Ferromagnetic Quantum Critical Point Research Articles

High temperature spin-triplet topological superconductivity in K2Cr3As3

Spin-triplet superconductors are novel materials capable of harboring Majorana bound states that can be used in topological quantum computing. However, such bulk materials are still rare. Here we review the results that established K2Cr3As3 as a spin-triplet superconductor with transition temperature Tc as high as 6.5 K. We focus on the multiple-phases feature, and its exquisite distance to a ferromagnetic quantum critical point which is likely responsible for the high Tc . We touch on the topological aspects of the superconducting state, and suggest that it is a new route to the technical implementation using a topological spin-triplet superconductor at the highest temperature ever.

Interplay of superconductivity and localization near a two-dimensional ferromagnetic quantum critical point

We study the superconducting instability of a two-dimensional disordered Fermi liquid weakly coupled to the soft fluctuations associated with proximity to an Ising-ferromagnetic quantum critical point. We derive interaction-induced corrections to the Usadel equation governing the superconducting gap function, and show that diffusion and localization effects drastically modify the interplay between fermionic incoherence and strong pairing interactions. In particular, we obtain the phase diagram, and demonstrate that (i) there is an intermediate range of disorder strength where superconductivity is enhanced, eventually followed by a tendency towards the superconductor-insulator transition at stronger disorder; and (ii) diffusive particle-particle modes (so-called ``Cooperons'') acquire anomalous dynamical scaling $z=4$, indicating strong non-Fermi liquid behavior.

Evolution of short-range magnetic correlations in ferromagnetic Ni-V alloys

We experimentally study how the magnetic correlations develop in a binary alloy close to the ferromagnetic quantum critical point with small-angle neutron scattering (SANS). Upon alloying the itinerant ferromagnet nickel with vanadium, the ferromagnetic order is continuously suppressed. The critical temperature Tc vanishes when vanadium concentrations reach the critical value of xc=0.116 indicating a quantum critical point separating the ferromagnetic and paramagnetic phases. Earlier magnetization and $\mu$SR data have indicated the presence of magnetic inhomogeneities in Ni(1-x)V(x) and, in particular, recognize the magnetic clusters close to xc, on the paramagnetic and on the ferromagnetic sides with nontrivial dynamical properties [R. Wang et al., Phys. Rev. Lett. 118, 267202 (2017)]. We present the results of SANS study with full polarization analysis of polycrystalline Ni(1-x)V(x) samples with x=0.10 and x=0.11 with low critical temperatures Tc below 50 K. For both Ni-V samples close to xc we find isotropic magnetic short-range correlations in the nanometer-scale persisting at low temperatures. They are suppressed gradually in higher magnetic fields. In addition, signatures of long-range ordered magnetic domains are present below Tc. The fraction of these magnetic clusters embedded in the ferromagnetic ordered phase grows towards xc and agrees well with the cluster fraction estimate from the magnetization and $\mu$SR data. Our SANS studies provide new insights into the nature of the inhomogeneities in a ferromagnetic alloy close to a quantum critical point.

Proximity of superconducting LaCoSi to a ferromagnetic quantum critical point.

The physical characteristics of the 4 K superconductor LaCoSi are studied using first-principles density functional theory inside the local density approximation (LDA) framework. We discover that LDA predicts a ferromagnetic ground state for LaCoSi, which is in disagreement with the experiments. Even though LDA rarely overestimates the local magnetic moment associated with the magnetic ion in itinerant systems, such occurrences highlight the significance of spin fluctuations in the system. In this view, the Ginzburg-Landau free energy expansion and its variation as a function of pressure are used to calculate the amplitude of the zero-point fluctuations. Based on our calculations, we contend that the superconductivity associated with LaCoSi is closely related to a ferromagnetic quantum critical point, making it an intriguing candidate for the category of quantum materials.

Avoided ferromagnetic quantum critical point in CeZn

Cubic CeZn shows a structural phase transition under pressure, and it modifies the ground state from an antiferromagnetic (AFM) state to a ferromagnetic (FM) state. To investigate how the FM state terminates at a quantum phase transition, we measured the electrical resistivity under pressure for a single crystal CeZn. The transition temperature into the FM state decreases monotonously with increasing pressure, accompanied by the pronounced Kondo effect, but a drastic change in the field response occurs before the ordered phase terminates. This result suggests that the FM quantum critical point is avoided by the appearance of an AFM-like state.

Instability of the ferromagnetic quantum critical point and symmetry of the ferromagnetic ground state in two-dimensional and three-dimensional electron gases with arbitrary spin-orbit splitting

In this work we revisit itinerant ferromagnetism in 2D and 3D electron gases with arbitrary spin-orbit splitting and strong electron-electron interaction. We identify the resonant scattering processes close to the Fermi surface that are responsible for the instability of the ferromagnetic quantum critical point at low temperatures. In contrast to previous theoretical studies, we show that such processes cannot be fully suppressed even in presence of arbitrary spin-orbit splitting. A fully self-consistent non-perturbative treatment of the electron-electron interaction close to the phase transition shows that these resonant processes always destabilize the ferromagnetic quantum critical point and lead to a first-order phase transition. Characteristic signatures of these processes can be measured via the non-analytic dependence of the spin susceptibility on magnetic field both far away or close to the phase transition.

Metamagnetism and tricritical behavior in the Kondo lattice model

The phase diagram of the Kondo lattice model is explored around the ferromagnetic region, including an external magnetic field, and allowing the coexistence of ferromagnetism and Kondo effect ($\mathrm{FM}+\mathrm{K}$). Considering the combined effect of temperature and pressure, the evolution of the $\mathrm{FM}+\mathrm{K}$ phase yields a wing structure phase diagram with a tricritical point and a ferromagnetic quantum critical end point. The evolution of the spin-selective Kondo insulator phase, inside the coexistence region, introduces another critical end point. The results show a correspondence with the experimental phase diagram of heavy-fermion compounds, in particular, the ferromagnetic superconductor ${\mathrm{UGe}}_{2}$.

Suppression of ferromagnetism governed by a critical lattice parameter in CeTiGe3 with hydrostatic pressure or V substitution

We combine structural and magnetic measurements to compare the different magnetic phase diagrams between the pressure and substitution studies in ${\mathrm{CeTiGe}}_{3}$. We report on the structural, magnetic, and electrical transport properties of single crystals of ${\mathrm{CeTi}}_{1\ensuremath{-}x}{\mathrm{V}}_{x}{\mathrm{Ge}}_{3}$ ($x=0$, 0.1, 0.2, 0.3, 0.4, 0.9, and 1), and of polycrystalline samples ($x=0.5$, 0.6, 0.7, 0.8), as well as structural properties of ${\mathrm{CeTiGe}}_{3}$ under pressure up to $9\phantom{\rule{0.16em}{0ex}}\mathrm{GPa}$. The ferromagnetic ordering in ${\mathrm{CeTiGe}}_{3}$ is suppressed with V doping in ${\mathrm{CeTi}}_{1\ensuremath{-}x}{\mathrm{V}}_{x}{\mathrm{Ge}}_{3}$, and suggests a possible ferromagnetic quantum critical point near $x=0.45$. We perform a detailed crystalline electric field (CEF) analysis, and the magnetic susceptibility data in pure ${\mathrm{CeTiGe}}_{3}$ and ${\mathrm{CeVGe}}_{3}$ can be well explained by the CEF model. The proposed CEF energy levels suggest that there is a gradual change of the ground state from $|\ifmmode\pm\else\textpm\fi{}5/2\ensuremath{\rangle}$ in ${\mathrm{CeTiGe}}_{3}$ to $|\ifmmode\pm\else\textpm\fi{}1/2\ensuremath{\rangle}$ in ${\mathrm{CeVGe}}_{3}$, and a suppression of CEF splitting energies near the quantum critical region. When hydrostatic pressure is used instead of chemical substitution, the quantum critical point is avoided by the appearance of magnetic phases above around $4.1\phantom{\rule{0.16em}{0ex}}\mathrm{GPa}$. In the substitution study, the ferromagnetic and antiferromagnetic regions are well separated, whereas they touch in the pressure study. We observe a different trend in the temperature dependence of the resistivity maximum in both studies, suggesting that the CEF splitting energy is suppressed by V substitution but enhanced by pressure. We also observe different responses in lattice constants between the two studies, highlighting the fact that substitution effects cannot be reduced to chemical pressure effects only. Nevertheless, when the magnetic phase diagrams of both hydrostatic pressure and substitution are compared, we find a common critical lattice constant $c=5.78\phantom{\rule{0.16em}{0ex}}\AA{}$ where the ferromagnetic ordering is suppressed in both studies.

Superconductivity near the (2+1)-Dimensional Ferromagnetic Quantum Critical Point

We utilize both analytical and numerical methods to study the superconducting transition temperature T c near a fermionic quantum critical point (QCP) using a model constructed by Xu et al. [Phys. Rev. X 7, 031059 (2017)] as an example. In this model, the bosonic critical fluctuation plays the role of pairing glue for the Cooper pairs, and we use a Bardeen–Cooper–Schrieffer-type mean-field theory to estimate T c. We further argue that the T c computed from the BCS theory approximates a pseudogap temperature T PG, instead of the Berezinskii–Kosterlitz–Thouless transition temperature T KT, which is confirmed by our determinant quantum Monte Carlo simulation. Moreover, due to the fact that electron density of state starts to deplete at T PG, the critical scaling of the underlying QCP is also affected below T PG. Thus, when studying the critical behavior of fermionic QCPs, we need to monitor that the temperature is above T PG instead of T KT. This was often ignored in previous studies.

Effect of chemical disorder on Griffiths phase in weak itinerant ferromagnetic Ni92−xCuxCr8 alloy

We report magnetic and thermal properties of Cu substituted Ni92−xCuxCr8 polycrystalline alloys close to their critical concentration (xc~18%), where ferromagnetic order disappears. From the detailed analysis of field and temperature dependent magnetization data weak itinerant ferromagnetic character has been identified for the compositions below xc. Spin-fluctuations theory using the Ginzburg–Landau formalism further revealed the contributions of spin fluctuations, which increase near xc. Specific heat data shows unusual low-temperature variation with an enhanced Sommerfeld coefficient and non Fermi-liquid behavior due to strong magnetic fluctuations near xc. The magnetization data and the linear term of the specific heat follow the theoretical predictions of a ferromagnetic quantum critical point within the experimental uncertainties. The exponent of the power-law M(H) ∝Hλ fits to low-temperature magnetic isotherms and its variation with composition indeed suggests a possibility of quantum Griffiths phase in these alloy compositions. Finally, this study shows that the Cu substituted Ni-Cr system shows Griffiths phase at critical point even after the reduction of disorder.

Hyperscaling analysis of a disorder-induced ferromagnetic quantum critical point in Ni1−xRhx with x=0.375

Here we report on hyperscaling analysis on thermodynamic measurements as a function of temperature and magnetic field for Ni$_{1-x}$Rh$_{x}$ with $x = 0.375$ where a ferromagnetic quantum critical point has been recently identified [Phys. Rev. Lett. $\textbf{124}$, 117203 (2020)]. The obtained critical exponents agree well with the theory proposed by Belitz, Kirkpatrick, and Vojta for disorder tuned quantum critical point in the preasymptotic region.

Dynamical exponent of a quantum critical itinerant ferromagnet: A Monte Carlo study

We consider the effect of the coupling between 2D quantum rotors near an XY ferromagnetic quantum critical point and spins of itinerant fermions. We analyze how this coupling affects the dynamics of rotors and the self-energy of fermions.A common belief is that near a $q=0$ ferromagnetic transition, fermions induce an $\Omega/q$ Landau damping of rotors (i.e., the dynamical critical exponent is $z=3$) and Landau overdamped rotors give rise to non-Fermi liquid fermionic self-energy $\Sigma\propto \omega^{2/3}$. This behavior has been confirmed in previous quantum Monte Carlo (QMC) studies.Here we show that for the XY case the behavior is different.We report the results of large scale quantum Monte Carlo simulations,which show that at small frequencies $z=2$ and $\Sigma\propto \omega^{1/2}$. We argue that the new behavior is associated with the fact that a fermionic spin is by itself not a conserved quantity due to spin-spin coupling to rotors, and a combination of self-energy and vertex corrections replaces $1/q$ in the Landau damping by a constant. We discuss the implication of these results to experiments.

CeAu2In4: A candidate of quasi-one-dimensional antiferromagnetic Kondo lattice* *Project supported by the National Natural Science Foundation of China (Grant Nos. 11774404 and 52088101), the National Key R&D Program of China (Grant No. 2017YF A0303100), and the Chinese Academy of Sciences through the Strategic Priority Research Program (Grant No. XDB33000000).

Needle-like single crystals of CeAu2In4 have been grown from In flux and characterized as a new candidate of quasi-one-dimensional Kondo lattice compound by crystallographic, magnetic, transport, and specific-heat measurements down to very low temperatures. We observe an antiferromagnetic transition at T N ≈ 0.9 K, a highly non-mean-field profile of the corresponding peak in specific heat, and a large Sommerfeld coefficient γ = 369 mJ⋅mol−1⋅K−2. The Kondo temperature T K is estimated to be 1.1 K, being low and comparable to T N. While Fermi liquid behavior is observed deep into the magnetically ordered phase, the Kadowaki–Woods ratio is much reduced relative to the expected value for Ce compounds with Kramers doublet ground state. Markedly, this feature shares striking similarities to that of the prototypical quasi-one-dimensional compounds YbNi4P2 and CeRh6Ge4 with tunable ferromagnetic quantum critical point. Given the shortest Ce–Ce distance along the needle direction, CeAu2In4 appears to be an interesting model system for exploring antiferromagnetic quantum critical behaviors in a quasi-one-dimensional Kondo lattice with enhanced quantum fluctuations.

Anisotropic c-f Hybridization in the Ferromagnetic Quantum Critical Metal CeRh_{6}Ge_{4}.

Heavy fermion compounds exhibiting a ferromagnetic quantum critical point have attracted considerable interest. Common to two known cases, i.e., CeRh_{6}Ge_{4} and YbNi_{4}P_{2}, is that the 4f moments reside along chains with a large interchain distance, exhibiting strong magnetic anisotropy that was proposed to be vital for the ferromagnetic quantum criticality. Here, we report an angle-resolved photoemission study on CeRh_{6}Ge_{4} in which we observe sharp momentum-dependent 4f bands and clear bending of the conduction bands near the Fermi level, indicating considerable hybridization between conduction and 4f electrons. The extracted hybridization strength is anisotropic in momentum space and is obviously stronger along the Ce chain direction.The hybridized 4f bands persist up to high temperatures, and the evolution of their intensity shows clear band dependence. Our results provide spectroscopic evidence for anisotropic hybridization between conduction and 4f electrons in CeRh_{6}Ge_{4}, which could be important for understanding the electronic origin of the ferromagnetic quantum criticality.

Localized 4f-electrons in the quantum critical heavy fermion ferromagnet CeRh6Ge4

Ferromagnetic quantum critical points were predicted to be prohibited in clean itinerant ferromagnetic systems, yet such a phenomenon was recently revealed in CeRh6Ge4, where the Curie temperature can be continuously suppressed to zero under a moderate hydrostatic pressure. Here we report the observation of quantum oscillations in CeRh6Ge4 from measurements using the cantilever and tunnel-diode oscillator methods in fields up to 45 T, clearly demonstrating that the ferromagnetic quantum criticality occurs in a clean system. In order to map the Fermi surface of CeRh6Ge4, we performed angle-dependent measurements of quantum oscillations at ambient pressure, and compared the results to density functional theory calculations. The results are consistent with the Ce 4f electrons remaining localized and not contributing to the Fermi surface, suggesting that localized ferromagnetism is a key factor for the occurrence of a ferromagnetic quantum critical point in CeRh6Ge4.

Avoided ferromagnetic quantum critical point in pressurized La5Co2Ge3

We present the pressure-temperature phase diagram ${\mathrm{La}}_{5}{\mathrm{Co}}_{2}{\mathrm{Ge}}_{3}$ up to $\ensuremath{\sim}5$ GPa, which was constructed from magnetization, resistivity, and specific heat measurements. At ambient pressure, ${\mathrm{La}}_{5}{\mathrm{Co}}_{2}{\mathrm{Ge}}_{3}$ is an itinerant ferromagnet with a Curie temperature ${T}_{\text{C}}\ensuremath{\sim}$ 4 K. Upon increasing pressure up to $\ensuremath{\sim}1.7$ GPa, ${T}_{\text{C}}$ is suppressed down to $\ensuremath{\sim}3$ K. Upon further increasing pressure, our results suggest that ${\mathrm{La}}_{5}{\mathrm{Co}}_{2}{\mathrm{Ge}}_{3}$ enters a different low-temperature ground state. The corresponding transition temperature ${T}^{*}$ has a nonmonotonic pressure dependence up to $\ensuremath{\sim}5$ GPa. Our results demonstrate that the ferromagnetic quantum critical point in ${\mathrm{La}}_{5}{\mathrm{Co}}_{2}{\mathrm{Ge}}_{3}$ is avoided by the appearance of a different, likely magnetically ordered, state that has an antiferromagnetic component.

Interaction-Induced Metallicity in a Two-Dimensional Disordered Non-Fermi Liquid.

The interplay of interactions and disorder in two-dimensional (2D) electron systems has actively been studied for decades. The paradigmatic approach involves starting with a clean Fermi liquid and perturbing the system with both disorder and interactions. Instead, we start with a clean non-Fermi liquid near a 2D ferromagnetic quantum critical point and consider the effects of disorder. In contrast with the disordered Fermi liquid, we find that our model does not suffer from runaway flows to strong coupling and the system has a marginally stable fixed point with perfect conduction.

Pressure-induced suppression of ferromagnetism in CePd2P2

The correlated electron material CePd$_2$P$_2$ crystallizes in the ThCr$_2$Si$_2$ structure and orders ferromagnetically at 29 K. Lai et al. [Phys. Rev. B 97, 224406 (2018)] found evidence for a ferromagnetic quantum critical point induced by chemical compression via substitution of Ni for Pd. However, disorder effects due to the chemical substitution interfere with a simple analysis of the possible critical behavior. In the present work, we examine the temperature - pressure - magnetic field phase diagram of single crystalline CePd$_2$P$_2$ to 25 GPa using a combination of resistivity, magnetic susceptibility, and x-ray diffraction measurements. We find that the ferromagnetism appears to be destroyed near 12 GPa, without any change in the crystal structure.

Identification of non-Fermi liquid fermionic self-energy from quantum Monte Carlo data

Quantum Monte Carlo (QMC) simulations of correlated electron systems provide unbiased information about system behavior at a quantum critical point (QCP) and can verify or disprove the existing theories of non-Fermi liquid (NFL) behavior at a QCP. However, simulations are carried out at a finite temperature, where quantum critical features are masked by finite-temperature effects. Here, we present a theoretical framework within which it is possible to separate thermal and quantum effects and extract the information about NFL physics at T = 0. We demonstrate our method for a specific example of 2D fermions near an Ising ferromagnetic QCP. We show that one can extract from QMC data the zero-temperature form of fermionic self-energy Σ(ω) even though the leading contribution to the self-energy comes from thermal effects. We find that the frequency dependence of Σ(ω) agrees well with the analytic form obtained within the Eliashberg theory of dynamical quantum criticality, and obeys ω2/3 scaling at low frequencies. Our results open up an avenue for QMC studies of quantum critical metals.

Simulating disordered quantum Ising chains via dense and sparse restricted Boltzmann machines.

In recent years, generative artificial neural networks based on restricted Boltzmann machines (RBMs) have been successfully employed as accurate and flexible variational wave functions for clean quantum many-body systems. In this article, we explore their use in simulations of disordered quantum Ising chains. The standard dense RBM with all-to-all interlayer connectivity is not particularly appropriate for large disordered systems, since in such systems one cannot exploit translational invariance to reduce the amount of parameters to be optimized. To circumvent this problem, we implement sparse RBMs, whereby the visible spins are connected only to a subset of local hidden neurons, thus reducing the amount of parameters. We assess the performance of sparse RBMs as a function of the range of the allowed connections, and we compare it with that of dense RBMs. Benchmark results are provided for two sign-problem-free Hamiltonians, namely pure and random quantum Ising chains. The RBM Ansätzes are trained using the unsupervised learning scheme based on projective quantum Monte Carlo (PQMC) algorithms. We find that the sparse connectivity facilitates the training process and allows sparse RBMs to outperform their dense counterparts. Furthermore, the use of sparse RBMs as guiding functions for PQMC simulations allows us to perform PQMC simulations at a reduced computational cost, avoiding possible biases due to finite random-walker populations. We obtain unbiased predictions for the ground-state energies and the magnetization profiles with fixed boundary conditions, at the ferromagnetic quantum critical point. The magnetization profiles agree with the Fisher-de Gennes scaling relation for conformally invariant systems, including the scaling dimension predicted by the renormalization-group analysis.