Robust spin correlations at high magnetic fields in the harmonic honeycomb iridates

Beyond Kitaev physics in strong spin-orbit coupled magnets

We review the recent advances and current challenges in the field of strong spin-orbit coupled Kitaev materials, with a particular emphasis on the physics beyond the exactly-solvable Kitaev spin liquid point. To this end, we present a comprehensive overview of the key exchange interactions in candidate materials with a specific focus on systems featuring effectiveJeff=1/2magnetic moments. This includes, but not limited to,5d5iridates,4d5ruthenates and3d7cobaltates. Our exploration covers the microscopic origins of these interactions, along with a systematic attempt to map out the most intriguing correlated regimes of the multi-dimensional parameter space. Our approach is guided by robust symmetry and duality transformations as well as insights from a wide spectrum of analytical and numerical studies. We also survey higher spin Kitaev models and recent exciting results on quasi-one-dimensional models and discuss their relevance to higher-dimensional models. Finally, we highlight some of the key questions in the field as well as future directions.

Possible intermediate quantum spin liquid phase in α-RuCl3 under high magnetic fields up to 100 T

Pursuing the exotic quantum spin liquid (QSL) state in the Kitaev material α-RuCl3 has intrigued great research interest recently. A fascinating question is on the possible existence of a field-induced QSL phase in this compound. Here we perform high-field magnetization measurements of α-RuCl3 up to 102 T employing the non-destructive and destructive pulsed magnets. Under the out-of-plane field along the c* axis (i.e., perpendicular to the honeycomb plane), two quantum phase transitions are uncovered at respectively 35 T and about 83 T, between which lies an intermediate phase as the predicted QSL. This is in sharp contrast to the case with in-plane fields, where a single transition is found at around 7 T and the intermediate QSL phase is absent instead. By measuring the magnetization data with fields tilted from the c* axis up to 90° (i.e., in-plane direction), we obtain the field-angle phase diagram that contains the zigzag, paramagnetic, and QSL phases. Based on the K-J-Γ-[Formula: see text] model for α-RuCl3 with a large Kitaev term we perform density matrix renormalization group simulations and reproduce the quantum phase diagram in excellent agreement with experiments.

Large tunneling magnetoresistance in van der Waals magnetic tunnel junctions based on FeCl2 films with interlayer antiferromagnetic couplings

Antiferromagnets (AFMs) are some of the most promising candidates for next-generation magnetic memory technology owing to their advantages over conventional ferromagnets (FMs), such as zero stray field and THz-range magnetic resonance frequency. Motivated by the recent synthesis of FeCl₂ films with interlayer AFM and intralayer FM couplings, we investigated the magnetic properties of few-layer FeCl₂ and the spin-dependent transmissions of graphite/bilayer FeCl₂/graphite and Au/n-layer FeCl₂/Au magnetic tunnel junctions (MTJs) using first-principles calculations combined with the nonequilibrium Green's function. The interlayer AFM coupling of FeCl₂ is certified to be stable and independent of the stacking orders and relative displacement between layers. Furthermore, based on the Au electrode with better conductive performance than the graphite electrode and monolayer 1T-FeCl₂ with complete spin polarization, high Curie temperature and large magnetic anisotropic energy, a high tunnel magnetoresistance (TMR) ratio of 2.7 × 10³% is achieved in Au/bilayer FeCl₂/Au MTJs at zero bias and it increases with different layers of FeCl₂ (n = 2-10). These excellent spin transport properties of Au/n-layer FeCl₂/Au MTJs based on two-dimensional (2D) AFM barriers with out-of-plane magnetization directions suggest their great potential for application in high-reliability, high-speed and high-density spintronic devices.

The Magnetic Genome of Two-Dimensional van der Waals Materials

Magnetism in two-dimensional (2D) van der Waals (vdW) materials has recently emerged as one of the most promising areas in condensed matter research, with many exciting emerging properties and significant potential for applications ranging from topological magnonics to low-power spintronics, quantum computing, and optical communications. In the brief time after their discovery, 2D magnets have blossomed into a rich area for investigation, where fundamental concepts in magnetism are challenged by the behavior of spins that can develop at the single layer limit. However, much effort is still needed in multiple fronts before 2D magnets can be routinely used for practical implementations. In this comprehensive review, prominent authors with expertise in complementary fields of 2D magnetism (i.e., synthesis, device engineering, magneto-optics, imaging, transport, mechanics, spin excitations, and theory and simulations) have joined together to provide a genome of current knowledge and a guideline for future developments in 2D magnetic materials research.

Low-field magnetic anisotropy of Sr2IrO4

Magnetic anisotropy in strontium iridate (Sr₂IrO₄) is essential because of its strong spin-orbit coupling and crystal field effect. In this paper, we present a detailed mapping of the out-of-plane (OOP) magnetic anisotropy in Sr₂IrO₄for different sample orientations using torque magnetometry measurements in the low-magnetic-field region before the isospins are completely ordered. Dominant in-plane anisotropy was identified at low fields, confirming thebaxis as an easy magnetization axis. Based on the fitting analysis of the strong uniaxial magnetic anisotropy, we observed that the main anisotropic effect arises from a spin-orbit-coupled magnetic exchange interaction affecting the OOP interaction. The effect of interlayer exchange interaction results in additional anisotropic terms owing to the tilting of the isospins. The results are relevant for understanding OOP magnetic anisotropy and provide a new way to analyze the effects of spin-orbit-coupling and interlayer magnetic exchange interactions. This study provides insight into the understanding of bulk magnetic, magnetotransport, and spintronic behavior on Sr₂IrO₄for future studies.

Sawtooth Torque in Anisotropic j_{eff}=1/2 Magnets: Application to α-RuCl_{3}

The so-called "Kitaev candidate" materials based on 4d^{5} and 5d^{5} metals have recently emerged as magnetic systems displaying strongly anisotropic exchange interactions reminiscent of the Kitaev's honeycomb model. Recently, these materials have been shown to commonly display a distinct sawtooth angular dependence of the magnetic torque over a wide range of magnetic fields. While higher order chiral spin interactions have been considered as a source of this observation, we show here that bilinear anisotropic interactions and/or g anisotropy are each sufficient to explain the observed torque response, which may be distinguished on the basis of high-field measurements. These findings unify the understanding of magnetic torque experiments in a variety of Kitaev candidate materials.

Resonant torsion magnetometry in anisotropic quantum materials

Unusual behavior in quantum materials commonly arises from their effective low-dimensional physics, reflecting the underlying anisotropy in the spin and charge degrees of freedom. Here we introduce the magnetotropic coefficient k = ∂²F/∂θ², the second derivative of the free energy F with respect to the magnetic field orientation θ in the crystal. We show that the magnetotropic coefficient can be quantitatively determined from a shift in the resonant frequency of a commercially available atomic force microscopy cantilever under magnetic field. This detection method enables part per 100 million sensitivity and the ability to measure magnetic anisotropy in nanogram-scale samples, as demonstrated on the Weyl semimetal NbP. Measurement of the magnetotropic coefficient in the spin-liquid candidate RuCl₃ highlights its sensitivity to anisotropic phase transitions and allows a quantitative comparison to other thermodynamic coefficients via the Ehrenfest relations.

Correlated states in β-Li2IrO3 driven by applied magnetic fields

Magnetic honeycomb iridates are thought to show strongly spin-anisotropic exchange interactions which, when highly frustrated, lead to an exotic state of matter known as the Kitaev quantum spin liquid. However, in all known examples these materials magnetically order at finite temperatures, the scale of which may imply weak frustration. Here we show that the application of a relatively small magnetic field drives the three-dimensional magnet β-Li₂IrO₃ from its incommensurate ground state into a quantum correlated paramagnet. Interestingly, this paramagnetic state admixes a zig-zag spin mode analogous to the zig-zag order seen in other Mott-Kitaev compounds. The rapid onset of the field-induced correlated state implies the exchange interactions are delicately balanced, leading to strong frustration and a near degeneracy of different ground states.

Materials with a Kitaev spin liquid ground state are sought after as models of quantum phases but candidates so far form either zig-zag or incommensurate magnetic order. Ruiz et al. find a crossover between these states in β-Li₂IrO₃ under weak magnetic fields, indicating strongly frustrated spin interactions.