Self-consistent Renormalization Research Articles

Superconductivity and Pseudogap in Quasi-Two-Dimensional Metals around the Antiferromagnetic Quantum Critical Point

Spin fluctuations (SF) and SF-mediated superconductivity (SC) in quasi-two-dimensional metals around the antiferrromagnetic (AF) quantum critical point (QCP) are investigated by using the self-consistent renormalization theory for SF and the strong coupling theory for SC. We introduce a parameter y0 as a measure for the distance from the AFQCP which is approximately proportional to (x-xc), x being the electron (e) or hole (h) doping concentration to the half-filled band and xc being the value at the AFQCP. We present phase diagrams in the T-y0 plane including contour maps of the AF correlation length and AF and SC transition temperatures TN and Tc, respectively. The Tc curve is dome-shaped with a maximum at around the AFQCP. The calculated one-electron spectral density shows a pseudogap in the high-density-of-states region near (pi,0) below around a certain temperature T* and gives a contour map at the Fermi energy reminiscent of the Fermi arc. These results are discussed in comparison with e- and h-doped high-Tc cuprates.

Magnetic-field-induced crossover from non-Fermi to Fermi liquid at the quantum critical point ofYbCu5−xAux

The temperature $(T)$ dependence of the muon and $^{63}\text{C}\text{u}$ nuclear spin-lattice relaxation rates $1/{T}_{1}$ in ${\text{YbCu}}_{4.4}{\text{Au}}_{0.6}$ is reported over nearly four decades. It is shown that for $T\ensuremath{\rightarrow}0$ $1/{T}_{1}$ diverges following the behavior predicted by the self-consistent renormalization (SCR) theory for a ferromagnetic quantum critical point. On the other hand, the static uniform susceptibility ${\ensuremath{\chi}}_{s}$ is observed to diverge as ${T}^{\ensuremath{-}2/3}$ and $1/{T}_{1}T\ensuremath{\propto}{\ensuremath{\chi}}_{s}^{2}$, a behavior which is not accounted for by SCR theory. The application of a magnetic field $H$ is observed to induce a crossover to a Fermi-liquid behavior and for $T\ensuremath{\rightarrow}0$ $1/{T}_{1}$ is found to obey the scaling law $1/{T}_{1}(H)=1/{T}_{1}(0){[1+{({\ensuremath{\mu}}_{B}H/{k}_{B}T)}^{2}]}^{\ensuremath{-}1}$.

Frustrated Magnetism in Vanadium Oxides

The effect of frustration in various localized and itinerant vanadium oxide compounds is discussed within next nearest neighbors Heisenberg and spin fluctuation models, respectively. In the localized moment case the S = 1/2 J1−J2-model on a square lattice exhibits a rich phase diagram with magnetic as well as exotic hidden order phases due to the interplay of frustration and quantum fluctuations. Their signatures in the high field magnetization and in magnetocaloric quantities are surveyed. The possible quantum phase transitions are discussed and applied to layered vanadium oxides of the type AA′VO(PO4)2 where A, A′ = Pb, Zn, Sr, Ba, Cd. In itinerant electron systems magnetic frustration may emerge as a result of electron correlations on a geometrically frustrated lattice. This mechanism causes enhanced spin fluctuations in a large region of momentum space and therefore can lead to a heavy fermion state at low temperatures as in the 3d spinel compound LiV2O4. The evidence from neutron scattering and NMR experiments is discussed within self-consistent renormalization theory based on local density approximation band structure calculations.

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.

Unusual temperature dependence in the low-temperature specific heat ofU3Ni5Al19

Specific heat has been measured down to 0.053 K on a single crystal of the heavy-fermion antiferromagnet ${\text{U}}_{3}{\text{Ni}}_{5}{\text{Al}}_{19}$ that orders at ${T}_{\text{N}}=23\text{ }\text{K}$. As has been previously reported, these data can be fitted between 0.4 and 4 K by the spin-fluctuation model of Moriya and Takimoto, which describes the contribution of weakly interacting critical spin fluctuations to the specific heat, $C$, where, as $T\ensuremath{\rightarrow}0$, $C/T={\ensuremath{\gamma}}_{0}\ensuremath{-}a\ensuremath{\surd}T$. However, below 0.35 K a noticeable divergence in $C/T\ensuremath{\sim}\text{log}\text{ }T$ dependence, consistent with the existence of strongly interacting fluctuations, is observed. This increase in the divergence of $C/T$ at the lowest temperatures---which is contrary to the self-consistent renormalization theory of Moriya and Takimoto, which predicts $\ensuremath{\surd}T$ dependence for $C/T$ as $T\ensuremath{\rightarrow}0$ and $\text{log}\text{ }T$ dependence at higher temperatures---has been measured as a function of magnetic field to further understand its origin. The field data in the low-temperature regime, where $C/T\ensuremath{\sim}\text{log}\text{ }T$ exhibit scaling with $\ensuremath{\Delta}B/{T}^{1.9}$, further evidence that there exist strongly interacting fluctuations below 0.35 K in ${\text{U}}_{3}{\text{Ni}}_{5}{\text{Al}}_{19}$.

Synthesis and Magnetic Properties of Ni3AlCx

The itinerant-electron ferromagnet Ni 3 Al and its carbon-intercalated compounds Ni 3 AlC x ( x = 0.01, 0.02, 0.04, 0.05, 0.08, and 0.1) were synthesized and investigated by magnetization measurements between 2 and 300 K with the magnetic field H up to 5 T and 27 Al NMR measurements at H = 7.4847 T. The Curie temperature is suppressed and disappears only by the carbon intercalation with x = 0.02. For the samples with x ≤0.02, the T 4/3 -temperature dependence of M s 2 ( M s : spontaneous magnetization) and χ 0 -1 (χ 0 : initial susceptibility) are newly observed, being consistent with the predication of the self-consistent renormalization theory of spin fluctuations for weak itinerant ferromagnets. The coupling constant between the 27 Al Knight shift and the bulk susceptibility of Ni 3 AlC 0.1 is three times larger than that of Ni 3 Al, suggesting the drastic change of the electronic state by the carbon intercalation.

Self-consistent renormalization theory of spin fluctuations in paramagnetic spinelLiV2O4

A phenomenological description for the dynamical spin susceptibility $\ensuremath{\chi}(\mathbf{q},\ensuremath{\omega};T)$ observed in inelastic neutron scattering measurements on powder samples of $\mathrm{Li}{\mathrm{V}}_{2}{\mathrm{O}}_{4}$ is developed in terms of the parametrized self-consistent renormalization (SCR) theory of spin fluctuations. Compatible with previous studies at $T\ensuremath{\rightarrow}0$, a peculiar distribution in $\mathbf{q}$ space of strongly enhanced and slow spin fluctuations at $q\ensuremath{\sim}{Q}_{c}\ensuremath{\simeq}0.6\phantom{\rule{0.3em}{0ex}}{\mathrm{\AA{}}}^{\ensuremath{-}1}$ in $\mathrm{Li}{\mathrm{V}}_{2}{\mathrm{O}}_{4}$ is involved to derive the mode-mode coupling term entering the basic equation of the SCR theory. The equation is solved self-consistently with the parameter values found from a fit of theoretical results to experimental data. For low temperatures, $T\ensuremath{\lesssim}30\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, where the SCR theory is more reliable, the observed temperature variations of the static spin susceptibility $\ensuremath{\chi}({Q}_{c};T)$ and the relaxation rate ${\ensuremath{\Gamma}}_{Q}(T)$ at $q\ensuremath{\sim}{Q}_{c}$ are well reproduced by those suggested by the theory. For $T\ensuremath{\gtrsim}30\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, the present SCR is capable of predicting only main trends in $T$ dependences of $\ensuremath{\chi}({Q}_{c};T)$ and ${\ensuremath{\Gamma}}_{Q}(T)$. The discussion is focused on a marked evolution (from $q\ensuremath{\sim}{Q}_{c}$ at $T\ensuremath{\rightarrow}0$ toward low $q$ values at higher temperatures) of the dominant low-$\ensuremath{\omega}$ integrated neutron scattering intensity $I(q;T)$.

Sharp superconductor–insulator transition in short wires

Recent experiments on short MoGe nanowires show a sharp superconductor–insulator transition tuned by the normal state resistance of the wire, with a critical resistance of R c ≈ R Q = h/(4 e 2). These results are at odds with a broad range of theoretical work on Josephson-like systems that predicts a smooth transition, tuned by the value of the resistance that shunts the junction. We develop a self-consistent renormalization group treatment of interacting phase-slips and their dual counterparts, correlated cooper pair tunneling, beyond the dilute approximation. This analysis leads to a very sharp transition with a critical resistance of R Q. The addition of the quasi-particles’ resistance at finite temperature leads to a quantitative agreement with the experimental results. This self-consistent renormalization group method should also be applicable to other physical systems that can be mapped onto similar sine-Gordon models, in the previously inaccessible intermediate-coupling regime.

Unusual Suppression of Low Energy Spin Excitations near Fermi Level inAFe4Sb12(A=Ca, Sr, and Ba) Probed by Sb-NQR

Sb nuclear quadrupole resonances (NQR) have been performed on the alkaline-earth filled skutterudite A Fe 4 Sb 12 ( A =Ca, Sr, and Ba) being close to ferromagnetic instabiity. No hyperfine splitting in NQR spectrum even at the lowest temperature (1.5 K) confirms an absence of uniform ferromagnetic order in these compounds. Above about T * ∼70 K, the nuclear spin–lattice relaxation rate divided by temperature, 1/ T 1 T , follows an empirical relationship 1/ T 1 T = a + b χ spin with respect to the Curie Weiss (CW) like T -dependence of the static spin susceptibility χ spin . The correlation between 1/ T 1 T and χ spin is consistent with the self-consistent renormalization (SCR) theory for the three-dimensional (3D) nearly ferromagnet despite the relatively large contribution of the first term not correlating to χ spin . However, below about T * , 1/ T 1 T exhibits a gap-like suppression with a gap magnitude of about 65 K. This unusual suppression of the low energy spin excitations is contrasting to the cas...

Spin dynamics in the diluted ferromagnetic Kondo lattice model

The interplay of disorder and competing interactions is investigated in the carrier-inducedferromagnetic state of the Kondo lattice model within a numerical finite-size study in whichimpurity positional disorder is treated exactly. Competition between impurityspin couplings with increasing hole doping results in a strong optimization ofTc at , highlighting the importance of compensation in diluted magnetic semiconductors. The estimatedTc is in good agreement with experimental results forGa1−xMnxAs for corresponding impurity concentration, hole bandwidth, and compensation. Dilution isshown to result in a sharply enhanced density of low-energy magnon modes extended overthe majority bulk spins and high-energy magnon modes localized over impurity spinclusters. The effects of these magnon properties on finite-temperature spin dynamics arestudied quantitatively using a locally self-consistent magnon renormalization scheme.The large enhancement in the density of low-energy magnetic excitations resultsin a rapid thermal decay of magnetization, which fits well with the Bloch formM0(1−BT3/2) at lowtemperature, with B of the same order of magnitude as obtained in recent superconductingquantum interference device (SQUID) magnetization measurements onGa1−xMnxAs samples. Furthermore, strong cluster couplings and correlations are shownto slow down the magnetization decay and prolong magnetic ordering nearTc, as is also observed in magnetization measurements.

Spin dynamics in a weakly itinerant magnet fromSi29NMR inMnSi

$^{29}\mathrm{Si}$ NMR spectra and nuclear spin-lattice relaxation rate measurements in $\mathrm{MnSi}$ paramagnetic phase are presented. The experimental results are analyzed in the framework of the self-consistent renormalization theory for spin fluctuations, and detailed estimates of microscopic parameters describing the $\stackrel{P\vec}{q}$ and frequency dependence of the dynamical spin susceptibility are obtained. It is shown, in the light of a comparison with neutron scattering results, that some early determined parameters need to be revised. Accordingly, also the derivation of Curie-Weiss law within this model should be critically reconsidered.

Clustering induced suppression of ferromagnetism in diluted magnets

Ferromagnetism in diluted magnets in the compensated regime p << x is shown to be suppressed by the formation of impurity spin clusters. The majority bulk spin couplings are shown to be considerably weakened by the preferential accumulation of holes in spin clusters, resulting in low-energy magnon softening and enhanced low-temperature decay of magnetic order. A locally self-consistent magnon renormalization analysis of spin dynamics shows that although strong intra-cluster correlations tend to prolong global order, T_c is still reduced compared to the ordered case.

Transport and magnetic properties in the Heusler-type Fe 2+xV 1−xAl under high pressure

We report magnetic susceptibility and electrical resistivity under high pressure on polycrystalline Fe 2+ x V 1− x Al, which exhibits the ferromagnetic transition at x > 0 . The pseudogap band structure, magnetic defects and lower number of conduction carrier seem to result in the spin fluctuation, the enhancement of thermoelectric power and other unique properties in this system. On the other hand, the excess V-atom brings about the variable range hopping conduction at lower temperature that is affected by external pressure. The pressure effects on the transition temperature, T c, and magnetization at low temperature reveal that the magnetism can be described by the self-consistent renormalization (SCR) theory.

Nearly ferromagnetic state probed by Sb-NQR in filled skutterudite [formula omitted

Sb-NQR measurements were performed to investigate the itinerant magnetism in LaFe 4 Sb 12 with rising temperature from 5 K to 300 K. The monotonic decrease of NQR frequency ν Q without changing the asymmetry parameter η = 0.367 ± 0.005 indicates an isotropic volume expansion with no change of local symmetry. The nuclear spin–lattice relaxation rate divided by temperature 1 / T 1 T is proportional to χ spin the spin component of the static susceptibility, being consistent with the nearly ferromagnetic state described by the self-consistent renormalization theory.

Erratum: “On the Theory of Spin Fluctuations around the Magnetic Instabilities Effects of Zero-Point Fluctuations”

Effects of temperature variation of the zero-point spin fluctuations on the self-consistent renormalization (SCR) theory of spin fluctuations around the magnetic instabilities are discussed. In two and three dimensional ferromagnets and three dimensional antiferromagnets the effect is mostly to renormalize the mode-mode coupling constant. The renormalized value, corresponding to the experimental value, has a finite upper bound corresponding to a divergent mean field value. In two-dimensional antiferromagnets the critical behaviors of the staggered susceptibility and the nuclear spin-lattice relaxation rate are modified by logarithmic corrections while this correction hardly appears in those of the electrical resistivity and the specific heat. The temperature variation of the mean square local amplitude of the spin density around the magnetic instability is studied by using a simple model for the dynamical susceptibility and is applied to discuss a general trend in the magneto-volume effects in weak itiner...

Canonical transformation theory for multireference problems

We propose a theory to describe dynamic correlations in bonding situations where there is also significant nondynamic character. We call this the canonical transformation (CT) theory. When combined with a suitable description of nondynamic correlation, such as given by a complete-active-space self-consistent Field (CASSCF) or density matrix renormalization group wave function, it provides a theory to describe bonding situations across the entire potential energy surface with quantitative accuracy for both dynamic and nondynamic correlation. The canonical transformation theory uses a unitary exponential ansatz, is size consistent, and has a computational cost of the same order as a single-reference coupled cluster theory with the same level of excitations. Calculations using the CASSCF based CT method with single and double operators for the potential energy curves for water and nitrogen molecules, the BeH(2) insertion reaction, and hydrogen fluoride and boron hydride bond breaking, consistently yield quantitative accuracies typical of equilibrium region coupled cluster theory, but across all geometries, and better than obtained with multireference perturbation theory.

Crossover between itinerant ferromagnetism and antiferromagnetic fluctuations in filled skutterudites MFe 4Sb 12 (M=Na, Ba, La) as determined by NMR

Nuclear resonance investigations on the 23Na and the 139La nuclei in filled skutterudites MFe 4Sb 12 (M=Na, La) are reported. In contrast to NaFe 4Sb 12 for the La compound the effective magnetic moment is remarkably lower and the Curie–Weiss temperature is negative which indicates antiferromagnetic correlations. The spin-lattice relaxation rates 1/ T 1 exhibit a qualitatively different temperature behavior which provides clear evidence for dissimilar types of itinerant magnetism in the two compounds. For NaFe 4Sb 12 1/ T 1 vs. T indicates itinerant ferromagnetism with ordering at T c = 8 5 K , whereas for the La 0.9Fe 4Sb 12 weak itinerant antiferromagnetism with no ordering is found. 1/ T 1 is analyzed in terms of Moriya's self-consistent renormalization theory (SCR) for itinerant magnetic materials.

Self-consistent Fermi surface renormalization of two coupled Luttinger liquids

Using functional renormalization group methods, we present a self-consistent calculation of the true Fermi momenta ${k}_{F}^{a}$ (antibonding band) and ${k}_{F}^{b}$ (bonding band) of two spinless interacting metallic chains coupled by small interchain hopping. In the regime where the system is a Luttinger liquid, we find that $\ensuremath{\Delta}={k}_{F}^{b}\ensuremath{-}{k}_{F}^{a}$ is self-consistently determined by $\ensuremath{\Delta}={\ensuremath{\Delta}}_{1}{[1+{g}_{0}^{2}\mathrm{ln}{({\ensuremath{\Lambda}}_{0}∕\ensuremath{\Delta})}^{2}]}^{\ensuremath{-}1}$, where ${g}_{0}$ is the dimensionless interchain backscattering interaction, ${\ensuremath{\Delta}}_{1}$ is the Hartree-Fock result for ${k}_{F}^{b}\ensuremath{-}{k}_{F}^{a}$, and ${\ensuremath{\Lambda}}_{0}⪢\ensuremath{\Delta}$ is an ultraviolet cutoff. For ${g}_{0}^{2}\mathrm{ln}{({\ensuremath{\Lambda}}_{0}∕{\ensuremath{\Delta}}_{1})}^{2}⪢1$ even weak interachain backscattering leads to a strong reduction of the distance between the Fermi momenta.

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 .

Edge States in Doped Antiferromagnetic Nanostructures

We study competition between different phases in a strongly correlated nanostructure with an edge. Making use of the self-consistent Green's function and density matrix renormalization group methods, we study a system described by the t-J(z) and t-J models on a strip of a square lattice with a linear hole density n(||). At intermediate interaction strength J/t we find edge stripelike states, reminiscent of the bulk stripes that occur at smaller J/t. We find that stripes attach to edges more readily than hole pairs, and that the edge stripes can exhibit a peculiar phase separation.