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We have investigated the electronic states of CeB$_6$ and have directly calculated the RKKY interaction on the basis of the 74-orbital effective Wannier model which includes 14 Ce-$f$ orbitals and 60 conduction ($c$) orbitals of Ce-$d,s$ and B-$p,s$ derived from the density-functional theory bandstructure calculation. By using not only the $c$-band dispersion but also the $f$-$c$ mixing matrix elements of the Wannier model, the realistic couplings for all 15 active multipole moments in $\Gamma_8$ quartet subspace are obtained in the wavevector $q$-space and real-space. Both of the $\Gamma_{5g}$ quadrupoles $(O_{yz},O_{zx},O_{xy})$ and the $\Gamma_{2u}$ octupole $T_{xyz}$ couplings are maximally enhanced with $q=(\pi,\pi,\pi)$ which naturally explains the phase II of the antiferro-quadrupolar ordering at $T_{Q}=3.2$ K, and are also enhanced with $q=(0,0,0)$ corresponding to the elastic softening of $C_{44}$. Also the couplings of the $\Gamma_{5u}$ octupoles $T_{x}^{\beta}$, $T_{y}^{\beta}$ and $T_{z}^{\beta}$ are quite large for $q=(\pi,0,0)$, $(0,\pi,0)$ and $(0,0,\pi)$, which yields the antiferro-octupolar ordering of a possible candidate for phase IV of Ce$_{x}$La$_{1-x}$B$_6$. The intersite vector dependence of the RKKY couplings exhibit different long-range, oscillating, isotropic and anisotropic behaviors depending on the types of the multipole moments. The present approach enables us to provide the information about the possible multipole ordering in an unbiased way and is easily available for other localized $f$ electron materials once the $c$ states and $f$-$c$ mixing elements are given from the bandstructure calculation., Comment: 10 pages, 7 figures, accepted for publication in J. Phys. Soc. Jpn

We report the de Haas–van Alphen effect study on the evolution of spin dependence of the effective mass in CeIn 3 and CeRu 2 (Si 1- x Ge x ) 2 by using physical and chemical pressures to control the relative strengths ot the Kondo effect and the RKKY interaction.

We have studied the magnetization, electrical resistivity and magnetic phase diagram of Pr x La 1- x B 6 . The x dependence of the incommensurate (IC) magnetic ordering temperature, T IC1 , is simi...

In order to determine a proper RKKY interaction model for CeB 6 , the general model Hamiltonian for Γ 8 quartet with nearest-neighbor interactions is investigated in terms of the constant coupling ...

We present recent advances in the magnetism and superconductivity of rare earth and uranium compounds. Heavy fermions are formed on the basis of the competition between the RKKY interaction and the Kondo effect in these compounds. The application of pressure to these compounds is useful to control the electronic states in the antiferromagnets CeRh 2 Si 2 and CeRhIn 5 , and the ferromagnet UGe 2 . The quadrupole interaction or the quadrupole Kondo effect is found to be responsible for heavy fermions in PrFe 4 P 12 . A rich variety of superconducting properties are demonstrated: superconductivity of CeCoIn 5 and CeRhIn 5 in the vicinity of a quantum critical point, coexistence of ferromagnetism and superconductivity in UGe 2 , and superconductivity based on the quadrupole fluctuations in PrOs 4 Sb 12 , together with the relation between the superconducting transition temperature and the quasi-two dimensionality of the electronic states.

The electrical resistivity, magnetic susceptibility and specific heat measurements were performed on Ce(Pd 1- x Cu x ) 2 Al 3 ( x =0.0–0.7) system to investigate the effects induced by Cu substitution in the heavy fermion compound CePd 2 Al 3 . A dramatic evolution of the magnetic properties was observed with the substitution of Pd by Cu: (1) a small amount of Cu ( x < 0.1) in CePd 2 Al 3 leads to a rapid decrease of the antiferromagnetic transition temperature T N ; (2) passing through a crossover region without a long-range magnetic order, a ferromagnetic-like state, which reveals an enhanced magnetic susceptibility and a distinct peak in the specific heat curve at low temperatures, occurs around x =0.1–0.4; (3) by furthering the substitution through a second crossover region, however, the antiferromagnetic ordering is recovered close to x =0.5–0.7. A decrease tendency of the Kondo temperature T K with increasing x is derived from the analysis on the specific heat results. It is suggested that the chang...

The quadrupolar phase transition of CeB 6 in high magnetic fields is studied by mapping the multipolar RKKY model to an effective orbital Hamiltonian. The fluctuation correction to the mean-field solution of the effective Hamiltonian is analyzed as a function of the strength and the direction of the magnetic field. The results are combined with the low-field analysis of the previous paper to obtain a possible high-field phase diagram for CeB 6 .

The single particle excitation spectrum of the periodic Anderson model in two dimensions is calculated by using the dynamical cluster approximation (DCA). The DCA method is an extention of the dyna...

The magnetization process of one-dimensional Kondo necklace model with next-nearest-neighbor interaction has been studied by the use of exact-diagonalization method. The magnetization plateaus appear at zero ( m =0) and at half ( m =1/2) of the saturation magnetization. The ground state in the absence of a magnetic field is regarded as an aggregate of intra-atomic Kondo singlets. On the other hand, the spin configuration at the 1/2-plateau represents the intra-chain dimer (σ-dimer) phase with broken translational symmetry. The picture for spin configurations in the uniform magnetic fields other than m =0 and 1/2 are also given. We also determined the phase diagram for the ground state of the system in the magnetic field.

A combination of the dense Kondo effect and Ruderman–Kittel–Kasuya–Yoshida interaction exhibited by an antiferromagnetic (AF) heavy-Fermion compound CeCuSb 2 ( T N =8 K) was investigated with the magnetic susceptibility χ and 63 Cu magnetic resonance measurements in the temperature range between 1.4 and 210 K. For temperatures above ∼25 K, characteristics of the localized 4 f spins are observed in the Curie–Weiss-type behavior of the Knight shift K and the strongly enhanced relaxation rate T 1 -1 . For the temperature below ∼25 K, the χ data tend toward a constant value, which is an indication of the onset of the heavy-Fermion state. The slope of the Knight shift versus susceptibility ( K -χ) plots decreases below ∼100 K, which is ascribed to the difference in the anisotropic hyperfine coupling to the crystal-field-split Γ 7 (ground state) and Γ 8 (excited state) wave functions of the Ce ions. The K -χ plots below ∼25 K exhibit another deviation from the linearity in opposite direction. We speculate that ...

The effect of multipolar fluctuations on the quadrupolar phase transition in CeB 6 is investigated. The d -1 -correction to the mean-field solution of the multipolar Ruderman–Kittel–Kasuya–Yoshida (RKKY) model is analyzed in terms of a generalized Landau expansion of free energy, with d being the spatial dimension. It is shown that the multipolar fluctuations become strong and field-dependent when the model is close to the SU(4)-symmetric limit. As a result, various unusual phenomena around the transition are shown to be reasonably explained within the RKKY model. The realistic form of the interactions for CeB 6 is discussed on the basis of a quantitative comparison with experiments.

The susceptibilities χ( q ) of heavy rare earth metals are calculated using the results of a linear muffin-tin orbital band structure method for the eigenvalues and eigenfunctions of each metal. The results of these calculations, including Gd, are very similar to those of yttrium. The variation of the susceptibilities with changes in the Fermi level is also investigated. The region of the Fermi surface called the “webbing” is thought to play a vital role in driving the exotic magnetic structures found in a number of the heavier rare earth metals. Our calculations don't show that the susceptibilities are very sensitive to the topology of the Fermi surface. It is argued that these results require an extension of conventional models of exchange interaction in heavy rare earth metals to include magnetic ordered band structure.

We developed a Monte Carlo method to study the magnetic and transport properties of low density carrier ferromagnetic (FM) semiconductors. The calculation is carried out for the two- and three-dimensional Ising spin system interacting with electrons through the s-d exchange coupling. When the temperature increases from T =0, the spontaneous magnetization of the local spins decreases appreciably in the low T range, and steeply at the Curie temperature ( T C ). The initial decrease is caused by the almost complete escape of electrons from the spin flipped sites, and accumulation in the FM region. The electron spin polarization is complete in the whole FM temperature range except very near T C . The Curie temperature shifts to low T side from the value estimated based on the RKKY model as the exchange constant increases. The critical-scattering-like peak of the resistivity appears near T C when the exchange interaction is not so strong, but it disappears when the interaction is strong. In the former cases, t...

We address the question as to why the ordering of O x y -type quadrupole moment predominates that of T x y z octupole moment at no applied field in CeB 6 , in spite of the same coupling constant predicted. In the mean field approximation (MFA), the same results are obtained for the quadrupolar and the octupolar interactions. If we go beyond the MFA to apply the constant coupling approximation, it is shown that the ordering of O x y is stabilized compared with that of T x y z , as far as each interaction is treated separately.

It is shown that the main origin of the hyperfine field at B nuclei in CeB 6 is the transferred hyperfine interaction of the nuclear moment with the electronic spin carried by the electrons in the 2 s and 2 p states of the B ion hybridized with the 4 f states of neighboring Ce ions. The dipole-dipole interaction with the magnetic moments of Ce ions also contributes substantially. In the antiferro-quadrupolar ordering phase II, it is essential to assume the ordering of Γ 5 -type moments. The reason why the RKKY interaction between the Γ 5 -type quadrupole moments is strongest is also discussed, on the basis of the estimate of the strength of p-f mixing which plays a vital role in many respects in CeB 6 .

Measurements of the magnetic susceptibility (2–300 K), electrical resistivity (70 mK–300 K), specific heat (70 mK–150 K) and thermoelectric power (0.3–300 K) have been carried out on Ce x La 1- x PdSn. For all these quantities, the crystalline electric field (CEF) effect on Ce 3+ state was observed: the CEF splitting scheme does not change much for x ≥0.3. The Neel temperature decreases monotonically with decreasing Ce concentration, and the long-range antiferromagnetic order disappears for x around 0.1. The thermoelectric power of Ce x La 1- x PdSn shows complicated structures at low temperatures. These results were discussed from the viewpoint of coexistence and competition between the RKKY interaction and the Kondo effect.

Four types of magnetic exchange interactions, which work between quasiparticles, are investigated within the theoretical framework of the virtual exchange of bosons or bosonic excitations. Three types of exchange interactions are due to the virtual exchange of high-energy spin excitations, pair excitations of electrons far from the chemical potential through the spin channels. They are characterized by a pair of intermediate states in the exchange process; the conventional superexchange interaction is characterized by a pair of occupied bands, an extended superexchange interaction by a pair of unoccupied bands, and an extended Ruderman-Kittel-Kasuya-Yosida (RKKY) exchange interaction by a pair of an occupied band and an unoccupied band. These three types of exchange interactions are present in both insulating and metallic states. The fourth one is a novel exchange interaction due to the virtual exchange of low-energy spin excitations, pair excitations of quasiparticles through the spin channels, and scale...

A theory of the antiferro-quadrupolar ordering in CeB 6 is developed in the framework of the Γ 8 -quartet basis. Possible ordered phases under the external magnetic field are classified in terms of their symmetry properties, and the relations between quadrupolar order parameters and field-induced moments are established. Then we formulate a mean-field theory of Ohkawa's RKKY model based on the group-theoretical consideration. The stability of the possible phases and the resulting phase diagrams are analyzed in connection with the character of quadrupolar moments, the influence of induced moments and the form of Zeeman term. Considering available experimental results, we introduce an improved model with asymmetric interactions and discuss the phase diagram of CeB 6 . The connection between magnetostriction and uniform quadrupolar moments is discussed.

Distributions of hyperfine magnetic fields were obtained for RKKY spin glass systems such as CuMn:Sn, AgMn:Sn, AuCr:Sn, AuMn:Sn and AuFe:Sn, together with some ternary alloys. These are classified into two groups: the one is expressed by a stable distribution and the other by the superposition of two types of distributions. The relation between the hyperfine field distribution in RKKY spin glasses and the stable distribution is discussed.

For cubic and hexagonal UAu 2 Sn, the specific heat and elastic modulus have been measured down to 1.3 K in the magnetic field up to 14 T. We have clarified that the 5 f electrons in the cubic and hexagonal phases are localized above 120 K and the both phases are characterized as a non-magnetic heavy-fermion system and an antiferromagnetic heavy-fermion system, respectively. In the cubic phase, the 5 f ground state in crystal-electric-field is determined to be a singlet, and the first excited state a triplet. In the hexagonal phase, both of the ground and first excited states are doublets and the ground doublet has an electronic multipolar degeneracy. The difference between the ground states of the two phases is discussed in terms of an electric multipole moment in addition to the competition between the Kondo effect and the RKKY interaction.

In this article we discuss the reflection positivity in spin space for the Heisenberg model and the Kondo Hamiltonian. We show that the ground state is unique for J ≠0 where J is the strength of the exchange interaction in the Heisenberg model or the exchange coupling between the localized spins and conduction electrons in the Kondo model. We introduce the Coulomb interaction U >0 between the conduction lectrons for the Kondo Hamiltonian to show the uniqueness of the ground state. We write the Hamiltonian in terms of fermions to express the exchange interactions and impose constraints. We employ the Lagrange-multiplier method to deal with the constraints in this work.

The Kondo effect in the system where localized spins are mutually coupled in investigated, taking account of the dynamics of internal magnetic fields applied to a scattering center. Results show that it is not the magnitude of internal magnetic fields but its fluctuation multiplied by a correlation time to determine whether the Kondo effect appears or not.

A trial is made for determining the origin of exchange interactions between spins of two intercalation compounds, Fe 0.05 TiS 2 and Co 0.1 TiS 2 , by comparing the change in spin glass transition temperature T g accompanying a change in conduction electron number. For the purpose of changing the conduction electron number, 5% of Ti are substituted by Ta. In Co 0.1 TiS 2 , T g changes and the RKKY interaction may be the dominant exchange interaction. In Fe 0.05 TiS 2 , although the change in T g is small, a tendency toward the RKKY interaction is suggested.

The maximum supercurrent I c passing through the S(Nb)-N(Cu doped with Mn)-S(Nb) junction made of Cu-clad Nb wire has been measured down to 30 mK, in order to investigate the relation between the superconducting proximity effect and the Kondo effect. The maximum supercurrent becomes small with an increase in Mn concentration and remarkably with a decrease in electronic mean free path in Cu. The electronic mean free path dependence of I c may be explained qualitatively in consideration of the spin flip scattering and the RKKY interaction of Mn impurities. The Meissner effect induced by the proximity effect in Cu-clad Nb wire can be understood through the behavior of the coherence length ξ N in Cu which is derived from I c .

Ferromagnetic resonance (FRM) measurements were made on [Ni 0.8 Fe 0.15 Co 0.05 /Cu/Co] multilayers in order to observe the coupling between ferromagnetic layers across Cu spacer. The resonant fields vary oscillatory with Cu spacer thickness. The FMR results were analyzed by the resonant model of a magnetically coupled two-layer system. By using a modified RKKY theory for interlayer exchange interaction and FMR results, the coupling constant, J , was determined as a function of Cu spacer thickness. The resonant field can be predicted for Cu spacer thickness and are well compared to the experimental values. In samples of antiferromagnetic coupling, the resonance mode of the magnetization flopping were observed at small applied fields.

Electrical resistivity is calculated on the basis of the effective nuclear Hamiltonian above and below the nuclear ordering temperature T c . The conduction electrons are scattered by the nuclear spins mediated by the f-electrons through the s-f exchange interaction and the hyperfine interaction. By the short range order, the resistivity increases or decreases from the value of the non-interacting nuclear spin system depending on the sign of the RKKY interaction and the size of k F . In low temperatures the resistivity is calculated by the spin wave approximation. The T -dependence reflects the crystal field anisotropy through the dispersion relation of the spin wave. It is shown also that the aspherical Coulomb interaction, which works sometimes to the resistivity at high temperatures, is not effective in this low temperature region.

The effective RKKY coupling constants are derived from the one dimensional 22-site Anderson lattice model with various band fillings in the fourth order perturbation with respect to d - f mixing element, assuming that the other parameters belong to the Kondo regime. The resulting RKKY lattice model has been exactly diagonalized in terms of Lanczos method. The ground state f -spin correlation functions are studied in detail. It is shown that a long range correlation is stabilized in the case of general filling of conduction band compared to the nearest-neighbor antiferromagnetic Heisenberg model, reflecting the coherent nature of RKKY coupling based on the Anderson lattice model.

We present a diagonalization study of the two-impurity Anderson model. We explore the competition between the Kondo effect and the Ruderman-Kittel-Kasuya-Yosida (RKKY) interactions. Over the entire range of the exchange coupling J between two magnetic impurities, we evaluate the susceptibilities. We find that the two-impurity state smoothly changes from a triplet-like state to a singlet-like one with the increase of J ; there is a smooth crossover from small into large coupling. In order to study this further, we consider the Anderson model with only even-parity-mixing term. In this model, there is a critical point J c ; the localized spins form a triplet for J J c . We also discuss, in the numerical diagonalization and a variational theory, the metamagnetic transition induced by the antiferromagnetic interactions in the two-impurity system.

We study the two-impurity Anderson model by the exact diagonalization method in small systems and the variational method. With varying of the exchange coupling J between two impurities, we evaluate the staggered susceptibility χ s to investigate the competition between the Kondo effect and the RKKY interaction effect. The staggered susceptibility in our calculations shows no anomalous behavior in contrast to the recent numerical renormalization group calculations. In order to study this further, we introduce the even-parity-mixing Anderson model. This model appears to show singularities in χ s and the ground-state energy at a point J = J c . We show that at this point, the ground state changes suddenly; the localized spins form a triplet for J J c . In the original two-impurity Anderson model, a crossover occurs around J c without singularity.

The proximity effect in Cu clad Nb wires of which Cu is doped with dilute magnetic impurities, has first been investigated in relation to the Kondo effect. As for Cu doped with dilute Fe, Co and Ni impurities, the probability of the spin flip scattering of conduction electrons, α, by Fe, Co and Ni impurities decreases linearly with decreasing temperature. As for Cu doped with dilute Mn impurities, the probability, α, by Mn impurities is concluded to be suppressed by the RKKY interaction between Mn impurities which depends on the electronic mean free path. The temperature dependence of the resistivity of the Mn alloy may be understood as a result of the coexistence of the dilute Kondo effect and the RKKY interaction between Mn impurities.

The exact numerical diagonalization of the 1-D Kondo lattice is done to obtain energies and correlation functions of this system. In this system the ground state changes from a ferromagnetic state in the low density limit of conduction electrons to a total spin singlet state for the half-filled conduction band. The main mechanism for the suppression of the total spin for half-filling is the antiferromagnetic correlation between the localized spins of nearest neighbor sites. However, the comparison of energies show that the Kondo effect also plays an important role. Increasing the magnetization of the 1-D Kondo lattice the system changes its nature and behaves as a simple spin system, which is determined only by the RKKY interaction.

A quantum mechanical phenomenology for heavy-fermion systems is formulated. The effective Lagrangian for low-energy excitations contains a localized spin-fluctuation part which is coupled with an itinerant fermion part. Each part represents the dual nature of strongly correlated f electrons. The coupling parameter is fixed by comparison with the Fermi-liquid theory for the Anderson model. The comparison also fixes the localized spin-fluctuation spectrum. As an advantage over the Fermi-liquid description the present model takes into account the RKKY interaction and non-linear effects of spin polarization. A formula for the magnetic equation of state is derived which is applicable to the metamagnetism and weak antiferromagnetism in heavy-fermion systems.

The internal field distribution for a Au 0.97 Fe 0.03 spin-glass system is obtained from the Mossbauer absorption experiment using a relation between a hyperfine field and an internal field, which holds in the case of RKKY interaction. The obtained distribution is well explained with the stable distribution with the characteristic index α of 0.86. It is shown that the internal field distribution is close to Lorentzian but far from Gaussian distribution.

Specific heat of a newly-found dense-Kondo system CeTIn (T=Ni, Pd, Pt) has been measured between 60 mK and 80 K. For CePdIn and CePtIn, the ratio of specific heat to temperature, C / T , increases remarkably below 10 K, indicating the heavy-fermion nature. On the other hand, no enhancement of C / T is observed for CeNiIn, suggesting the valence fluctuating state. A sharp peak in C / T is observed at 1.7 K for CePdIn, which is ascribed to an antiferromagnetic transition, whereas CePtIn does not show any signs of phase transition at least down to 60 mK. The variety of low-temperature behavior in CeTIn is discussed in terms of competition between the Kondo state and the RKKY interaction.

The magnetic correlations between Ce 4f electrons and conduction electrons in the new tetragonal compound CeRu2Al2B have been investigated by 27Al nuclear magnetic resonance (NMR). The 27Al NMR spin–lattice relaxation rate 1/T1 exhibits a large magnetic anisotropy for field directions. Within a localized moment picture, the Ce 4f spin-fluctuation rates Γ|| for the c-axis and Γ⊥ for the c-plane are evaluated by taking account of the magnetic anisotropy. The relation of \(\Gamma _{\parallel } \gg \Gamma _{ \bot }\), which holds in the entire temperature range, indicates that the c–f hybridization between the ligand conduction electrons and the Ce 4f electrons with the \(\Gamma _{7}^{(1)}\) crystal electric field ground state is anisotropic. From the temperature dependence of Γ, it is found that the Kondo effect dominates the Ruderman–Kittel–Kasuya–Yosida (RKKY) interaction at high temperatures, whereas below 60 K the RKKY interaction overcomes the Kondo effect and causes the magnetic order. These results in...

The spin polarization of conduction electrons in Gd is clearly observed in the magnetic Compton profile. The magnetic moment of the conduction electron is evaluated to be 0.53±0.08 µ B /atom, consistent with the bulk magnetic moment. The measurement is performed with circularly polarized synchrotron-radiation X-rays emitted from an elliptical multipole wiggler. A segmented Ge solid-state detector having thirteen elements is successfully used for high count-rate accumulation.

TiS2 crystallizes in a hexagonal CdI2 structure with repetitions of S-, Tiand S-layers. Various 3d transition metal atoms T are intercalated into van der Waals gaps between neighboring S-layers, which are called T-layers hereafter, forming TxTiS2. In the T-layers, T-atoms are located in ordered manners for x 1⁄4 1=4 and 1/3 and are randomly distributed for other values of x. As x increases in random FexTiS2 spin glass phase, then ferromagnetic phase appears. Motizuki and Suzuki performed band calculation studies of TiS2 and T1=3TiS2. 2) They found that the TiS2-band consists of, with increasing energy, a bonding band of mainly S-3p states hybridized with Ti-3d states, a nonbonding band of Ti-3d" states and an antibonding band of mainly Ti-3d states. In FexTiS2 the Fe-atom supplies two conduction electrons. According to the band calculation for Fe1=3TiS2, 2) the two electrons enter into the host TiS2-band nearly in a rigid-band manner, raising the Fermi level of the host TiS2-band. The Fe-atoms form the Fe-band. Although the energy of the Fe-band is close to that of the nonbonding Ti-3d" band, the degree of hybridization between the two bands is low because Tiand Fe-atoms are located in different layers. Furthermore, interaction between the Feband and the bonding TiS2-band, whose main contribution is from S-3p states, is expected to be weak because the energy of the Fe-band is much higher than that of the bonding TiS2band. Then it is expected that Fe behaves nearly as an Fe2þ ion, and the origin of the exchange interaction is expected to be the Ruderman–Kittel–Kasuya–Yosida (RKKY) interaction. These expectations may also be valid for random FexTiS2. In fact, from the values of paramagnetic effective moments of about 4:0 B/Fe in FexTiS2, Fe-atoms are presumed to be in a nearly divalent ionic state with S 1⁄4 2. Furthermore, it has been suggested that the dominant exchange interactions in Fe0:05TiS2 and Co0:1TiS2 are RKKY interactions. In the present paper, we try to explain the x-dependence of the asymptotic Curie temperature of the paramagnetic susceptibility of FexTiS2 (0 x 0:43) by the RKKY interaction. Letting Ji be the exchange interaction constant between an Fe-spin and its i-th neighbor Fe-spin, is expressed as

We have performed an extensive study on the electronic transport properties of Ce x La 1- x Ru 2 Si 2 . At zero field or under the fields parallel to the hard axis of magnetization, the residual resistivity, magnetoresistivity and Hall resistivity are found to be most enhanced around x = 0.85 in the antiferromagnetic state. On the other hand, the high magnetic field along the easy axis is effective to suppress the enhancement. The coherence temperature derived from the temperature variation of Hall coefficient becomes equal to the antiferromagnetic transition temperature at x = 0.85, indicating that the competition between the coherence of the Kondo singlet and the long range magnetic order is responsible for the enhancement. The competition is likely to affect also the magnetic properties in the antiferromagnetic state. The comparison with the de Haas–van Alphen effect measurements suggests that the enhancement is likely to be due to the increase in scattering. The present results are compared with the t...

A novel metallic silver chromate, Ag 2 CrO 2 , was synthesized using a high-pressure technique. Ag 2 CrO 2 crystallizes in trigonal symmetry with lattice parameters of a = 2.9271(1) A and c = 8.6721(4) A. The structure consists of CrO 2 and double Ag layers stacked alternately along the c -axis. The former realizes an S = 3/2 triangular-lattice Heisenberg system, while the latter provides itinerant electrons. Ag 2 CrO 2 exhibits an antiferromagnetic long-range order at T N = 24 K with the weak ferromagnetic moment. The resistivity shows a sudden drop at T N , suggesting a large s – d interaction (RKKY interaction) between the Cr 3 d localized spins on the triangular lattice and the Ag 5 s itinerant electrons. The RKKY interaction is responsible for releasing the magnetic frustration and the three-dimensional long-range ordering at T N .

We report on the synthesis and measurements of the magnetic susceptibility, electrical resistivity, and specific heat of R Os 2 Al 10 ( R =Pr, Nd, Sm, and Gd). All compounds are isostructural with a Kondo semiconductor CeOs 2 Al 10 showing an unusual phase transition at T 0 =28.6 K. For R =Pr, no magnetic transitions were observed down to 0.4 K, whereas compounds with R =Nd, Sm, and Gd undergo antiferromagnetic transitions at T N = 2.2, 12.5, and 18 K, respectively. Moreover, successive magnetic transitions occur for R =Sm and Gd. The resistivity of the compounds with R =Sm and Gd increases on cooling below T N due to the superzone-gap formation. The fact that T N =18 K for R = Gd is lower than T 0 for R = Ce indicates that the phase transition in CeOs 2 Al 10 is not originated from the RKKY interaction alone but from the anisotropic hybridization of the 4 f state with conduction bands.

In Ce(Pd 1- x M x ) 2 Al 3 (M=Ag, Cu), the (0,0,1/2)-antiferromagnetic (AF), ferromagnetic (F), and another AF orders are observed for x

Calculating the local spectral densities at magnetic adatoms, we estimate the variation in the Yosida–Kondo resonance due to the Ruderman–Kittel–Kasuya–Yosida (RKKY) interaction and the direct exchange between adatoms in systems of magnetic trimers on metal surfaces. The results show that the RKKY interaction leads to the gradual variation in Kondo temperature, and the direct exchange can be the origin of the drastic variation.

For a system of two magnetic adatoms on a metal surface at finite temperatures, we calculate the spectral density at adatom sites. At sufficiently low temperatures, the peak structure at the Fermi level, which originates from the coupling between the local moments of adatoms and conduction electrons, corresponds to the Yosida–Kondo resonance. In addition, we also consider the indirect Ruderman–Kittel–Kasuya–Yosida (RKKY) interaction between the adatoms, which is mediated by the conduction electrons of the metal surface, and depends strongly on the adatom separation. Under strong ferromagnetic (FM) RKKY interaction, the peak structure disappears, while under antiferromagnetic (AF) RKKY interaction, the width of the peak structure increases in comparison to that of the single adatom case. Our conclusion of the spectral density variation in the two dimensional system can be confirmed by experiments on the surface, for example by the scanning tunneling spectroscopy.

A possible spin-Peierls (dimerization) transition in Ce Compounds is investigated theoretically, in connection with the novel phase transition recently reported to occur in CeRu 2 Al 10 . It is pointed out that one-dimensional zigzag chains are profiled by connecting nearest-neighbor (n.-n.) Ce ions in this compound. If only the RKKY interactions between n.-n. Ce 3+ ions are considered in the mean-field approximation, a spin-Peierls transition occurs at T =27 K for the zero-temperature gap parameter Δ 0 =90 K, regardless of the magnetic anisotropy. The characteristics of CeRu 2 Al 10 can be accounted for semiquantitatively, including the finite value of susceptibility for T →0 K due to a Van-Vleck contribution of the excited states of the crystalline electric field at ≈10 2 K above the ground-state doublet.

Inelastic neutron scattering (INS) experiments have been performed on a V 3 triangular spin cluster. At the base temperature ( T = 0.7 K), the INS spectrum clearly exhibits a broad peak at \(\hbar\omega = 0.8\) meV. The peak was ascribed to the superposition of four magnetic excitations from two S total = 1/2 doublets to two S total = 3/2 doublets. From the observed peak position, width, and intensity, we confirmed a model Hamiltonian comprising anisotropic exchange and Dzyaloshinsky–Moriya (DM) interactions, and estimated the Hamiltonian parameters as J x = J y = -5.73 K, J z = -6.83 K, D 1,2 z = 0.261 K, and D 2,3 z = D 3,1 z = 0.287 K, where J α is the α-component of the exchange interactions and D i , j z represents the z -component of the DM vector between the i -th and j -th V 4+ ions. The resulting model Hamiltonian successfully reproduced the half-step magnetization process reported earlier as well as magnetic susceptibility.

Single crystals of Yb 2 (Pd 1- x Ni x ) 2 Sn with x =0, 0.1, and 0.2 were prepared to clarify the effects of pressure on Yb 2 Pd 2 Sn which is considered to reside near the quantum critical point. The magnetization and specific heat measurements revealed that their ground states are regarded as an S =1/2 XY-like spin system. Although nondoped Yb 2 Pd 2 Sn shows no magnetic transition down to 0.5 K owing to the Kondo effect, Ni-doped Yb 2 Pd 2 Sn exhibits a distinct magnetic transition. Furthermore, the magnetic susceptibility of Ni-doped Yb 2 Pd 2 Sn exhibits a broad peak in the temperature range higher than the magnetic transition temperature, which is not explained by the S =1/2 Coqblin–Schrieffer model, suggesting the effect of geometrical frustration arising from the characteristic structure of these compounds, i.e., the Shastry–Sutherland lattice.

We calculate the corresponding differential conductance (d I /d V ) spectra from scanning tunneling spectroscopy (STS) measurements for two magnetic atoms adsorbed on a metal surface. The formula for the d I /d V spectra is based on a model that explicitly takes into account the energy dependence of the electron tunneling matrices between the corresponding constituent components, viz. , the magnetic adatoms and metal surface. We find that the shape of the d I /d V spectra varies with the distance between the two magnetic adatoms. From considerations of the Ruderman–Kittel–Kasuya–Yosida (RKKY) interaction strength on the metal surface, we conclude that the ferromagnetic RKKY interaction sharpens the d I /d V peak structure, making it more pronounced. On the other hand, the antiferromagnetic RKKY interaction broadens the peak structure. This result agrees well with experimental results and confirms that the RKKY interaction causes the deformation of the observed STS peak structure.

Phosphorus-doped silicon (Si:P) is one of the most extensively studied condensed matter systems since a variety of physical phenomena accompanies with doping P in Si, such as impurity-band conduction, metal–insulator transition (M–I). Recently, it has attracted new interest for possible applications to quantum computer where P nuclear spins serve qubits and electron spins are completely polarized for isolated spins bound at the donor. This model of silconbased quantum computer requires NMR control of P nuclear spins under extreme conditions of several tesla magnetic field and millikelvin temperature. Spin dynamics of both nuclei and electrons are of great interest in this regard. However, despite a large amount of works devoted to the magnetic properties of Si:P, P-NMR has never been investigated under such experimental conditions. Here we present the P-NMR of metallic Si:P investigated at temperature between 40mK and 4K and a magnetic field of 7 T. We tried P-NMR in insulator Si:P but could not detect it. Our NMR data show several novel features in longitudinal relaxation time T1 and transverse relaxation time T2 associated with very low temperature and high magnetic field. We prepared a powdered sample from single crystalline silicon wafers with phosphorus dopant concentration of n 1⁄4 5:6 10 cm 3 which is above the critical concentration for M–I, nc ’ 3:7 10 cm . The dopant concentration of Si:P was determined by measuring room temperature resistivity with the Mousty scale. The sample was immersed in He–He mixture which was cooled by a dilution fridge. The NMR spectra at 120MHz were obtained by recording the spin-echo height with varying magnetic fields. The T2 was measured by decay of the echo height with varying time delay of the pulse sequence =2 . The T1 was obtained from the magnetization recovery after -pulse with varying waiting time t of the sequence t =2 . The NMR spectra were typical for metallic sample and did not depend on temperature. The linewidth of about 24mT and the Knight shift agree with those reported in the literature for similar dopant concentrations. The linewidth is believed to be determined by inhomogeneous broadening of hyperfine interactions. The longitudinal relaxation showed a substantial change only below 0.6K from the previous data. Nuclear magnetization was recovered in two steps, following double-exponential curves below 0.6K while the recovery followed single-exponential curves above 0.6K. Typical recovery curves are shown in the inset of Fig. 1. Below 0.6K, we obtained T1 separately for the fast and slow components of the relaxation, T1f and T1s. The T1f and T1s are plotted against temperatures in Fig. 1. T1f above 0.2K follows the Korringa’s relation as, T1T 1⁄4 ( is Korringa constant). It shows, however, a gradual deviation from the Korringa’s relation below 0.2K. The long T1s increases with decreasing temperature as T1s / T n with n ’ 1:3. A double-exponential form of recovery curve was observed only when the nuclear Zeeman bath decays through the electron bath to a third bath in series and the heat capacity of Zeeman bath, CN, becomes comparable to that of the electron bath, Ce. The second stage for the slow recovery process appeared in the magnetization recovery at T 1⁄4 0:6K when CN=Ce ’ 0:01 and [1 MðtÞ=M0] was measured in the range between 2 and 0.01. We understand that both the deviation of T1f from the Korringa’s relation and the appearance of long T1s arise from the large nuclear Zeeman heat capacity at high B=T . Because CN goes with ðB=TÞ while Ce with T , the temperature of electrons actually rises during nuclear spin relaxation when the electron system is decoupled to the third bath (He–He mixture bath) by T1s since T1f T1s. Due to heating up the electron temperature Te the nuclear spins relax at faster rate =Te than that expected from =T where Te > T . The T1s was first observed and was the time constant for the Zeeman and conduction electron baths to decay together to the He–He bath. The T1s is needed to cool down the nuclear spins at low temperatures and may be due to the Kapitza resistance between the sample and He–He mixture. Fig. 1. Longitudinal relaxation times T1f (circle) and T1s (square) with temperature. The inset shows the recovery curves. Dotted line represents the Korringa’s relation derived from the data above 1K. Solid line is a guide to the eye.

The ordering of the Ising model on a pyrochlore lattice interacting via the long-range RKKY interaction, which models a metallic pyrochlore magnet such as Pr 2 Ir 2 O 7 , is studied by Monte Carlo simulations. Depending on the parameter k F representing the Fermi wavevector, the model exhibits rich ordering behaviors.