Pseudo-Jahn-Teller Effect and Magnetoelastic Coupling in Spin-Orbit Mott Insulators

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.

Giant stress response of terahertz magnons in a spin-orbit Mott insulator

Magnonic devices operating at terahertz frequencies offer intriguing prospects for high-speed electronics with minimal energy dissipation However, guiding and manipulating terahertz magnons via external parameters present formidable challenges. Here we report the results of magnetic Raman scattering experiments on the antiferromagnetic spin-orbit Mott insulator Sr2IrO4 under uniaxial stress. We find that the energies of zone-center magnons are extremely stress sensitive: lattice strain of 0.1% increases the magnon energy by 40%. The magnon response is symmetric with respect to the sign of the applied stress (tensile or compressive), but depends strongly on its direction in the IrO2 planes. A theory based on coupling of the spin-orbit-entangled iridium magnetic moments to lattice distortions provides a quantitative explanation of the Raman data and a comprehensive framework for the description of magnon-lattice interactions in magnets with strong spin-orbit coupling. The possibility to efficiently manipulate the propagation of terahertz magnons via external stress opens up multifold design options for reconfigurable magnonic devices.

Controllable Emergent Spatial Spin Modulation in Sr_{2}IrO_{4} by In Situ Shear Strain

Symmetric anisotropic interaction can be ferromagnetic and antiferromagnetic at the same time but for different crystallographic axes. We show that the competition of anisotropic interactions of orthogonal irreducible representations can be a general route to obtain new exotic magnetic states. We demonstrate it here by observing the emergence of a continuously tunable 12-layer spatial spin modulation when distorting the square-lattice planes in the quasi-two-dimensional antiferromagnetic Sr_{2}IrO_{4} under in situ shear strain. This translation-symmetry-breaking phase is a result of an unusual strain-activated anisotropic interaction which is at the fourth order and competing with the inherent quadratic anisotropic interaction. Such a mechanism of competing anisotropy is distinct from that among the ferromagnetic, antiferromagnetic, and/or the Dzyaloshinskii-Moriya interactions, and it could be widely applicable and highly controllable in low-dimensional magnets.

Manifestation of the Jahn-Teller effect subject to quadraticT⊗e+t2problem in ultrasonic attenuation. Case study of CaF2:Cr crystal with isovalent and aliovalent substitution

A new approach is introduced to obtain information about the adiabatic potential energy surface of the Jahn-Teller (JT) complexes subject to theT⊗e+t2problem in doped crystals. It employs simulation of the contribution of the JT sub-system to ultrasonic attenuation with account of three mechanisms of relaxation and subsequent comparison with the experimental data on temperature dependence of the attenuation obtained with the use of doped crystal and nominally pure one. The approach has been applied to the CaF₂crystal doped with chromium. The experiment has been carried out at the frequencies of (13-158) × 10⁶Hz at low temperatures (4-170 K). Peak for all the ultrasonic normal modes propagating along the [110] axis has been observed at about 8 K. It has been considered as the JT effect manifestation by the sub-system of Cr²⁺F8-complexes. Symmetry properties of the global minima and saddle points have been identified, the JT stabilization energies and coordinates of the extrema points in the five-dimensional space of symmetrized displacements have been evaluated. Besides, a broad shoulder has been found at 15-40 K and attributed to contribution of the Cr³⁺F8-sub-system.

Proximate ferromagnetic state in the Kitaev model material α-RuCl3

α-RuCl₃ is a major candidate for the realization of the Kitaev quantum spin liquid, but its zigzag antiferromagnetic order at low temperatures indicates deviations from the Kitaev model. We have quantified the spin Hamiltonian of α-RuCl₃ by a resonant inelastic x-ray scattering study at the Ru L₃ absorption edge. In the paramagnetic state, the quasi-elastic intensity of magnetic excitations has a broad maximum around the zone center without any local maxima at the zigzag magnetic Bragg wavevectors. This finding implies that the zigzag order is fragile and readily destabilized by competing ferromagnetic correlations. The classical ground state of the experimentally determined Hamiltonian is actually ferromagnetic. The zigzag state is stabilized by quantum fluctuations, leaving ferromagnetism – along with the Kitaev spin liquid – as energetically proximate metastable states. The three closely competing states and their collective excitations hold the key to the theoretical understanding of the unusual properties of α-RuCl₃ in magnetic fields.

RuCl₃ has stood out as a prime candidate in the search for quantum spin liquids; however, its antiferromagnetic ordering at low temperature suggests deviations from typical QSL models. Here, using resonant inelastic x-ray scattering, the authors provide a comprehensive determination of the low energy effective Hamiltonian.

Ionic charge distributions in silicon atomic surface wires

Using a non-contact atomic force microscope (nc-AFM), we examine continuous dangling bond (DB) wire structures patterned on the hydrogen terminated silicon (100)-2 × 1 surface. By probing the DB structures at varying energies, we identify the formation of previously unobserved ionic charge distributions which are correlated to the net charge of DB wires and their predicted degrees of freedom in lattice distortions. Performing spectroscopic analysis, we identify higher energy configurations corresponding to alternative lattice distortions as well as tip-induced charging effects. By varying the length and orientation of these DB structures, we further highlight key features in the formation of these ionic surface phases.

Ligand dependent magnetism of theJeff= 3/2 Mott insulator Cs2MX6(M= Ta, Nb,X= Br, Cl)

Magnetic and structural properties of double perovskite type bromides Cs₂MBr₆(M= Ta, Nb), where Ta⁴⁺(5d¹) and Nb⁴⁺(4d¹) ions form the face centered cubic lattice, are investigated and compared with chlorides Cs₂MCl₆. Cs₂TaBr₆exhibits the effective magnetic moment of 0.24μ_B, which is much smaller than the spin only value of ad¹ion, 1.73μ_B, and comparable to 0.25μ_Bin Cs₂TaCl₆. On the other hand, the effective magnetic moment of Cs₂NbBr₆is 0.7μ_Band is substantially smaller than 1.0μ_Bin Cs₂NbCl₆. On cooling, successive structural and magnetic phase transitions accompanying the release of electronic entropy approximatelyRln 4 in total as expected for theJ_eff= 3/2 state are observed. The type of the ligand changes the temperature dependence of magnetic susceptibility at low temperature as well as its magnitude. The role of the ligands on the magnetism ofJ_eff= 3/2 Mott insulators are discussed in the light of metal-ligand hybridization and the electron-lattice coupling.

Strain engineering of the charge and spin-orbital interactions in Sr2IrO4

Understanding the relationship between entangled degrees of freedom (DOF) is a central problem in correlated materials and the possibility to influence their balance is promising toward realizing novel functionalities. In Sr₂IrO₄, the interaction between spin–orbit coupling and electron correlations induces an exotic ground state with magnetotransport properties promising for antiferromagnetic spintronics applications. Moreover, the coupling between orbital and spin DOF renders the magnetic structure sensitive to the Ir–O bond environment. To date, a detailed understanding of the microscopic spin-lattice and electron–phonon interactions is still lacking. Here, we use strain engineering to perturb the local lattice environment and, by tracking the response of the low-energy elementary excitations, we unveil the response of the microscopic spin and charge interactions.

In the high spin–orbit-coupled Sr₂IrO₄, the high sensitivity of the ground state to the details of the local lattice structure shows a large potential for the manipulation of the functional properties by inducing local lattice distortions. We use epitaxial strain to modify the Ir–O bond geometry in Sr₂IrO₄ and perform momentum-dependent resonant inelastic X-ray scattering (RIXS) at the metal and at the ligand sites to unveil the response of the low-energy elementary excitations. We observe that the pseudospin-wave dispersion for tensile-strained Sr₂IrO₄ films displays large softening along the [h,0] direction, while along the [h,h] direction it shows hardening. This evolution reveals a renormalization of the magnetic interactions caused by a strain-driven cross-over from anisotropic to isotropic interactions between the magnetic moments. Moreover, we detect dispersive electron–hole pair excitations which shift to lower (higher) energies upon compressive (tensile) strain, manifesting a reduction (increase) in the size of the charge gap. This behavior shows an intimate coupling between charge excitations and lattice distortions in Sr₂IrO₄, originating from the modified hopping elements between the t_2g orbitals. Our work highlights the central role played by the lattice degrees of freedom in determining both the pseudospin and charge excitations of Sr₂IrO₄ and provides valuable information toward the control of the ground state of complex oxides in the presence of high spin–orbit coupling.

Organic Multiferroic Magnetoelastic Complexes

The design of crystal structures aids the discovery of interesting physical phenomena in organic crystals. In this work, the optimization of the coronene-tetracyanoquinodimethane (TCNQ) structure generates non-degenerate energy levels of spin-up and spin-down electrons after charge transfer, producing spontaneous spin polarization, leading to pronounced ferromagnetism. The deformed crystal lattice can significantly affect the saturation magnetization of organic ferromagnets to present a remarkable magnetoelastic coupling. Furthermore, the magnetic-field-induced lattice shrinkage of the ferromagnetic crystals supports a spin-lattice-interaction-dependent magnetoelastic coupling. This concept of organic magnetoelastic coupling will pave the way for the rapid mechanical control of spin polarization in organic multiferroic magnetoelastic materials.

Comprehensive Electrical Control of Metamagnetic Transition of a Quasi-2D Antiferromagnet by In Situ Anisotropic Strain

Effective nonmagnetic control of the spin structure is at the forefront of the study for functional quantum materials. This study demonstrates that, by applying an anisotropic strain up to only 0.05%, the metamagnetic transition field of spin-orbit-coupled Mott insulator Sr₂ IrO₄ can be in situ modulated by almost 300%. Simultaneous measurements of resonant X-ray scattering and transport reveal that this drastic response originates from the complete strain-tuning of the transition between the spin-flop and spin-flip limits, and is always accompanied by large elastoconductance and magnetoconductance. This enables electrically controllable and electronically detectable metamagnetic switching, despite the antiferromagnetic insulating state. The obtained strain-magnetic field phase diagram reveals that C₄ -symmetry-breaking anisotropy is introduced by strain via pseudospin-lattice coupling, directly demonstrating the pseudo-Jahn-Teller effect of spin-orbit-coupled complex oxides. The extracted coupling strength is much weaker than the superexchange interactions, yet crucial for the spontaneous symmetry-breaking, affording the remarkably efficient strain-control.

Kitaev Spin Liquid in 3d Transition Metal Compounds

We study the exchange interactions and resulting magnetic phases in the honeycomb cobaltates. For a broad range of trigonal crystal fields acting on Co^{2+} ions, the low-energy pseudospin-1/2 Hamiltonian is dominated by bond-dependent Ising couplings that constitute the Kitaev model. The non-Kitaev terms nearly vanish at small values of trigonal field Δ, resulting in spin liquid ground state. Considering Na_{3}Co_{2}SbO_{6} as an example, we find that this compound is proximate to a Kitaev spin liquid phase, and can be driven into it by slightly reducing Δ by ∼20  meV, e.g., via strain or pressure control. We argue that, due to the more localized nature of the magnetic electrons in 3d compounds, cobaltates offer the most promising search area for Kitaev model physics.

Magnetic Anisotropy of a Quasi Two-Dimensional Canted Antiferromagnet

We report the control of the interplane magnetic exchange coupling in CaIrO₃ perovskite thin films and superlattices with SrTiO₃. By analyzing the anisotropic magneto-transport data, we demonstrate that a semimetallic paramagnetic CaIrO₃ turns into a canted antiferromagnetic Mott insulator at reduced dimensions. The emergence of a biaxial magneto-crystalline anisotropy indicates the canted moment responding to the cubic symmetry. Extending to superlattices and probing oxygen octahedral rotation by half-integer X-ray Braggs diffraction, a more complete picture about the canted moment evolution with interplane coupling can be understood. Remarkably, a rotation of the canted moments' easy axes by 45° is also observed by a sign reversal of the in-plane strain. These results demonstrate the robustness of anisotropic magnetoresistance in revealing quasi two-dimensional canted antiferromagnets, as well as valuable insights about quadrupolar magnetoelastic coupling, relevant for designing future antiferromagnetic spintronic devices.

Discovery of twin orbital-order phases in ferromagnetic semiconducting VI3 monolayer

Discovery of twin orbital-order ferromagnetic semiconducting phases in VI₃-like 2D systems.

Giant anisotropic magnetoresistance and nonvolatile memory in canted antiferromagnet Sr2IrO4

Antiferromagnets have been generating intense interest in the spintronics community, owing to their intrinsic appealing properties like zero stray field and ultrafast spin dynamics. While the control of antiferromagnetic (AFM) orders has been realized by various means, applicably appreciated functionalities on the readout side of AFM-based devices are urgently desired. Here, we report the remarkably enhanced anisotropic magnetoresistance (AMR) as giant as ~160% in a simple resistor structure made of AFM Sr₂IrO₄ without auxiliary reference layer. The underlying mechanism for the giant AMR is an indispensable combination of atomic scale giant-MR-like effect and magnetocrystalline anisotropy energy, which was not accessed earlier. Furthermore, we demonstrate the bistable nonvolatile memory states that can be switched in-situ without the inconvenient heat-assisted procedure, and robustly preserved even at zero magnetic field, due to the modified interlayer coupling by 1% Ga-doping in Sr₂IrO₄. These findings represent a straightforward step toward the AFM spintronic devices.

Critical fluctuations in the spin-orbit Mott insulator Sr3Ir2O7

X-ray magnetic critical scattering measurements and specific heat measurements were performed on the perovskite iridate [Formula: see text]. We find that the magnetic interactions close to the Néel temperature [Formula: see text] are three-dimensional. This contrasts with previous studies which suggest two-dimensional behaviour like Sr₂IrO₄. Violation of the Harris criterion ([Formula: see text]) means that weak disorder becomes relevant. This leads a rounding of the antiferromagnetic phase transition at [Formula: see text], and modifies the critical exponents relative to the clean system. Specifically, we determine that the critical behaviour of [Formula: see text] is representative of the diluted 3D Ising universality class.

Orbital Symmetry and Orbital Excitations in High-Tc Superconductors

We discuss a few possibilities of high- T c superconductivity with more than one orbital symmetry contributing to the pairing. First, we show that the high energies of orbital excitations in various cuprates suggest a simplified model with a single orbital of x 2 − y 2 symmetry doped by holes. Next, several routes towards involving both e g orbital symmetries for doped holes are discussed: (i) some give superconductivity in a CuO 2 monolayer on Bi2212 superconductors, Sr 2 CuO 4 − δ , Ba 2 CuO 4 − δ , while (ii) others as nickelate heterostructures or Eu 2 − x Sr x NiO 4 , could in principle realize it as well. At low electron filling of Ru ions, spin-orbital entangled states of t 2 g symmetry contribute in Sr 2 RuO 4 . Finally, electrons with both t 2 g and e g orbital symmetries contribute to the superconducting properties and nematicity of Fe-based superconductors, pnictides or FeSe. Some of them provide examples of orbital-selective Cooper pairing.