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DOE OSTI2023

The primordial black holes that disappeared: connections to dark matter and MHz-GHz gravitational Waves

In the post-LIGO era, there has been a lot of focus on primordial black holes (PBHs) heavier than ~10 15 g as potential dark matter (DM) candidates. We point out that the branch of the PBH family that disappeared — PBHs lighter than ~10 9 g that ostensibly Hawking evaporated away in the early Universe — also constitute an interesting frontier for DM physics. Hawking evaporation itself serves as a portal through which such PBHs can illuminate new physics, for example by emitting dark sector particles. Here, taking a simple DM scalar singlet model as a template, we compute the abundance and mass of PBHs that could have provided, by Hawking evaporation, the correct DM relic density. We consider two classes of such PBHs: those originating from curvature perturbations generated by inflation, and those originating from false vacuum collapse during a first-order phase transition. For PBHs of both origins we compute the gravitational wave (GW) signals emanating from their formation stage: from second-order effects in the case of curvature perturbations, and from sound waves in the case of phase transitions. The GW signals have peak frequencies in the MHz-GHz range typical of such light PBHs. We compute the strength of such GWs compatible with the observed DM relic density, and find that the GW signal morphology can in principle allow one to distinguish between the two PBH formation histories.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

Quantum membrane phases in synthetic lattices of cold molecules or Rydberg atoms

Here, we calculate properties of dipolar interacting ultracold molecules or Rydberg atoms in a semisynthetic three-dimensional configuration—one synthetic dimension plus a two-dimensional real-space optical lattice or periodic microtrap array—using the stochastic Green's function quantum Monte Carlo method. Through a calculation of thermodynamic quantities and appropriate correlation functions, along with their finite-size scalings, we show that there is a second-order transition to a low-temperature phase in which two-dimensional “sheets” form in the synthetic dimension of internal rotational or electronic states of the molecules or Rydberg atoms, respectively. Simulations for different values of the interaction V, which acts between atoms or molecules that are adjacent both in real and synthetic space, allow us to compute a phase diagram. We find a finite-temperature transition at sufficiently large V as well as a quantum phase transition—a critical value V c below which the transition temperature vanishes.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2024

Origin of spin-driven ferroelectricity and effect of external pressure on the complex magnetism of the 6⁢ H perovskite Ba 3 ⁢Ho⁢Ru 2⁢ O 9

The compound Ba 3 HoRu 2 O 9 magnetically orders at 50 K (T N1 ), followed by another complex magnetic ordering at 10.2 K (T N2 ). The second magnetic phase transition was characterized by the coexistence of two competing magnetic ground states associated with two different magnetic wave vectors (K 1 = 0.5 0 0 and K 2 = 0.25 0.25 0). The multiferroicity and magnetoelectric coupling were predicted below T N2 in these 4d-based materials. Here, in this work, we have discussed the origin of spin-driven ferroelectricity, which is not known yet, and the nature of magnetoelectric domains. We have investigated the compound through time-of-flight neutron diffraction, synchrotron x-ray diffraction (XRD), ac susceptibility, frequency-dependent complex dielectric spectroscopy, and dc magnetization under external pressure. We have demonstrated that the noncollinear structure involving two different magnetic ions, Ru (4d) and Ho (4f), breaks the spatial inversion symmetry via inverse Dzyaloshinskii-Moriya (DM) interaction through strong 4d-4f magnetic correlation, which shifts the oxygen atoms and results in nonzero polarization. Such an observation of inverse DM interaction from two different magnetic ions which cause ferroelectricity is rarely observed. The stronger spin-orbit coupling of 4d orbital might play a major role in creating DM interaction of noncollinear spins. We have systematically studied the spin and dipolar dynamics, which exhibit intriguing behavior with shorter coherence lengths of second magnetic phase associated with the k 2 wave vector. The results manifest the development of finite-size magnetoelectric domains instead of true long-range ordering, which justifies the experimentally obtained low value of ferroelectric polarization. The lattice parameters and volume show a sharp anomaly at T N2 obtained by analyzing the temperature-dependence XRD, which is consistent with the ferroelectric transition, predicting a noncentrosymmetric space group, $P\bar{6}2c$, for this compound. Furthermore, we have investigated the effect of external pressure on this complex magnetism. The result reveals an enhancement of ordering temperature by the application of external pressure (~1.6 K/GPa). The external pressure might favor stabilizing the magnetic ground state associated with second magnetic phase. Our study shows an unconventional mechanism of spin-driven ferroelectricity involving inverse DM interaction between Ru (4d) and Ho (4f) magnetic ions due to strong 4d-4f cross coupling.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2026

Universal CMB 𝐵-mode spectrum from early causal tensor sources

Many early Universe scenarios predict postinflationary tensor perturbations from causality-limited, subhorizon sources. While the microphysical details may be different, as long as these sources are bounded in duration and correlation length, their tensor power spectra exhibit a universal scaling behavior at small wave number: 𝒫 ℎ ⁡(𝑘)∝𝑘 3 , corresponding to white noise on superhorizon scales at the time of production. If these early causal tensor sources (ECTs) exclusively produce gravitational waves before redshift 𝑧 ∼10 5 , this scaling is realized on all of the scales observed in the CMB, and thus yields a universal multipole distribution for the 𝐵-mode angular power spectrum. Unlike the scale-invariant distributions of inflationary 𝐵 modes, ECTs generically predict enhanced power on small scales and suppressed power on large scales, which allows these source classes to be distinguished given measurements over a sufficient range of angular scales. In this paper, we introduce a unified framework for characterizing ECTs and demonstrate how their universal infrared scaling manifests in low-frequency observables, including CMB 𝐵 modes and stochastic gravitational wave spectral densities. We illustrate this mapping with representative case studies of this universality class involving first-order phase transitions, topological defects, and enhanced scalar perturbations, which source tensor modes at second order in perturbation theory.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2023

Theory of criticality for quantum ferroelectric metals

A variety of compounds, for example, doped paraelectrics and polar metals, exhibit both ferroelectricity and correlated electronic phenomena such as low-density superconductivity and anomalous transport. Characterizing such properties is tied to understanding the quantum dynamics of inversion symmetry breaking in the presence of itinerant electrons. Here, we present a comprehensive analysis of the properties of a metal near a quantum critical transition to a ferroelectric state, in both two and three dimensions. In this study, starting from a minimal model of electrons coupled to a transverse polar phonon via a Rashba-type spin-orbit interaction, we compute the dynamical response of both electrons and phonons. We find that the system can evince both Fermi and non-Fermi liquid phases, as well as enhanced pairing in both singlet and triplet channels. Furthermore, we systematically compute corrections to one-loop theory and find a tendency to quantum order-by-disorder, leading to a phase diagram that can include second-order, first-order, and finite-momentum phase transitions. Finally, we show that the entire phase diagram can be controlled via application of external strain, either compressive or volume-preserving. Our results provide a map of the dynamical and thermodynamical phase space of quantum ferroelectic metals, which can serve in characterizing existing materials and in seeking applications for quantum technologies.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

Ferroelectric phase-transition frustration near a tricritical composition point

Phase transition describes a mutational behavior of matter states at a critical transition temperature or external field. Despite the phase-transition orders are well sorted by classic thermodynamic theory, ambiguous situations interposed between the first- and second-order transitions were exposed one after another. Here, we report discovery of phase-transition frustration near a tricritical composition point in ferroelectric Pb(Zr 1-x Ti x )O 3 . Our multi-scale transmission electron microscopy characterization reveals a number of geometrically frustrated microstructure features such as self-assembled hierarchical domain structure, degeneracy of mesoscale domain tetragonality and decoupled polarization-strain relationship. Associated with deviation from the classic mean-field theory, dielectric critical exponent anomalies and temperature dependent birefringence data unveil that the frustrated transition order stems from intricate competition of short-range polar orders and their decoupling to long-range lattice deformation. With supports from effective Hamiltonian Monte Carlo simulations, our findings point out a potentially universal mechanism to comprehend the abnormal critical phenomena occurring in phase-transition materials.

42 ENGINEERING↗

DOE OSTI2020

Ca 2 MnO 4 structural path: Following the negative thermal expansion at the local scale

The oxygen octahedral rotations in Ca 2 MnO 4 , the first member of the CaO(CaMnO 3 )n Ruddlesden-Popper family, is probed through a set of complementary techniques, including temperature-dependent neutron and x-ray diffraction, combined with local probe studies and ab initio calculations. Here we demonstrate the enhancement of the uniaxial negative thermal expansion coefficient from -1.26 ± 0.25 to -21 ± 1.8 ppm/K at the second order I4 1 /acd to I4/mmm structural phase transition, providing direct evidence for the corkscrew atomic mechanism. We establish, also, that the predicted I4/mmm high symmetry is attained around 1050 K. At lower temperatures, within the 10–1000 K temperature range, our first-principles calculations and detailed analysis of the Ca local environment reveals that the reported Aba2 structural phase, coexisting with the I4 1 /acd one, cannot describe correctly this compound. On the other hand, our data allow for the coexistence of the locally identical I4 1 /acd and Acam structural phases.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

NASA NTRS1988

Star formation via the phase transition of an adiabatic gas

An analytic model based on a second-order accurate global virial analysis is used to describe two stable equilibrium states for rotating gas clouds: a pressure-supported, diffuse state and a rotationally supported, compact state. Diffuse and compact equilibrium sequences are identified along which slow, secular evolution of a gas cloud can occur. A virial analysis provides analytic expressions for the limiting masses of gas clouds at points of dynamical instability. The minimum mass below which external triggers of any amplitude cannot effectively induce star formation is identified for adiabatic gas clouds. It is suggested that fluctuations in the ISM of some galaxies may actually cause star formation to proceed primarily via a phase transition, rather than via the classical Jeans instability.

Tohline, Joel E.↗

DOE OSTI2023

Vacancy-tuned magnetism in LaMn x Sb 2

The layered AMP 2 (A = alkali-earth or rare-earth atom, M = transition metal, P = Sb, Bi) compounds are widely studied for their rich magnetism and electronic structure topology. We provide a detailed characterization of the magnetic and transport properties of LaMn x Sb 2 , an understudied member of the AMP 2 family. LaMn x Sb 2 forms with intrinsic Mn vacancies, and we demonstrate that by varying the starting ratio of La, Mn, and Sb, we can synthetically control the Mn occupancy and produce single crystals with x = 0.74 – 0.97. Magnetization and transport measurements indicate LaMn x Sb 2 has a rich temperature-composition (T–x) magnetic phase diagram with physical properties strongly influenced by the Mn occupancy. LaMn x Sb 2 orders antiferromagnetically at T 1 = 130–180 K, where T 1 increases with x. Below T 1 , the T–x phase diagram is complicated. At high x, there is a second transition T 2 that decreases in temperature as x is lowered, vanishing below x ≤ 0.85. A third, first-order, transition T 3 is detected at x ≈ 0.92, and the transition temperature increases as x is lowered, crossing above T 2 near x ≈ 0.9. On moving below x < 0.79, here we find the crystal structure changes from the P 4/nmm arrangement to an I$\bar{4}$2m structure with partially ordered Mn vacancies. The change in crystal structure results in the sudden appearance of two new low-temperature phases and a crossover between regimes of negative and positive magnetoresistance when x ≤ 0.78. Finally, we provide powder neutron diffraction for x = 0.93, and find that the high-x compositions first adopt a G-type antiferromagnetic structure with the Mn moments aligned within the ab plane, which is followed upon further cooling by a second transition to a different, noncollinear structure where the moments are rotated within the basal plane. Our results demonstrate that LaMn x Sb 2 is a highly tunable material with six unique magnetically ordered phases, depending on T and x.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

Formation of short-range magnetic order and avoided ferromagnetic quantum criticality in pressurized LaCrGe 3

LaCrGe 3 has attracted attention as a paradigm example of the avoidance of ferromagnetic (FM) quantum criticality in an itinerant magnet. In this work, we combined thermodynamic (specific heat and thermal expansion), transport, x-ray, and neutron scattering as well as μSR measurements to obtain insights on the temperature-pressure phase diagram of LaCrGe 3 . Consistent with previous studies of the phase diagram by transport measurements, our thermodynamic data shows clearly that the FM transition at T FM changes its character from second order to first order when it is suppressed to low temperatures by pressure. In addition, previous studies demonstrated that for high pressures a new phase occurs below T 2 , which was proposed to be a long-wavelength antiferromagnetic state (AFM q ). In this paper, we provide evidence from our thermodynamic data that this phase transition is preceded by yet another phase transition at T 1 >T 2 . Our μSR data indicate that full magnetic volume fraction is only established below T 2 , but that this magnetism is characterized by a short correlation length. Within the experimental resolution, our neutron-scattering data is not able to identify any magnetic Bragg peaks. Overall, the microscopic magnetic data is therefore consistent with the formation of FM clusters in the proximity of the avoided FM quantum critical point in LaCrGe 3 . This conclusion is at odds with the previous proposal of AFM q order and raises questions on the role of disorder in this stochiometric compound.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2023

Strain-tuned quantum criticality in electronic Potts-nematic systems

Motivated by recent observations of threefold rotational symmetry breaking in twisted moiré systems, cold-atom optical lattices, quantum Hall systems, and triangular antiferromagnets, we phenomenologically investigate the strain-temperature phase diagram of the electronic 3-state Potts-nematic order. While in the absence of strain the quantum Potts-nematic transition is first-order, quantum critical points (QCP) emerge when uniaxial strain is applied, whose nature depends on whether the strain is compressive or tensile. In one case, the nematic amplitude jumps between two non-zero values while the nematic director remains pinned, leading to a symmetry-preserving metanematic transition that terminates at a quantum critical end-point. For the other type of strain, the nematic director unlocks from the strain direction and spontaneously breaks an in-plane twofold rotational symmetry, which in twisted moiré superlattices triggers an electric polarization. Such a piezoelectric transition changes from first to second-order upon increasing strain, resulting in a quantum tricritical point. Using a Hertz-Millis approach, we show that these QCPs share interesting similarities with the widely studied Ising-nematic QCP. The existence of three minima in the nematic action also leaves fingerprints in the strain-nematic hysteresis curves, which display multiple loops. At non-zero temperatures, because the upper critical dimension of the 3-state Potts model is smaller than three, the Potts-nematic transition is expected to remain first-order in 3D, but to change to second-order in 2D. As a result, the 2D strain-temperature phase diagram displays two first-order transition wings bounded by lines of critical end-points or tricritical points, reminiscent of the phase diagram of metallic ferromagnets. Furthermore, we discuss how our results can be used to unambiguously identify spontaneous Potts-nematic order.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2025

Asymmetry of the Ferroelectric Phase Transition in BaTiO 3

Symmetry changes during phase transformations fundamentally determine the behavior of thermodynamic systems, governing phenomena as diverse as water evaporation, fermion condensation, and epidemic spreading. Phase transitions are conventionally divided into two classes, and this classification is typically assumed to remain invariant upon reversing the transition. Here, an asymmetric phase transformation is uncovered in the ferroelectric–paraelectric transition of single-crystal BaTiO 3 , a model system for first-order transitions. Under slow temperature variation (≤0.1 °C min −1 ), thermodynamic, dielectric, and domain-structure measurements reveal that the ferroelectric-to-paraelectric transition exhibits latent heat, phase coexistence, and a discontinuous order parameter, while these signatures are absent upon cooling. Complementary phase-field simulations demonstrate similar behavior, attributing it to distinct elastic strain energy accumulation and release during heating and cooling. These findings reveal a first-order character upon heating but a second-order-like behavior upon cooling, challenging the conventional paradigm of symmetric phase-transition classification and suggesting new possibilities for ferroelectric-based energy storage.

Hershkovitz, Asaf [Technion-Israel Institute of Te↗

DOE OSTI2021

Quantum phase transitions in long-range interacting hyperuniform spin chains in a transverse field

Hyperuniform states of matter are characterized by anomalous suppression of long-wavelength density fluctuations. While most of the interesting cases of disordered hyperuniformity are provided by complex many-body systems such as liquids or amorphous solids, classical spin chains with certain long-range interactions have been shown to demonstrate the same phenomenon. Such spin-chain systems are ideal models for exploring the effects of quantum mechanics on hyperuniformity. It is well-known that the transverse field Ising model shows a quantum phase transition (QPT) at zero temperature. Under the quantum effects of a transverse magnetic field, classical hyperuniform spin chains are expected to lose their hyperuniformity. High-precision simulations of these cases are complicated because of the presence of highly nontrivial long-range interactions. We perform an extensive analysis of these systems using density matrix renormalization group simulations to study the possibilities of phase transitions and the mechanism by which they lose hyperuniformity. Even for a spin chain of length 30, we see discontinuous changes in properties like the “τ order metric” of the ground state, the measure of hyperuniformity, and the second cumulant of the total magnetization along the x-direction, all suggestive of first-order QPTs. An interesting feature of the phase transitions in these disordered hyperuniform spin chains is that, depending on the parameter values, the presence of a transverse magnetic field may lead remarkably to an increase in the order of the ground state as measured by the “τ order metric,” even if hyperuniformity is lost. Therefore, it would be possible to design materials to target specific novel quantum behaviors in the presence of a transverse magnetic field. Our numerical investigations suggest that these spin chains can show no more than two QPTs. We further analyze the long-range interacting spin chains via the Jordan-Wigner mapping onto a system of spinless fermions, showing that under the pairwise-interaction approximation and a mean-field treatment, there can be at most two quantum phase transitions. Here, based on these numerical and theoretical explorations, we conjecture that for spin chains with long-range pair interactions that have convergent cosine transforms, there can be a maximum of two quantum phase transitions at zero temperature.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

QCD Equation of State and Phase Diagram from Holographic Black Holes

By using the AdS/CFT correspondence, we construct an Einstein-Maxwell-Dilaton model to map the thermodynamics of strongly interacting matter. The holographic model, constrained to reproduce the lattice QCD equation of state at zero baryon chemical potential, predicts a critical end point and a first order phase transition line. We also obtain the equation of state of the model for a large region of the phase diagram. We characterize the crossover transition region by two lines, one associated to the inflection of the second order baryon susceptibility, and another one associated to the minimum of the square of the speed of sound along trajectories of constant entropy per baryon number. We observe that both lines merge at the critical point.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

NASA NTRS1973

Certain characteristics and capture regions of nonlinear vibrating systems

Free vibrations of a system and vibrations which are multiples of them in frequency are discussed. The corresponding periodic forced vibrations of the type n/m (n is the number of periods of disturbance between periods of movement and m is the number of periods of movement in one period of disturbance), generated by a harmonic or close to harmonic disturbance, are propagated close to the corresponding curves of the free vibrations and their frequency multiples. It has been proposed that investigation of transitional modes of motion and capture regions be carried out by precise methods in phase space, with the least number of coordinates. Thus, for example, for nonautonomous second order equations (for example, the Duffing equations), in place of three variables (coordinates, velocity, phases), it is proposed to use two: velocity during transition of the coordinate through zero and phase.

Ragulskene, V. L.↗

DOE OSTI2022

Orbital-induced crossover of the Fulde-Ferrell-Larkin-Ovchinnikov phase into Abrikosov-like states.

The Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state can emerge in superconductors for which the orbital critical field exceeds the Pauli limit. Here, we present angular-resolved specific-heat data of the quasi-two-dimensional organic superconductor ??-(ET)2Cu(NCS )2 , with a focus on high fields in the regime of the FFLO transition. For an increasing out-of-plane tilt of the applied magnetic field, which leads to an increase of orbital contributions, we found that the nature of the superconducting transition changes from second to first order and that a further transition appears within the high-field superconducting phase. However, the superconducting state above the Pauli limit is stable for field tilt of several degrees. Since any finite perpendicular component of the magnetic field necessarily leads to quantization of the orbital motion, the resulting vortex lattice states compete with the modulated order parameter of the FFLO state leading to complex high-field superconducting phases. By solving the linearized self-consistency equation within weak-coupling BCS theory, we show that our results are clear experimental evidence of an orbital-induced transformation of the FFLO order parameter into Abrikosov-like states of higher Landau levels.

Kotte, Tommy↗

DOE OSTI2021

Pressure-induced order–disorder transitions in β-In 2 S 3 : an experimental and theoretical study of structural and vibrational properties

We report this joint experimental and theoretical study of the structural and vibrational properties of β-In 2 S 3 upon compression shows that this tetragonal defect spinel undergoes two reversible pressure-induced order–disorder transitions up to 20 GPa. We propose that the first high-pressure phase above 5.0 GPa has the cubic defect spinel structure of α-In 2 S 3 and the second high-pressure phase ($\phi$-In 2 S 3 ) above 10.5 GPa has a defect α-NaFeO 2 -type (R$\bar{3}$) structure. This phase, related to the NaCl structure, has not been previously observed in spinels under compression and is related to both the tetradymite structure of topological insulators and to the defect LiTiO 2 phase observed at high pressure in other thiospinels. Structural characterization of the three phases shows that α-In 2 S 3 is softer than β-In 2 S 3 while $\phi$-In 2 S 3 is harder than β-In 2 S 3 . Vibrational characterization of the three phases is also provided, and their Raman-active modes are tentatively assigned. Our work shows that the metastable α phase of In 2 S 3 can be accessed not only by high temperature or varying composition, but also by high pressure. On top of that, the pressure-induced β–α–$\phi$ sequence of phase transitions evidences that β-In 2 S 3 , a B III 2 X V 3 compound with an intriguing structure typical of A II B III 2 X VI 4 compounds (intermediate between thiospinels and ordered-vacancy compounds) undergoes: (i) a first phase transition at ambient pressure to a disordered spinel-type structure (α-In 2 S 3 ), isostructural with those found at high pressure and high temperature in other B III 2 X V 3 compounds; and (ii) a second phase transition to the defect α-NaFeO 2 -type structure ($\phi$-In 2 S 3 ), a distorted NaCl-type structure that is related to the defect NaCl phase found at high pressure in A II B III 2 X VI 4 ordered-vacancy compounds and to the defect LiTiO 2 -type phase found at high pressure in A II B III 2 X VI 4 thiospinels. This result shows that In 2 S 3 (with its intrinsic vacancies) has a similar pressure behaviour to thiospinels and ordered-vacancy compounds of the A II B III 2 X VI 4 family, making β-In 2 S 3 the union link between such families of compounds and showing that group-13 thiospinels have more in common with ordered-vacancy compounds than with oxospinels and thiospinels with transition metals.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1980

Phase transitions in the ordered compound TiAl and in alloys having it as a base

The combined effect of alloying and heat treatment on the order-disorder transition in TiAl of stoichiometric composition was investigated. It is concluded from the data obtained that the TiAl 1 to TiAl 2 transition is a phase transition of the second kind. A phase transition was observed in TiAl of equiatomic composition in the 450-550 C temperature range. The introduction of niobium into the ordered compound TiAl of stoichiometric composition, instead of titanium or aluminum atoms, leads to partial softening. In this case, the effect of niobium atoms on softening of the alloys was greater when the niobium was introduced in place of aluminum atoms.

Zelenkov, I. A.↗