Persistent Detwinning of Iron-Pnictide EuFe_{2}As_{2} Crystals by Small External Magnetic Fields

Perspective: probing elasto-quantum materials with x-ray techniques andin situanisotropic strain

Anisotropic lattice deformation plays an important role in the quantum mechanics of solid state physics. The possibility of mediating the competition and cooperation among different order parameters by applyingin situstrain/stress on quantum materials has led to discoveries of a variety of elasto-quantum effects on emergent phenomena. It has become increasingly critical to have the capability of combining thein situstrain tuning with x-ray techniques, especially those based on synchrotrons, to probe the microscopic elasto-responses of the lattice, spin, charge, and orbital degrees of freedom. Herein, we briefly review the recent studies that embarked on utilizing elasto-x-ray characterizations on representative material systems and demonstrated the emerging opportunities enabled by this method. With that, we further discuss the promising prospect in this rising area of quantum materials research and the bright future of elasto-x-ray techniques.

Strain-switchable field-induced superconductivity

Field-induced superconductivity is a rare phenomenon where an applied magnetic field enhances or induces superconductivity. Here, we use applied stress as a control switch between a field-tunable superconducting state and a robust non-field-tunable state. This marks the first demonstration of a strain-tunable superconducting spin valve with infinite magnetoresistance. We combine tunable uniaxial stress and applied magnetic field on the ferromagnetic superconductor Eu(Fe0.88Co0.12)2As2 to shift the field-induced zero-resistance temperature between 4 K and a record-high value of 10 K. We use x-ray diffraction and spectroscopy measurements under stress and field to reveal that strain tuning of the nematic order and field tuning of the ferromagnetism act as independent control parameters of the superconductivity. Combining comprehensive measurements with DFT calculations, we propose that field-induced superconductivity arises from a novel mechanism, namely, the uniquely dominant effect of the Eu dipolar field when the exchange field splitting is nearly zero.

Effect of antifluorite layer on the magnetic order in Eu-based 1111 compounds, EuTAsF (T = Zn, Mn, and Fe)

The 1111 compounds with an alternating sequence of fluorite and antifluorite layers serve as structural hosts for the vast family of Fe-based superconductors. Here, we use neutron powder diffraction and density-functional-theory (DFT) band-structure calculations to study magnetic order of Eu²⁺ in the [EuF]⁺ fluorite layers depending on the nature of the [TAs]^- antifluorite layer that can be non-magnetic semiconducting (T = Zn), magnetic semiconducting (T = Mn), or magnetic metallic (T = Fe). Antiferromagnetic transitions at T_N ∼ 2.4-3 K due to an ordering of the Eu²⁺ magnetic moments were confirmed in all three EuTAsF compounds. Whereas in EuTAsF (T = Zn and Mn), the commensurate k₁ = (½ ½ 0) stripe order pattern with magnetic moments within the a-b plane is observed, the order in EuFeAsF is incommensurate with k = (0 0.961(1) ½) and represents a cycloid of Eu²⁺ magnetic moments confined within the bc-plane. Additionally, the Mn²⁺ sublattice in EuMnAsF features a robust G-type antiferromagnetic order that persists at least up to room temperature, with magnetic moments along the c-direction. Although DFT calculations suggest stripe antiferromagnetic order in the Fe-sublattice of EuFeAsF as the ground state, neutron diffraction reveals no evidence of long-range magnetic order associated with Fe. We show that the frustrating interplane interaction J₃ between the adjacent [EuF]⁺ layers is comparable with in-plane J₁-J₂ interactions already in the case of semiconducting fluorite layers [TAs]^- (T = Zn and Mn) and becomes dominant in the case of the metallic [FeAs]^- ones. The latter, along with a slight orthorhombic distortion, is proposed to be the origin of the incommensurate magnetic structure observed in EuFeAsF.

Lattice disorder effect on magnetic ordering of iron arsenides

This study investigates magnetic ordering temperature in nano- and mesoscale structural features in an iron arsenide. Although magnetic ground states in quantum materials can be theoretically predicted from known crystal structures and chemical compositions, the ordering temperature is harder to pinpoint due to potential local lattice variations that calculations may not account for. In this work we find surprisingly that a locally disordered material can exhibit a significantly larger Néel temperature (T_N) than an ordered material of precisely the same chemical stoichiometry. Here, a EuFe₂As₂ crystal, which is a ‘122’ parent of iron arsenide superconductors, is found through synthesis to have ordering below T_N = 195 K (for the locally disordered crystal) or T_N = 175 K (for the ordered crystal). In the higher T_N crystals, there are shorter planar Fe-Fe bonds [2.7692(2) Å vs. 2.7745(3) Å], a randomized in-plane defect structure, and diffuse scattering along the [00 L] crystallographic direction that manifests as a rather broad specific heat peak. For the lower T_N crystals, the a-lattice parameter is larger and the in-plane microscopic structure shows defect ordering along the antiphase boundaries, giving a larger T_N and a higher superconducting temperature (T_c) upon the application of pressure. First-principles calculations find a strong interaction between c-axis strain and interlayer magnetic coupling, but little impact of planar strain on the magnetic order. Neutron single-crystal diffraction shows that the low-temperature magnetic phase transition due to localized Eu moments is not lattice or disorder sensitive, unlike the higher-temperature Fe sublattice ordering. This study demonstrates a higher magnetic ordering point arising from local disorder in 122.

Two types of magnetic shape-memory effects from twinned microstructure and magneto-structural coupling in Fe1+y Te

Magnetic shape memory (MSM) refers to a change in shape and/or size of a magnetic material upon applying a magnetic field. There are 2 types of MSM effects; the first one occurs in a twinned magnetically ordered material, in which the crystallographic axes are irreversibly reoriented by the applied magnetic field. In the second type, the applied field drives a magnetoelastic phase transition. In certain iron tellurides Fe_1+yTe, both types of MSM occur. Notably, the first antiferromagnetic compound found to display an MSM effect is a parent material to the well-studied high-T_c cuprate superconductor La_2−xSr_xCuO₄. Observation of MSM effects in 2 known material families related to high-T_c superconductors points to a prominent role of electron–phonon coupling arising through the spin–orbit interactions.

A detailed experimental investigation of Fe_1+yTe (y = 0.11, 0.12) using pulsed magnetic fields up to 60 T confirms remarkable magnetic shape-memory (MSM) effects. These effects result from magnetoelastic transformation processes in the low-temperature antiferromagnetic state of these materials. The observation of modulated and finely twinned microstructure at the nanoscale through scanning tunneling microscopy establishes a behavior similar to that of thermoelastic martensite. We identified the observed, elegant hierarchical twinning pattern of monoclinic crystallographic domains as an ideal realization of crossing twin bands. The antiferromagnetism of the monoclinic ground state allows for a magnetic-field–induced reorientation of these twin variants by the motion of one type of twin boundaries. At sufficiently high magnetic fields, we observed a second isothermal transformation process with large hysteresis for different directions of applied field. This gives rise to a second MSM effect caused by a phase transition back to the field-polarized tetragonal lattice state.

Dichotomy between in-plane magnetic susceptibility and resistivity anisotropies in extremely strained BaFe2As2

High-temperature superconductivity in the Fe-based materials emerges when the antiferromagnetism of the parent compounds is suppressed by either doping or pressure. Closely connected to the antiferromagnetic state are entangled orbital, lattice, and nematic degrees of freedom, and one of the major goals in this field has been to determine the hierarchy of these interactions. Here we present the direct measurements and the calculations of the in-plane uniform magnetic susceptibility anisotropy of BaFe₂As₂, which help in determining the above hierarchy. The magnetization measurements are made possible by utilizing a simple method for applying a large symmetry-breaking strain, based on differential thermal expansion. In strong contrast to the large resistivity anisotropy above the antiferromagnetic transition at T _N, the anisotropy of the in-plane magnetic susceptibility develops largely below T _N. Our results imply that lattice and orbital degrees of freedom play a subdominant role in these materials.Interplay between lattice, orbital, magnetic and nematic degrees of freedom is crucial for the superconductivity in Fe-based materials. Here, the authors demonstrate the subdominant roles of pure lattice distortions and/or orbital ordering in BaFe₂As₂ by characterizing the in-plane magnetic susceptibility anisotropy.

Two-Dimensional Massless Dirac Fermions in Antiferromagnetic AFe_{2}As_{2} (A=Ba,Sr)

We report infrared studies of AFe_{2}As_{2} (A=Ba, Sr), two representative parent compounds of iron-arsenide superconductors, at magnetic fields (B) up to 17.5 T. Optical transitions between Landau levels (LLs) were observed in the antiferromagnetic states of these two parent compounds. Our observation of a sqrt[B] dependence of the LL transition energies, the zero-energy intercepts at B=0  T under the linear extrapolations of the transition energies and the energy ratio (∼2.4) between the observed LL transitions, combined with the linear band dispersions in two-dimensional (2D) momentum space obtained by theoretical calculations, demonstrates the existence of massless Dirac fermions in the antiferromagnet BaFe_{2}As_{2}. More importantly, the observed dominance of the zeroth-LL-related absorption features and the calculated bands with extremely weak dispersions along the momentum direction k_{z} indicate that massless Dirac fermions in BaFe_{2}As_{2} are 2D. Furthermore, we find that the total substitution of the barium atoms in BaFe_{2}As_{2} by strontium atoms not only maintains 2D massless Dirac fermions in this system, but also enhances their Fermi velocity, which supports that the Dirac points in iron-arsenide parent compounds are topologically protected.

Determination of the resistivity anisotropy of orthorhombic materials via transverse resistivity measurements

Measurements of the resistivity anisotropy can provide crucial information about the electronic structure and scattering processes in anisotropic and low-dimensional materials, but quantitative measurements by conventional means often suffer very significant systematic errors. Here we describe a novel approach to measuring the resistivity anisotropy of orthorhombic materials, using a single crystal and a single measurement that is derived from a π4 rotation of the measurement frame relative to the crystallographic axes. In this new basis, the transverse resistivity gives a direct measurement of the resistivity anisotropy, which combined with the longitudinal resistivity also gives the in-plane elements of the conventional resistivity tensor via a 5-point contact geometry. This is demonstrated through application to the charge-density wave compound ErTe₃, and it is concluded that this method presents a significant improvement on existing techniques, particularly when measuring small anisotropies.

Europium-based iron pnictides: a unique laboratory for magnetism, superconductivity and structural effects

Despite decades of intense research, the origin of high-temperature superconductivity in cuprates and iron-based compounds is still a mystery. Magnetism and superconductivity are traditionally antagonistic phenomena; nevertheless, there is basically no doubt left that unconventional superconductivity is closely linked to magnetism. But this is not the whole story; recently, also structural effects related to the so-called nematic phase gained considerable attention. In order to obtain more information about this peculiar interplay, systematic material research is one of the most important attempts, revealing from time to time unexpected effects. Europium-based iron pnictides are the latest example of such a completely paradigmatic material, as they display not only spin-density-wave and superconducting ground states, but also local Eu²⁺ magnetism at a similar temperature scale. Here we review recent experimental progress in determining the complex phase diagrams of europium-based iron pnictides. The conclusions drawn from the observations reach far beyond these model systems. Thus, although europium-based iron pnictides are very peculiar, they provide a unique platform to study the common interplay of structural-nematic, magnetic and electronic effects in high-temperature superconductors.