SCR Theory Research Articles

Weak itinerant magnetic behaviour in Al substituted Ni 92 Cr 8 alloys

In the present work we report low temperature magnetic properties of Ni92−xAlxCr8 alloys. It is found that the Curie temperature and spontaneous magnetization (MSP) get suppressed around xC ≈ 7. From the analysis of the temperature and field dependent magnetization data we have obtained high value of Rhodes–Wohlfarth ratio, which indicates the weak itinerant ferromagnetic behavior for samples below xC. This is further supported by analysing the temperature variation of MSP in the framework of spin fluctuations, SCR theory. Furthermore, the Ginzburg-Landau formalism-based on spin fluctuation theory revealed that the contribution of spin fluctuations at low temperature increases as we approach xC.

International Workshop on Itinerant-Electron Magnetism

PrefaceIn these several decades, a lot of important approaches have been conducted in order to understand the itinerant-electron magnetism. Among them epoch-making was the great success of the spin-fluctuation theory for weak itinerant ferro- and antiferromagnets by Moriya and his coworkers based upon the self-consistent renormalization of spin fluctuations since 1973 (the SCR theory of spin fluctuations). Afterwards, the spin fluctuation theory has been developed toward the unified theory between the weakly itinerant and localized moment regimes in the metallic magnets in a phenomenological way by Moriya and Takahashi (1978). Then, the SCR theory has been developed and rearranged in a quantitative way by Takahashi and Moriya in 1985, by which we can compare the experiments and the SCR theory quantitatively by means of a set of (several numbers of) spin-fluctuation parameters.Furthermore, Takahashi has developed the spin-fluctuation theory in different approaches with some assumptions: the total spin-fluctuation amplitude conservation (TAC) and global consistency (GC) so far (1986 ∼ present), which possibly leads us to the unified picture of metallic magnetism with a wide variety of itinerant-electron magnets based upon the spin-fluctuation approaches.Since the novel superconductors with the magnetic origins have been discovered in the strongly correlated electron systems, e.g., the Heavy-Fermion compounds and intermetallics, the organic systems, the high-Tc cuprates, and Fe pnictides, moreover the electron correlations and interplays between the itinerant magnetism and the exotic superconductivity have been important, and the itinerant-electron characteristics have recently become one of the most important problems in the solid state sciences.In organizing the International Workshop on Itinerant-Electron Magnetism, which was held during September 25-27, 2015 in the seminar house of Graduate School of Science, Kyoto University, Kyoto, Japan, we had a plan to bring together an international group of leading theoreticians and experimental scientists on magnetism to discuss advanced topics in condensed matter physics, especially related to spin fluctuations in itinerant-electron magnetism including exotic superconductivity with magnetic pairing mechanism of electron pairs, and to shape the future development of this field. We also plan to invite young scientists as well as graduate students. We hoped that such young scientists have chance to talk with invited speakers and organizers on their own interests.Finally, this workshop is also organized in commemoration of Prof. Y. Takahashi’s retirement from University of Hyogo, Japan.(Kazuyoshi Yoshimura)

Chiral Magnetism in an Itinerant Helical Magnet, MnSi — An Extended 29Si NMR Study —

The microscopic magnetism in the helical, the conical and the ferro-magnetically polarized phases in an itinerant helical magnet, MnSi, has been studied by an extended 29Si NMR at zero field and under external magnetic fields. The temperature dependence of staggered moment, M_Q(T), determined by the 29Si NMR frequency, nu(T), and nuclear relaxation rate, 1/T_1(T) is in general accord with the SCR theory for weak itinerant ferromagnetic metals and its extension. The external field dependence of resonance frequency, nu(H), follows a vector sum of the contributions from atomic hyperfine and macroscopic fields with a field induced moment characteristic to the itinerant magnets. A discontinuous jump of the resonance frequency at the critical field, H_c, between the conical and the polarized phases has also been found that suggests a first order like change of the electronic states at H_c.

Pressure-Induced Quantum Critical Point in Ferromagnet U4Ru7Ge6

The electrical resistivity ρ of the ferromagnet U 4 Ru 7 Ge 6 has been studied under high pressure up to ∼4.5 GPa by using an indenter-type high-pressure cell. The Curie temperature T C = 11.2 K at ambient pressure decreases monotonously with increasing pressure, and seems to disappear at ∼2.6 GPa, where an enhancement of the coefficient A assuming Fermi liquid regime is observed. This result indicates a presence of a quantum critical point (QCP) of U 4 Ru 7 Ge 6 at around 2.6 GPa. In addition, non-Fermi liquid behavior (ρ∼ T 5/3 ) predicted by the SCR theory of three dimensional ferromagnet is also observed near the QCP.

Quantum critical behavior in the heavy Fermion single crystal Ce(Ni0.935Pd0.065)2Ge2

We have performed magnetic susceptibility, specific heat, resistivity, and inelastic neutron scattering measurements on a single crystal of the heavy Fermion compound Ce(Ni0.93BPd0.06B)2Ge2, which is believed to be close to a quantum critical point (QCP) at T = 0. At lowest temperature(1.8-3.5 K), the magnetic susceptibility behaves as χ(T) − χ(0) ∝ T−1/6 with χ(0) = 0.032 × 10−6 m3/mole (0.0025 emu/mole). For T < 1 K, the specific heat can be fit to the formula ΔC/T = γ0 − T1/2 with γ0 of order 700 mJ/mole-K2. The resistivity behaves as ρ = ρ0 + AT3/2 for temperatures below 2 K. This low temperature behavior for γ(T) and ρ(T) is in accord with the SCR theory of Moriya and Takimoto[1]. The inelastic neutron scattering spectra show a broad peak near 1.5 meV that appears to be independent of Q; we interpret this as Kondo scattering with TK = 17 K. In addition, the scattering is enhanced near Q=(1/2, 1/2, 0) with maximum scattering at ΔE = 0.45 meV; we interpret this as scattering from antiferromagnetic fluctuations near the antiferromagnetic QCP.

Spin fluctuations probed by NMR in paramagnetic spinelLiV2O4: a self-consistent renormalization theory

Low-frequency spin fluctuation dynamics in paramagnetic spinelLiV2O4, a rare 3d-electron heavy-fermion system, is investigated. A parametrizedself-consistent renormalization (SCR) theory of the dominant AFM spin fluctuations isdeveloped and applied to describe temperature and pressure dependences of thelow-T nuclear spin–latticerelaxation rate 1/T1 in this material. The experimental data for1/T1 availabledown to ∼1 K are well reproduced by the SCR theory, showing the development of AFM spin fluctuationsas the paramagnetic metal approaches a magnetic instability under the applied pressure. Thelow-T upturn of 1/T1T detected below 0.6 K under the highest applied pressure of 4.74 GPa isexplained as the nuclear spin relaxation effect due to the spin freezingof magnetic defects unavoidably present in the measured sample ofLiV2O4.

Magnetic properties of weak itinerant electron ferromagnets Fe xCo 1−xSi under high pressure

High-pressure AC magnetic susceptibility measurements have been carried out for the weak itinerant-electron ferromagnet Fe x Co 1− x Si with x = 0.3 , 0.4, 0.5 and 0.7 using a cubic anvil apparatus up to 7.5 GPa in the temperature range from 4.2 to 300 K in order to investigate their itinerant-electron ferromagnetic character under high pressure. The slope of the curves of the temperature dependence of the susceptibility around the Curie temperature T C was found to become steeper with pressure for the alloys with x=0.4 and 0.5. It suggests a change in the magnetic phase transition from the second to the first order to occur at higher pressure for these alloys by analogy from the case of MnSi that is a weak itinerant-electron ferromagnet with the same crystal structure as Fe x Co 1− x Si. It was found that for all alloys T C obeys 3 4 power law of pressure derived from the SCR theory. Pressure derivative of the ratio T C/ T 0, where T 0 is the spin fluctuation parameter, was roughly estimated for all alloys using the data of the macroscopic magnetic measurements.

SPIN FLUCTUATIONS AND ANHARMONICITY IN ITINERANT ELECTRON MAGNETISM

The paper overviews recent investigations of thermodynamics and magnetic dynamics of itinerant electron magnets with strongly coupled (anharmonic) spin fluctuations (SF). A novel classification scheme for SF, dependent on their spatial dispersion and quantum effects is presented, including the generalized Fermi liquid (FL), soft-mode (SM), and localized moments (LM) regimes. It is shown that the conventional SCR theory of Moriya holds only in the weak coupling limit of the SM regime and cannot be applied to real magnets where spin anharmonicity induced by zero-point SF is expected to be strong. To account for the effects of strong spin anharmonicity, a variational SM theory of SF is presented. These effects essentially influence thermodynamics of itinerant magnets and affect the criterion for magnetic instabilities, equations of state, low temperature specific heat, non-FL and quantum critical behavior, etc. Nonlinear magnetic dynamics of itinerant magnets is analyzed based on the phenomenological spin-invariant dynamical equations both in the spin wave and relaxational regimes. Macroscopic magnetic dynamics and different mechanisms of magnon damping in the spin wave regime are shown to be essentially different from the results arising for the Heisenberg magnets. The relaxational regime may be strongly influenced by nonlinear effects of mode-mode couplings. The spectrum of overdamped longitudinal SF is shown to be radically changed due to their scattering by magnons, which may result in a quasielasic peak in the SF spectrum and inelastic SF near the magnon frequencies, depending on nonlinear coupling. The quasielastic SF are suppressed at low temperatures and develop at elevated temperatures, dominating near the Curie point. The results are applied to the magnetoresistive manganites.

23Na NMR investigations of the itinerant ferromagnets NaFe 4Sb 12 and Na 0.5Ca 0.5Fe 4Sb 12

A 23Na ( I = 3 2 ) NMR study is presented on the itinerant ferromagnets NaFe 4Sb 12 and the isostructural Ca-substituted compound Na 0.5Ca 0.5Fe 4Sb 12 performed in 7.05 and 11.74 T in the temperature range from 4 to 300 K. Both compounds show a bulk ferromagnetism below 85 K. Static (Knight-shift) and dynamic (spin-lattice relaxation) measurements are described in the framework of the SCR theory for itinerant d band metals.

Pseudospin dynamical susceptibility based on the two-orbital Anderson lattice model of [formula omitted]-singlet ground state with antiferromagnetic Hund's-rule coupling

We investigate the pseudospin dynamical susceptibility based on the two-orbital Anderson lattice model of 5 f 2 -singlet ground state with the antiferromagnetic Hund's-rule coupling. We use the energy level scheme of 5 f 2 -state in the body-centered tetragonal crystalline field that are obtained by diagonalizing the pseudospin Hamiltonian i.e. the Hamiltonian of the antiferromagnetic Hund's-rule coupling. This energy level scheme is denoted by the two orbitals of two 5f-electrons and the pseudospins. We investigate the pseudospin dynamical susceptibility based on this two-orbital Anderson lattice model with two 5f-electrons with the pseudospins within the self-consistent renormalization theory of spin fluctuations (SCR theory). The SCR theory enables us to treat the pseudospin dynamical susceptibility beyond the random phase approximation. From the investigations it is possible for us to analyze the results of neutron scattering experiments of URu 2 Si 2 and the ones of nuclear spin lattice relaxation rates in nuclear magnetic resonance of URu 2 Si 2 .

Magnetic - nonmagnetic transition of U3P4 at high pressures

The transport properties of the itinerant ferromagnet U3P4 have been studied at high pressures up to 6.0 GPa using a diamond anvil cell. The Curie temperature TC decreases with increasing pressure, but then TC cannot be assigned above 4.0 GPa. The coefficient A, assuming the Fermi liquid behavior (p(T) = p0 + AT2) at low temperatures, shows a maximum at 5.3 GPa. The temperature dependence of the resistivity at 5.0 GPa follows T5/3 which is expected in the SCR theory of a three dimensional ferromagnet. From these results, it is concluded that the ferromagnetic-nonmagnetic transition exists at around 5.0 GPa.

Exotic superconducting phase inCeCu2Si2close to antiferromagnetism: A Cu-NQR study under hydrostatic pressure

We report Cu nuclear-quadrupole-resonance results under pressure on a homogeneous CeCu2Si2 (Tc = 0.65 K) that revealed critical magnetic fluctuations at the border to an antiferromagnetic phase. This exotic superconducting phase evolves into the typical heavy-fermion superconducting phase at minute pressures exceeding Pc ~ 0.2 GPa. The nuclear spin-lattice relaxation data in a pressure range 0.85 - 2.58 GPa are shown to be accountable by the SCR theory based on the nearly antiferromagnetic Fermi-liquid model. In 0 < P < Pc ~ 0.2 GPa, by contrast, we conclude that the exotic superconducting phase manifests itself under the unconventional normal state where antiferromagnetic waves propagate over a long range without any trace of antiferromagnetic order and thereby the heavy-fermion state breaks up.

NMR study of itinerant heavy electron system Ce(Ru 1− xRh x) 2Si 2

Spin-lattice relaxation times ( T 1) of 29Si in Ce( Ru 1−x Rh x) 2 Si 2 (x=0, 0.03 and 0.05) were measured in the temperature range between 0.35 and 60 K. Temperature dependences of T 1 do not obey the Korringa relation, and are well described by the effect of spin fluctuations based on the SCR theory. The best-fitted parameters to the observed T 1 are close to the values obtained by the specific heat and the susceptibility measurements. 29Si NMR and 101Ru NQR observed below T N∼2 K for x=0.05 have shown the characteristic line shapes associated with the occurrence of longitudinal incommensurate SDW.

μSR study on SDW transition in Ce(Ru 0.95Rh 0.05) 2Si 2

ZF-μSR measurement on Ce(Ru 0.95Rh 0.05) 2Si 2 single-crystalline sample with incident muon beam along both the a- and c-axis showed an exponential relaxation above about T N=2.0 K and two component relaxations were found below 2.0 K. One is a Gaussian relaxation signal which is the precursor of SDW ordering and the other is an exponential relaxation due to the fluctuation of 4f-electron moment. The Gaussian relaxation rate σ increases steeply with decreasing temperature, reflecting the broad field distribution under SDW ordering, and vanishes below 1.8 K. The exponential relaxation rate λ showed critical slowing down with SDW ordering near T N for both a- and c-axis. These behaviors were analyzed by the SCR theory with finite ordering temperature.

Ru NQR studies in La- and Ge-doped CeRu 2Si 2

We report 101Ru NQR studies in substituted systems of a non-magnetic heavy fermion compound CeRu 2Si 2, Ce 1− x La x Ru 2Si 2 ( x=0.05, 0.08) and CeRu 2(Si 1− z Ge z ) 2 ( z=0.05, 0.078). The Kondo temperature T K and the characteristic temperature of the Fermi liquid T FL, estimated from the 101Ru nuclear spin–lattice relaxation rate 1/ T 1, decrease with increasing x or z. A magnetic ordering is observed for z=0.078. The SCR theory is applied for an interpretation of the T-dependence in 1/ T 1, and it is suggested that the magnetic to non-magnetic transition against x or z may occur as a first-order type in these systems without passing through the quantum critical point ( T N→0).

Unified theory of dynamical mean field and self-consistently renormalized spin-fluctuations

A unified theory of the dynamical mean-field and the self-consistently renormalized spin-fluctuations (SCR) for strongly correlated electron systems is proposed. Starting from the iterative perturbation theory, local dynamical magnetic susceptibility χ L( ω) is constructed with inclusion of the vertex corrections, and the effect of spin fluctuations is incorporated in the form similar to the SCR theory. Temperature dependence of specific heat and electrical resistivity are calculated to be proportional to T(1− const. T ) and T 3/2, respectively, at the quantum critical point and low temperatures.

NMR study of the spin fluctuation in Ce(Ru 1− xRh x) 2Si 2

Spin-lattice relaxation times ( T 1) were measured on x=0.03 and x=0.05 samples of Ce(Ru 1− x Rh x ) 2Si 2 in a temperature range between 1.5 and 60 K. Temperature dependences of T 1 in both samples do not obey the Korringa relation, and are well described by the SCR theory for an antiferromagnetic ground state. Four parameters of y 0, y 1, T 0, T A obtained by the best fitting have close values obtained by specific heat experiments. The positive y 0 value in x=0.05 means that the sample of x=0.05 has no magnetic ordering at finite temperature, which contradicts with the experimental results of neutron diffraction, specific heat and susceptibility.

Magnetic correlations and quantum criticality in the insulating antiferromagnetic, insulating spin liquid, renormalized Fermi liquid, and metallic antiferromagnetic phases of the Mott systemV2O3

Magnetic correlations in all four phases of pure and doped vanadium sesquioxide V_2O_3 have been examined by magnetic thermal neutron scattering. While the antiferromagnetic insulator can be accounted for by a Heisenberg localized spin model, the long range order in the antiferromagnetic metal is an incommensurate spin-density-wave, resulting from a Fermi surface nesting instability. Spin dynamics in the strongly correlated metal are dominated by spin fluctuations in the Stoner electron-hole continuum. Furthermore, our results in metallic V_2O_3 represent an unprecedentedly complete characterization of the spin fluctuations near a metallic quantum critical point, and provide quantitative support for the SCR theory for itinerant antiferromagnets in the small moment limit. Dynamic magnetic correlations for energy smaller than k_BT in the paramagnetic insulator carry substantial magnetic spectral weight. However, the correlation length extends only to the nearest neighbor distance. The phase transition to the antiferromagnetic insulator introduces a sudden switching of magnetic correlations to a different spatial periodicity which indicates a sudden change in the underlying spin Hamiltonian. To describe this phase transition and also the unusual short range order in the paramagnetic state, it seems necessary to take into account the orbital degrees of freedom associated with the degenerate d-orbitals at the Fermi level in V_2O_3.

Spin Fluctuation and Magnetic Phase Transition in Itinerant Heavy Electron System Ce(Ru1-xRhx)2Si2(x=0, 0.03 and 0.05)

The specific heats and the susceptibilities of Ce(Ru 1- x Rh x ) 2 Si 2 single crystals ( x = 0, 0.03 and 0.05) were studied between 0.1 and 10 K. The magnetic ground state of Ce(Ru 1- x Rh x ) 2 Si 2 is found to be a Fermi liquid even near the critical concentration x =0.03. x = 0.05 compound takes place a spin density wave transition at around 2 K, which is an antiferromagnetic order of itinerant heavy electrons by nesting in the Fermi liquid state. The low temperature behavior of the specific heat and the susceptibility were well explained by the effect of spin fluctuations based on the SCR theory.

Aniomalous metallic state in LiV 2O 4

Nuclear magnetic resonance (NMR) for 7Li nuclei was performed in vanadium spinel, LiV 2O 4. An anomalous temperature dependence of the relaxation time T 1 was observed. Namely, the relaxation rate 1/ T 1 first increases with increasing temperature and then decreases below about 50 K. Such an anomalous temperature dependence may reflect the critical behavior around the ferromagnetic instability predicted by the SCR theory.