Ferromagnetic Quantum Critical Point Research Articles

Phase diagram of CeVSb3under pressure and its dependence on pressure conditions

We present temperature dependent resistivity and ac-calorimetry measurements of CeVSb3 under pressure up to 8 GPa in a Bridgman anvil cell modified to use a liquid medium and in a diamond anvil cell using argon as a pressure medium, respectively. We observe an initial increase of the ferromagnetic transition temperature Tc with pressures up to 4.5 GPa, followed by decrease of Tc on further increase of pressure and finally its disappearance, in agreement with the Doniach model. We infer a ferromagnetic quantum critical point around 7 GPa under hydrostatic pressure conditions from the extrapolation to 0 K of Tc and the maximum of the A coefficient from low temperature fits of the resistivity \rho (T)=\rho_{0}+AT^{n}. No superconductivity under pressure was observed down to 0.35 K for this compound. In addition, differences in the Tc(P) behavior when a slight uniaxial component is present are noticed and discussed and correlated to choice of pressure medium.

Signatures of a quantum Griffiths phase in a d-metal alloy close to its ferromagneticquantum critical point

We report magnetization measurements close to the ferromagnetic quantum phase transition of the d-metal alloyNi1 − xVx at a vanadiumconcentration of xc≈11.4%. Inthe diluted regime (x > xc), the temperature (T)and magnetic field (H) dependences of the magnetization are characterized by nonuniversal power laws and displayH/T scaling in a wide temperature and field range. The exponents vary strongly withx and follow the predictions of a quantum Griffiths phase. We also discuss the deviations andlimits of the quantum Griffiths phase as well as the phase boundaries due to bulk andcluster physics.

Ferromagnetic quantum critical point induced by dimer-breaking in SrCo2(Ge1−xPx)2

Instead of the usual chemical doping or applied pressure methods for controlling quantum phase transitions, it’s now possible to break chemical bonds to tune into a ferromagnetic quantum critical point. In contrast to classical phase transitions driven by temperature,a quantum critical point (QCP) defines a transition at zero temperature that is driven by non-thermal parameters1,2,3. In the known quantum critical d-electron systems, tuning the electronic bandwidth by means of changing the applied pressure or unit-cell dimensions, or tuning the d-state population, is used to drive the criticality4,5,6. Here we describe how a novel chemical parameter, the breaking of bonds in Ge–Ge dimers that occurs within the intermetallic framework in SrCo2(Ge1−xPx)2, results in the appearance of a ferromagnetic (FM) QCP. Although both SrCo2P2 and SrCo2Ge2 are paramagnetic, weak itinerant ferromagnetism unexpectedly develops during the course of the dimer breaking, and a QCP is observed at the onset of the FM phase. The use of chemical bond breaking as a tuning parameter to induce QCP opens an avenue for designing and studying novel magnetic materials.

Upper Critical Field in Superconductors Near Ferromagnetic Quantum Critical Points: UCoGe

We study the strong-coupling superconductivity near ferromagnetic quantum critical points, mainly focusing on the upper critical fields $H_{c2}$. Based on our simple model calculations, we discuss experimentally observed unusual behaviors of $H_{c2}$ in a recently discovered ferromagnetic superconductor UCoGe. Especially, the large anisotropy between $H_{c2}\parallel a$-axis and $H_{c2}\parallel c$-axis, and the strong-coupling behaviors in $H_{c2}^{\parallel a}$ are investigated. We also examine effects of non-analytic corrections in the spin susceptibility on the superconductivity, which can arise from effective long range interactions due to particle-hole excitations.

Quantum phase transitions in single-crystalMn1−xFexSiandMn1−xCoxSi: Crystal growth, magnetization, ac susceptibility, and specific heat

We report the magnetization, ac susceptibility, and specific heat of optically float-zoned single crystals of ${\text{Mn}}_{1\ensuremath{-}x}{\text{Fe}}_{x}\text{Si}$ and ${\text{Mn}}_{1\ensuremath{-}x}{\text{Co}}_{x}\text{Si}$ for temperatures down to $\ensuremath{\sim}2\text{ }\text{K}$ and magnetic fields up to 9 T. The suppression of the helimagnetic transition temperature ${T}_{1}$ above a critical composition ${x}_{1}$, as seen in the magnetization, ac susceptibility, and specific heat, suggests the existence of a quantum phase transition at ${x}_{1}$. A Vollhardt invariance at a temperature ${T}_{2}>{T}_{1}$, which may be attributed to the Dzyaloshinsky-Moriya (DM) spin-orbit interactions, is also suppressed with increasing $x$ and vanishes above a concentration ${x}_{2}$, where ${x}_{2}>{x}_{1}$. When suppressing the effects of the DM interactions in an applied magnetic field, the magnetization for sufficiently large fields shares the signatures expected of an underlying putative ferromagnetic quantum critical point for a critical concentration ${x}_{c}$, where ${x}_{1}<{x}_{c}<{x}_{2}$. As a function of normalized concentration $x/{x}_{c}$, where ${x}_{c}^{\text{Co}}\ensuremath{\approx}0.084$ and ${x}_{c}^{\text{Fe}}\ensuremath{\approx}0.192$, the properties of ${\text{Mn}}_{1\ensuremath{-}x}{\text{Fe}}_{x}\text{Si}$ and ${\text{Mn}}_{1\ensuremath{-}x}{\text{Co}}_{x}\text{Si}$ are essentially identical with ${x}_{1}/{x}_{c}\ensuremath{\approx}0.78$ and ${x}_{2}/{x}_{c}\ensuremath{\approx}1.17$. Taken together, our study identifies ${\text{Mn}}_{1\ensuremath{-}x}{\text{Fe}}_{x}\text{Si}$ and ${\text{Mn}}_{1\ensuremath{-}x}{\text{Co}}_{x}\text{Si}$ as model systems in which the influence of DM interactions on ferromagnetic quantum criticality may be studied.

Non-Fermi-Liquid Behavior on an Iron-Based Itinerant Electron Magnet Fe3Mo3N

We report magnetic, calorimetric, and transport properties of an iron-based itinerant electron magnet Fe 3 Mo 3 N. Magnetic susceptibility shows a Curie–Weiss behavior at high temperatures and takes a broad maximum at around 75 K. The absence of magnetic long range order was confirmed by 57 Fe-Mössbauer and neutron diffraction measurements. C / T shows a divergent behavior following -log T at low temperatures and reaches 128 mJ/(f.u.mol K 2 ) at 0.5 K. The deviation from the T 2 power law of resistivity also suggests a non-Fermi-liquid (NFL) behavior. The observed C / T and χ are enhanced compared with the values estimated from the theoretical density of states, suggesting a strong magnetic enhancement. The NFL behaviors indicate that Fe 3 Mo 3 N is one of the ideal systems located in the vicinity of the ferromagnetic quantum critical point.

Ferromagnetic and ferroelectric quantum phase transitions

AbstractThe applicability of mean field models of ferroelectric and ferromagnetic quantum critical points is examined for a selection of d‐electron systems. Crucially, we find that the tendency of the effective interaction between critical fluctuation modes to become attractive and anomalous as the ordering temperatures tend to absolute zero results in particularly complex and striking phenomena. The multiplicity of quantum critical fields at the border of metallic ferromagnetism, in particular, is discussed here.

Vertex corrections for impurity scattering at a ferromagnetic quantum critical point

We study the renormalization of a non-magnetic impurity's scattering potential due to the presence of a massless collective spin mode at a ferromagnetic quantum critical point. To this end, we compute the lowest order vertex corrections in two- and three-dimensional systems, for arbitrary scattering angle and frequency of the scattered fermions, as well as band curvature. We show that only for backward scattering in D=2 does the lowest order vertex correction diverge logarithmically in the zero frequency limit. In all other cases, the vertex corrections approach a finite (albeit possibly large) value in the zero frequency limit. We demonstrate that vertex corrections are strongly suppressed with increasing curvature of the fermionic bands. Moreover, we show how the frequency dependence of vertex corrections varies with the scattering angle. We also discuss the form of higher order ladder vertex corrections and show that they can be classified according to the zero-frequency limit of the lowest order vertex correction. We show that even in those cases where the latter is finite, summing up an infinite series of ladder vertex diagrams can lead to a strong enhancement (or divergence) of the impurity's scattering potential. Finally, we suggest that the combined frequency and angular dependence of vertex corrections might be experimentally observable via a combination of frequency dependent and local measurements, such as scanning tunneling spectroscopy on ordered impurity structures, or measurements of the frequency dependent optical conductivity.

Publisher’s Note: Spin Conservation and Fermi Liquid near a Ferromagnetic Quantum Critical Point [Phys. Rev. Lett.103, 216401 (2009)

Publisher’s Note: Spin Conservation and Fermi Liquid near a Ferromagnetic Quantum Critical Point [Phys. Rev. Lett.<b>103</b>, 216401 (2009)

Spin Conservation and Fermi Liquid near a Ferromagnetic Quantum Critical Point

We propose a new low-energy theory for itinerant fermions near a ferromagnetic quantum critical point. We show that the full low-energy model includes, in addition to conventional interaction via spin fluctuations, another type of interaction, whose presence is crucial for the theory to satisfy SU(2) spin conservation. We demonstrate the consistency between a loopwise expansion and a Fermi liquid description for the full model. We further show that, prior to the ferromagnetic instability, the system develops a Pomeranchuk-type instability into a state with zero magnetization but with p-wave deformations of the Fermi surfaces of spin-up and spin-down electrons (a spin nematic).

Thermoelectric properties ofCe(La)Fe4Sb12skutterudites under a magnetic field

We show that ${\text{LaFe}}_{4}{\text{Sb}}_{12}$ is a ferromagnetic quantum critical point system and that ${\text{CeFe}}_{4}{\text{Sb}}_{12}$ is a moderate heavy fermion compound. This is supported by our thermoelectric and thermodynamic experiments under magnetic field on both compounds, and a comparison with other physical properties of these compounds. For ${\text{LaFe}}_{4}{\text{Sb}}_{12}$, the quenching of the ferromagnetic spin fluctuations explains both the negative magnetothermopower and the decrease in the electronic heat capacity under magnetic field. We propose that the negative magnetothermopower is a generic property of compounds with ferromagnetic spin fluctuations when the diffusion term by spin fluctuations dominates at low temperature. On the other hand these critical ferromagnetic fluctuations are smeared out in ${\text{CeFe}}_{4}{\text{Sb}}_{12}$ due to the antiferromagnetic coupling between the $d$ electrons of Fe and the $4f$ electron of Ce. As a result, ${\text{CeFe}}_{4}{\text{Sb}}_{12}$ is a moderate heavy fermion compound with Kondo temperature ${T}_{K}$ of about 80 K, which is consistent with the fact that cerium is almost trivalent in this material, and the partially screened magnetic moment of the cerium ions at $T⪡{T}_{k}$ is $0.3{\ensuremath{\mu}}_{\text{B}}$. Finally, in both compounds, the power laws observed at low temperature in the lattice thermal conductivity ${\ensuremath{\kappa}}_{l}$ could be explained by electron-phonon scattering.

Enhancement of Superconductivity near the Ferromagnetic Quantum Critical Point in UCoGe

We report a high-pressure single crystal study of the superconducting ferromagnet UCoGe. Measurements of the ac susceptibility and resistivity under pressures up to 2.2 GPa show ferromagnetism is smoothly depressed and vanishes at a critical pressure p(c) = 1.4 GPa. Near the ferromagnetic critical point superconductivity is enhanced. Upper-critical field measurements under pressure show B(c2)(0) attains remarkably large values, which provides solid evidence for spin-triplet superconductivity over the whole pressure range. The obtained p-T phase diagram reveals superconductivity is closely connected to a ferromagnetic quantum-critical point hidden under the superconducting "dome."

Fermionic propagators for two-dimensional systems with singular interactions

We analyze the form of the fermionic propagator for two-dimensional fermions interacting with massless overdamped bosons. Examples include a nematic and Ising ferromagnetic quantum-critical points and fermions at a half-filled Landau level. Fermi-liquid behavior in these systems is broken at criticality by a singular self-energy, but the Fermi surface remains well defined. These are strong-coupling problems with no expansion parameter other than the number of fermionic species, $N$. The two known limits, $N⪢1$ and $N=0$, show qualitatively different behavior of the fermionic propagator $G({ϵ}_{k},\ensuremath{\omega})$. In the first limit, $G({ϵ}_{k},\ensuremath{\omega})$ has a pole at some ${ϵ}_{k}$; in the other it is analytic. We analyze the crossover between the two limits. We show that the pole survives for all $N$, but at small $N$ it only exists in a range $O({N}^{2})$ near the mass shell. At larger distances from the mass shell, the system evolves and $G({ϵ}_{k},\ensuremath{\omega})$ becomes regular. At $N=0$, the range where the pole exists collapses and $G({ϵ}_{k},\ensuremath{\omega})$ becomes regular everywhere.

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 $1/{T}_{1}(H)=1/{T}_{1}(0){[1+{({\ensuremath{\mu}}_{B}H/{k}_{B}T)}^{2}]}^{\ensuremath{-}1}$.

Muon spin relaxation study of non-Fermi-liquid behavior near the ferromagnetic quantum critical point inCePd0.15Rh0.85

The low-energy spin dynamics near the ferromagnetic quantum critical point in ${\text{CePd}}_{0.15}{\text{Rh}}_{0.85}$ have been investigated using zero-field (ZF) and longitudinal-field muon spin relaxation $(\ensuremath{\mu}\text{SR})$ measurements over a temperature range of 60 mK to 4 K and in applied fields up to 2500 G. The ZF-$\ensuremath{\mu}\text{SR}$ measurements reveal a considerable slowing down of the spin fluctuations with decreasing temperatures below 2 K. There is no clear sign of either static long-range magnetic ordering or spin freezing down to 60 mK. The temperature dependence of the ZF-muon depolarization rate $(\ensuremath{\lambda})$ exhibits a power-law behavior, $\ensuremath{\lambda}(T)\ensuremath{\sim}{T}^{\ensuremath{-}n}$ with $n\ensuremath{\sim}0.8$, while the field dependence at 0.1 K reveals a time-field scaling of the muon relaxation function, ${P}_{z}(t,H)={P}_{z}(t/{H}^{\ensuremath{\gamma}})$ with $\ensuremath{\gamma}\ensuremath{\sim}1.0\ifmmode\pm\else\textpm\fi{}0.1$. Furthermore, the exponent derived from the ZF-$\ensuremath{\mu}\text{SR}$ data agrees well with the power-law behavior of the temperature-dependent susceptibility, $\ensuremath{\chi}(T)\ensuremath{\sim}{T}^{\ensuremath{-}\ensuremath{\alpha}}$ $(\ensuremath{\alpha}\ensuremath{\sim}\ensuremath{-}0.6\ifmmode\pm\else\textpm\fi{}0.1)$, the $E/T$ scaling of the neutron dynamical susceptibility, as well as the magnetization-field-temperature scaling $({\ensuremath{\gamma}}_{m}\ensuremath{\sim}0.8\ifmmode\pm\else\textpm\fi{}0.1)$, obtained from the same sample. The $\ensuremath{\mu}\text{SR}$ results of ${\text{CePd}}_{0.15}{\text{Rh}}_{0.85}$ are discussed in the context of systems exhibiting non-Fermi-liquid behavior.

Interaction correction of conductivity near a ferromagnetic quantum critical point

We calculate the temperature dependence of conductivity due to interaction correction for a disordered itinerant electron system close to a ferromagnetic quantum critical point, which occurs due to a spin-density wave instability. In the quantum critical regime, the crossover between diffusive and ballistic transport occurs at a temperature T* = 1/[{tau}{gamma}(e{sub F}{tau}){sup 2}], where {gamma} is the parameter associated with the Landau damping of the spin fluctuations, {tau} is the impurity scattering time, and E{sub F} is the Fermi energy. For a generic choice of parameters, T* is a few orders of magnitude smaller than the usual crossover scale 1/{tau}. In the ballistic quantum critical regime, the conductivity has a T{sup (d-1)/3} temperature dependence where d is the dimensionality of the system. In the diffusive quantum critical regime, we get T{sup 1/4} dependence in three dimensions and In{sup 2} T dependence in two dimensions. Away from the quantum critical regime, we recover the standard results for a good metal.

Magnetic instability of weak ferromagnetic [formula omitted] under pressure

Ground state properties of intermetallic YCo 9 Si 4 are investigated by means of temperature-dependent electrical resistivity measurements under pressure using both a diamond-anvil cell and a piston-cylinder cell. At ambient pressure, YCo 9 Si 4 shows weak itinerant ferromagnetism below 25 K with an ordered moment of about 1.6 μ B / f . u . The temperature-dependent electrical resistivity exhibits below 10 K a power-law behavior R ( T ) = R 0 + AT n . The exponent n changes from n ≃ 1.7 at ambient pressure to about 1.5 at 6 GPa, referring to non-Fermi liquid behavior. The characteristic temperature decreases with pressure, implying a decrease of the ferromagnetic transition with pressure as well. The initial decrease of the ordering temperature is d T C / d p ≃ - 2 K / GPa . Both, the pressure-dependent evolution of T C as well as of the coefficients A and n indicate that a ferromagnetic quantum critical point will be reached under pressure of the order of 6 GPa.

Evidence for a ferromagnetic quantum critical point in URhGe doped with Ru

We have investigated the evolution of ferromagnetic order in the correlated metal series URh 1− x Ru x Ge. Magnetization, transport and specific heat measurements provide convincing evidence for a ferromagnetic quantum critical point at the critical concentration x c=0.38. Here we report ac-susceptibility and magnetization measurements on selected samples with Ru doping concentrations near the critical point.

Quantum critical phenomena of ferromagnetic [formula omitted

We have performed specific heat C and magnetic susceptibility χ measurements on the pseudo-binary alloys CePt 1 - x Rh x , synthesized by mixing CePt (a ferromagnetic Kondo-lattice system) and CeRh (an intermediate valence system). As Rh is substituted for Pt, CePt 1 - x Rh x shows a continuous change in the ground state from ferromagnetic order ( T C ∼ 6 K at x = 0 ) to a nonmagnetic valence-fluctuation state for x > 0.8 . We found a non-Fermi-liquid-like behavior which is characterized by the power law T dependence of C ( T ) and χ ( T ) , for a wide x range above the ferromagnetic quantum critical point ( x c ∼ 0.8 ) .

Helimagnetism and weak ferromagnetism in edge-shared chain cuprates

The present understanding of a novel growing class of chain cuprates with intriguing magnetic properties is reviewed. Among them, several undoped edge-shared CuO 2 chain compounds show at low temperature a clear tendency to helicoidal magnetical ordering with acute pitch angles and sometimes also to weak ferromagnetism. Our analysis is based on the isotropic 1D frustrated J 1 – J 2 Heisenberg model with ferromagnetic (FM) 1st neighbor and antiferromagnetic 2nd neighbor exchange. The achieved assignment is supported by microscopic calculations of the electronic and magnetic structure. We consider Na ( Li ) Cu 2 O 2 , LiVCuO 4 as the best studied helimagnets, Li 2 ZrCuO 4 and other systems close to a FM quantum critical point, as well as Li 2 CuO 2 with FM inchain ordering. The interplay of frustrated inchain couplings, anisotropy and interchain exchange is discussed.