RKKY Research Articles

Carrier-induced ferromagnetism in two-dimensional magnetically doped semiconductor structures

We show theoretically that the magnetic ions, randomly distributed in a two-dimensional (2D) semiconductor system, can generate a ferromagnetic long-range order via the RKKY interaction. The main physical reason is the discrete (rather than continuous) symmetry of the 2D Ising model of the spin-spin interaction mediated by the spin-orbit coupling of 2D free carriers, which precludes the validity of the Mermin-Wagner theorem. Further, the analysis clearly illustrates the crucial role of the molecular field fluctuations as opposed to the mean field. The developed theoretical model describes the desired magnetization and phase-transition temperature ${T}_{c}$ in terms of a single parameter, namely, the chemical potential $\ensuremath{\mu}$. Our results highlight a pathway to reach the highest possible ${T}_{c}$ in a given material as well as an opportunity to control the magnetic properties externally (e.g., via a gate bias). Numerical estimations show that magnetic impurities such as ${\mathrm{Mn}}^{2+}$ with spins $S=5/2$ can realize ferromagnetism with ${T}_{c}$ close to room temperature.

Effect of midgap states on the magnetic exchange interaction mediated by a d -wave superconductor

We theoretically study the indirect interaction between two ferromagnetic contacts located on the surface of a $d$-wave superconductor. When the magnets are connected to a $\{010\}$ edge of the superconductor we find an oscillating RKKY interaction that varies in sign as the distance between the magnetic contacts is varied. However, when coupling the magnets to an $\{110\}$ edge of the superconductor, we find that the presence of midgap states qualitatively changes the results. The ground state of the system is then found to always favor alignment of the magnets as this configuration most strongly suppresses the midgap states, leading to a larger condensation energy which dominates over the intrinsic RKKY interaction.

Coexistence of Charge Order and Antiferromagnetic Order in an Extended Periodic Anderson ModelSupported by the National Natural Science Foundation of China (Grant Nos. 11974048 and 11974049), and the Beijing Science Foundation (Grant No. 1192011).

The competition between the RKKY interaction and the Kondo effect leads to a magnetic phase transition, which occurs ubiquitously in heavy fermion materials. However, there are more and more experimental evidences indicating that the valence fluctuation plays an essential role in the Ce- and Y-based compounds. We study an extended periodic Anderson model (EPAM) which includes the onsite Coulomb repulsion Ucf between the localized electrons and conduction electrons. By employing the density matrix embedding theory, we investigate the EPAM in the symmetric case at half filling. By fixing the onsite Coulomb repulsion U of the localized electrons to an intermediate value, the interplay between the RKKY interaction, the Kondo effect and the Coulomb repulsion Ucf brings rich physics. We find three different phases, the antiferromagnetic phase, the charge order phase and paramagnetic phase. When the hybridization strength V between the localized orbital and the conduction orbital is small, the Kondo effect is weak so that the AF phase and the CO phase are present. The phase transition between the two long-range ordered phase is of first order. We also find a coexistence region between the two phases. As V increases, the Kondo effect becomes stronger, and the paramagnetic phase appears between the other two phases.

Mn-induced Fermi-surface reconstruction in the SmFeAsO parent compound

The electronic ground state of iron-based materials is unusually sensitive to electronic correlations. Among others, its delicate balance is profoundly affected by the insertion of magnetic impurities in the FeAs layers. Here, we address the effects of Fe-to-Mn substitution in the non-superconducting Sm-1111 pnictide parent compound via a comparative study of SmFe_{1-x}Mn_{x}AsO samples with x(text{Mn})= 0.05 and 0.10. Magnetization, Hall effect, and muon-spin spectroscopy data provide a coherent picture, indicating a weakening of the commensurate Fe spin-density-wave (SDW) order, as shown by the lowering of the SDW transition temperature T_text{SDW} with increasing Mn content, and the unexpected appearance of another magnetic order, occurring at T^{*} approx 10 and 20 K for x=0.05 and 0.10, respectively. We attribute the new magnetic transition at T^{*}, occurring well inside the SDW phase, to a reorganization of the Fermi surface due to Fe-to-Mn substitutions. These give rise to enhanced magnetic fluctuations along the incommensurate wavevector varvec{Q}_2 =(pi pm delta ,pi pm delta ), further increased by the RKKY interactions among Mn impurities.

Kondo holes in strongly correlated impurity arrays: RKKY-driven Kondo screening and hole-hole interactions

The emerging and screening of local magnetic moments in solids has been investigated for more than 60 years. Local vacancies as in graphene or in Heavy Fermions can induce decoupled bound states that lead to the formation of local moments. In this paper, we address the puzzling question how these local moments can be screened and what determines the additionally emerging low temperature scale. We review the initial problem for half-filled conduction bands from two complementary perspectives: By a single-particle supercell analysis in the uncorrelated limit and by the Lieb-Mathis theorem for systems with a large Coulomb interaction $U$. We proof that the stable local moments are subject to screening by three different mechanisms. Firstly the local moments are delocalized by a finite $U$ beyond the single-particle bound state. We find a Kosterlitz-Thouless type transition governed by an exponentially suppressed low energy scale of a counterintuitive Kondo form with $J_{\rm eff} \propto U^n$ for small $U$, where $n>1$ depends on the precise model. Secondly, we show that away from half-filling the local moment phase becomes unstable and is replaced by two types of singlet phases that are adiabatically connected. At a critical value for the band center, the physics is governed by an exponentially suppressed Kondo scale approaching the strong coupling phase that is replaced by an singlet formation via antiferromagnetic RKKY interaction for large deviation from the critical values. Thirdly, we show that the local magnetic moment can be screened by a Kondo hole orbital at finite energy, even though the orbital occupation is negligible: An additional low energy scale emerges below which the localized moment is quenched. Similarities to the experimental findings in Ce$_{1-x}$La$_x$Pd$_3$ are pointed out.

Magnetic structure and crystal field excitations of NdOs2Al10: a neutron scattering study

We have investigated the magnetic properties of a polycrystalline sample of NdOs2Al10 using neutron diffraction and inelastic neutron scattering, magnetic susceptibility and heat capacity measurements. The magnetic susceptibility data reveal an antiferromagnetic transition at T N1 = 2.2 K while the heat capacity data which extend to lower temperatures show a further transition at T N2 = 1.1 K. The INS measurements detect four well-resolved crystal field excitations at 7.4, 12.4, 17.6 meV and 19.2 meV at 5 K. The positions and intensities of the observed CEF excitations and the temperature dependence of previously published single crystal susceptibility data are analysed based on the orthorhombic CEF model of the J = 9/2 ground state multiplet of Nd3+ ion. The neutron diffraction study reveals the magnetic structure at T = 1.6 K to be of sine wave type (κ = [0, 0.723, 0]) with an ordered state moment of μ Nd 3+ = 1.59(1) μ B aligned along the a-axis in agreement with the single ion crystal field anisotropy. This indicates that the magnetism of NdOs2Al10 is governed by the RKKY interactions in agreement with other RT 2Al10 (R = Nd, Sm, Tb, T = Fe, Ru and Os), but different to that of R = Ce based compounds where anisotropic two ions interaction as well as Kondo interaction govern the anomalous direction of the ordered state moment.

Specific heat of Cu substituted GdNiSi

The specific heat of magnetic regenerator materials affects the efficiency of cryocoolers below 10 K. GdNiSi with the orthorhombic TiNiSi-type structure shows antiferromagnetic order at 11 K. To tune the magnetic transition temperature below 10 K, Cu substituted GdNiSi alloys were prepared. Powder X-ray diffraction and specific heat measurements were performed to study the effect of Cu substitution on the crystal structure and magnetic transition temperature. Increasing Cu content, the secondary phase which may be the hexagonal BeZrSi-type GdNi1−x Cu x Si is observed. The peak of the specific heat for x ≤ 0.2 was shifted higher temperature (13 K) due to the magnetic transition, though the unit cell volume of the TiNiSi-type structure slightly increased with increasing x. This result possibly originates from the increase of the RKKY interaction for the sinusoidal curve due to an increase of the intersite distance of Gd-ions.

Multi-layer transition and the magnetic properties of a spin-1/2 Ashkin Teller model with RKKY interaction: A Monte Carlo study

The effects of RKKY interaction and the influence of the four spin interaction J4, on the multi-layer transition and magnetic properties of a spin-1/2 Ashkin Teller model of a ferromagnetic system shaped by two magnetic multi-layer materials, of different thicknesses, separated by a non-magnetic spacer of thickness M, are examined using Monte Carlo simulations. The system presents a new partially ordered phase <σS>, for various values of J4/J2, and exhibits behavior typical of a second-order phase transition. It is found that the transition temperatures of the two blocks are strongly dependent on the thickness of the magnetic layers N and the four-spin coupling J4/J2, while they do not depend on the non-magnetic spacer and the Fermi level kf. Finally, We have obtained a critical thickness ML of the non-magnetic spacer above which the multi-layer blocks undergo a transition separately at different temperatures, for J4/J2=3 and kf=0.2.

Anisotropic ferroelectric distortion effects on the RKKY interaction in topological crystalline insulators

Manipulation of electronic and magnetic properties of topological materials is a topic of much interest in spintronic and valleytronic applications. Perturbation tuning of multiple Dirac cones on the (001) surface of topological crystalline insulators (TCIs) is also a related topic of growing interest. Here we show the numerical evidence for the ferroelectric structural distortion effects on the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between two magnetic impurity moments on the SnTe (001) and related alloys. The mirror symmetry breaking between Dirac cones induced by the ferroelectric distortion could be divided into various possible configurations including the isotropically gapped, coexistence of gapless and gapped, and anisotropically gapped phases. Based on the retarded perturbed Green’s functions of the generalized gapped Dirac model, we numerically find the RKKY response for each phase. The distortion-induced symmetry breaking constitutes complex and interesting magnetic responses between magnetic moments compared to the pristine TCIs. In the specific case of coexisted gapless and gapped phases, a nontrivial behavior of the RKKY interaction is observed, which has not been seen in other Dirac materials up until now. For two impurities resided on the same sublattices, depending on the distortion strength, magnetic orders above of a critical impurity separation exhibit irregular ferromagnetic ⇔ antiferromagnetic phase transitions. However, independent of the impurity separation and distortion strength, no phase transition emerges for two impurities resided on different sublattices. This essential study sheds light on magnetic properties of Dirac materials with anisotropic mass terms and also makes TCIs applications relatively easy to understand.

Ferrielectric properties of a bilayer structure with RKKY-like interaction: A Monte Carlo study

The ferrielectric properties of a bilayer structure separate by electrical insulating layers, with RKKY interactions in the Blume–Capel model. The system is composed of two interacting A (spin S=5∕2) and B (spin σ=2) planes in which the intralayer couplings are ferroelectric while the interlayer interactions are antiferroelectric. The temperature dependence of the ferroelectricity of a bilayer structure separate by electrical insulating layers, with RKKY interactions in the Blume–Capel model has been investigated. The effects of external longitudinal electric (EZ) and crystal anisotropy DA and DB fields have been investigated. On the other hand, the variation of total and partial polarizations with exchange coupling interactions JA, JB, JRKKY, crystal and external longitudinal electric fields was discussed. Finally, the influence of the exchange interactions and crystal field on the critical temperatures of the system and hysteresis cycles has been examined.

4f -block elemental-atom-embedded gh−C3N4 monolayers: Large magnetic moment, high-temperature ferromagnetism, and huge magnetic anisotropy energy

Two-dimensional (2D) magnetic materials with strong magnetism, long magnetic relaxation times, high temperature ferromagnetism, and large magnetic anisotropy energy (MAE) are promising for applications of nanoscale spintronic devices. Using the spin-orbital coupling density functional theory (DFT) calculations, we investigate the structural stability, electronic structures, and magnetic properties of graphenelike carbon-nitride ($\mathrm{gh}\text{\ensuremath{-}}{\mathrm{C}}_{3}{\mathrm{N}}_{4}$) sheets with the adsorption of whole series of $4f$-block elemental (lanthanide; Ln) atoms. Our results demonstrate that Ln atoms can be stably embedded into/above the center of the cavity of $\mathrm{gh}\text{\ensuremath{-}}{\mathrm{C}}_{3}{\mathrm{N}}_{4}$ monolayer and significantly affect the electronic and magnetic properties. Upon single Ln atom adsorption, all Ln@$\mathrm{gh}\text{\ensuremath{-}}{\mathrm{C}}_{3}{\mathrm{N}}_{4}$ systems show metal character, large spin and orbital magnetic moments, and most of them favor the long-range ferromagnetic ordering. Interestingly, Pr, Nd, Ho adsorbates would possess total magnetic moments of 1.09, 1.47, 6.13 ${\ensuremath{\mu}}_{B}$, high Curie temperatures (${T}_{c}$) of 593, 699, 700 K, large MAEs of 4.89, $\ensuremath{-}17.88$, 21.31 meV/Ln atom, respectively. Based on the electronic structure analyses, we propose that the $4f$ electron hopping between the occupied and unoccupied states around the Fermi level contributes to the large MAE, significant intratomic Ln-$sd$ orbital hybridization with N-$2p$ orbital hybridization gives rise to structural stability, and the coexistence of superexchange and RKKY interactions determines the long-term ferromagnetic coupling between Ln atoms. The present study demonstrates that Ln@$\mathrm{gh}\text{\ensuremath{-}}{\mathrm{C}}_{3}{\mathrm{N}}_{4}$ sheets have significant promise for applications in spintronics such as high density memory devices or for magnetic random access memory.

Spin accumulation induced anisotropic RKKY interaction

In a spin-valve structure, the magnetizations of the ferromagnetic layer are influenced by the RKKY exchange interaction. The RKKY exchange interaction is an indirect exchange interaction mediated by the conduction electron of the non-magnetic spacer. The RKKY exchange interaction has been widely studied both theoretically and experimentally. However, the effect of the spin accumulation in the spacer on the exchange interaction has not been studied yet. While the spin accumulation in the non-magnetic spacer is generally small, recent experiment show that non-magnetic metallic layer in magnetic multilayers can have a large spin accumulation. Utilizing linear response theory, we discuss the effect of the spin accumulation on the spin density of the conduction electron in the spacer and show that the spin accumulation induces an anisotropic exchange.

Evolution of helimagnetic correlations when approaching the quantum critical point of Mn1−xFexSi

We present a comprehensive investigation of the evolution of helimagnetic correlations in Mn$_{1-x}$Fe$_x$Si with increasing doping. By combining polarised neutron scattering and high resolution Neutron Spin Echo spectroscopy we investigate three samples with $x$=0.09, 0.11 and 0.14, i.e. with compositions on both sides of the concentration $x^* \sim 0.11$ where the helimagnetic Bragg peaks disappear and between $x^*$ and the quantum critical concentration $x_C \sim 0.17$, where $T_C$ vanishes. We find that the abrupt disappearance of the long range helical periodicity at $x^*$, does not affect the precursor fluctuating correlations. These build up with decreasing temperature in a similar way as for the parent compound MnSi. Also the dynamics bears strong similarities to MnSi. The analysis of our results indicates that frustration, possibly due to achiral RKKY interactions, increases with increasing Fe doping. We argue that this effect explains both the expansion of the precursor phase with increasing $x$ and the abrupt disappearance of long range helimagnetic periodicity at $x^*$.

RKKY Interaction of Magnetic Impurities in Node-Line Semimetals

Motivated by the recent upsurge in research of three-dimensional topological semimetals (SMs), we theoretically study the RKKY interaction between magnetic impurities in node-line SMs with and without the chirality and obtain the analytical expressions. We find that unique toroidal Fermi surface (FS) in nodal-line SMs, distinctly different from the spheroid FS in the SMs with the point nodes, has significant influences on the RKKY interaction, leading to strong anisotropic oscillation and unique decay features. In the direction perpendicular to node-line plane, as usual, there is only one oscillation period related to the Fermi energy. In contrast, in the node-line plane, the RKKY interaction form a beating pattern and oscillates more rapidly with two distinct periods: one is coming from the Fermi energy and the other is from the radius of node-line. More importantly, inside nodal-line SMs bulk, the decay rate of RKKY interaction manifests a typical two-dimensional feature for impurities aligned along the direction perpendicular to nodal-line plane. Furthermore, the magnetic interactions in nodal-line SMs with linear and quadratic dispersions in the nodal-line plane are compared. We also discuss the possible application of the present theory on realistic NLSM ZrSiSe. Our results shed the light for application of magnetically doped node-line SMs in spintronics.

Kondo effect and RKKY interaction assisted by magnetic anisotropy in a frustrated magnetic molecular device at zero and finite temperature.

Molecular magnetic compounds, which combine the advantages of nanoscale behaviors with the properties of bulk magnetic materials, are particularly attractive in the fields of high-density information storage and quantum computing. Before molecular electronic devices can be fabricated, a crucial task is the measurement and understanding of the transport behaviors. Herein, we consider a magnetic molecular trimer sandwiched between two metal electrodes, and, with the aid of the sophisticated full density matrix numerical renormalization group (FDM-NRG) technique, we study the effect of magnetic anisotropy on the charge transport properties, illustrated by the local density of states (LDOS, which is proportional to the differential conductance), the Kondo effect, and the temperature and inter-monomer hopping robustness. Three kinds of energy peaks are clarified in the LDOS: the Coulomb, the Kondo and the Ruderman-Kittel-Kasuya-Yosida (RKKY) peaks. The local magnetic moment and entropy go through four different regimes as the temperature decreases. The Kondo temperature TK could be described by a generalized Haldane's formula, revealing in detail the process where the local moment is partially screened by the itinerant electrons. A relationship between the width of the Kondo resonant peak WK and TK is built, ensuring the extraction of TK from WK in an efficient way. As the inter-monomer hopping integral varies, the ground state of the trimer changes from a spin quadruplet to a magnetically frustrated phase, then to an orbital spin singlet through two first order quantum phase transitions. In the first two phases, the Kondo peak in the transmission coefficient reaches its unitary limit, while in the orbital spin singlet, it is totally suppressed. We demonstrate that magnetic anisotropy may also induce the Kondo effect, even without Coulomb repulsion, hence it is replaceable in the many-body behaviours at low temperature.

Prediction of room-temperature ferromagnetism and large perpendicular magnetic anisotropy in a planar hypercoordinate FeB3 monolayer.

Two-dimensional (2D) magnets simultaneously possessing a high transition temperature and large perpendicular magnetic anisotropy are extremely rare, but essential for highly efficient spintronic applications. By using ab initio and global minimization approaches, we for the first time report a completely planar hypercoordinate metalloborophene (α-FeB3) with high stability, unusual stoichiometry and exceptional magnetoelectronic properties. The α-FeB3 monolayer exhibits room-temperature ferromagnetism (Tc = 480 K), whose origin is first revealed by the B-mediated RKKY interaction in the 2D regime. Its perpendicular magnetic anisotropy is almost six times larger than that of the experimentally realized 2D CrI3 and Fe3GeTe2. Moreover, metallic α-FeB3 shows n- and p-type Dirac transport with a high Fermi velocity in both spin channels. Our results not only highlight a promising 2D ferromagnet for advanced spintronics, but also pave the way for exploring novel 2D magnetism in boron-based magnetic allotropes.

Impurities in three-dimensional quadratic band-touching Luttinger semimetals: Friedel and RKKY oscillations

We investigate the response of 3D Luttinger semimetals to localized charge and spin impurities as a function of doping. The strong spin-orbit coupling of these materials strongly influences the Friedel oscillations and RKKY interactions. This can be seen at short distances with an $1/r^4$ divergence of the responses, and anisotropic behavior. Certain of the spin-orbital signatures are robust to temperature, even if the charge and spin oscillations are smeared out, and give an unusual diamagnetic Pauli susceptibility. We compare our results to the experimental literature on the bismuth-based half-Heuslers such as YPtBi and on the pyrochlore iridate Pr$_2$Ir$_2$O$_7$.

Anisotropic RKKY interaction in doped magnetic ordered bilayer graphene

Abstract We study exchange interaction between two magnetic impurities, i.e. (the Ruderman-Kittel-Kasuya-Yosida [RKKY]), in doped biased bilayer graphene by directly computing Green's function within full band method. Tight binding model Hamiltonian in the presence of magnetic long range ordering has been applied to describe electron dynamics. RKKY interaction as a function of distance between localized moments has been analyzed. It has been shown that a field induced ferromagnetic ordering along the z-axis mediates an anisotropic interaction which corresponds to a XXZ model interaction between two magnetic moments. Such field induced ferromagnetic ordering is due to external magnetic field. The exchange interaction along arbitrary direction between two magnetic moments, has been obtained using the static spin susceptibilities of gapped graphene structure. The effects of spin polarization on the dependence of exchange interaction on distance between moments are investigated via calculating correlation function of spin density operators. Our results show the chemical potential impacts the spatial behavior of RKKY interaction. Moreover bias voltage effects on RKKY interaction have been investigated for both stacking types of bilayer graphene.

Surface chiral superconductivity in odd-parity nematic superconductors with magnetic impurities

We study odd-parity nematic superconductivity in doped topological insulators in presence of surface magnetic impurities. The peculiar surface subgap spectrum, characterized by a Majorana flatband, nodal cones and the surface states of the parent topological insulator, gives rise to an overall ferromagnetic RKKY interactions between the surface impurities. An additional coupling between the impurities and a preemptive chiral order parameter promote a surface time-reversal symmetry breaking solution at the surface of the system. We discuss the relevant scenarios and suggest to engineer surface chiral superconductivity by properly choosing magnetic adatoms with highly anisotropic exchange coupling.

Spin-glass phase transition revealed in transport measurements

We have measured the resistivity of magnetically doped Ag:Mn mesoscopic wires as a function of temperature and magnetic field. The doping has been made using ion implantation, allowing a distribution of the dopants in the middle of the sample. Comparison with an undoped sample, used as a reference sample, shows that the resistivity of the doped sample exhibits nonmonotonic behavior as a function of both magnetic field and temperature, revealing the competition between the Kondo effect and the RKKY interactions between spins. This proves that transport measurements are still a reliable probe of the spin-glass transition in nanoscopic metallic wire doped using implantation.