The Casimir force between dielectric bodies is well-understood, but not the Casimir force inside a dielectric, in particular its renormalization. We develop and analyze a simple model for the Casimir forces inside a medium that is completely free of renormalization and show then how renormalization emerges. We consider a one-dimensional chain of point particles interacting with each other by scattering the zero-point fluctuations of the electromagnetic field confined to one dimension. We develop a fast, efficient algorithm for calculating the forces on each particle and apply it to study the macroscopic limit of infinitely many, infinitely weak scatterers. The force density converges for piecewise homogeneous media but diverges in inhomogeneous media, which would cause instant collapse in theory. We argue that short-range counterforces in the medium prevent this collapse in reality. Their effect appears as the renormalization of the Casimir stress in dielectrics. Our simple model also allows us to derive an elementary analog of the trace anomaly of quantum fields in curved space.

We revisit the intriguing magnetic behavior of the paradigmatic itinerant frustrated magnet $\mathrm{Sr}{\mathrm{Co}}_2{\mathrm{As}}_2$, which shows strong and competing magnetic fluctuations yet does not develop long-range magnetic order. By calculating the static spin susceptibility $\chi \left(\mathbf{q}\right)$ within a realistic 16-orbital Hubbard-Hund model, we determine the leading instability to be ferromagnetic (FM). We then explore the effect of doping and calculate the critical Hubbard interaction strength $U_c$ that is required for the development of magnetic order. We find that $U_c$ decreases under electron doping and with increasing Hund's coupling $J$, but increases rapidly under hole doping. This suggests that magnetic order could possibly emerge under electron doping but not under hole doping, which agrees with experimental findings. We map out the leading magnetic instability as a function of doping and Hund's coupling and find several antiferromagnetic phases in addition to FM. We also quantify the degree of itinerant frustration in the model and resolve the contributions of different orbitals to the magnetic susceptibility. Finally, we discuss the dynamic spin susceptibility $\chi (\mathbf{q},\omega )$ at finite frequencies, where we recover the anisotropy of the peaks at ${\mathbf{Q}}_{\pi }=(\pi ,0)$ and $(0,\pi )$ observed by inelastic neutron scattering that is associated with the phenomenon of itinerant magnetic frustration. By comparing results between theory and experiment, we conclude that the essential experimental features of doped ${\mathrm{SrCo}}_2{\mathrm{As}}_2$ are well captured by an itinerant Hubbard-Hund multiorbital model if one considers a small shift of the chemical potential towards hole doping.

The Li-Haldane correspondence [Phys. Rev. Lett. 101, 010504 (2008)] is often used to help identify wave functions of $(2+1)$-dimensional chiral topological phases (i.e., with nonzero chiral central charge) by studying low-lying entanglement spectra (ES) on long cylinders of finite circumference. Here we consider such ES of states [in fact, of wave functions of certain projected entangled pair states (PEPSs)] that are not chiral (i.e., having zero chiral central charge) but which strongly break time-reversal as well as reflection symmetry, while preserving their product, thus exhibiting the same symmetry properties as a chiral topological state. This leads to ES which have branches of both right- and left-moving chiralities, but with vastly different velocities. For circumferences much smaller than the inverse entanglement gap scale, the low-lying ES appear chiral in some topological sectors, and precisely follow the Li-Haldane state counting of a truly chiral phase. On its face, this could lead one to mistakenly identify the phase as chiral. However, by considering the ES in all possible sectors, one can observe distinct differences from a chiral phase. We explore this phenomenon in the setting of an SU(3) spin liquid PEPS studied by Kurečić et al. [Phys. Rev. B 99, 045116 (2019)], where the topologically trivial sector appeared to have the characteristic Li-Haldane counting of a chiral $\mathrm{SU}\left(3\right)$-level-one [$\mathrm{SU}{\left(3\right)}_1$] conformal field theory (CFT). In fact, the PEPS has $D\left({\mathbb{Z}}_3\right)$ topological order, with nine sectors. We compute the ES in minimally entangled states corresponding to all these sectors, which map to the nine anyon types of doubled $\mathrm{SU}\left(3\right)$-level-one Chern-Simons topological field theory. The state countings of the ES in all sectors are exactly consistent with our expectation: specifically, the ES contain representations of global SU(3) symmetry from the tensor products of the (lowest-lying) multiplet of primary states of a “high-velocity” chiral $\mathrm{SU}{\left(3\right)}_1$ CFT with the full content of a “low-velocity” chiral $\mathrm{SU}{\left(3\right)}_1$ CFT sector, a nonchiral structure beyond that observable in the topologically trivial sector of the ES.

We report the successful synthesis of a new $4d$-based polycrystalline inverse Heusler alloy ${\mathrm{Fe}}_2\mathrm{RuGe}$ by an arc melting process and have studied in detail its structural, magnetic and transport properties complemented with first-principles calculations. X-ray and neutron diffraction, extended x-ray absorption fine structure, and ${}^{57}\mathrm{Fe}$ Mössbauer spectroscopic studies confirm the single-phase nature of the system where the Fe and Ru atoms are randomly distributed in the $4c$ and $4d$ Wyckoff positions in a ratio close to 50:50. The formation of the disordered structure is also confirmed by the theoretical energy minimization calculation. Despite the random cross-site disorder of Fe and Ru atoms, magnetic measurements suggest not only a high Curie temperature of $\sim 860$ K, but also a large saturation magnetic moment $\sim 4.9{\mu }_B$ per formula unit at 5 K, considerably exceeding the theoretical limit (4 ${\mu }_B$ per formula unit) predicted by the Slater-Pauling rule. Only a few Fe-based inverse Heusler alloys are known to exhibit such high Curie temperatures. Neutron diffraction analysis coupled with the isothermal magnetization value indicates that the magnetic moments in ${\mathrm{Fe}}_2\mathrm{RuGe}$ are associated with Fe atoms only, which is also confirmed by Mössbauer spectrometry. Interestingly, in comparison to the cubic or hexagonal phase of the parent compound, ${\mathrm{Fe}}_3\mathrm{Ge}$, the Curie temperature of ${\mathrm{Fe}}_2\mathrm{RuGe}$ has increased significantly despite the substitution of the nonmagnetic yet isoelectronic element Ru in this structurally disordered compound. Our theoretical calculation reveals that the large Fe moment ($\sim 2.8{\mu }_B$/Fe) on the $4b$ site can be attributed to a charge transfer from this Fe site towards its Ru neighbors while a significant moment ($\sim 2{\mu }_B$/Fe) is kept on the other Fe sites. Instead of expected Slater-Pauling value of $4{\mu }_B$/f.u., the substantially increased observed total magnetic moment of $\sim 4.9{\mu }_B$/f.u. is due to these electron charge transfers, which have not been previously reported in other ferromagnetic Heusler systems.

Over the past few decades, tremendous efforts have been devoted to understanding self-duality at the quantum critical point, which enlarges the global symmetry and constrains the dynamics. A one-dimensional spin chain is an ideal platform for the theoretical investigation of these exotic phenomena, due to powerful simulation methods such as the density matrix renormalization group. Deconfined quantum criticality with self-duality at the critical point has been found in an extended short-range spin chain. In this work, we employ large-scale density matrix renormalization group simulations to investigate a critical spin chain with long-range power-law interaction $V\left(r\right)\sim 1/r^{\alpha }$. Remarkably, we reveal that the long-range interaction drives the original deconfined criticality towards a first-order phase transition as $\alpha$ decreases. More strikingly, the emergent self-duality leads to an enlarged symmetry and manifests at these first-order critical points. This discovery is reminiscent of self-duality protected multicritical points, and it provides an example of the critical line with generalized symmetry. Our work has far-reaching implications for ongoing experimental efforts in Rydberg atom quantum simulators.

Rhombohedral trilayer graphene (rTG) has recently emerged as a new playground for exploring flatband-induced exotic quantum phenomena and sparked considerable concern. However, the experimental accessing of local quantum behaviors such as the quantum confinement of flatband electrons in rTG has been highly limited so far. Here, using scanning tunneling microscopy and spectroscopy, we study the quantum confinement and interference of quasiparticles in rTG via Fabry-Pérot-like resonators. The resonators are formed by narrow rTG terraces with different geometries. In a narrow rectangular terrace (∼50-nm width) made by two parallel step edges, we observe quantum confined states, which can be accurately replicated by the Fabry-Pérot model. These confined states are highly governed by the transmission and scattering from the electronic states of adjacent graphene layers, leading to significant broadening and suppression of the flatband peak in rTG. The effective length of the flatband suppression is determined to be ∼15–30 nm for different step edges. Furthermore, we reveal the quasiparticle interference around two intersecting step edges, whose features can be well simulated by a developed Fabry-Pérot model. These findings not only uncover the fundamental properties of quasiparticle interference in confined rTG systems, but also provide important insight into the interactions between the flatband electrons of rTG and their surrounding environments.

We prove both analytically and numerically that the total angular momentum of a molecular system undergoing adiabatic Born-Oppenheimer dynamics is conserved only when pseudomagnetic Berry forces are taken into account. This finding sheds light on the nature of Berry forces for molecular systems with spin-orbit coupling and highlights how ab initio Born-Oppenheimer molecular dynamics simulations can successfully capture the entanglement of spin and nuclear degrees of freedom as modulated by electronic interactions in the adiabatic limit.

The discovery of all-optical ultrafast deterministic magnetization switching has opened up new possibilities for manipulating magnetization in devices using femtosecond laser pulses. Previous studies on single pulse all-optical helicity-independent switching (AO-HIS) have mainly focused on perpendicularly magnetized thin films. This work presents a comprehensive study on AO-HIS for in-plane magnetized ${\mathrm{Gd}}_{\mathrm{x}}{\mathrm{Co}}_{100-\mathrm{x}}$ thin films. Deterministic single femtosecond laser pulse toggle magnetization switching is demonstrated in a wider concentration range $(x=10-25\%)$ compared to the perpendicularly magnetized counterparts with GdCo thicknesses up to 30 nm. The switching time strongly depends on the ${\mathrm{Gd}}_{\mathrm{x}}{\mathrm{Co}}_{100-\mathrm{x}}$ concentration, with lower Gd concentration exhibiting shorter switching times (less than 500 fs). Our findings in this geometry provide insights into the underlying mechanisms governing single pulse AO-HIS, which challenge existing theoretical predictions. Moreover, in-plane magnetized ${\mathrm{Gd}}_{\mathrm{x}}{\mathrm{Co}}_{100-\mathrm{x}}$ thin films offer extended potential for optospintronic applications compared to their perpendicular magnetized counterparts.

Spinel structure ${\mathrm{CuCr}}_2{X}_4$ where $X$ is a chalcogen are ferromagnetic metals with Curie temperatures at or above room temperature. Experiments show that these compounds can be alloyed with halogens while preserving the ferromagnetic ordering. This alloying changes the carrier concentration and yields semiconductors for 25% halogen substitution on the chalcogen site in at least some cases. Here, we establish the electronic structures and related properties of ${\mathrm{CuCr}}_2{\mathrm{S}}_3\mathrm{Cl}$, ${\mathrm{CuCr}}_2{\mathrm{Se}}_3\mathrm{Br}$, and ${\mathrm{CuCr}}_2{\mathrm{Te}}_3\mathrm{I}$. ${\mathrm{CuCr}}_2{\mathrm{S}}_3\mathrm{Cl}$ and ${\mathrm{CuCr}}_2{\mathrm{Se}}_3\mathrm{Br}$ are ferromagnetic semiconductors with moderate band gaps and spin-polarized band edges. In contrast, ${\mathrm{CuCr}}_2{\mathrm{Te}}_3\mathrm{I}$ is found to be a semimetal, with nearly compensating Fermi surfaces. Calculations with spin-orbit coupling show an extraordinary sensitivity of the Fermi surfaces to the magnetization direction in this cubic material due to the details of the band crossings near the zone center. As a result, ${\mathrm{CuCr}}_2{\mathrm{Te}}_3\mathrm{I}$ is expected to show unusual anisotropic transport.

The magnetism and magnetocaloric effect in double perovskites is an alluring area of research due to its tunable nature. In particular, the exchange interactions and local ordering of magnetic sublattices are sensitive to the chemical substitution, synthesis/growth conditions, and strain. Here we study the effect of strain on magnetism in ${\mathrm{Gd}}_2{\mathrm{NiMnO}}_6$ double perovskite thin films grown using pulsed laser deposition on ${\mathrm{SrTiO}}_3$ (001) substrate. Magnetostructural study finds tensile strain to be the origin of perpendicular magnetic anisotropy in ${\mathrm{Gd}}_2{\mathrm{NiMnO}}_6$. Further, the anisotropic nature prevails in magnetocaloric effect as well. Magnetic entropy change along the in-plane direction is observed to be 21.82 J ${\mathrm{Kg}}^{-1}{\mathrm{K}}^{-1}$, which reduces to 9.84 J ${\mathrm{Kg}}^{-1}{\mathrm{K}}^{-1}$ along the out-of-plane direction. Our theoretical calculation reveals a ferrimagnetic ground state of ${\mathrm{Gd}}_2{\mathrm{NiMnO}}_6$. The relative spin orientation of Ni and Mn changes from parallel configuration for strained ${\mathrm{Gd}}_2{\mathrm{NiMnO}}_6$ to antiparallel configuration for strain-relaxed ${\mathrm{Gd}}_2{\mathrm{NiMnO}}_6$.

Ballistic hot electrons are extracted from a magnetic tunnel junction and injected into a metallic base with energies ranging from 0.65 to 2.8 eV. The energy and wave vector analysis made by a low height Si/Cu Schottky barrier allows one to disentangle the different contributions to the scattering. The hot electrons transport is interpreted as being mainly influenced by inelastic scattering. An explicit transport model reproduces our measurements and explains them as resulting directly from an electron-electron inelastic scattering process related to the $sp$ and $d$ bands of the ferromagnetic material involved.

In the first of two articles, we present here a mesoscopic micromagnetic approach for simulating materials composed of ferromagnetic and antiferromagnetic phases. Starting with the atomistic modeling of quasi-one-dimensional systems, we explicitly show how the material parameters for the mesoscopic model of an antiferromagnet can be derived. The comparison between magnetization profiles obtained in atomistic and mesoscopic calculations (using a Heusler alloy as an example) proves the validity of our method. This approach opens up the possibility to recover the details of the magnetization distribution in ferromagnetic/antiferromagnetic materials with the resolution of a few nanometers covering length scales up to several hundreds of nanometers.

In the second part of this publication we present simulation results for two three-dimensional models of Heusler-type alloys obtained by the mesoscopic micromagnetic approach. In the first model we simulate the magnetization reversal of a single ferromagnetic (FM) inclusion within a monocrystalline antiferromagnetic (AFM) matrix, revealing the evolution of the complex magnetization distribution within this inclusion when the external field is changed. The main result of this “monocrystalline” model is the absence of any hysteretic behavior by the magnetization reversal of the FM inclusion. Hence, this model is unable to reproduce the basic experimental result for the corresponding nanocomposite—hysteresis in the magnetization reversal of FM inclusions with a vertical shift of the corresponding loops. To explain this latter feature, in the second model we introduce a polycrystalline AFM matrix, with exchange interactions between AFM crystallites and between the FM inclusion and these crystallites. We show that within this model we can not only reproduce the hysteretic character of the remagnetization process, but also achieve a semiquantitative agreement with the experimentally observed hysteresis loop, assuming that the concentration of FM inclusions strongly fluctuates. These findings demonstrate the reliability of our enhanced micromagnetic model and set the basis for its applications in future studies of Heusler alloys and FM/AFM nanocomposites.

We study the phase diagram of the Yao-Lee model with Kitaev-type spin-orbital interactions in the presence of Dzyaloshinskii-Moriya interactions and external magnetic fields. Unlike the Kitaev model, the Yao-Lee model can still be solved exactly under these perturbations due to the enlarged local Hilbert space. Through a variational analysis, we obtain a rich ground-state phase diagram that consists of a variety of vison crystals with periodic arrangements of background ${\mathbb{Z}}_2$ flux (i.e., visons). With an out-of-plane magnetic field, these phases have gapped bulk and chiral edge states, characterized by a Chern number $\nu$ and an associated chiral central charge $c_{-}=\nu /2$ of edge states. We also find helical Majorana edge states that are protected by magnetic mirror symmetry. For the bilayer systems, we find that interlayer coupling can also stabilize new topological phases. Our results spotlight the tunability and the accompanying rich physics in exactly solvable spin-orbital generalizations of the Kitaev model.

Electron charge density is a fundamental physical quantity, determining various properties of matter. In this study, we have proposed a deep learning model for accurate charge-density prediction. Our model naturally preserves physical symmetries and can be effectively trained from one-shot density functional theory calculation toward high accuracy. It captures detailed atomic environment information, ensuring accurate predictions of charge density across bulk, surface, molecules, and amorphous structures. This implementation exhibits excellent scalability and provides efficient analyses of material properties in large-scale condensed matter systems.

A method is presented that allows for efficient evaluation of spin-orbit coupling (SOC) in density-functional-theory calculations. In the so-called second-variational scheme, where Kohn-Sham functions obtained in a scalar-relativistic calculation are employed as a basis for the spin-orbit-coupled problem, we introduce a rich set of local orbitals as additional basis functions. Also, relativistic local orbitals can be used. The method is implemented in the all-electron full-potential code exciting. We show that, for materials with strong SOC effects, this approach can reduce the overall basis-set size and thus computational costs tremendously.

We propose a theoretical framework to investigate elementary excitations at finite temperatures within a localized electron model that describes the interactions between multiple degrees of freedom, such as quantum spin models and Kugel-Khomskii models. Thus far, their excitation structures have been mainly examined using the linear flavor-wave theory, an $\mathrm{SU}(N$) generalization of the linear spin-wave theory. This technique introduces noninteracting bosonic quasiparticles as elementary excitations from the ground state, thereby elucidating numerous physical phenomena, including excitation spectra and transport properties characterized by topologically nontrivial band structures. Nevertheless, the interactions between quasiparticles cannot be ignored in systems exemplified by $S=1/2$ quantum spin models, where strong quantum fluctuations are present. Recent studies have investigated the effects of quasiparticle damping at zero temperature in such models. In our study, extending this approach to the flavor-wave theory for general localized electron models, we construct a comprehensive method to calculate excitation spectra with the quasiparticle damping at finite temperatures. We apply our method to the Kitaev model under magnetic fields, a typical example of models with topologically nontrivial magnon bands. Our calculations reveal that chiral edge modes undergo significant damping in weak magnetic fields, amplifying the damping rate by the temperature increase. This effect is caused by collisions with thermally excited quasiparticles. Since our approach starts from a general Hamiltonian, it will be widely applicable to other localized systems, such as spin-orbital coupled systems derived from multi-orbital Hubbard models in the strong-correlation limit.

The interest in the physical properties of kagome lattices has risen considerably. In addition to the synthesis of new materials, the possibility of realizing ultracold atoms on an optical kagome lattice (KL) raises interesting issues. For instance, by considering the Hubbard model on an anisotropic KL, with a hopping $t^{\prime }$ along one of the directions, one is able to interpolate between the Lieb lattice ($t^{\prime }=0$) and the isotropic KL ($t^{\prime }=t$). The ground state of the former is a ferrimagnetic insulator for any on-site repulsion $U$, while the latter displays a transition between a paramagnetic metal and a Mott insulator. One may thus consider $t^{\prime }$ to be a parameter controlling the degree of magnetic frustration in the system. By means of extensive quantum Monte Carlo simulations, we examine the magnetic properties and some transport properties as $t^{\prime }$ varies between these limits in order to set up a phase diagram in the $(U/t,t^{\prime }/t)$ parameter space. As an auxiliary response, analysis of the average sign of the fermionic determinant provides consistent predictions for critical points in the phase diagram. We observe a metal-insulator transition occurring at some critical point $U_c^{\mathrm{M}}\left(t^{\prime }\right)$, which increases monotonically with $t^{\prime }$, from the unfrustrated lattice limit. In addition, we find that the boundary between the ferrimagnetic insulator and the Mott insulator rises sharply with $t^{\prime }$.

The $\mathrm{N}{V}^{-}$ color center in diamond has been extensively investigated for applications in quantum sensing, computation, and communication. Nonetheless, charge-state decay from the $\mathrm{N}{V}^{-}$ to its neutral counterpart the $\mathrm{N}{V}^0$ detrimentally affects the robustness of the $\mathrm{N}{V}^{-}$ center and remains to be fully overcome. In this work, we provide an ab initio formalism for accurately estimating the rate of charge-state decay of color centers in wide band gap semiconductors. Our formalism employs density functional theory calculations in the context of thermal equilibrium. We illustrate the method using the transition of $\mathrm{N}{V}^{-}$ to $\mathrm{N}{V}^0$ in the presence of substitutional N [see Z. Yuan et al., Phys. Rev. Res. 2, 033263 (2020)].