Antiferromagnetic Quantum Phase Transition Research Articles

Antiferromagnetism of CeCd0.67As2 existing deep inside the narrow gap semiconducting state

Single crystals of $R$Cd$_{0.67}$As$_2$ ($R$ = La and Ce) have been synthesized by high temperature ternary melt and their physical properties have been explored by means of magnetization, specific heat, electrical resistivity, Hall coefficient, and thermoelectric power measurements. $R$Cd$_{0.67}$As$_2$ compounds indicate a (structural) phase transition at high temperatures, accompanied by a remarkable increase of the electrical resistivity with an extremely low carrier concentration. CeCd$_{0.67}$As$_2$ exhibits a large magnetic anisotropy and an antiferromagnetic (AFM) order below $T_{N} = 4$~K. Magnetic susceptibility curves, together with magnetization isotherms and specific heat, are analyzed by the point charge model of crystalline electric field (CEF). In the paramagnetic state, the observed magnetic properties can be well explained by the CEF effects, implying that the 4$f$ moments remain localized. Electrical resistivity measurements, together with Hall resistivity and thermoelectric power, also suggest highly localized 4$f$ electrons, where Kondo contributions are negligible. The low temperature physical properties manifest strong magnetic field dependencies. For $H \perp c$, $T_{N}$ shifts to lower temperature as magnetic field increases, and eventually disappears at $H_{c} \sim 60$~ kOe. Inside the AFM state, three metamagnetic transitions are clearly evidenced from the magnetization isotherms. The RKKY interaction may be responsible for the AFM ordering in CeCd$_{0.67}$As$_2$, however it would have to be mediated by extremely low charge carriers. Although the AFM ordering temperature in CeCd$_{0.67}$As$_2$ can be continuously suppressed to zero, no AFM quantum phase transition is expected due to the lack of conduction electron clouds to screen the 4$f$ moments.

Quantum Phase Transition and Quantum Correlation in the Two-dimensional Honeycomb-bilayer Lattice Antiferromagnet

Quantum Phase Transition and Quantum Correlation in the Two-dimensional Honeycomb-bilayer Lattice Antiferromagnet

Modeling Unconventional Superconductivity at the Crossover between Strong and Weak Electronic Interactions.

High-temperature superconductivity emerges in many different quantum materials, often in regions of the phase diagram where the electronic kinetic energy is comparable to the electron-electron repulsion. Describing such intermediate-coupling regimes has proven challenging as standard perturbative approaches are inapplicable. Here, we employ quantum MonteCarlo methods to solve a multiband Hubbard model that does not suffer from the sign problem and in which only repulsive interband interactions are present. In contrast to previous sign-problem-free studies, we treat magnetic, superconducting, and charge degrees of freedom on an equal footing. We find an antiferromagnetic dome accompanied by a metal-to-insulator crossover line in the intermediate-coupling regime, with a smaller superconducting dome appearing in the metallic region. Across the antiferromagnetic dome, the magnetic fluctuations change from overdamped in the metallic region to propagating in the insulating region. Our findings shed new light on the intertwining between superconductivity, magnetism, and charge correlations in quantum materials.

Quantum Griffiths phase near an antiferromagnetic quantum critical point: Muon spin relaxation study of Ce(Cu1−xCox)2Ge2

The antiferromagnetic order in the heavy-fermion compound ${\mathrm{CeCu}}_{2}{\mathrm{Ge}}_{2}$ can be suppressed by Co-doping, and at critical composition ${x}_{c}=0.6$ (${T}_{N}\phantom{\rule{0.16em}{0ex}}\ensuremath{\rightarrow}0$ K) a quantum critical point has been observed. We have performed zero-field (ZF) and longitudinal-field muon spin relaxation ($\ensuremath{\mu}\mathrm{SR}$) measurements on polycrystalline samples of $\mathrm{Ce}{({\mathrm{Cu}}_{1\ensuremath{-}x}{\mathrm{Co}}_{x})}_{2}{\mathrm{Ge}}_{2}$ ($x=0,0.2,0.6,1$) over a temperature range of 100 mK to 10 K and in applied fields from 0 up to 3000 G. Above any ordering temperature, the muon relaxation spectra can be described by a Gaussian-Kubo-Toyabe times exponential line shape. Below the magnetic ordering temperature (i.e., for $x<0.6$), an additional Gaussian relaxation is observed. The zero-field muon relaxation rate suggests the presence of antiferromagnetic ordering below 4 and 0.8 K for $x=0$ and 0.2 samples, respectively. For $x=0.6$, the magnetic order is completely suppressed, and the quantum critical point is accompanied by non-Fermi-liquid behavior, manifested in the power-law divergence of exponential depolarization, i.e., $\ensuremath{\lambda}\phantom{\rule{0.16em}{0ex}}\ensuremath{\propto}\phantom{\rule{0.16em}{0ex}}{T}^{0.55}$. The relaxation rate of $x=0.6$ obeys the time-field scaling relation ${G}_{z}(t,H)={G}_{z}(t/{H}^{\ensuremath{\gamma}})$, which is considered to be a characteristic feature of quantum critical magnetic fluctuations. Furthermore, for $x=0.6$, the exponent of isotherm magnetization, $M\ensuremath{\sim}{H}^{\ensuremath{\eta}}$, and magnetization-field-temperature scaling is consistent with the ZF-$\ensuremath{\mu}\mathrm{SR}$ data. These results provide strong evidence for the formation of a quantum Griffiths phase near the antiferromagnetic quantum phase transition.

Evolution of charge order topology across a magnetic phase transition in cuprate superconductors

Charge order is now accepted as an integral constituent of cuprate high-temperature superconductors, one that is intimately related to other instabilities in the phase diagram including antiferromagnetism and superconductivity. Unlike nesting-induced Peierls-like density waves, the charge correlations in the CuO2 planes have been predicted to display a rich momentum space topology depending on the detailed fermiology of the system. However, to date charge order has only been observed along the high-symmetry Cu-O bond directions. Here, using resonant soft X-ray scattering, we investigate the evolution of the full momentum space topology of charge correlations in Ln2CuO4 (Ln=Nd, Pr) as a function of intrinsic electron doping. We report that, upon electron doping the parent Mott insulator, charge correlations first emerge in a hitherto-unobserved form, with full (Cinf) rotational symmetry in momentum-space. At higher doping levels, the orientation of charge correlations is sharply locked to the Cu-O bond high-symmetry directions, restoring a more conventional bidirectional charge order with enhanced correlation lengths. Through charge susceptibility calculations, we closely reproduce the drastic evolution in the topology of charge correlations across an antiferromagnetic quantum phase transition, highlighting the interplay between spin and charge degrees of freedom in electron-doped cuprates. Finally, using the established link between charge correlations and the underlying fermiology, we propose a revised phase diagram of Ln2CuO4 with a superconducting region extending toward the Mott limit.

Effect of the exchange interaction anisotropy on the magnetic quantum phase transitions in dimerized antiferromagnets

We present a theoretical description of a quantum phase transition in a dimerized antiferromagnet, induced by an external magnetic field. The description of such transitions is constructed by determining the minimum of the Lagrange function which depends on the parameters of the ground-state crystal wavefunction. We determine that during a crystal transition from the singlet state of the dimer to the state with a noncollinear spin orientation, an order-order type phase transition occurs. We show that in the case of a single-axis character of the exchange anisotropy, the location of the quantum phase transition critical point is affected by the spin-spin interactions inside the dimer. Additionally, analogous to the classical Néele antiferromagnets, single-axis type anisotropic spin-spin interactions between dimers, shift the point of the spin-flip transition from the noncollinear antiferromagnetic phase to the ferromagnetic phase.

Electronic in-plane symmetry breaking at field-tuned quantum criticality in CeRhIn5.

Electronic nematic materials are characterized by a lowered symmetry of the electronic system compared to the underlying lattice, in analogy to the directional alignment without translational order in nematic liquid crystals. Such nematic phases appear in the copper- and iron-based high-temperature superconductors, and their role in establishing superconductivity remains an open question. Nematicity may take an active part, cooperating or competing with superconductivity, or may appear accidentally in such systems. Here we present experimental evidence for a phase of fluctuating nematic character in a heavy-fermion superconductor, CeRhIn5 (ref. 5). We observe a magnetic-field-induced state in the vicinity of a field-tuned antiferromagnetic quantum critical point at Hc ≈ 50 tesla. This phase appears above an out-of-plane critical field H* ≈ 28 tesla and is characterized by a substantial in-plane resistivity anisotropy in the presence of a small in-plane field component. The in-plane symmetry breaking has little apparent connection to the underlying lattice, as evidenced by the small magnitude of the magnetostriction anomaly at H*. Furthermore, no anomalies appear in the magnetic torque, suggesting the absence of metamagnetism in this field range. The appearance of nematic behaviour in a prototypical heavy-fermion superconductor highlights the interrelation of nematicity and unconventional superconductivity, suggesting nematicity to be common among correlated materials.

Holographic model for antiferromagnetic quantum phase transition induced by magnetic field

We propose a gravity dual of antiferromagnetic quantum phase transition induced by magnetic field and study the critical behavior around the quantum critical point. It turns out that the boundary critical theory is a strong coupling theory with dynamic exponent $z=2$ and that the hyperscaling law is violated and logarithmic corrections appear near the quantum critical point. Some novel scaling relations are predicated, which can be tested by experiment data in the future. We also make some comparison with experimental data on low-dimensional magnets ${\mathrm{BiCoPO}}_{5}$ and pyrochlores ${\mathrm{Er}}_{2\ensuremath{-}2x}{\mathrm{Y}}_{2x}{\mathrm{Ti}}_{2}{\mathrm{O}}_{7}$.

Holographic antiferromagnetic quantum criticality andAdS2scaling limit

A holographic description on the antiferromagnetic quantum phase transition (QPT) induced by the magnetic field and the criticality in the vicinity of the quantum critical point have been investigated numerically recently. In this paper, we show that the properties of QPT in this holographic model are governed by a CFT dual to the emergent ${\mathrm{AdS}}_{2}$ in the IR region, which confirms that the dual boundary theory is a strong coupling theory with dynamic exponent $z=2$ and logarithmic corrections appearing. We also compare them with the results from the Hertz model by solving the RG equation at its upper critical dimension and with some experimental data from pyrochlores ${\mathrm{Er}}_{2\ensuremath{-}2x}{\mathrm{Y}}_{2x}{\mathrm{Ti}}_{2}{\mathrm{O}}_{7}$ and ${\mathrm{BiCoPO}}_{5}$.

Critical quasiparticles in single-impurity and lattice Kondo models

Quantum criticality in systems of local moments interacting with itinerant electrons has become an important and diverse field of research. Here we review recent results which concern (a) quantum phase transitions in single-impurity Kondo and Anderson models and (b) quantum phase transitions in heavy-fermion lattice models which involve critical quasiparticles. For (a) the focus will be on impurity models with a pseudogapped host density of states and their applications, e.g., in graphene and other Dirac materials, while (b) is devoted to strong-coupling behavior near antiferromagnetic quantum phase transitions, with potential applications in a variety of heavy-fermion metals.

Emergence of localized magnetic moments near antiferromagnetic quantum criticality

We revisit an antiferromagnetic quantum phase transition with $\mathbit{Q}=2{\mathbit{k}}_{F}$, where $\mathbit{Q}$ is an ordering wave vector and ${\mathbit{k}}_{F}$ is a Fermi momentum. Reformulating the Hertz-Moriya-Millis theory within the strong-coupling approach to diagonalize the spin-fermion coupling term and performing the scaling analysis for an effective-field theory with quantum corrections in the Eliashberg approximation, we propose an interacting fixed point for this antiferromagnetic quantum phase transition, where antiferromagnetic spin fluctuations become locally critical to interact with renormalized electrons. The emergence of local quantum criticality suggests a mechanism of $\ensuremath{\omega}/T$ scaling for antiferromagnetic quantum criticality, generally forbidden in the context of the Hertz-Moriya-Millis theory.

Quantum Quench in an Atomic One-Dimensional Ising Chain

We study nonequilibrium dynamics for an ensemble of tilted one-dimensional atomic Bose-Hubbard chains after a sudden quench to the vicinity of the transition point of the Ising paramagnetic to antiferromagnetic quantum phase transition. The quench results in coherent oscillations for the orientation of effective Ising spins, detected via oscillations in the number of doubly occupied lattice sites. We characterize the quench by varying the system parameters. We report significant modification of the tunneling rate induced by interactions and show clear evidence for collective effects in the oscillatory response.

Sign-Problem–Free Quantum Monte Carlo of the Onset of Antiferromagnetism in Metals

The quantum theory of antiferromagnetism in metals is necessary for our understanding of numerous intermetallic compounds of widespread interest. In these systems, a quantum critical point emerges as external parameters (such as chemical doping) are varied. Because of the strong coupling nature of this critical point and the "sign problem" plaguing numerical quantum Monte Carlo (QMC) methods, its theoretical understanding is still incomplete. Here, we show that the universal low-energy theory for the onset of antiferromagnetism in a metal can be realized in lattice models, which are free from the sign problem and hence can be simulated efficiently with QMC. Our simulations show Fermi surface reconstruction and unconventional spin-singlet superconductivity across the critical point.

Dzyaloshinsky-Moriya Interaction Estimated by AFMR of Kagome Like Substance Cu2O(SO4) Observed at 1.8K

Dolerophanite Cu2O(SO4) is one of model substances for S = 1/2 kagome like antiferromagnet. Although many X-ray diffraction studies have been performed on natural mineral Cu2O(SO4), little is known about its magnetic property. Therefore, the multi-frequency electron spin resonance (ESR) measurements of dolerophanite powder sample have been performed using pulsed magnetic fields up to 16 T in the frequency range from 50 GHz to 315 GHz in the temperature range from 1.8 K to 86 K Antiferromagnetic resonance (AFMR) has been observed below TN = 20 K, which is consistent with the previous magnetic susceptibility result by Asano et al. Moreover, the frequency-field relation at 1.8 K suggests typical easy-plane type AFMR with Dzyaloshinsky-Moriya (DM) interaction, which is also consistent with the weak ferromagnetism below TN suggested by Asano et al. As the estimation of DM interaction is very important to discuss the quantum phase transition in kagome antiferromagnet as suggested by Cépas et al. [2008, Phys. Rev. B 78 140405(R)], we have estimated the D term of DM interaction as 6.98 ± 0.01 K from our AFMR results.

Non-Fermi liquid transport and "universal" ratios in quantum Griffiths phases

We use the semi-classical Boltzmann equation to investigate transport properties such as electrical resistivity, thermal resistivity, thermopower, and the Peltier coefficient of disordered metals close to an antiferromagnetic quantum phase transition. In the quantum Griffiths phase, the electrons are scattered by spin-fluctuations in the rare regions. This leads to singular temperature dependencies not just at the quantum critical point, but in the entire Griffiths phase. We show that the resulting non-universal power-laws in transport properties are controlled by the same Griffiths exponent λ which governs the thermodynamics. λ takes the value zero at the quantum critical point and increases throughout the Griffiths phase. We also study some of the "universal" ratios commonly used to characterize Fermi-liquid behavior.

Critical quasiparticle theory applied to heavy fermion metals near an antiferromagnetic quantum phase transition

We use the recently developed critical quasiparticle theory to derive the scaling behavior associated with a quantum critical point in a correlated metal. This is applied to the magnetic-field induced quantum critical point observed in YbRh(2)Si(2), for which we also derive the critical behavior of the specific heat, resistivity, thermopower, magnetization and susceptibility, the Grüneisen coefficient, and the thermal expansion coefficient. The theory accounts very well for the available experimental results.

Comment on “Quantum phase transition in the four-spin exchange antiferromagnet”

In a recent paper [Phys. Rev. B 80, 174403 (2009)] Kotov et al. studied the paramagnetic-to-antiferromagnetic transition in the $J\text{\ensuremath{-}}Q$ model. Their findings were claimed to be in ``fairly good agreement'' with previous quantum Monte Carlo (QMC) results. In this Comment we show that the above claim is misleading and in reality their phase transition point is not only far from the corresponding QMC value but also lies in a region of parameter space not yet explored in the literature. We also show that their reference dimer state is unstable against formation of a plaquette condensate, which could in part explain the large fluctuations they found.

On the theory of the magnetization of dimerized magnets

To describe a quantum phase transition in a dimerized antiferromagnet, the formalism of the Landau theory of phase transitions has been applied. The energy of the ground state is minimized by varying the parameter of the mixing of the wavefunctions with different multiplicities. The critical behavior of the parameter of the wavefunction is responsible for the critical behavior of the observables.

Quantum phase transition in the four-spin exchange antiferromagnet

We study the $S=1/2$ Heisenberg antiferromagnet on a square lattice with nearest-neighbor and plaquette four-spin exchanges [introduced by A. W. Sandvik, Phys. Rev. Lett. 98, 227202 (2007).] This model undergoes a quantum phase transition from a spontaneously dimerized phase to N\'eel order at a critical coupling. We show that as the critical point is approached from the dimerized side, the system exhibits strong fluctuations in the dimer background, reflected in the presence of a low-energy singlet mode, with a simultaneous rise in the triplet quasiparticle density. We find that both singlet and triplet modes of high density condense at the transition, signaling restoration of lattice symmetry. In our approach, which goes beyond mean-field theory in terms of the triplet excitations, the transition appears sharp; however since our method breaks down near the critical point, we argue that we cannot make a definite conclusion regarding the order of the transition.

Analysis of the Antiferromagnetic Phase Transitions of the 2D Kondo Lattice

We study the antiferromagnetic quantum phase transition of a 2D Kondo-Heisenberg square lattice using the nonlinear sigma model. A renormalization group analysis of the competing Kondo-RKKY interaction is carried out to one-loop order in the expansion, and a new quantum critical point (QCP) strongly affected by Kondo fluctuations is found. Near this QCP, the spin-wave velocity scales logarithmically, i.e., breakdown of hydrodynamic behavior, and the spin wave is logarithmically frozen out. The renormalization group results also allow us to propose a new phase diagram near the antiferromagnetic fixed point of this 2D Kondo lattice model.