Ruderman-Kittel-Kasuya-Yosida Research Articles

The prolonged decay of RKKY interactions by interplay of relativistic and non-relativistic electrons in semi-Dirac semimetals

The Ruderman–Kittel–Kasuya–Yosida (RKKY) interaction has been extensively explored in isotropic Dirac systems with linear dispersion, which typically follows an exponent decaying rate with the impurity distance R, i.e., J ∝ 1/R d (1/R 2d−1) in d-dimensional systems at finite (zero) Fermi energy. This fast decay makes it rather difficult to be detected and limits its application in spintronics. Here, we theoretically investigate the influence of anisotropic dispersion on the RKKY interaction, and find that the introduction of non-relativistic dispersion in semi-Dirac semimetals (S-DSMs) can significantly prolong the decay of the RKKY interaction and can remarkably enhance the Dzyaloshinskii–Moriya interaction around the relativistic direction. The underlying physics is attributed to the highly increased density of states in the linear-momentum direction as a result of the interplay of relativistic and non-relativistic electrons. Furthermore, we propose a general formula to determine the decaying rate of the RKKY interaction, extending the typical formula for isotropic DSMs. Our results suggest that the S-DSM materials are a powerful platform to detect and control the magnetic exchange interaction, superior to extensively adopted isotropic Dirac systems.

Frustration-controlled quantum phase transition between multiple singular two-stage Kondo behaviors in a tetrahedral quadruple quantum dot structure

Semiconductor quantum dots are considered to be promising candidates for the hardware of quantum information technology and optoelectronic devices. Herein, motivated by a tetrahedrally shaped colloidal quadruple quantum dot structure made from In-based III--V semiconductors, which has been synthesized very recently by Leemans et al. [J. Am. Chem. Soc., 143, 4290 (2021)], we provide timely insight into the electronic transport and the quantum phase transition (QPT) for such an architecture. When the interdot hopping between different side dots (${t}_{2}$) is absent, a singular two-stage Kondo effect is revealed for small central-side coupling ${t}_{1}$. The two screening processes are separated by an energy scale of the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction, and the fitting parameters deviate from the regular ones of the side-coupled double dot system. The RKKY interaction and temperature are well illustrated by functions of ${t}_{1}^{4}/(U{T}_{K1}^{2})$, where $U$ and ${T}_{K1}$ are the on-site electron-electron repulsion and the first Kondo temperature, respectively. When ${t}_{2}$ turns on, the ground state of the side dots transits from a spin quadruplet to a magnetic frustration phase, and then to a singlet, through two first-order QPTs. In the frustration phase, another new two-stage Kondo effect is demonstrated, which includes the process of screening the local spin on the central dot firstly, and then that on the neighborless side dot is screened at a lower temperature. Both the Kondo temperatures are found to be rather sensitive to ${t}_{2}$. When ${t}_{2}$ is large enough, the reappearance of the regular Kondo effect is found. With fixed ${t}_{2}=0$, charging the central dot triggers a transition from an antiferromagnetic correlation among the side dots to a ferromagnetic one, accompanied by a Kondo behavior in the central dot. We adopt the state-of-the-art numerical renormalization group method to implement the above behaviors, combined with analytical arguments.

Stray field and combined effects on device miniaturization of the magnetic tunnel junctions

Magneto-static stray field (H stray) interactions become an important issue when perpendicular CoFeB/MgO magnetic tunnel junctions (MTJs) are miniaturized. This raises the issue of which of the two mainstream etching processes, the pillar structure and the step structure, is better able to retain MTJ performance at extremely small scales. In the current study, we first simulated H stray effects as a function of Ruderman–Kittel–Kasuya–Yosida strength within a synthetic antiferromagnetic structure for the two structures. Our results revealed that H stray interactions were less influential (in terms of offset field) in step MTJs than in pillar MTJs during MTJ miniaturization. This is in good agreement with experimental results. This finding is further supported by adding Dzyaloshinskii–Moriya interactions into the free-layer of the two structures. We further simulated thermal stability with the inclusion of H stray for 30 nm MTJs. We found that adding etching damage effects (i.e. assuming both anisotropy constant and saturation magnetization of the free layer had some degree of loss) into the model of the pillar MTJ was necessary to obtain a trend that is close to the experimental results of thermal stability. This information can provide some guidance on the technical choices for the MTJ miniaturization.

Emergent magnonic singularities in anti parity-time symmetric synthetic antiferromagnets

We study the impact of the transition across the anti-parity-time (anti-) symmetry breaking point on the low-energy spin excitations in a synthetic antiferromagnet (SyAFM) that consists of two magnetic layers coupled antiferromagnetically via the Ruderman–Kittel–Kasuya–Yosida (RKKY) interaction. When varying the interlayer (RKKY) coupling strength a degeneracy point (exceptional point) is reached beyond which the system enters the anti- symmetry-broken phase. This phase is marked by the emergence of a finite net magnetization and low-lying excitations beyond the Goldstone modes in the anti- symmetry-preserved phase. For systems hosting an interfacial Dzyaloshinskii–Moriya interaction, we find a bound state in the continuum with a maximal coherent superposition of SyAFM excitations without any radiation. Analytical results for linearized models are corroborated with full numerical micromagnetic simulations endorsing the robustness and generalities of the theory predictions.

The Study of Diluted Magnetic Semiconductor: The Case of Manganese Doped Gallium Nitride

The diluted magnetic semiconductor, (Ga, Mn) N has recently attracted intense research interest for the purpose of spintronics application. The material is believed to circumvent the difficulty of combining data processing and mass storage facilities in a single crystal besides solving non-volatility problems. The concentration x, of Mn that substitutes for a fraction of Ga in the compound is thought to contribute a large concentration of magnetic moments and holes. The material studied is focused on dilute magnetic semiconductors (DMS) like <i>Ga_1-XMn<SUB>X</SUB>N</i> that play a key role in semiconductor spintronics. Due to their ferromagnetic properties they can be used in magnetic sensors and as spin injectors. The basic problems for applications are, however, the relatively low Curie temperatures of these systems. Therefore, we focus on the understanding of the magnetic properties and on a reliable calculation of Curie temperatures from first principles. We have developed a theoretical framework for calculating critical temperatures by combining first principles calculations and in terms of the Ruderman–Kittel–Kasuya–Yosida quantum spin model in Green’s function approach. Magnetic properties of the group-III nitride semiconductors are introduced here with basic material parameters (temperature, concentration, heat capacity, etc. Temperature dependencies of the spin wave specific heat, inverse magnetic susceptibility and reduced magnetization are determined. Therefore, the dependence of the Neel temperature on the manganese ion concentration is linear thus for our calculation the highest Neel temperature obtained T=146.3k within the concentration of 0.2.

Effect of In or Ge substitution on magnetic ordering in TmGa(In/Ge) compounds

The effect of In or Ge substitution for Ga on magnetic ordering in TmGa(In/Ge) compounds was systematically investigated, where three samples of TmGa, TmGa0.9In0.1 and TmGa0.9Ge0.1 were successfully synthesized. For TmGa, two transitions from ferromagnetic (FM) to antiferromagnetic (AFM) phase at TFA = 12.6 K and from AFM to paramagnetic (PM) phase at TN = 15.6 K were clearly identified. For TmGa0.9In0.1, it shows similar magnetic transitions with TFA = 10.6 K and TN = 14.2 K. For TmGa0.9Ge0.1, Ge substitution plays an effective role on the magnetic ordering, where only one transition from AFM-to-PM occurs and the transition from FM-to-AFM disappears. Variable temperature XRD experiments confirm that the bond length between the nearest neighboring Tm atoms undergoes a sharp change around TFA with increasing temperature. The magnetic ordering and transition in TmGa(In/Ge) compounds can be well explained by lattice distortion based on Ruderman–Kittel–Kasuya–Yosida (RKKY) indirect exchange interactions. Furthermore, In or Ge substitution has a great influence on the magnetocaloric effect as well.

Floquet control of indirect exchange interaction in periodically driven two-dimensional electron systems

We present a theory for the Ruderman–Kittel–Kasuya–Yosida (RKKY) interaction mediated by a two-dimensional (2D) electron system subjected to periodic driving. This is demonstrated for a 2D metal with two ferromagnetic chains deposited in parallel. Our calculations reveal new non-analytic features in the time-averaged spin susceptibility. For weak light–matter coupling, the RKKY interaction shows oscillations with a period tunable by the light amplitude and frequency. For stronger light–matter coupling, the interaction becomes non-oscillatory and remains purely ferromagnetic. Our findings open a path forward for realizing dynamic control of the indirect exchange interaction in 2D magnetic structures.

Evidence of symmetry lowering in antiferromagnetic metal TmB12 with dynamic charge stripes

Precise angle-resolved magnetoresistance (ARMR) and magnetization measurements have revealed (i) strong charge transport and magnetic anisotropy and (ii) emergence of a huge number of magnetic phases in the ground state of isotopically 11B-enriched single crystals of TmB12 antiferromagnetic (AF) metal with fcc crystal structure and dynamic charge stripes. We analyze for the first time the angular H–φ phase diagrams of AF state of Tm11B12 reconstructed from experimental ARMR and magnetization data arguing that the symmetry lowering leads to the appearance of several radial phase boundaries between different phases in the AF state. It is proposed that the suppression of the indirect Ruderman–Kittel–Kasuya–Yosida (RKKY) exchange along ⟨110⟩ directions between nearest neighboring magnetic moments of Tm3+ ions and subsequent redistribution of conduction electrons to quantum fluctuations of the electron density (dynamic stripes) are the main factors responsible for the anisotropy. Essential (more than 25% at T = 2 K) anisotropy of the Neel field in the (110) plane was found in Tm11B12 unlike to isotropic AF–P boundary in the H–φ phase diagrams of Ho11B12. Magnetoresistance components are discussed in terms of charge carrier scattering on the spin density wave, itinerant ferromagnetic nano-domains and on-site Tm3+ spin fluctuations.

RKKY Exchange Bias Mediated Ultrafast All‐Optical Switching of a Ferromagnet

AbstractThe discovery of ultrafast helicity‐independent all‐optical switching (HI‐AOS), as well as picosecond all‐electrical switching of a ferrimagnet, has inspired the ultrafast spintronics community to explore ultrafast switching of a ferromagnet to achieve practical ultrafast storage and memory devices. Two explored mechanisms of HI‐AOS of a ferromagnet in ferromagnet‐ferrimagnet heterostructure are: a) exploiting the indirect exchange coupling with and b) injection of non‐local spin current originated from a switching ferrimagnet. In this manuscript, exchange mediated HI‐AOS of a Ruderman–Kittel–Kasuya–Yosida (RKKY) exchange coupled “[Co/Pt]‐multilayers/Pt spacer/CoGd” heterostructure is demonstrated. The authors have measured layer‐resolved static magnetic properties, single‐shot HI‐AOS, and magnetization dynamics of the ferromagnetic Co/Pt multilayers (MLs), that are ferromagnetically or antiferromagnetically coupled with ferrimagnetic CoGd layers. Time‐resolved magnetization dynamics reveal a 3.5 ps switching time of the Co/Pt MLs, which is the fastest switching of a ferromagnet reported to date. Employing an extended microscopic three‐temperature model, the temporal dynamics of the exchange coupled ferromagnet–ferrimagnet heterostructure are simulated, qualitatively and quantitatively explaining the experimental switching phenomena. This work experimentally as well as theoretically establishes the mechanism of exchange mediated all‐optical switching of ferromagnet‐ferrimagnet heterostructures, which can be integrated with a magnetic tunnel junction for efficient reading after ultrafast energy‐efficient switching.

RKKY coupled local-moment magnetism in NaFe1−xCuxAs

A central question in a large class of strongly correlated electron systems, including heavy fermion compounds and iron pnictides, is the identification of different phases and their origins. It has been shown that the antiferromagnetic (AFM) phase in some heavy fermion compounds is induced by Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between localized moments, and that the competition between this interaction and Kondo effect is responsible for quantum criticality. However, conclusive experimental evidence of the RKKY interaction in pnictides is lacking. Here, using high resolution $^{23}$Na NMR measurements on lightly Cu-doped metallic single crystals of NaFe$_{1-x}$Cu$_{x}$As ~($x \approx 0.01$) and numerical simulation, we show direct evidence of the RKKY interaction in this pnictide system. Aided by computer simulation, we identify the $^{23}$Na NMR satellite resonances with the RKKY oscillations of spin polarization at Fe sites. Our $^{23}$Na spin-lattice and spin-spin relaxation data exhibits signature of an itinerant and inhomogeneous AFM phase in this system, accompanied by a simulation of Cu-induced perturbation to the ordered moments on the Fe sites. Our NMR results indicate coexistence of local and itinerant magnetism in lightly Cu-doped NaFe$_{1-x}$Cu$_{x}$As.

Room temperature CPP-giant magnetoresistance in Ni/Cu multilayered nanowires

Current-flow perpendicular to the layer planes giant magnetoresistance (CPP-GMR) of Ni/Cu multilayered nanowires (NWs) grown by an alternating current (AC) pulsed electrodeposition technique into anodic aluminum oxide (AAO) template with a pore diameter of 50 ± 5 nm is studied at room temperature. The method used for obtaining GMR percentage is the 2-probe resistance measurement of the contact of released and aligned NWs on a glass substrate in the presence of a magnetic field. The structure and thickness of layers are investigated by X-ray diffraction (XRD) and transmission electron microscopy (TEM), indicating the formation of well-ordered multilayers. The magnetic properties are studied by a vibrating sample magnetometer (VSM) and the first-order reversal curve (FORC) analysis. The maximum CPP-GMR of Ni/Cu multilayered NWs is obtained to be 2.6% for 17 and 2.7 nm thick Ni and Cu layers, respectively. The results show that Ruderman–Kittel–Kasuya–Yosida (RKKY) variation behavior of GMR values as a function of Cu spacer thickness is in accordance with theoretical models.

Unconventional magnetic order emerging from competing energy scales in the new RRh3Si7 intermetallics ( R = Gd-Yb)

The competition between Ruderman-Kittel-Kasuya-Yosida (RKKY), crystal electric field (CEF), and Kondo energy scales has recently emerged at the heart of complex magnetism in several Ce- or Yb-based intermetallics. Hard axis magnetic order has been observed in a handful of these compounds, independent of the crystal symmetry, size of the ordered moment, or the relative scale of the Kondo and magnetic ordering temperatures. This raises the question of the role of each energy scale in driving the ground state properties. In focusing on a single class of compounds, the rhombohedral R${\mathrm{Rh}}_{3}{\mathrm{Si}}_{7}$, we compare the anisotropy and magnetic ground states in members of this series with only RKKY interactions (R = Gd), or RKKY and CEF effects (R = Tb-Tm), with the behavior of the R = Yb compound, where all three energy scales (RKKY, CEF, Kondo) are at play. Moreover, we extend the comparison to two other isostructural Kondo systems ${\mathrm{YbIr}}_{3}{\mathrm{Si}}_{7}$ and ${\mathrm{YbIr}}_{3}{\mathrm{Ge}}_{7}$, where hard axis magnetic order is also observed. The non-Kondo compounds R${\mathrm{Rh}}_{3}{\mathrm{Si}}_{7}$ (R = Tb-Tm) lack the complexity of magnetic order along the hard CEF axis, pointing to the dominant role of the Kondo effect in driving this magnetic order. However, the CEF-RKKY competition is still responsible for complex magnetic ground states, and it appears that the electronic and magnetic degrees of freedom are entangled in all magnetic members of this series of compounds.

Controlling the RKKY interaction and heat transport in a Kitaev spin liquid via Z2 flux walls

Kitaev spin liquids (KSLs) contain both itinerant Majorana fermions and localized ${\mathbb{Z}}_{2}$ flux excitations. The mobile fermions transport energy, while the fluxes hinder heat flow. By controlling the flux configuration, one can separate a KSL into different domains via ${\mathbb{Z}}_{2}$ flux walls. We show that at low temperatures, the wall significantly suppresses the Majorana-mediated Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction and blocks the heat transfer between domains.

Magnetic imaging of various topological spin textures and their dynamics

Nanometer-scale vortex-like topological spin textures, such as magnetic skyrmion and antiskyrmion, have recently attracted enormous attention owing to their topological nature and emergent electromagnetic properties. To confirm such minute twisted spin textures and their dynamics under external stimuli, real-space imaging techniques with high spatial resolution and high recording speed are required.To realize the Bloch-type magnetic skyrmion with a topological number of − 1 (where spins swirl from the north-pole in the core to the south-pole in the peripheral, and wrap a sphere), we have developed a technique allowing not only to create skyrmions via precise control of the magnetic field in a standard transmission electron microscope (TEM), but also to directly demonstrate their twisted textures and dynamics. We employed a phase imaging technique, called differential-phase contrast, in the scanning TEM mode to quantitatively characterize Néel-type magnetic twists, such as Bloch lines, that constitute the antiskyrmion with a topological number + 1. Furthermore, we took advantage of cryogenic high-resolution Lorentz TEM to probe atomic-scale skyrmions in a centrosymmetric magnet with a Ruderman–Kittel–Kasuya–Yosida coupling.To manipulate and track individual skyrmions and their lattice using a relatively low electric current, combined with field-quenching of skyrmions, we designed a thin FeGe microdevice having a notch, in which the spin current was localized in the specific area near a corner of the notch. Using this device, we tracked drift, Hall, and torque motions of single 80-nm-sized skyrmions and their bunches using electric current densities three orders of magnitude lower than those required to manipulate magnetic domain walls.

Low-Energy Picosecond Magnetic Switching for Synthetic Ferrimagnetic Free Layer Utilizing the Electric-Field-Tuned RKKY Effect

The processional switching mechanism governs magnetic switching in magnetic tunnel junctions (MTJs) in the sub-nanosecond range, which limits the application of spin transfer torque magnetic random access memory (STT-MRAM) in the ultrafast region. In this paper, we propose a new picosecond magnetic switching mechanism in a synthetic antiferromagnetic (SAF) structure using the adjustable Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction controlled by an external electric field (E-field). It is shown that along with the sign change of the RKKY interaction in the SAF structure with an external E-field, the critical switching current density can be significantly reduced by one order of magnitude compared to that of a normal MTJ design at 100 ps; thus, this novel STT-MRAM can be written with a very low switching current density to avoid the MTJ breakdown problem and reduce the writing energy. To understand the physical origin of this abnormal phenomenon, a toy model is proposed in which the external-E-field-controlled sign change of the RKKY interaction in the SAF structure provides an extra contribution to the total energy that helps thespins overcome the energy barrier and break the processional switching mechanism.

Molecular-Field Approximation in the Theory of Ferromagnetic Phase Transition in Diluted Magnetic Semiconductors

In this pedagogical paper, the comparative analysis of two common approaches describing the ferromagnetic phase transition in diluted magnetic semiconductors (DMS) is expounded in terms of the Weiss field approximation. Assuming a finite spin polarization of the magnetic ions, the treatment of carrier-ion exchange interaction in the first order evokes a homogeneous Weiss molecular field that polarizes the spins of free carriers. In turn, this spin polarization of the free carriers exerts the effective field that may stabilize the DMS spin polarization belowa critical temperature TC. The treatment of such self-consistent spontaneous DMS magnetization can be done in terms of the spin-spin interaction independent of the inter-ion distance and the infinitesimal in thermodynamic limit. On the other hand, by additionally accounting for the second-order effects of the carrier-ion exchange interaction, we can treat a Weiss field in terms of the Ruderman–Kittel–Kasuya–Yosida indirect spin-spin interaction, which oscillates and does not disappear at finite inter-ion distances in the case of a finite concentration of carriers. These both approaches result in the same Curie temperature TC provided a non-correlated homogeneous random distribution of the localized spin moments over the sample volume. We discuss the origin of such coincidence and show when this is not a case in other more realistic models of the conducting DMSs.

Electrical control of Ruderman–Kittel–Kasuya–Yosida exchange interaction in zigzag edge MoS2 nanoflakes

In this study, we investigate the spin–spin correlation of two magnetic impurities in zigzag edge MoS2 nanoflakes using a three-orbital tight-binding model. In particular, we consider the dependence of the Ruderman–Kittel–Kasuya–Yosida (RKKY) interaction on the local electric field strength for providing a degree of tunability in triangular and rectangular nanoflakes. Our results indicate that manipulating the local electric field at the zigzag edges could allow the control of all the different components of the RKKY interaction in MoS2 nanoflakes. Interestingly, the Dzyaloshinskii–Moriya JDM oscillates but does not decay due to strong spin–orbit coupling. Moreover, the electric field induces a sizable JDM interaction as a function of the magnetic separation along zigzag edges for various Fermi energies. Our findings provide a method for enhancing the RKKY exchange interactions with magnetic arrays in these materials.

Prioritization of the influence of different exchange interactions and uniaxial anisotropy on the generation and morphology of skyrmions

Different magnetic interactions and anisotropy in the multi-layer structure have different effects on the formation and morphology of skyrmions under zero field. In this paper, we show that the Ruderman–Kittel–Kasuya–Yosida (RKKY) coupling plays a dominant role in the generation of skyrmions but has no significant effect on the size of skyrmions. When the RKKY coupling is weak, if the Dzyaloshinskii–Moriya interaction (DMI) is strong enough, some irregular cruciform domain states can be formed. With the increase of the DMI, the shape of skyrmions is altered from Néel skyrmions to skyrmioniums, and when the Heisenberg exchange is relatively low, complex domain states, such as the labyrinth are formed. However, when the Heisenberg coupling is comparatively high, the spin states of the Néel-skyrmions are reversed. Both the Heisenberg exchange interaction and uniaxial anisotropy have a positive influence on reducing the diameters of skyrmions. However, skyrmions are difficult to generate when the Heisenberg exchange and anisotropy are strong enough. We find the prioritization of the effects of different magnetic interactions and uniaxial anisotropy on the formation and morphology of skyrmions by analyzing the energy diagrams, combined with the magnetization configuration in different pairs of the exchange interactions and anisotropy, in which the RKKY coupling has the greatest influence, followed by the DMI, then the Heisenberg exchange and finally the uniaxial anisotropy.

Two-dimensional parabolic Dirac system in the presence of nonmagnetic and magnetic impurities

We theoretically investigate the effect of the nonmagnetic and magnetic impurities to the 2D parabolic Dirac system. The induced charge density by the charged impurity is obtained by the linear response theory within the random phase approximation. We also calculate in-detail, the Ruderman–Kittel–Kasuya–Yosida (RKKY) interaction between two magnetic impurities placed within the 2D sheet of the Dirac materials with isotropic and anisotropic dispersion. For the anisotropic dispersion, the RKKY interaction is also anisotropic and related to the lattice parameters which can be obtained through the DFT calculation or the experiments. The features of the RKKY interaction also can be treated as a signature of the topological phase transition as well as the change of Berry curvature. Our results are also illuminating to the study of the static screening and the RKKY interaction of the isotropic or anisotropic 3D Dirac/Weyl semimetals or the 2D transition metal dichalcogenide family.

Inhomogeneous Kondo destruction by RKKY correlations

The competition between the indirect exchange interaction (IEC) of magnetic impurities in metals and the Kondo effect gives rise to a rich quantum phase diagram, the Doniach Diagram (Doniach, 1977). A Kondo screened phase is separated from a spin ordered phase when the local exchange coupling J and the concentration of magnetic moments nM are varied. In disordered metals, both the Kondo temperature and the IEC are widely distributed due to the scattering of the conduction electrons from the impurity potential. Therefore, it is a question of fundamental importance, how this Doniach diagram is modified by the disorder, and if one can still identify separate phases. Recently, Nejati et al. (2017) investigated the effect of Ruderman–Kittel–Kasuya–Yosida (RKKY) correlations on the Kondo effect of two magnetic impurities, renormalizing the Kondo interaction based on the Bethe–Salpeter equation and performing the poor men’s renormalization group (RG) analysis with the RKKY-renormalized Kondo coupling. In the present study, we extend this theoretical framework, allowing for different Kondo temperatures of two RKKY-coupled magnetic impurities due to different local exchange couplings and density of states. As a result, we find that the smaller one of the two Kondo temperatures is suppressed more strongly by the RKKY interaction, thereby enhancing their initial inequality. In order to find out if this relevance of inequalities between Kondo temperatures modifies the distribution of the Kondo temperature in a system of a finite density of randomly distributed magnetic impurities, we present an extension of the RKKY coupled Kondo RG equations. We discuss the implication of these results for the interplay between Kondo coupling and RKKY interaction in disordered electron systems and the Doniach diagram in disordered electron systems.