co/CC composite annealed at 800°C (Co/CC-800) achieves minimum reflection loss (−40.69 dB) and 120% effective absorption bandwidth extension (6.16 GHz) as a filler, and exhibits superior electromagnetic interference shielding effectiveness (46.66 dB) as an integrated component. Significantly, Co/CC-800 demonstrated robust photothermal and electrothermal conversion capabilities, ensuring operational stability in ice-covered and humid harsh environments. This work pioneers a pore-structure-mediated strategy to harmonize dielectric–magnetic synergy, providing a new paradigm for designing advanced multifunctional electromagnetic protection materials.

dielectric‐magnetic synergy↗
DOE OSTI2025

Unusual Ferromagnetic Band Evolution and High Curie Temperature in Monolayer 1T‐CrTe2 on Bilayer Graphene

2D van der Waals ferromagnets hold immense promise for spintronic applications due to their controllability and versatility. Despite their significance, the realization and in-depth characterization of ferromagnetic materials in atomically thin single layers, close to the true 2D limit, has been scarce. Here, a successful synthesis of monolayer (ML) 1T-CrTe2 is reported on a bilayer graphene (BLG) substrate via molecular beam epitaxy. Using angle-resolved photoemission spectroscopy and magneto-optical Kerr effect measurements, that the ferromagnetic transition is observed at the Curie temperature (TC) of 150 K in ML 1T-CrTe2 on BLG, accompanied by unconventional temperature-dependent band evolutions. The spectroscopic analysis and first-principle calculations reveal that the ferromagnetism may arise from Goodenough-Kanamori super-exchange and double-exchange interactions, enhanced by the lattice distortion and the electron doping from the BLG substrate. These findings provide pivotal insight into the fundamental understanding of mechanisms governing 2D ferromagnetism and offer a pathway for engineering higher TC in 2D materials for future spintronic devices.

Park, Kyoungree↗
DOE OSTI2025

Magnet-superconductor hybrid quantum systems: a materials platform for topological superconductivity

Magnet–superconductor hybrid (MSH) systems have recently emerged as one of the most significant developments in condensed matter physics. This has generated, in the last decade, a steadily rising interest in the understanding of their unique properties. They have been proposed as one of the most promising platforms for the establishment of topological superconductivity, which holds high potential for application in future quantum information technologies. Their emergent electronic properties stem from the exchange interaction between the magnetic moments and the superconducting condensate. Given the atomic-level origin of such interaction, it is of paramount importance to investigate new magnet–superconductor hybrids at the atomic scale. In this regard, scanning tunneling microscopy (STM) and spectroscopy are playing a crucial role in the race to unveil the fundamental origin of the unique properties of MSH systems, with the aim to discover new hybrid quantum materials capable of hosting topologically non-trivial unconventional superconducting phases. In particular, the combination of STM studies with tight-binding model calculations have represented, so far, the most successful approach to unveil and explain the emergent electronic properties of MSHs. The scope of this review is to offer a broad perspective on the field of MSHs from an atomic-level investigation point-of-view. The focus is on discussing the link between the magnetic ground state hosted by the hybrid system and the corresponding emergent superconducting phase. This is done for MSHs with both one-dimensional (atomic chains) and two-dimensional (atomic lattices and thin films) magnetic systems proximitized to conventional s-wave superconductors. We present a systematic categorization of the experimentally investigated systems with respect to defined experimentally accessible criteria to verify or falsify the presence of topological superconductivity and Majorana edge modes. The discussion will start with an introduction to the physics of Yu–Shiba–Rusinov bound states at magnetic impurities on superconducting surfaces. This will be used as a base for the discussion of magnetic atomic chains on superconductors, distinguishing between ferromagnetic, antiferromagnetic and non-collinear magnetic ground states. A similar approach will be used for the discussion of magnetic thin film islands on superconductors. Given the vast number of publications on the topic, we limit ourselves to discuss works which are most relevant to the search for topological superconductivity.

Majorana states↗
DOE OSTI2020

Linear in temperature resistivity in the limit of zero temperature from the time reparameterization soft mode

The most puzzling aspect of the ‘strange metal’ behavior of correlated electron compounds is that the linear in temperature resistivity often extends down to low temperatures, lower than natural microscopic energy scales. We consider recently proposed deconfined critical points (or phases) in models of electrons in large dimension lattices with random nearest-neighbor exchange interactions. The criticality is in the class of Sachdev–Ye–Kitaev models, and exhibits a time reparameterization soft mode representing gravity in dual holographic theories. We compute the low temperature resistivity in a large M limit of models with SU(M) spin symmetry, and find that the dominant temperature dependence arises from this soft mode. The resistivity is linear in temperature down to zero temperature at the critical point, with a co-efficient universally proportional to the product of the residual resistivity and the co-efficient of the linear in temperature specific heat. We argue that the time reparameterization soft mode offers a promising and generic mechanism for resolving the strange metal puzzle.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

The magnetic order in multiferroic DyMnO 3

We report that with flexibility in tuning their electric and magnetic properties, multiferroics can be used in information exchange and storage in ways that are very different from the present electronic materials. Here we use resonant soft X-ray scattering spectroscopy to study the F-type (0,τ,0) and C-type (0, 1–2τ, 0) diffraction peaks from sinusoidal antiferromagnetic spin order in multiferroic DyMnO 3 . By comparing the temperature dependence of ordering wave vectors τ, peak intensities I, and correlation lengths λ measured at Mn L 2 - , O K-, and Dy M 5 -edges, we show that the nearly perfect locking between the ordering wave vectors from Dy 4f states and Mn 3d orbitals manifesting the second harmonic diffraction peak implies the notable orbital involvement in the coupling between Mn and Dy spins. Our DFT calculations further suggest that the lattice response to different antiferromagnetic ground states (A-type versus E-type) is much weaker in TbMnO 3 , in agreement with previous claim that the symmetric exchange interaction can be an important factor for understanding the ferroelectricity in DyMnO 3 than in TbMnO 3 .

36 MATERIALS SCIENCE↗