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Nematic antiferromagnetism and deconfined criticality from the interplay between electron-phonon and electron-electron interactions

Systems with strong electron-phonon couplings typically exhibit various forms of charge order, while strong electron-electron interactions lead to magnetism. In this work, we use determinant quantum Monte Carlo calculations to solve a model on a square lattice with a caricature of these interactions. In the limit where electron-electron interactions dominate it has antiferromagnetic order, while where electron-phonon coupling dominates there is columnar valence-bond-solid (VBS) order. We find an intervening phase that hosts coexisting nematic and antiferromagnetic orders. We have also found evidence of a Landau-forbidden continuous quantum phase transition with an emergent O(4) symmetry between the VBS and the nematic antiferromagnetic phases.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Tensor renormalization group approach to the $O(2)$ models via symmetry-twisted partition functions

We investigate critical phenomena in the $O(2)$ models using symmetry-twisted partition functions that can be efficiently computed within the tensor renormalization group framework. We first demonstrate, taking the three-dimensional model as an example, that symmetry-twisted partition functions detect the spontaneous breaking of global continuous symmetry. We then consider the same model in two dimensions, where the Berezinskii--Kosterlitz--Thouless (BKT) transition occurs. Since symmetry-twisted partition functions directly provide the helicity modulus at a finite twist angle, we determine the BKT transition point. These results are presented based on Ref.~\cite{Akiyama:2026dzg}. Finally, in addition to the original paper~\cite{Akiyama:2026dzg}, we apply this approach to the two-dimensional generalized $O(2)$ model and confirm that it successfully identifies the phase transitions between the ferromagnetic and nematic phases, as well as between the nematic and paramagnetic phases.

Akiyama, Shinichiro [Tsukuba U., CCS; Tokyo U., IC↗

Competing magnetic orders in quantum critical Sr 3 Ru 2 O 7

We investigated Sr 3 RuO 7 , a quantum critical metal that shows a metamagnetic quantum phase transition and electronic nematicity, through density functional calculations. These predict a ferromagnetic ground state in contrast to the experimentally observed paramagnetism, raising the question of competing magnetic states and associated fluctuations that may suppress magnetic order. We did a search to identify such low-energy antiferromagnetically ordered metastable states. We find that the lowest-energy antiferromagnetic state has a striped order. This corresponds to the E-type order that has been shown to be induced by Mn alloying. We also note significant transport anisotropy in this E-type ordered state. Furthermore, these results are discussed in relation to experimental observations.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Surface tension-driven convection phenomena

The techniques for measuring surface tension-driven flow are reported. In addition to the fairly standard crossed beam LDV method, methods using ripplon scattering which do not require seeding of the fluid were developed. These methods can be used to determine thermophysical properties of the surface, such as surface tension, viscosity, and local temperature. This technique was utilized to observe the change in surface tension associated with the nematic to isotropic phase transition of para-azoxydianisole at 134 C. The ripplon scattering methods become difficult for surface velocities below 1 mm/sec because of the overlapping spectra. Careful analysis procedures could extend this to smaller flows, but the more conventional LDV techniques with seeded flows are the method of choice for slow flows.

Mann, J. A., Jr.↗

Quantum spin nematic phase in a square-lattice iridate

Spin nematic is a magnetic analogue of classical liquid crystals, a fourth state of matter exhibiting characteristics of both liquid and solid. Particularly intriguing is a valence-bond spin nematic, in which spins are quantum entangled to form a multipolar order without breaking time-reversal symmetry, but its unambiguous experimental realization remains elusive. Here, in this study, we establish a spin nematic phase in the square-lattice iridate Sr 2 IrO 4 , which approximately realizes a pseudospin one-half Heisenberg antiferromagnet in the strong spin-orbit coupling limit. Upon cooling, the transition into the spin nematic phase at T C approximate to 263 K is marked by a divergence in the static spin quadrupole susceptibility extracted from our Raman spectra and concomitant emergence of a collective mode associated with the spontaneous breaking of rotational symmetries. The quadrupolar order persists in the antiferromagnetic phase below TN approximate to 230 K and becomes directly observable through its interference with the antiferromagnetic order in resonant X-ray diffraction, which allows us to uniquely determine its spatial structure. Further, we find using resonant inelastic X-ray scattering a complete breakdown of coherent magnon excitations at short-wavelength scales, suggesting a many-body quantum entanglement in the antiferromagnetic state. Taken together, our results reveal a quantum order underlying the Neel antiferromagnet that is widely believed to be intimately connected to the mechanism of high-temperature superconductivity. We establish a spin nematic phase in the square-lattice iridate Sr 2 IrO 4 and find a complete breakdown of coherent magnon excitations at short-wavelength scales, suggesting a many-body quantum entanglement in the antiferromagnetic state.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

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↗

Field-tuned ferroquadrupolar quantum phase transition in the insulator TmVO 4

We report results of low-temperature heat-capacity, magnetocaloric-effect, and neutron-diffraction measurements of TmVO 4 , an insulator that undergoes a continuous ferroquadrupolar phase transition associated with local partially filled 4 f orbitals of the thulium (Tm 3 + ) ions. The ferroquadrupolar transition, a realization of Ising nematicity, can be tuned to a quantum critical point by using a magnetic field oriented along the c axis of the tetragonal crystal lattice, which acts as an effective transverse field for the Ising-nematic order. In small magnetic fields, the thermal phase transition can be well described by using a semiclassical mean-field treatment of the transverse-field Ising model. However, in higher magnetic fields, closer to the field-tuned quantum phase transition, subtle deviations from this semiclassical behavior are observed, which are consistent with expectations of quantum fluctuations. Although the phase transition is driven by the local 4 f degrees of freedom, the crystal lattice still plays a crucial role, both in terms of mediating the interactions between the local quadrupoles and in determining the critical scaling exponents, even though the phase transition itself can be described via mean field. In particular, bilinear coupling of the nematic order parameter to acoustic phonons changes the spatial and temporal fluctuations of the former in a fundamental way, resulting in different critical behavior of the nematic transverse-field Ising model, as compared to the usual case of the magnetic transverse-field Ising model. Our results establish TmVO 4 as a model material and electronic nematicity as a paradigmatic example for quantum criticality in insulators.

36 MATERIALS SCIENCE↗

Absence of E 2 g Nematic Instability and Dominant A 1 g Response in the Kagome Metal CsV 3 Sb 5

Ever since the discovery of the charge density wave (CDW) transition in the kagome metal CsV 3 Sb 5 , the nature of its symmetry breaking has been under intense debate. While evidence suggests that the rotational symmetry is already broken at the CDW transition temperature ( T CDW ), an additional electronic nematic instability well below T CDW has been reported based on the diverging elastoresistivity coefficient in the anisotropic channel ( m E 2 g ). Verifying the existence of a nematic transition below T CDW is not only critical for establishing the correct description of the CDW order parameter, but also important for understanding low-temperature superconductivity. Here, we report elastoresistivity measurements of CsV 3 Sb 5 using three different techniques probing both isotropic and anisotropic symmetry channels. Contrary to previous reports, we find the anisotropic elastoresistivity coefficient m E 2 g is temperature independent, except for a step jump at T CDW . The absence of nematic fluctuations is further substantiated by measurements of the elastocaloric effect, which show no enhancement associated with nematic susceptibility. On the other hand, the symmetric elastoresistivity coefficient m A 1 g increases below T CDW , reaching a peak value of 90 at T * = 20 K . Our results strongly indicate that the phase transition at T * is not nematic in nature and the previously reported diverging elastoresistivity is due to the contamination from the A 1 g channel. Published by the American Physical Society 2024

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Quantitative relationship between structural orthorhombicity, shear modulus, and heat capacity anomaly of the nematic transition in iron-based superconductors

Electronic nematicity in iron pnictide materials has been extensively studied by various experimental techniques, yet its heat capacity anomaly at the phase transition has not been examined quantitatively. In this paper, we review the thermodynamic description of nematicity in Ba(Fe 1- x Cox) 2 As 2 using the Landau free energy, which defines the behavior of three thermodynamic quantities: the structural orthorhombicity that develops below the nematic transition, the softening shear modulus above the transition, and the discontinuous heat capacity at the transition. We derive a quantitative relationship between these three quantities, which is found to hold for a range of dopings. We report this result shows that the nematic transition is exceedingly well described by a mean-field model in the underdoped regime of the phase diagram.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Elastocaloric evidence for a multicomponent superconductor stabilized within the nematic state in Ba(Fe 1− x Co x ) 2 As 2

The iron-based high-$T_c$ superconductors (SCs) exhibit rich phase diagrams with intertwined phases, including magnetism, nematicity, and superconductivity. The superconducting $T_c$ in many of these materials is maximized in the regime of strong nematic fluctuations, making the role of nematicity in influencing the superconductivity a topic of intense research. Here, in this study, we use the AC elastocaloric effect (ECE) to map out the phase diagram of Ba(Fe 1− x Co x ) 2 As 2 near optimal doping. The ECE signature at $T_c$ on the overdoped side, where superconductivity condenses without any nematic order, is quantitatively consistent with other thermodynamic probes that indicate a single-component superconducting state. In contrast, on the slightly underdoped side, where superconductivity condenses within the nematic phase, ECE reveals a second thermodynamic transition proximate to and below $T_c$. We rule out magnetism and reentrant tetragonality as the origin of this transition and find that our observations strongly suggest a phase transition into a multicomponent superconducting state. This implies the existence of a subdominant pairing instability that competes strongly with the dominant $s^±$ instability. Our results highlight the significant role of nematic order in determining the pairing symmetry close to optimal doping in this extensively studied iron-based SC, while also demonstrating the power of ECE in uncovering strain-tuned phase diagrams of quantum materials.

Ghosh, Sayak [Stanford University, CA (United Stat↗

Multiple Charge Density Waves and Superconductivity Nucleation at Antiphase Domain Walls in the Nematic Pnictide Ba 1– x Sr x Ni 2 As 2

How superconductivity interacts with charge or nematic order is one of the great unresolved issues at the center of research in quantum materials. Ba 1– x Sr x Ni 2 As 2 (BSNA) is a charge ordered pnictide superconductor recently shown to exhibit a sixfold enhancement of superconductivity due to nematic fluctuations near a quantum phase transition (at $x_c$ = 0.7). The superconductivity is, however, anomalous, with the resistive transition for $0.4 < x < x_c$ occurring at a higher temperature than the specific heat anomaly. Here, using x-ray scattering, we discovered a new charge density wave (CDW) in BSNA in this composition range. The CDWis commensurate with a period of two lattice parameters, and is distinct from the two CDWs previously reported in this material. We argue that the anomalous transport behavior arises from heterogeneous superconductivity nucleating at antiphase domain walls in this CDW. We also present new data on the incommensurate CDW, previously identified as being unidirectional, showing that it is a rotationally symmetric “4$\textit{Q}$” state with $C_4$ symmetry. Our study establishes BSNA as a rare material containing three distinct CDWs, and an exciting test bed for studying coupling between CDW, nematic, and SC orders.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Growth of Nanocrystal Superlattices from Liquid Crystals

The growth of superlattices (SLs) made from self-assembled nanocrystals (NCs) is a powerful method for creating new materials and gaining insight into fundamental molecular dynamics. Previous explorations of NCSL syntheses have mostly compared them to crystallization. However, NCSL synthesis has not broadly shown cooling crystallization from saturated solutions as a reversible crystallization–dissolution process. We demonstrate the reversible growth of NCSLs by dispersing NCs in liquid crystal (LC) “smart solvents,” and harnessing the transitions between the isotropic and nematic phases of the LCs. The growth mode and morphology can be tuned. Furthernore, this process is a model platform for studying crystallization and demonstrates great potential in manufacturing NCSLs as colloidal crystals through liquid-phase epitaxy or colloidal synthesis.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

Spontaneous orbital polarization in the nematic phase of FeSe

The origin of nematicity in FeSe remains a critical outstanding question towards understanding unconventional superconductivity in proximity to nematic order. To understand what drives the nematicity, it is essential to determine which electronic degree of freedom admits a spontaneous order parameter independent from the structural distortion. In this work, we use X-ray linear dichroism at the Fe K pre-edge to measure the anisotropy of the 3d orbital occupation as a function of in situ applied stress and temperature across the nematic transition. Along with using X-ray diffraction to precisely quantify the strain state, we reveal a lattice-independent, spontaneously ordered orbital polarization within the nematic phase, as well as an orbital polarizability that diverges as the transition is approached from above. These results provide strong evidence that spontaneous orbital polarization serves as the primary order parameter of the nematic phase.

36 MATERIALS SCIENCE↗

Phase diagram of generalized XY model using the tensor renormalization group

We use the higher-order tensor renormalization group method to study the two-dimensional generalized XY model that admits integer and half-integer vortices. This model is the deformation of the classical XY model and has a rich phase structure consisting of nematic, ferromagnetic, and disordered phases and three transition lines belonging to the Berezinskii-Kosterlitz-Thouless and Ising class. We explore the model for a wide range of temperatures, T , and the deformation parameter, Δ , and compute specific heat along with integer and half-integer magnetic susceptibility, finding both Berezinskii-Kosterlitz-Thouless-like and Ising-like transitions and the region where they meet. Published by the American Physical Society 2024

2-dimensional systems↗

Discovery of spontaneous mesoscopic strain waves in nematic domains using dark-field x-ray microscopy

Electronic nematic order arises when correlated electrons spontaneously break the rotational symmetry of a crystal lattice. When electronic nematic order couples bilinearly to symmetry-breaking lattice strain, both appear together at a single ferroelastic phase transition, producing structural twin domains with distinct orientations of the nematic director. While the effects of applied strain on these domains are well established, the intrinsic behavior of spontaneous subdomain strain fields has remained unexplored. Here, we report the discovery of spontaneous mesoscopic strain waves within individual nematic domains of an iron-based superconductor, observed using dark-field x-ray microscopy (DFXM). Using this advanced full-field imaging technique, we visualize subdomain strain modulations emerging concurrently with nematic order. Elastic compatibility relations governing inhomogeneous strains provide a natural mechanism for the strain waves. Our findings reveal a broadly relevant form of strain self-organization and position DFXM as a powerful probe of the local interplay between lattice strain and electronic order.

36 MATERIALS SCIENCE↗

Hydrostatic and Uniaxial Pressure Tuning of Iron-Based Superconductors: Insights into Superconductivity, Magnetism, Nematicity, and Collapsed Tetragonal Transitions

Iron-based superconductors are well-known for their intriguing phase diagrams, which manifest a complex interplay of electronic, magnetic and structural degrees of freedom. Among the phase transitions observed are superconducting, magnetic, and several types of structural transitions, including a tetragonal-to-orthorhombic and a collapsed-tetragonal transition. In particular, the widely-observed tetragonal-to-orthorhombic transition is believed to be a result of an electronic order that is coupled to the crystalline lattice and is, thus, referred to asnematic transition. Nematicity is therefore a prominent feature of these materials, which signals the importance of the coupling of electronic and lattice properties. Correspondingly, these systems are particularly susceptible to tuning via pressure (hydrostatic, uniaxial, or some combination). We review efforts to probe the phase diagrams of pressure-tuned iron-based superconductors, with a strong focus on our own recent insights into the phase diagrams of several members of this mate-rial class under hydrostatic pressure. These studies on FeSe, Ba(Fe 1-x Co x ) 2 As 2 , Ca(Fe 1-x Co x ) 2 As 2 and CaK(Fe 1-x Ni x ) 4 As 4 were, to a significant extent, made possible by advances of what measurements can be adapted to the use under differing pressure environments. We point out the potential impact of these tools for the study of the wider class of strongly correlated electron systems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗