RKKY Research Articles

Kondo scenario of the \u03b3\u2013\u03b1 phase transition in single crystalline cerium thin films

The physical mechanism driving the γ–α phase transition of face-centre-cubic (fcc) cerium (Ce) remains controversial until now. In this work, high-quality single crystalline fcc–Ce thin films were grown on Graphene/6H-SiC(0001) substrate, and explored by XRD and ARPES measurement. XRD spectra showed a clear γ–α phase transition at Tγ−α ≈ 50 K, which is retarded by strain effect from substrate comparing with Tγ−α (about 140 K) of the bulk Ce metal. However, APRES spectra did not show any signature of α-phase emerging in the surface-layer from 300 to 17 K, which implied that α-phase might form at the bulk-layer of our Ce thin films. Besides, an evident Kondo dip near Fermi energy was observed in the APRES spectrum at 80 K, indicting the formation of Kondo singlet states in γ–Ce. Furthermore, the DFT + DMFT calculations were performed to simulate the electronic structures and the theoretical spectral functions agreed well with the experimental ARPES spectra. In γ–Ce, the behavior of the self-energy’s imaginary part at low frequency not only confirmed that the Kondo singlet states emerged at TKS ≥ 80 K, but also implied that they became coherent states at a lower characteristic temperature (Tcoh ~40 K) due to the indirect RKKY interaction among f–f electrons. Besides, Tcoh from the theoretical simulation was close to Tγ−α from the XRD spectra. These issues suggested that the Kondo scenario might play an important role in the γ–α phase transition of cerium thin films.

An Origin of Dzyaloshinskii–Moriya Interaction at Graphene-Ferromagnet Interfaces Due to the Intralayer RKKY/BR InteractionSupported by the National Natural Science Foundation of China (Grant Nos. 11404043 and 1160041160), the Key Technology Innovations Project to Industries of Chongqing (Grant No. cstc2016zdcy-ztzx0067), and the Graduate Research Innovation Project of Chongqing (Grants No. CYS18253).

We present a theory of both the itinerant carrier-mediated RKKY interaction and the virtual excitations-mediated Bloembergen–Rowland (BR) interaction between magnetic moments in graphene induced by proximity effect with a ferromagnetic film. It is shown that the RKKY/BR interaction consists of the Heisenberg, Ising, and Dzyaloshinskii–Moriya (DM) terms. In the case of the nearest distance, we estimate the DM term from the RKKY/BR interaction is about 0.13 meV for the graphene/Co interface, which is consistent with the experimental result of DM interaction 0.16±0.05 meV. Our calculations indicate that the intralayer RKKY/BR interaction may be a possible physical origin of the DM interaction in the graphene-ferromagnet interface. This work provides a new perspective to comprehend the DM interaction in graphene/ferromagnet systems.

RKKY interaction in a doped pseudospin-1 fermion system at finite temperature

We study the RKKY interaction of magnetic impurities in the $\alpha-\mathcal{T}_3$ model which hosts pseudospin-1 fermions with two dispersive and one flat bands. By using the effective low-energy Hamiltonian we calculate the RKKY coupling for impurities placed on the same or different sublattices. We find that there are three types of interaction, which depend on the model parameter defining the relative strength of hoppings between sublattices, two of them can be reduced to graphene case while the third one is new and is due to the presence of a flat zero-energy band. We derive general analytical expressions for the RKKY interaction in terms of Mellin-Barnes type integrals and analyze different limiting cases. The cases of finite chemical potential and temperature, as well as asymptotic at large distances are considered. We show that the interaction between impurities located at different rim sites displays a very strong temperature dependence at small doping being a direct consequence of the flat band. The subtleties of the theorem for signs of the RKKY interaction at zero doping, as applied to the $\mathcal{T}_3$ lattice, related to the existence of a dispersionless flat band are discussed.

RKKY Interaction in a One-Dimensional Crystal Taking into Account Disorder and Temperature

An analytical expression for the energy of indirect exchange interaction of two magnetic impurities in a one-dimensional crystal has been obtained taking into account both disorder and temperature. The inclusion of even a weak disorder in a one-dimensional crystal leads to the localization of charge carriers in it and, as a result, to the suppression of the long-range indirect exchange interaction (RKKY interaction) between two magnetic impurities at the localization length of charge carriers. An increase in the temperature, in turn, causes the disappearance of electron density coherence, which provides the RKKY interaction. It has been shown that these two effects are independent of each other and exponentially suppress the exchange interaction with an increase in the distance between the impurities. Another important manifestation of disorder is a change in the power dependence on the distance between the impurities: the RKKY interaction decreases with distance faster than 1/r.

Formation of magnetization plateaus in the 3D Ising model with the long-range RKKY interaction: application to rare-earth tetraborides

The standard Metropolis algorithm and the parallel tempering method are used to study the influence of the long-range RKKY interaction on the formation of magnetization plateaus in the 3D Ising model with magnetically coupled Shastry-Sutherland layers. It is shown that depending on the Fermi momentum k F the model exhibits the rich spectrum of magnetic solutions which is demonstrated by the appearance of the large number of magnetization plateaus on the magnetization curves. In particular, the following set of individual fractional magnetization plateaus with macroscopic stability regions is observed: m ∕m s = 1/8, 1/7, 1/6, 1/5, 2/9, 1/4, 1/3, 3/8, 2/5, 5/12, 3/7, 1/2, 5/9 and 2/3. In the regime of k F ~ 2π ∕1.24, corresponding to the real situation in TmB 4 , we have confirmed the existence of the magnetization plateau with m ∕m s = 1∕8, the nature of which was intensively discussed in recent experimental works. Since the change of k F can be induced by doping, our results provide predictions of the complete sequences of magnetization plateaus that could appear in tetraboride solid solutions. And finally, the current results are confronted with our previous ones obtained for the two-dimensional Ising model with the RKKY interaction in order to reveal the role of system dimension on the formation of magnetization plateaus.

Skyrmion Crystal from RKKY Interaction Mediated by 2D Electron Gas.

We consider a C_{6} invariant lattice of magnetic moments coupled via a Kondo exchange J with a 2D electron gas (2DEG). The effective Ruderman-Kittel-Kasuya-Yosida interaction between the moments stabilizes a magnetic skyrmion crystal in the presence of magnetic field and easy-axis anisotropy. An attractive aspect of this mechanism is that the magnitude of the magnetic ordering wave vectors, Q_{ν} (ν=1, 2, 3), is dictated by the Fermi wave number k_{F}: |Q_{ν}|=2k_{F}. Consequently, the topological contribution to the Hall conductivity of the 2DEG becomes of the order of the quantized value, e^{2}/h, when J is comparable to the Fermi energy ε_{F}.

Evolution of the magnetic and magnetocaloric properties of Gd6YPd3 alloys originating from structural modifications

The Gd6YPd3 alloys were synthesized in various forms/structural states and with various quenching rates, utilizing mould casting and melt-spinning, in order to determine the influence of microstructure on the magnetic and magnetocaloric properties. The magnetic and magnetocaloric properties clearly depend on the grain size and structural disorder. The Curie temperature of melt-spun Gd6YPd3 is equal to 115 K although the rapidly cooled cast (rc-cast) orders ferromagnetically at 305 K. The magnetic and magnetocaloric properties clearly depend on the grain size and varying degree of structural disorder. The rc-cast Gd6YPd3 exhibits -ΔSm value of 4.13 Jkg-1K−1 and relative cooling power (RCP) value of ~ 805 J/kg, for the magnetic field changes of 0–5 T. The structurally disordered Gd6YPd3 ribbon exhibits considerable -ΔSm value reaching 8.18 Jkg-1K−1 and large RCP of ~ 891 Jkg−1. Such significant changes are caused by the modification of spatial range of the ferromagnetic and RKKY interactions.

Changes of orbital electron correlations due to the coupling between quantum dots and Majorana zero modes

We present a detailed analysis about the changes of the orbital electron-correlation effects in one quantum-dot circuit, by considering finite couplings between the quantum dots and Majorana zero modes (MZMs). It is found that the dot-MZM couplings complicate the orbital-Kondo effect, because the orbital correlation occurs between the localized states in the quantum dots and the continuum hybridized states induced by the indirect metal-MZM couplings. When two of such correlation exist in pair, they have an opportunity to induce a long-range RKKY correlation, which is related to the MZMs. Further investigation shows that this RKKY interaction leads to the anomalous fractional Josephson effect. Our work can be helpful in clarifying the influence of MZM on the orbital electron correlation effects.

Influence of the Long-Range RKKY Interaction on a Formation of Magnetization Plateaus in the Generalised Ising Model on the Shastry-Sutherland Lattice

Influence of the Long-Range RKKY Interaction on a Formation of Magnetization Plateaus in the Generalised Ising Model on the Shastry-Sutherland Lattice

Exact Green's function approach to RKKY interactions

The Green's function~(GF) of two localized magnetic moments embedded in the electron gas is calculated exactly. The electrons are treated in the effective mass approximation and the magnetic moments are coupled with electrons by a delta-like~$s-d$ interaction. The resulting GF is obtained by the exact summation of the Born series using a generalization of the method developed by Slater-Koster and Ziman to non-commuting spin operators with the use of the Woodbury identities. The exact GF crucially depends on the value of the one-electron GF at the origin, denoted as~$g_0$. The Born series is convergent only if~$g_0$ is finite, which holds for electrons in parabolic energy bands in~$1D$, but not in~$2D$ and~$3D$. In the general case, the exact GF includes nonlinear combination of localized spins operators. A method of calculating matrix elements of these operators is given. For spins~$S_a=S_b = 1/2$ the exact GF is expressed as a linear combination of components of~$\hS_a, \hS_b$, and the exact range function~${\cal J}(r)$ is obtained as a double integral over analytical expression. For electron energy~$E=0$ and~$J g_0/2 = 2$ or~$J g_0/2=-2/3$ the range function and GF are singular. Poles of GF occur in the vicinities of singularity points and the resulting energies of bound states are calculated. There are three regimes of~$J$. For small $J$ the range function resembles RKKY one: it has the same period~$\pi/k_F$, the same decay character and a slightly different amplitude, usually within a few percent. This regime occurs for most frequently in the nature. For~$|J|$ comparable to~$|g_0|^{-1}$ the exact range function differs qualitatively from RKKY one,. For large $|J|$ the exact range function oscillates with the same period and power-like decay as the usual RKKY function but it has much lower amplitude decaying with growing~$|J|$.

Magnetic orders induced by RKKY interaction in Tsai-type quasicrystalline approximant Au-Al-Gd

Recent experimental study on Tsai-type quasicrystalline approximant Au-Al-Gd has revealed the presence of magnetic orders and phase transitions with changing the Au/Al concentration. Motivated by the experiment, we theoretically investigate whether a successive change of magnetic orders occurs in a minimal magnetic model including the RKKY interaction only. We find that the model induces multifarious magnetic orders depending on the Fermi wavenumber and gives a good starting point for understanding the experimental observation. In addition, we predict the presence of an undiscovered novel magnetic order called cuboc order at large Fermi wavenumber region.

Anisotropic RKKY interactions mediated by j=32 quasiparticles in half-Heusler topological semimetals

We theoretically explore the RKKY interaction mediated by spin-3/2 quasiparticles in half-Heusler topological semimetals in quasi-two-dimensional geometries. We find that while the Kohn-Luttinger terms gives rise to generalized Heisenberg coupling of the form ${\cal H}_{\rm RKKY} \propto {\sigma}_{1,i} {\cal I}_{ij} {\sigma}_{2,j}$ with a symmetric matrix ${\cal I}_{ij}$, addition of small antisymmetric linear spin-orbit coupling term leads to Dzyaloshinskii-Moriya (DM) coupling with an antisymmetric matrix ${\cal I}'_{ij}$. We demonstrate that besides the oscillatory dependence on the distance, all coupling strengths strongly depend on the relative orientation of the two impurities with respect to the lattice. This yields a strongly anisotropic behavior for ${\cal I}_{ij}$ such that by only rotating one impurity around another at a constant distance, we can see further oscillations of the RKKY couplings. This unprecedented effect is unique to our system which combines spin-orbit coupling with strongly anisotropic Fermi surfaces. We further find that all of the RKKY terms have two common features: a tetragonal warping in their map of spatial variations, and a complex beating pattern. Intriguingly, all these features survive in all dopings and we see them in both electron- and hole-doped cases. In addition, due to the lower dimensionality combined with the effects of different spin-orbit couplings, we see that only one symmetric off-diagonal term, ${\cal I}_{xy}$ and two DM components ${\cal I}'_{xz}$ and ${\cal I}'_{yz}$ are nonvanishing, while the remaining three off-diagonal components are identically zero. This manifests another drastic difference of RKKY interaction in half-Heusler topological semimetals compared to the electronic systems with spin-1/2 effective description.

Large negative magnetoresistance in the antiferromagnetic rare-earth dichalcogenide EuTe2

We report the synthesis and characterization of a rare-earth dichalcogenide EuTe$_2$. An antiferromagnetic transition was found at T$_M$ = 11 K. The antiferromagnetic order can be tuned by an applied magnetic field to access a first-order spin flop transition and a spin flip transition. These transitions are associated with a giant negative magnetoresistance with a value of nearly 100\%. Heat capacity measurements reveal strong electronic correlations and a reduced magnetic entropy. Furthermore, density functional theory calculations demonstrate that the electrons near the Fermi surface mainly originate from the Te 5$p$ orbitals and the magnetism is dominated by localized electrons from the Eu 4$f$ orbitals. These results suggest that both the RKKY and Kondo interactions between the local moments and itinerant electrons play crucial roles in the magnetism and large negative magnetoresistance of EuTe$_2$.

Magnetic properties of Co-doped Eu8Ga16Ge30 type-I clathrate

Type-I Eu8Ga16Ge30 clathrate is a stable functional material with special magnetocaloric properties, mainly derived from the 4f magnetism of Eu ions. However, the influence of cage atoms, especially 3d magnetic atoms, on the magnetic properties of Eu8Ga16Ge30 is still lackof study. Co-doped Eu8Ga15Co1Ge30 was synthesized creatively by using arc method. It's magnetic properties have been investigated and compared with that of Co-free Eu8Ga16Ge30. Because Co ion has magnetic moment, its joining will introduce a new 3d-4f interaction into the lattice. This study can enrich the understanding of RKKY interaction between Eu ions with larger distances. The substitution of Co for Ga atoms on the cage frame results in the decrease of the ferromagnetic ordering temperature (TC) from 34.7 to 31.1 K. By fitting the M−H curves using Brillouin function, the exchange parameter λ was obtained. The decrease of λ from 0.25 to 0.21 T·emu−1·g due to the Co doping is thought to be the inherentreason of the TC decrease. For a magnetic field change from 0 to 3 T, the maximum magnetic entropy change -ΔSMmax around TC for Eu8Ga15Co1Ge30 is 5.92 J/kg·K, which is a little smaller than the value 6.0 J/kg·K of Eu8Ga16Ge30. This could be attributed to the decrease of the saturation magnetic moment. The critical exponents β, γ and δ around TC, the -ΔSM(H) behaviors below, at and above TC are analyzed and discussed.

Spin liquid mediated RKKY interaction

We propose an RKKY-type interaction that is mediated by a spin liquid. If a spin liquid exists such an interaction could leave a fingerprint by ordering underlying localised moments such as nuclear spins. This interaction has a unique phenomenology that is distinct from the RKKY interaction found in fermionic systems; most notably the lack of a Fermi surface and absence of the requirement for itinerant electrons, since most spin liquids are insulators. We demonstrate that the interaction is predominately shaped by the lattice symmetries of the underlying spin liquid. As a working example we investigate the possible ordering of nuclear spins that interact through an underlying lattice of the two-dimensional spin-1/2 kagome antiferromagnet (KHAF), although the treatment remains general and can be extended to other spin liquids and dimensions. We find that several different nuclear spin orderings minimise the RKKY-type energy induced by the KHAF but are unstable due to a zero-energy flat magnon band in linear spin-wave theory. Despite this we show that a small magnetic field is able to gap out this magnon spectrum resulting in an intricate nuclear magnetism.

Use of density functional theory to investigate the optical and magnetic behaviours of Ge1-xMnxTe half-metallic ferromagnets

Ge1-xMnxTe-based IVVI ferromagnetic semiconductors are attractive due to their versatile material properties. In this study, we investigate the physical properties of Ge1-xMnxTe with xMn≤ 0.50 using density functional theory. The dominant exchange splitting caused by pd-hybridisation mediates ferromagnetism that is consistent with the stable ferromagnetic (FM) states, as observed using structural optimisations. The presence of holes due to the half-metallic character suggests that RKKY interactions stabilise FM states. The absorption edges lie in the infrared energy range and are influenced by the crystal symmetry, and the compounds exhibit strong absorption of visible and UV energies. The narrow band gaps extracted from the band structures and the Tauc plots show similar variations with the Mn content, and hence suggest applications in optoelectronic devices.

The Impact of the Composition Effect on Ferromagnetic Properties of Tb2Co2Ga

The ferromagnetic properties of Tb2Co2Ga, crystallizing into an orthorhombic W2CoB2-type structure, were investigated by preparing 11 polycrystalline samples with different starting atomic compositions. We found that Tb2Co2Ga possesses a homogeneity range in the ternary phase diagram. The Curie temperature TC is sensitive to the atomic composition and ranges rather widely, i.e., from 75 to 145 K. For the samples with a TC above 90 K, the nearest Tb–Tb and the Tb–Co distances would be important factors deciding TC, considering the RKKY interaction through the hybridization between Tb and Co atoms. An anisotropic change of two kinds of Co–Tb–Co angles in the octahedron formed by two Tb and four Co atoms occurs in the samples with a TC lower than 90 K. Such a change of octahedral parameters seems to be related to a difference of shapes in the ac magnetization anomaly at TC between the samples in the lowest TC (~ 75 K) group and those in the other groups.

Probing and dressing magnetic impurities in a superconductor

We propose a method to probe and control the interactions between an ensemble of magnetic impurities in a superconductor via microwave radiation. Our method relies upon the presence of sub-gap Yu-Shiba-Rusinov (YSR) states associated with the impurities. Depending on the sign of the detuning, radiation generates either a ferro- or antiferromagnetic contribution to the exchange interaction. This contribution can bias the statistics of the random exchange constants stemming from the RKKY interaction. Moreover, by measuring the microwave response at the YSR resonance, one gains information about the magnetic order of the impurities. To this end, we estimate the absorption coefficient as well as the achievable strength of the microwave-induced YSR-interactions using off-resonant radiation. The ability to utilize microwave fields to both probe and control impurity spins in a superconducting host may open new paths to studying metallic spin glasses.

Contrasting exchange interactions in the new R3Pd5 (R = Tb, Dy, Ho, Er) compounds. Multiple magnetic transitions, spin-reorientation and frustration, as revealed by temperature dependent neutron diffraction studies: A question of sublattices?

In a recent work we have reported the formation and the crystal structure of the new family of compounds R3Pd5 (R = Sc, Y, Gd–Lu; Pu3Pd5-type, oS32, spacegroup 63, Cmcm). DFT calculations for Gd3Pd5 and heat capacity and magnetic measurements for Tb3Pd5, Dy3Pd5, Ho3Pd5 and Er3Pd5 were able to discriminate at least two distinct antiferromagnetic transitions at low temperatures; at the same time these data suggested these separate magnetic orderings to be likely associated to the two structurally different rare earth sublattices (4c and 8e, respectively). The magnetic structures of the R3Pd5 compounds, with R = Tb, Dy, Ho, Er, have been now investigated in this work. High-resolution and high-intensity neutron powder diffraction data were recorded for the four compounds of the series. The results reveal that the magnetic structures adopted are significantly diverse and their temperature dependence more complex than originally deduced from magnetic and heat capacity measurements. Tb3Pd5 is in fact the only of the four compounds where the rare earth sublattices order independently with two different magnetic propagation vectors on the two sites (k1 = [1 0 ½] for Tb2 and k2 = [kx 0 0] or k3 = [1 0 0] for Tb1). In Dy3Pd5 both sublattices follow the propagation vector k = [kx 0 0], with the second transition corresponding to a spin reorientation. In Ho3Pd5 ordering of both sublattices follow the k = [1 0 0] propagation vector; the second transition seen in the magnetic and heat capacity data corresponds to an accelerated increase in the magnetic moment of the Ho2 sublattice. The case of Er3Pd5 is special as it is the sole case where one of the rare earth sublattices does not order down to T = 1.5 K; here the second transition determined from the magnetic data corresponds to a change of the magnetic propagation vector from k1 = [kx 0 kz] to k2 = [1 0 0], both only acting on the Er2 sublattice. Irrespectively of the very similar structures not even two of the four studied R3Pd5 compounds show identical magnetic structures on either of the two sublattices. These strong variations have to be connected to changes in the RKKY interactions induced by the progressive filling of the f-orbitals of the heavy rare earth ions and the concomitant changes of the crystal electric fields.

Spin channel induced directional dependent spin exchange interactions between divacantly substituted Fe atoms in graphene

In this study, we investigate the isolated magnetic interactions between two identical Fe atoms divacantly-substituted into graphene. Using density functional theory, we simulated the electronic and magnetic properties for a supercell of graphene with spatial variation of the Fe atoms along either the armchair or zig-zag directions. Overall, we find that the exchange interaction between the two Fe atoms fluctuates from ferromagnetic to antiferromagnetic as a function of the spatial distance in the armchair direction. Given the induced magnetic moment and increased density of states at the Fermi level by the surrounding carbon atoms, we conclude that an RKKY-like interaction may characterize the exchange interactions between the Fe atoms. Furthermore, we examined the same interactions for Fe atoms along the zig-zag direction in graphene and found no evidence for an RKKY interaction as this system shows standard superexchange between the transition-metal impurities. Therefore, we determine that Fe-substituted graphene produces a directional-dependent spin interaction, which may provide stability to spintronic and multifunctional devices and applications for graphene.