Ferromagnetic Quantum Critical Point Research Articles

Low Curie temperature ferromagnetic phase in SmPt2Cd20 possibly accompanied by strong quantum fluctuations

Electrical resistivity, magnetization and specific heat have been measured for single crystals of SmPt$_{2}$Cd$_{20}$. It has been found that SmPt$_{2}$Cd$_{20}$ exhibits a ferromagnetic (FM) transition at $T_{\rm C} = 0.64$ K, the lowest among cubic compounds. Specific heat divided by temperature increases with decreasing temperature even below $T_{\rm C}$ and attains 4.5 J/mol K$^{2}$ at 0.26 K, implying substantial magnetic quantum fluctuations. An analysis of the magnetic entropy suggests the crystalline-electric-field splitting of the Sm $J = 5/2$ multiplet with a $\Gamma_{7}$ doublet ground state and a $\Gamma_8$ quartet excited state (the excitation energy of $\sim30$ K). The electrical resistivity shows a power-law behavior with $T^{0.74}$ below 2 K without showing any noticeable anomaly at $T_{\rm C}$. SmPt$_{2}$Cd$_{20}$ is regarded as a rare cubic system that is located in the vicinity of a FM quantum critical point.

Quantum critical behavior in the asymptotic limit of high disorder in the medium entropy alloy NiCoCr0.8

The behavior of matter near a quantum critical point is one of the most exciting and challenging areas of physics research. Emergent phenomena such as high-temperature superconductivity are linked to the proximity to a quantum critical point. Although significant progress has been made in understanding quantum critical behavior in some low dimensional magnetic insulators, the situation in metallic systems is much less clear. Here, we demonstrate that NiCoCrx single crystal alloys are remarkable model systems for investigating quantum critical point physics in a metallic environment. For NiCoCrx alloys with x ≈ 0.8, the critical exponents associated with a ferromagnetic quantum critical point are experimentally determined from low temperature magnetization and heat capacity measurements. All of the five exponents (γT ≈ 1/2, βT ≈ 1, δ ≈ 3/2, νzm ≈ 2, {bar {rm alpha}}T ≈ 0) are in remarkable agreement with predictions of Belitz–Kirkpatrick–Vojta theory in the asymptotic limit of high disorder. Using these critical exponents, excellent scaling of the magnetization data is demonstrated with no adjustable parameters. We also find a divergence of the magnetic Gruneisen parameter, consistent with a ferromagnetic quantum critical point. This work therefore demonstrates that entropy stabilized concentrated solid solutions represent a unique platform to study quantum critical behavior in a highly tunable class of materials.

Magnetic properties of exchange-enhanced Pauli paramagnetic metals AeCo2P2 (Ae = Sr, Ba)

We have synthesized single crystals of AeCo2P2 (Ae = Sr, Ba) and polycrystalline powder sample of Sr1−xBaxCo2P2, and measured their magnetic properties. SrCo2P2 shows an itinerant-electron metamagnetic transition at Hc = 600 kOe and its temperature dependent magnetic susceptibility shows characteristic two anomalies at Tmax1 = 25 and Tmax2 = 115 K, suggesting it is in the vicinity of a ferromagnetic quantum critical point. While, BaCo2P2 does not show the metamagnetic transition with the applied field up to 600 kOe, and its magnetic susceptibility shows only one anomaly corresponding to Tmax1 at 33 K. In addition, the Weiss temperature of Sr1−xBaxCo2P2, decreases to negative as x increases. These results indicate the system recede from the quantum critical point by the Ba substitution.

Magnetic order and spin dynamics across a ferromagnetic quantum critical point:μSRinvestigations ofYbNi4(P1−xAsx)2

In the quasi-1D heavy-fermion system YbNi$_4$(P$_{1-x}$As$_x$)$_2$ the presence of a ferromagnetic (FM) quantum critical point (QCP) at $x_c$ $\approx 0.1$ with unconventional quantum critical exponents in the thermodynamic properties has been recently reported. Here, we present muon-spin relaxation ($\mu$SR) experiments on polycrystals of this series to study the magnetic order and the low energy 4$f$-electronic spin dynamics across the FM QCP. The zero field $\mu$SR measurements on pure YbNi$_4$(P$_{2}$ proved static long range magnetic order and suggested a strongly reduced ordered Yb moment of about 0.04$\mu_B$. With increasing As substitution the ordered moment is reduced by half at $x = 0.04$ and to less than 0.005 $\mu_B$ at $x=0.08$. The dynamic behavior in the $\mu$SR response show that magnetism remains homogeneous upon As substitution, without evidence for disorder effect. In the paramagnetic state across the FM QCP the dynamic muon-spin relaxation rate follows 1/$T_{1}T\propto T^{-n}$ with $1.01 \pm 0.04 \leq n \leq 1.13 \pm 0.06$. The critical fluctuations are very slow and are even becoming slower when approaching the QCP.

Ferromagnetic quantum critical behavior in heavy-fermion compounds CeTi1−xNixGe3

The measurements on magnetization (M), resistivity (ρ) and specific heat (C) were carried out for the ferromagnetic CeTi NixGe3 (0.0 x 0.45) system. It was found that the Curie temperature, TC, decreases with increasing Ni content, x, and reaches zero kelvin near a critical content xcr = 0.44. A new phase diagram is constructed based on these measurements. The non-Fermi liquid (nFL) behavior in ρ(T), and (T0/T) relationship in C/T in the samples near xcr, demonstrate that strong spin fluctuation emerges in these samples, indicating that they are near a quantum critical point (QCP). Our results indicate that CeTi NixGe3 may provide another platform to study exotic quantum phenomena near ferromagnetic QCP.

Avoided ferromagnetic quantum critical point: Antiferromagnetic ground state in substituted CeFePO

AbstractWe have investigated single crystals of two substitution series Ce(Ru1−x Fex)PO and CeFe(As1−y Py)O in the vicinity to the quantum critical material CeFePO by means of magnetic‐susceptibility and specific‐heat measurements. We observe an antiferromagnetic ground state in the vicinity of the quantum critical point, with pronounced metamagnetic transitions for , which is the magnetically hard direction. Our results verify that a ferromagnetic quantum critical point is avoided in substituted CeFePO, because we clearly demonstrate that the ferromagnetic ground state changes into an antiferromagnetic one, when approaching the quantum critical point.Temperature–substitution phase diagram of the series Ce(Ru1−x Fex)PO and CeFe(As1−y Py)O.

Crystal growth by Bridgman and Czochralski method of the ferromagnetic quantum critical material YbNi4P2

The tetragonal YbNi4P2 is one of the rare examples of compounds that allow the investigation of a ferromagnetic quantum critical point. We report in detail on two different methods which have been used to grow YbNi4P2 single crystals from a self-flux. The first, a modified Bridgman method, using a closed crucible system yields needle-shaped single crystals oriented along the [001]-direction. The second method, the Czochralski growth from a levitating melt, yields large single crystals which can be cut in any desired orientation. With this crucible-free method, samples without flux inclusions and a resistivity ratio at 1.8K of RR1.8K=17 have been grown.

Tuning the ferromagnetic phase in the CDW compound SmNiC2 via chemical alloying.

We report a study on tuning the charge density wave (CDW) ferromagnet SmNiC2 to a weakly coupled superconductor by substituting La for Sm. X-ray diffraction measurements show that the doped compounds obey Vegard’s law, where La (Lu) alloying expands (shrinks) the lattice due to its larger (smaller) atomic size than Sm. In the series Sm1−xLaxNiC2, CDW transition (TCDW = 148 K) for SmNiC2 is gradually suppressed, while the ferromagnetic (FM) ordering temperature (TC) at 17 K slightly increases up to x = 0.3. For x > 0.3, TC starts to decrease and there is no signature that could be related with the CDW phase. Electrical resistivity, magnetic susceptibility and specific heat measurements point toward the possible presence of a FM quantum critical point (QCP) near x = 0.92, where the TC is extrapolated to zero temperature. Superconductivity in LaNiC2 (Tsc = 2.9 K) is completely suppressed with small amount of Sm inclusion near the proposed FM critical point, indicating a competition between the two ordered phases. The tunable lattice parameters via chemical substitution (La,Lu) and the ensuing change among the ordered phases of ferromagnetism, CDW and superconductivity underscores that SmNiC2 provides a rich avenue to study the rare example of a FM QCP, where the broken symmetries are intricately correlated.

Topological properties of ferromagnetic superconductors

A variety of heavy fermion superconductors, such as UCoGe, UGe$_2$, and URhGe exhibit a striking coexistence of bulk ferromagnetism and superconductivity. In these systems, the magnetic moment decreases with pressure, and vanishes at a ferromagnetic quantum critical point (qcp). Remarkably, the superconductivity in UCoGe varies smoothly with pressure across the qcp and exists in both the ferromagnetic and paramagnetic regimes. We argue that in UCoGe, spin-orbit interactions stabilize a time-reversal invariant odd-parity superconductor in the high pressure paramagnetic regime. Based on a simple phenomenological model, we predict that the transition from the paramagnetic normal state to the phase where superconductivity and ferromagnetism coexist, is a first-order transition.

Incommensurate spin density wave at a ferromagnetic quantum critical point in a three-dimensional parabolic semimetal

We explore the ferromagnetic quantum critical point in a three-dimensional semimetallic system with upward- and downward-dispersing bands touching at the Fermi level. Evaluating the static spin susceptibility to leading order in the coupling between the fermions and the fluctuating ferromagnetic order parameter, we find that the ferromagnetic quantum critical point is masked by an incommensurate, longitudinal spin density wave phase. We first analyze an idealized model which, despite having strong spin-orbit coupling, still possesses O(3) rotational symmetry generated by the total angular momentum operator. In this case, the direction of the incommensurate spin density wave propagation can point anywhere, while the magnetic moment is aligned along the direction of propagation. Including symmetry-allowed anisotropies in the fermion dispersion and the coupling to the order parameter field, however, the ordering wavevector instead breaks a discrete symmetry and aligns along either the [111] or [100] direction, depending on the signs and magnitudes of these two types of anisotropy.

Evolution of ferromagnetic and non-Fermi-liquid states with doping: The case of Ru-doped UCoGe

We have investigated the impact of Ru substitution for Co on the behavior of the ferromagnetic superconductor UCoGe by performing x-ray diffraction, magnetization, specific heat and electrical resistivity measurements on polycrystalline samples of the $\mathrm{UCo}_{1-x}\mathrm{Ru}_{x}\mathrm{Ge}$ series ($0\geq x\leq0.9$). The initial Ru substitution up to $x\approx0.1$ leads to a simultaneous sharp increase of the Curie temperature and spontaneous magnetization up to maximum values of $T_{\mathrm{C}}=8.6 K$ and $M_{\mathrm{S}}=0.1 \mu_{\mathrm{B}}$ per formula unit, respectively, whereas superconductivity vanishes already for $x\approx0.03$. Further increase of the Ru content beyond $x\approx0.1$ leads to a precipitous decrease of both, $T_{\mathrm{C}}$ and $M_{\mathrm{S}}$ towards a ferromagnetic quantum critical point (QCP) at $x_{\mathrm{cr}}=0.31$. Consequently the $T-x$ magnetic phase diagram consists of a well-developed ferromagnetic dome. We discuss the evolution of ferromagnetism with $x$ on the basis of band structure changes due to varying 5$f$-ligand hybridization. This scenario is supported by the results of electronic structure calculations and consideration of the simplified periodic Anderson model. The analysis of the temperature dependencies of the electrical resistivity and heat capacity at low temperatures of the samples in the vicinity of the QCP reveals a non-Fermi liquid behavior and assigns the ferromagnetic quantum phase transition to be most likely of a continuous Hertz-Millis type.

Competing ground states in transition metal oxides: Behavior of itinerant Sr1−x Ca x RuO3 close to the classical and quantum critical ferromagnetic phase transition

The ferromagnetic (FM) phase transition of the itinerant electron-system Sr1−x Ca x RuO3 can be tuned by chemical composition resulting in a quantum critical point (QCP) at the critical concentration x c ≈ 0.7. Applying epitaxial pressure at constant x leads to a reduction of the Curie temperature T C which is found to be proportional to the shrinkage of the unit-cell volume V uc , shifting x c to higher values for tensile strained films. Surprisingly, the tetragonal distortion seems to play here only a minor role. With increasing x the critical scaling of the order parameter shows unusual behavior. The magnetic critical exponents β, γ, and δ change systematically from typical mean-field values at x = 0 with increasing x towards β = 1, γ = 0.9 and δ = 1.6 at x = 0.7. The results are discussed with respect to a crossover from mean-field-like behavior at x = 0 to a line of fixed points that might emerge in the strong-disorder limit as the system approaches the QCP at or near x c . Magnetic inhomogeneities are indeed suggested by a non-vanishing magnetic moment at x c and the evidence of a Griffiths phase as well as glass-like behavior close to x c . Although spin fluctuations certainly play an important role around x c as proposed previously, our highly accurate data of the magnetization M(T,B) and specific heat C(T,B) for x = 0.7 suggest dynamic scaling with an unusual dynamic exponent z = 1.8, incompatible with standard spin-fluctuation theories at a ferromagnetic QCP.

Magnetism in Na-filled Fe-based skutterudites.

The interplay of superconductivity and magnetism is a subject of ongoing interest, stimulated most recently by the discovery of Fe-based superconductivity and the recognition that spin-fluctuations near a magnetic quantum critical point may provide an explanation for the superconductivity and the order parameter. Here we investigate magnetism in the Na filled Fe-based skutterudites using first principles calculations. NaFe4Sb12 is a known ferromagnet near a quantum critical point. We find a ferromagnetic metallic state for this compound driven by a Stoner type instability, consistent with prior work. In accord with prior work, the magnetization is overestimated, as expected for a material near an itinerant ferromagnetic quantum critical point. NaFe4P12 also shows a ferromagnetic instability at the density functional level, but this instability is much weaker than that of NaFe4Sb12, possibly placing it on the paramagnetic side of the quantum critical point. NaFe4As12 shows intermediate behavior. We also present results for skutterudite FeSb3, which is a metastable phase that has been reported in thin film form.

A ferromagnetic quantum critical point in heavy-fermion iron oxypnictide CeFe1−xCrxPO

We report crystallographic and magnetic properties of layered iron oxypnictide CeFe1−xCrxPO (x = 0.000–0.692). Interlayer distances between Ce2O2 and (Fe1−xCrx)2P2 layers increase as a function of x, suggesting suppression of Kondo coupling among hybridized conducting orbitals and localized Ce 4f orbitals. CeFe1−xCrxPO (x = 0.100–0.384) exhibits finite ferromagnetic transition temperatures (Tcurie) obtained by Arrott plots, although 57Fe Mössbauer spectra reveal paramagnetic Fe sublattice at T ≥ 4.2 K. These results indicate that the ferromagnetic phase transitions of samples are mainly due to Ce sublattice. For the samples with x ≥ 0.500, no ferromagnetic order is observed down to 2 K. These results verify that ferromagnetic quantum critical points of CeFe1−xCrxPO appear at 0.045 ≤ x ≤ 0.100 and 0.384 ≤ x ≤ 0.500.

Pressure-induced ferromagnetic quantum criticality in the low-carrier system CeP

We have already obtained the tentative pressure (P)-temperature (T) magnetic phase diagram of the antiferromagnetic (AF) semimetal CeP with strongly localized 4f electrons by measurements of the only T-dependence of the electrical resistivity, ρ(T), up to 8 GPa. In order to get further reliability, we performed the simultaneous measurements of the T- dependent real part of the AC magnetic susceptibility, χ'AC(T), and ρ(T) at P ≲ 2.5 GPa. As a result, the temperature which give the resistive anomaly was found to be the exact transition temperature from the paramagnetic (PM) phase to the magnetically ordered state, even in P > 2.5 GPa. The detailed magnetic structures (MSs) is already clarified by the neutron diffraction (ND) experiments under high pressures up to 1.7GPa by Kohgi et al. and up to 5.6 GPa by Goncharenko et al. The careful comparison between our macroscopic P-T magnetic phase diagram and the microscopic MSs elucidated the new facts: in the high-P region, the induction of the pure ferromagnetic (FM) phase for P ≳ 4 GPa is revealed to cause a rapid decrease in the Curie temperature TC and the Ce localized magnetic moment (LM); and furthermore, the TC is observed to vanish at a critical pressure PC ≈ (5.5±0.1) GPa together with the LM. We report the convincing basis for the presence of a P-induced FM quantum critical point (FM- QCP) and the possibility of localized-delocalized transition of the Ce-4f states approximately at the FM-QCP in the semi-metallic LM system CeP with the extremely low-carrier density.

Pairing gaps near ferromagnetic quantum critical points

We address the quantum-critical behavior of two-dimensional itinerant ferromagnetic systems described by spin-fermion models in which fermions interact with close-to-critical bosonic modes. We consider Heisenberg ferromagnets, Ising ferromagnets, and the Ising nematic transition. Mean-field theory close to the quantum critical point predicts a superconducting gap with spin-triplet symmetry for the ferromagnetic systems and a singlet gap for the nematic scenario. Studying fluctuations in this ordered phase using a nonlinear sigma model, we find that these fluctuations are not suppressed by any small parameter. As a result, we find that a superconducting quasi-long-range order is still possible in the Ising-like models but long-range order is destroyed in Heisenberg ferromagnets.

Evolution of magnetism in UCoGe and UCoAl with Ru doping**Invited talk at the 7th International Workshop on Advanced Materials Science and Nanotechnology IWAMSN2014, 2–6 November, 2014, Ha Long, Vietnam.

Intriguing magnetic properties of the UCo1−xRuxGe and UCo1−xRuxAl pseudoternary systems studied on single crystals are presented and discussed in terms of anisotropic 5f-ligand hybridization as the principal driving mechanism. Ferromagnetism of the ferromagnetic superconductor UCoGe is initially stabilized by Ru substitutions for Co (superconductivity suppressed already for x > 0.01) providing maximum Curie temperature (TC), spontaneous magnetic moment (μs) and magnetic entropy (Smag) for 10% Ru. Further increasing Ru concentration leads to gradual suppression of these parameters towards a ferromagnetic quantum critical point (FM QCP) at ≈0.31. Non-Fermi liquid scaling of specific heat and electrical resistivity is observed in the vicinity of FM QCP. The itinerant electron metamagnet UCoAl is transformed to a ferromagnet by only 0.5% Ru substituted for Co. The ferromagnetism is suppressed for x > 0.7. On the descending branch of the dome-like T − x magnetic phase diagram two distinctly different ferromagnetic phases are observed. The strong magnetocrystalline anisotropy leaving the hard magnetization directions Pauli paramagnetic like irrespective of magnetic ground states projected exclusively in the easy magnetization directions is accounted to the anisotropic 5f-5f wave-function overlap and 5f-ligand hybridization, and 5f-electron orbital moment.

Spin-Fluctuation Effects Near the Quantum Phase Transition of the Ising-Type Itinerant Ferromagnet URhAl

We performed high-pressure resistivity measurements for an Ising-type itinerant ferromagnet URhAl at low temperatures down to 40 mK. In URhAl, the Curie temperature (TC) is sufficiently suppressed with increasing pressure and TC suddenly disappears at the critical pressure Pc ∼ 5.2GPa. Above Pc, we observed the large enhancement of the A coefficient of AT2 resistivity term, which is defined below T*(P). Near Pc, the exponent (n) of resistivity, ρ(T) = ρ0 + A’Tn, approaches n ∼ 5/3, which is suggested from the spin-fluctuation theory for a three dimensional itinerant ferromagnetic system. We observed the non-Fermi-liquid behavior of resistivity under high pressure far above Pc up to ∼ 7.5GPa. On the other hand, the critical behaviors of T*(P) and A(P) for URhAl do not obey the spin-fluctuation theory for a ferromagnetic quantum critical point, where the Curie temperature vanishes as a second-order phase transition. The sudden disappearance of TC support the change of nature of transition from second-order to first-order in URhAl near Pc. Furthermore, the pressure dependences of A(P) and ρ0(P) are asymmetric around Pc, and these behaviors might be explained by a remarkable Fermi-surface change, which accompanies the ferromagnetic-paramagnetic quantum phase transition in URhAl.

Probing the magnetic phases in the Ni-V alloy close to the disordered ferromagnetic quantum critical point with μSR

Zero (ZF) and longitudinal field (LF) muon spin relaxation data of the d-metal alloy Ni1-xVx are presented at several vanadium concentrations x below and above the critical xc ≈ 11 % where long-range ferromagnetic (FM) order is suppressed. The clear single precession frequency observed for Ni, as expected for a homogeneous FM, changes to rather damped osciallation with small V substitution at x = 4 %, confirming magnetic inhomogeneities caused by the less magnetic V environments in the magnetic Ni matrix. Furthermore, local fields and spatial field distributions can be estimated to characterize different inhomogeneous regimes developing with x in the FM phase of Ni1-xVx. In the regime of x = 7 – 10 % a Kubo Toyabe function well describes the low temperature ZF and LF asymmetry data supporting a static Gaussian field distribution. Closer to the quantum critical concentration a single scale static Kubo Toyabe function with one field distribution is not sufficient to describe the muon relaxation. These data indicate that further changes in spatial distributions and dynamics are evolving as expected within the critical regime of a disordered quantum critical point.

Observation of two ferromagnetic phases inFe3Mo3N

We report alloying-induced and field-induced ferromagnetism in the $\ensuremath{\eta}$-carbide-type compound ${\mathrm{Fe}}_{3}{\mathrm{Mo}}_{3}\mathrm{N}$, which shows a non-Fermi-liquid behavior in the vicinity of a ferromagnetic quantum critical point. Co substitution induces ferromagnetism in ${(\mathrm{Fe}}_{1\ensuremath{-}x}{\mathrm{Co}}_{x})$${}_{3}{\mathrm{Mo}}_{3}\mathrm{N}$ in the composition range $0.05\ensuremath{\le}x\ensuremath{\le}0.60$. With increasing $x$, the magnetism varies from the Curie-Weiss-type paramagnetism with a maximum in the temperature dependence of the magnetic susceptibility to another paramagnetism without the maximum via a weak ferromagnetism. An itinerant electron metamagnetic transition is observed for low $x$ at a magnetic field of $\ensuremath{\sim}$14 T. The magnetic phase diagram, in which the alloying-induced and the field-induced ferromagnetic phases are separated, is different from conventional phase diagrams for weak ferromagnets. Taking account of the fact that a magnetic field induces a Fermi-liquid behavior, the quantum criticality for pure ${\mathrm{Fe}}_{3}{\mathrm{Mo}}_{3}\mathrm{N}$ appears to be dominated by the dispersive spin fluctuations observed in the alloying-induced ferromagnetic phase.