arXiv subjects

D. Belitz

Publications and source records attributed to D. Belitz.

At least 37 records · Page 2Linked to original sources

arXiv2019

Soft Modes and Nonanalyticities in a Clean Dirac Metal

We consider the effects of the electron-electron interaction in a clean Dirac metal, i.e., a Dirac system with the chemical potential not tuned to the Dirac point. We introduce the notion of a Dirac Fermi liquid (DFL) and discuss the soft two-particle excitations in such systems, which are qualitatively different from the corresponding excitations in a conventional, or Landau, Fermi liquid (LFL). These soft excitations lead to nonanalytic dependencies of observables, including the density of states, the spin susceptibility, and the specific heat, on the temperature, magnetic field, and wave number, which first appear at second order in the interaction. We determine and discuss the nature of these nonanalyticities in a DFL and compare them with the corresponding effects in a LFL. Our results are based on very general arguments regarding the existence and nature of the soft modes, and corroborated by explicit perturbative calculations. We also discuss their consequences for magnetic quantum phase transitions in Dirac metals.

cond-mat.str-el↗

arXiv2018

Anomalous Transport Behavior in Quantum Magnets

Transport behavior characterized by a low-temperature electrical resistivity that displays a power-law behavior $ρ(T\to 0) \propto T^s$ with an exponent $s<2$, is commonly observed in magnetic materials in both the magnetic and nonmagnetic phases. We give a pedagogical overview of this phenomenon that summarizes both the experimental situation and the state of its theoretical understanding. We also put it in context by drawing parallels with unusual power-law transport behavior in other systems.

cond-mat.str-el↗

arXiv2018

Generic non-Fermi-liquid behavior of the resistivity in magnets with ferromagnetic, helical, or skyrmionic order

The electrical resistivity of several relatively clean metallic ferromagnets, as well as the helimagnet MnSi, is commonly observed to exhibit non-Fermi-liquid behavior at low temperatures. This behavior, which is found in both ordered and disordered phases, and both near and away from the magnetic transition, remains a major unsolved problem. We derive and discuss three novel mechanisms underlying such behavior that are based on electron scattering mediated by the exchange of (1) ferromagnons or (2) skyrmionic fluctuations, both in conjunction with weak disorder, or (3) helimagnons in clean systems. Since the magnetic transition in weakly disordered sytems is generically discontinuous, static droplets of the ordered phase can exist within the disordered phase, making the mechanisms viable there as well. We compare our theoretical results with existing experimental ones and suggest additional experiments.

cond-mat.str-el↗

arXiv2017

Quantum triple point and quantum critical endpoints in metallic magnets

In low-temperature metallic magnets, ferromagnetic (FM) and antiferromagnetic (AFM) orders can exist in a single system in different parts of the phase diagram as a function of some control parameter. These phases can be adjacent, or exist concurrently, resulting in a phase transition between a FM phase and an AFM one, or between a phase of concurrent FM and AFM order and either of the pure phases. We show that universal quantum fluctuations qualitatively alter the known phase diagrams for classical magnets: They shrink the region of concurrent FM and AFM order, change various transitions from second to first order, and, in the presence of a magnetic field, lead to either a quantum triple point where the FM, AFM and paramagnetic phases coexist, or to a quantum critical end point.

cond-mat.str-el↗

arXiv2017

Spin dynamics of antiferromagnets in the presence of a homogeneous magnetization

We use general hydrodynamic equations to determine the long-wavelength spin excitations in isotropic antiferromagnets in the presence of a homogeneous magnetization. The latter may be induced, such as in antiferromagnets in an external magnetic field, or spontaneous, such as in ferrimagnetic or canted phases that are characterized by the coexistence of antiferromagnetic and ferromagnetic order. Depending on the physical situation, we find propagating spin waves that are gapped in some cases and gapless in others, diffusive modes, or relaxational modes. The excitation spectra turn out to be qualitatively different depending on whether or not the homogeneous magnetization is a conserved quantity. The results lay the foundation for a description of a variety of quantum phase transitions, including the transition from a ferromagnetic metal to an antiferromagnetic one, and the spin-flop transitions that are observed in some antiferromagnets. They also are crucial for incorporating weak-localization and Altshuler-Aronov effects into the descriptions of quantum phases in both clean and disordered magnetic metals.

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arXiv2016

Scaling Theory of a Compressibility-Driven Metal-Insulator Transition in a Two-Dimensional Electron Fluid

We present a scaling description of a metal-insulator transition in two-dimensional electron systems that is driven by a vanishing compressibility rather than a vanishing diffusion coefficient. A small set of basic assumptions leads to a consistent theoretical framework that is compatible with existing transport and compressibility measurements, and allows to make predictions for other observables. We also discuss connections between these ideas and other theories of transitions to an incompressible quantum fluid.

cond-mat.str-el↗

arXiv2016

Magnon-induced long-range correlations and their neutron-scattering signature in quantum magnets

We consider the coupling of the magnons in both quantum ferromagnets and antiferromagnets to the longitudinal order-parameter fluctuations, and the resulting nonanalytic behavior of the longitudinal susceptibility. In classical magnets it is well known that long-range correlations induced by the magnons lead to a singular wave-number dependence of the form $1/k^{4-d}$ in all dimensions 2<d<4, for both ferromagnets and antiferromagnets. At zero temperature we find a profound difference between the two cases. Consistent with naive power counting, the longitudinal susceptibility in a quantum antiferromagnet scales as $k^{d-3}$ for 1<d<3, whereas in a quantum ferromagnet the analogous result, $k^{d-2}$, is absent due to a zero scaling function. This absence of a nonanalyticity in the longitudinal susceptibility is due to the lack of magnon number fluctuations in the ground state of a quantum ferromagnet; correlation functions that are sensitive to other fluctuations do exhibit the behavior predicted by simple power counting. Also of interest is the dynamical behavior as expressed in the longitudinal part of the dynamical structure factor, which is directly measurable via neutron scattering. For both ferromagnets and antiferromagnets there is a logarithmic singularity at the magnon frequency with a prefactor that vanishes as $T\to 0$. In the antiferromagnetic case there also is a nonzero contribution at T=0 that is missing for ferromagnets. Magnon damping due to quenched disorder restores the expected scaling behavior of the longitudinal susceptibility in the ferromagnetic case; it scales as $k^{d-2}$ if the order parameter is not conserved, or as $k^d$ if it is. Detailed predictions are made for both two- and three-dimensional systems at both T=0 and in the limit of low temperatures, and the physics behind the various nonanalytic behaviors is discussed.

cond-mat.stat-mech↗

arXiv2016

The quantum ferromagnetic transition in a clean Kondo lattice is discontinuous

The Kondo-lattice model, which couples a lattice of localized magnetic moments to conduction electrons, is often used to describe heavy-fermion systems. Because of the interplay between Kondo physics and magnetic order it displays very complex behavior and is notoriously hard to solve. The ferromagnetic Kondo-lattice model, with a ferromagnetic coupling between the local moments, describes a phase transition from a paramagnetic phase to a ferromagnetic one as a function of either temperature or the ferromagnetic local-moment coupling. At zero temperature, this is a quantum phase transition that has received considerable attention. It has been theoretically described to be continuous, or second order. Here we show that this belief is mistaken; in the absence of quenched disorder the quantum phase transition is first order, in agreement with experiments, as is the corresponding transition in other metallic ferromagnets.

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arXiv2016

Droplet formation near first-order phase transitions: A mechanism for heterogeneity and phase separation away from the coexistence curve

Phase separation, i.e., the coexistence of two different phases, is observed in many systems away from the coexistence curve of a first-order transition, leading to a stable heterogeneous phase or region. Examples include various quantum ferromagnets, heavy-fermion systems, rare-earth nickelates, and others. These observations seem to violate basic notions of equilibrium thermodynamics, which state that phase separation can occur only on the coexistence curve. We show theoretically that quenched disorder allows for phase separation away from the coexistence curve even in equilibrium due to the existence of stable minority-phase droplets within the majority phase. Our scenario also answers a related question: How can a first-order transition remain sharp in the presence of quenched disorder without violating the rigorous lower bound $ν\geq 2/d$ for the correlation-length exponent? We discuss this scenario in the context of experimental results for a large variety of systems.

cond-mat.str-el↗

arXiv2015

Exponent relations at quantum phase transitions, with applications to metallic quantum ferromagnets

Relations between critical exponents, or scaling laws, at both continuous and discontinuous quantum phase transitions are derived and discussed. In general there are multiple dynamical exponents at these transitions, which complicates the scaling description. Some rigorous inequalities are derived, and the conditions needed for these inequalities to be equalities are discussed. New scaling laws involving the specific-heat exponents are derived and and contrasted with their counterparts at classical phase transitions. We also generalize the ideas of Fisher and Berker and others for applying (finite-size) scaling theory near a classical first-order transition to the quantum case. We then apply and illustrate all of these ideas by using the quantum ferromagnetic phase transition in metals as an explicit example. This transition is known to have multiple dynamical scaling exponents, and in general it is discontinuous in clean systems, but continuous in disordered ones. Furthermore, it displays many experimentally relevant crossover phenomena that can be described in terms of fixed points, originally discussed by Hertz, that ultimately become unstable asymptotically close to the transition and give way to the asymptotic fixed points. These fixed points provide a rich environment for illustrating the general scaling concepts and exponent relations. We also discuss the quantum-wing critical point at the tips of the tricritical wings associated with the discontinuous quantum ferromagnetic transition from a scaling point of view.

cond-mat.stat-mech↗

arXiv2015

Metallic Quantum Ferromagnets

This review gives an overview of the quantum phase transition (QPT) problem in metallic ferromagnets, discussing both experimental and theoretical aspects. These QPTs can be classified with respect to the presence and strength of quenched disorder: Clean systems generically show a discontinuous, or first-order, QPT from the ferromagnetic state to a paramagnetic one as a function of some control parameter, as predicted by theory. Disordered systems are much more complicated, depending on the disorder strength and the distance from the QPT. In many disordered materials the QPT is continuous, or second order, and Griffiths-phase effects coexist with QPT singularities near the transition. In other systems the transition from the ferromagnetic state at low temperatures is to a different type of long-range order, such as an antiferromagnetic or a spin-density-wave state. In still other materials a transition to a state with glass-like spin dynamics is suspected. The review provides a comprehensive discussion of the current understanding of these various transitions, and of the relation between experimental and theoretical developments.

cond-mat.str-el↗

arXiv2015

Quantum Correlations in Metals that Grow in Time and Space

We show that the correlations of electrons with a fixed energy in metals have very anomalous time and space dependences. Due to soft modes that exist in any Fermi liquid, combined with the incomplete screening of the Coulomb interaction at finite frequencies, the correlations in 2-d systems grow with time as $t^2$. In the presence of disorder, the spatial correlations grow as the distance squared. Similar, but in general weaker, effects are present in 3-d systems and in the absence of quenched disorder. We propose ways to experimentally measure these anomalous correlations.

cond-mat.str-el↗

arXiv2015

Third law of thermodynamics and the shape of the phase diagram for systems with a first-order quantum phase transition

The Third Law of Thermodynamics constrains the phase diagram of{systems with a first-order quantum phase transition. For zero conjugate field, the coexistence curve has an infinite slope at T=0. If a tricritical point exists at T>0, then the associated tricritical wings are perpendicular to the T=0 plane, but not to the zero-field plane. These results are based on the third law and basic thermodynamics only, and are completely general. As an explicit example we consider the ferromagnetic quantum phase transition in clean metals, where a first-order quantum phase transition is commonly observed.

cond-mat.stat-mech↗

arXiv2014

Pre-asymptotic critical behavior and effective exponents in disordered metallic quantum ferromagnets

We determine the pre-asymptotic critical behavior at the quantum ferromagnetic transition in strongly disordered metals. We find that it is given by effective power laws, in contrast to the previously analyzed asymptotic critical behavior, which is valid only in an unobservably small region. The consequences for analyzing experiments are discussed, in particular ways to distinguish between critical behavior and Griffiths-phase effects.

cond-mat.str-el↗

arXiv2014

Disorder dependence of the ferromagnetic quantum phase transition

We quantitatively discuss the influence of quenched disorder on the ferromagnetic quantum phase transition in metals, using a theory that describes the coupling of the magnetization to gapless fermionic excitations. In clean systems, the transition is first order below a tricritical temperature T_tc. Quenched disorder is predicted to suppress T_tc until it vanishes for residual resistivities rho_0 on the order of several microOhmcm for typical quantum ferromagnets. We discuss experiments that allow to distinguish the mechanism considered from other possible realizations of a first-order transition.

cond-mat.str-el↗

arXiv2014

Electronic relaxation rates in metallic ferromagnets

We show that the single-particle and transport relaxation rates in ferromagnetic metals, which determine the thermal and electrical conductivity, respectively, at asymptotically low temperature do not obey a power law as previously thought, but rather show an exponential temperature dependence. The reason is the splitting of the conduction band that inevitably results from a nonzero magnetization. At higher temperatures there is a sizable temperature window where the transport rate shows a T^2 temperature dependence, in accord with prior results. This window is separated from the asymptotic regime by a temperature scale that is estimated to range from tens of mK to tens of K for typical ferromagnets. We motivate and derive a very general effective theory for metallic magnets that we then use to derive these results. Comparisons with existing experiments are discussed, and predictions for future experiments at low temperatures are made.

cond-mat.str-el↗

arXiv2013

Nonanalyticities in a Strongly Correlated Fermi Liquid: Corrections to Scaling at the Fermi-Liquid Fixed Point

We use scaling and renormalization-group techniques to analyze the leading nonanalyticities in a Fermi liquid. We show that a physically motivated scaling hypothesis reproduce the results known from perturbation theory for the density of states, the density-of-states fluctuations, the specific heat, the spin susceptibility, and the nematic magnetic susceptibility. We also discuss the absence of nonanalytic terms in the density susceptibility. We then use a recent effective field theory for clean electron systems to derive the scaling hypothesis by means of renormalization-group techniques. This shows that the exponents (although not the prefactors) of the nonanalyticities that were previously derived by means of perturbative techniques are indeed exact, and can be understood as the leading corrections to scaling at the stable Fermi-liquid fixed point.

cond-mat.str-el↗

arXiv2012

Anomalous Density-of-States Fluctuations in Two-Dimensional Clean Metals

It is shown that density-of-states fluctuations, which can be interpreted as the order-parameter susceptibility χ_OP in a Fermi liquid, are anomalously strong as a result of the existence of Goldstone modes and associated strong fluctuations. In a 2-d system with a long-range Coulomb interaction, a suitably defined χ_OP diverges as 1/T^2 as a function of temperature in the limit of small wavenumber and frequency. In contrast, standard statistics suggest χ_OP = O(T), a discrepancy of three powers of T. The reasons behind this surprising prediction, as well as ways to observe it, are discussed.

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