Recently, there has been a drive towards the realization of topological phases beyond conventional electronic materials, including phases defined in more than three dimensions. We propose a versatile and experimentally realistic approach of realizing a large variety of multicomponent topological phases in two-dimensional (2D) photonic crystals with quasiperiodically modulated defects. With a length scale introduced by a background resonator lattice, the defects are found to host various effective orbitals of $s$-, $p$-, and $d$-type symmetries, thus providing a monolithic platform for realizing multicomponent topological states without requiring separate internal degrees of freedom in the physical setup. Notably, by coupling the defect modulations diagonally, we report the realization of “entangled” 4D quantum Hall (QH) phases which cannot be factorized into two copies of 2D QH phases, each described by the first Chern number. The structure of this nonfactorizability can be quantified by a classical entanglement entropy inspired by quantum information theory. In another embodiment, we present 4D $p$-orbital nodal lines in a nonsymmorphic photonic lattice, hosting boundary states with an exotic manifold. Our simple and versatile approach holds the promise of topological optoelectronic and photonic applications such as one-way optical fibers.

We present magnetic measurements on ${\mathrm{Nd}}_2{\mathrm{NiMnO}}_6$ which exhibits a well-known insulating paramagnetic state to an insulating ferromagnetic state transition when cooled below 200 K. Beyond this basic fact, there is a great deal of diversity in the reported magnetic properties and interpretation of specific anomalies observed in the magnetic data of this compound below the Curie temperature. We address specifically two anomalies discussed in the past, namely, a spin-glass like behavior observed in some samples near 100 K and a downturn in the magnetization with a lowering of the temperature below approximately 50 K. We show for the first time that the application of an increasing magnetic field can systematically change the low-temperature behavior to make the down-turn in the magnetization into an upturn. With the help of first principle calculations and extensive simulations along with our experimental observations, we provide a microscopic understanding of all magnetic properties observed in this interesting system to point out that the glassiness around 100 K is absent in well-ordered samples and that the low-temperature magnetic anomaly below 50 K is a consequence of a ferromagnetic coupling of the Nd spin moments with the spin of the Ni-Mn ordered sublattice without giving rise to any ordering of the Nd sublattice that remains paramagnetic, contrary to earlier claims. We explain this counter-intuitive interpretation of a ferromagnetic coupling of Nd spins with Ni-Mn spin giving rise to a decrease in the total magnetic moment by noting the less than half-filled $4f$ occupation of Nd that ensures orbital and spin moments of Nd to be opposite to each other due to the spin-orbit coupling. Since the ground state total magnetic moment of Nd has a contribution from the orbital moment, that is larger than the spin moment, the total moment of Nd is indeed pointing in a direction opposite to the direction of spin moments of the Ni-Mn sublattice as a consequence of the ferromagnetic exchange coupling between Nd and Ni-Mn spins.

We use Ru $L_3$-edge (2838.5 eV) resonant inelastic x-ray scattering (RIXS) to quantify the electronic structure of ${\mathrm{Ca}}_2{\mathrm{RuO}}_4$, a layered $4d$-electron compound that exhibits a correlation-driven metal-insulator transition and unconventional antiferromagnetism. We observe a series of Ru intraionic transitions whose energies and intensities are well described by model calculations. In particular, we find a $J=0\to 2$ spin-orbit excitation at 320 meV, as well as Hund's-rule driven $S=1\to 0$ spin-state transitions at 750 and 1000 meV. The energy of these three features uniquely determines the spin-orbit coupling, tetragonal crystal-field energy, and Hund's rule interaction. The parameters inferred from the RIXS spectra are in excellent agreement with the picture of excitonic magnetism that has been devised to explain the collective modes of the antiferromagnetic state. $L_3$-edge RIXS of Ru compounds and other $4d$-electron materials thus enables direct measurements of interactions parameters that are essential for realistic model calculations.

We explore the impact of a Rashba-type spin-orbit interaction in the conduction band on the spin dynamics of hot excitons in diluted magnetic semiconductor quantum wells. In materials with strong spin-orbit coupling, we identify parameter regimes where spin-orbit effects greatly accelerate the spin decay and even change the dynamics qualitatively in the form of damped oscillations. Furthermore, we show that the application of a small external magnetic field can be used to either mitigate the influence of spin-orbit coupling or entirely remove its effects for fields above a material-dependent threshold.

Owing to the ultrashort timescales of ballistic electron transport, relaxation dynamics of hot nonequilibrium electrons is conventionally considered local. Utilizing propagating surface plasmon-polaritons (SPs) in metal-dielectric heterostructures, we demonstrate that both local (relaxation) and nonlocal (transport) hot electron dynamics contribute to the transient optical response. The data obtained in two distinct series of pump-probe experiments demonstrate a strong increase in both nonthermal electron generation efficiency and nonlocal relaxation timescales at the SP resonance. We develop a simple kinetic model incorporating a SP excitation, where both local and nonlocal electron relaxation in metals are included, and analyze nonequilibrium electron dynamics in its entirety in the case of collective electronic excitations. Our results elucidate the role of SPs in nonequilibrium electron dynamics and demonstrate rich perspectives of ultrafast plasmonics for tailoring spatiotemporal distribution of hot electrons in metallic nanostructures.

The spontaneous onset of the spin-nematic order in spin-chain systems is studied. The ordering persists due to distortions of either magnetic ions, or ligands taking part in the superexchange between magnetic ions. The spin-nematic order yields a nonzero biaxial magnetic anisotropy for the spin chain, violating the U(1) symmetry. The influence of the external magnetic field and nonzero temperature is considered. We predict how the spin-nematic ordering can manifest itself in the temperature and magnetic field behavior of magnetoacoustic characteristics.

The discovery of ${\mathrm{FeO}}_2$ containing more oxygen than hematite $\left({\mathrm{Fe}}_2{\mathrm{O}}_3\right)$, which was previously believed to be the most oxygen rich iron compound, has important implications for the study of deep lower mantle compositions. Compared to other iron compounds, there are limited reports on ${\mathrm{FeO}}_2$, making studies of its physical properties of great interest in fundamental condensed matter physics and geoscience. Even the oxidation state of Fe in ${\mathrm{FeO}}_2$ is the subject of debate in theoretical works and there have not been reports from experimental electronic and magnetic properties measurements. Here, we report the pressure-induced spin state transition from synchrotron experiments and our computational results explain the underlying mechanism. Using density functional theory and dynamical mean field theory, we calculated spin states of Fe with volume and Hubbard interaction $U$ change, which clearly demonstrate that Fe in ${\mathrm{FeO}}_2$ consists of Fe(II) and peroxide ${\mathrm{O}}_2^{2-}$. Our paper suggests that the localized nature of both Fe $3d$ orbitals and ${\mathrm{O}}_2$ molecular orbitals should be correctly treated for unveiling the structural and electronic properties of ${\mathrm{FeO}}_2$.

The underdoped phase diagram of the iron-based superconductors exemplifies the complexity common to many correlated materials. Indeed, multiple ordered states that break different symmetries but display comparable transition temperatures are present. Here we argue that such a complexity can be understood within a simple unifying framework. This framework, built to respect the symmetries of the nonsymmorphic space group of the FeAs/Se layer, consists of primary magnetically ordered states and their vestigial phases that intertwine spin and orbital degrees of freedom. All vestigial phases have Ising-like and zero wave-vector order parameters, described in terms of composite spin order and exotic orbital-order patterns such as spin-orbital loop currents, staggered atomic spin-orbit coupling, and emergent Rashba- and Dresselhaus-type spin-orbit interactions. Moreover, they host unusual phenomena, such as the electronematic effect, by which electric fields act as transverse fields to the nematic order parameter, and the ferro-Néel effect, by which a uniform magnetic field induces Néel order. We discuss the experimental implications of our findings to iron-based superconductors and possible extensions to other correlated compounds with similar space groups.

Prethermalization, where quasisteady states are realized in the intermediate long-time regime (prethermal regime), in periodically driven (Floquet) systems is an important phenomenon since it provides a platform for nontrivial Floquet many-body physics. In this Rapid Communication, we consider Floquet systems with dual energy scales: The Hamiltonian consists of two different terms whose amplitude is either comparable to or much smaller than the frequency. As a result, when the larger-amplitude drive induces a ${\mathbb{Z}}_N$ symmetry operation, we obtain the effective static Hamiltonian respecting the emergent ${\mathbb{Z}}_N$ symmetry in high-frequency expansions, which describes the dynamics of such Floquet systems in the prethermal regime. As an application of our formulation, our formalism gives a general way to analyze time crystals in prethermal regimes in terms of the static effective Hamiltonian. We also provide an application to Floquet engineering, with which we can perform the simultaneous control of phases and symmetries of the systems. For example, this enables us to control symmetry protected topological phases even when the original system does not respect the symmetry.

We measure the transverse relaxation of the spin state of an ensemble of ground-state rubidium atoms trapped in solid parahydrogen at cryogenic temperatures. We find the spin dephasing time of the ensemble ($T_2^{*}$) is limited by inhomogeneous broadening. We determine that this broadening is dominated by electrostaticlike interactions with the host matrix, and can be reduced by preparing nonclassical spin superposition states. Driving these superposition states gives significantly narrower electron paramagnetic resonance lines and the longest reported electron spin $T_2^{*}$ in any solid-phase system other than solid helium.

Topological protection offers unprecedented opportunities for wave manipulation and energy transport in various fields of physics, including elasticity, acoustics, quantum mechanics, and electromagnetism. Distinct classes of topological waves have been investigated by establishing analogs with the quantum, spin, and valley Hall effects. We here propose and experimentally demonstrate the possibility of supporting multiple classes of topological modes within a single platform. Starting from a patterned elastic plate featuring a double Dirac cone, we create distinct topological interfaces by lifting such degeneracy through selective breaking of symmetries across the thickness and in the plane of the plate. We observe the propagation of a new class of heterogeneous helical-valley edge waves capable of isolating modes on the basis of their distinct polarization, i.e., the specific mode wave field distribution within the unit cell. Our results show the onset of wave splitting resulting from the interaction of multiple topological equal-frequency wave modes, which may have significance in applications involving elastic beam splitters, switches, and filters.

We study the formation of band gap bound states induced by a non-Hermitian impurity embedded in a Hermitian system. We show that a pair of bound states emerges inside the band gap when a parity-time $\left(\mathcal{PT}\right)$ imaginary potential is added in strongly coupled bilayer lattices and the bound states become strongly localized when the system approaches the exceptional point. As a direct consequence of such $\mathcal{PT}$ impurity-induced bound states, an impurity array can be constructed and protected by energy gap. The effective Hamiltonian of the impurity array is non-Hermitian Su-Schrieffer-Heeger type and hosts Dirac probability-preserving dynamics. We demonstrate the conclusion by numerical simulations for the quantum transport of wave packet in right-angle bends waveguide and $Y$-beam splitter. Our finding provides an alternative way to fabricate quantum device by non-Hermitian impurity.

In search of a quantum phase transition between the two-dimensional ($2\mathrm{D}$) ferromagnetism of ${\mathrm{CaCo}}_{2-y}{\mathrm{As}}_2$ and stripe-type antiferromagnetism in ${\mathrm{SrCo}}_2{\mathrm{As}}_2$, we instead find evidence for $1\mathrm{D}$ magnetic frustration between magnetic square Co layers. We present neutron-diffraction data for ${\mathrm{Ca}}_{1-x}{\mathrm{Sr}}_x{\mathrm{Co}}_{2-y}{\mathrm{As}}_2$ that reveal a sequence of $x$-dependent magnetic transitions which involve different stacking of $2\mathrm{D}$ ferromagnetically aligned layers with different magnetic anisotropy. We explain the $x$-dependent changes to the magnetic order by utilizing classical analytical calculations of a $1\mathrm{D}$ Heisenberg model where single-ion magnetic anisotropy and frustration of antiferromagnetic nearest- and next-nearest-layer exchange interactions are all composition dependent.

From the pioneering work of Winter [Phys. Rev. 124, 452 (1961)], a magnetic domain wall of Bloch type is known to host a special wall-bound spin-wave mode, which corresponds to spin waves being channeled along the magnetic texture. Using micromagnetic simulations, we investigate spin waves traveling inside Bloch walls formed in thin magnetic media with perpendicular-to-plane magnetic anisotropy and we show that their propagation is actually strongly nonreciprocal, as a result of dynamic dipolar interactions. We investigate spin-wave nonreciprocity effects in single Bloch walls, which allows us to clearly pinpoint their origin, as well as in arrays of parallel walls in stripe domain configurations. For such arrays, a complex domain-wall-bound spin-wave band structure develops, some aspects of which can be understood qualitatively from the single-wall picture by considering that a wall array consists of a sequence of up/down and down/up walls with opposite nonreciprocities. Circumstances are identified in which the nonreciprocity is so extreme that spin-wave propagation inside individual walls becomes unidirectional.

Uranium mononitride (UN) displays a spin-flop-like transition for magnetic field applied along all principal crystallographic directions just below 60 T. Here, we report on ultrasound and magnetocaloric-effect results for UN in pulsed magnetic fields up to 65 T. The field-induced phase transition causes a discontinuous temperature decrease, indicating a larger magnetic entropy above the transition. Furthermore, we find pronounced anomalies in the acoustic properties, which signals strong spin-lattice interactions. A further anomaly observed at fields slightly above the transition is likely related to the formation of magnetic domains. A model based on the exchange-striction coupling mechanism well reproduces the strong renormalization of the acoustic properties.

To study the mutual interaction between unconventional superconductivity and magnetic order through an interface, we fabricate hybrid Kondo superlattices consisting of alternating layers of the heavy-fermion superconductor ${\mathrm{CeCoIn}}_5$ and the antiferromagnetic (AFM) heavy-fermion metal ${\mathrm{CeIn}}_3$. The strength of the AFM fluctuations is tuned by applying hydrostatic pressure to the ${\mathrm{CeCoIn}}_5\left(m\right)/{\mathrm{CeIn}}_3\left(n\right)$ superlattices with $m$ and $n$ unit-cell-thick layers of ${\mathrm{CeCoIn}}_5$ and ${\mathrm{CeIn}}_3$, respectively. The superconductivity in ${\mathrm{CeCoIn}}_5$ and the AFM order in ${\mathrm{CeIn}}_3$ coexist in spatially separated layers in the whole thickness and pressure ranges. At ambient pressure, the Néel temperature $T_N$ of the ${\mathrm{CeIn}}_3$ block layers (BLs) of ${\mathrm{CeCoIn}}_5\left(7\right)/{\mathrm{CeIn}}_3\left(n\right)$ shows little dependence on the thickness $n$, in sharp contrast to ${\mathrm{CeIn}}_3\left(n\right)/{\mathrm{LaIn}}_3\left(4\right)$ superlattices, where $T_N$ is strongly suppressed with decreasing $n$. This suggests that each ${\mathrm{CeIn}}_3$ BL is magnetically coupled by the Ruderman-Kittel-Kasuya-Yosida interaction through the adjacent ${\mathrm{CeCoIn}}_5$ BL and a three-dimensional magnetic state is formed. With applying pressure to ${\mathrm{CeCoIn}}_5\left(7\right)/{\mathrm{CeIn}}_3\left(13\right)$, $T_N$ of the ${\mathrm{CeIn}}_3$ BLs is suppressed up to 2.4 GPa, showing a similar pressure dependence to that of bulk ${\mathrm{CeIn}}_3$ single crystals. An analysis of the upper critical field reveals that the superconductivity in the ${\mathrm{CeCoIn}}_5$ BLs is barely influenced by the AFM fluctuations in the ${\mathrm{CeIn}}_3$ BLs, even when the ${\mathrm{CeIn}}_3$ BLs are in the vicinity of the AFM quantum critical point. This is in stark contrast to ${\mathrm{CeCoIn}}_5/{\mathrm{CeRhIn}}_5$ superlattices, in which the superconductivity in the ${\mathrm{CeCoIn}}_5$ BLs is profoundly affected by AFM fluctuations in the ${\mathrm{CeRhIn}}_5$ BLs. The present results show that although AFM fluctuations are injected into the ${\mathrm{CeCoIn}}_5$ BLs from the ${\mathrm{CeIn}}_3$ BLs through the interface, they barely affect the force that binds superconducting electron pairs. These results demonstrate that two-dimensional AFM fluctuations are essentially important for the pairing interactions in ${\mathrm{CeCoIn}}_5$.

The existence of a spectral gap above the ground state has far-reaching consequences for the low-energy physics of a quantum many-body system. A recent work of Movassagh [R. Movassagh, Phys. Rev. Lett. 119, 220504 (2017)] shows that a spatially random local quantum Hamiltonian is generically gapless. Here we observe that a gap is more common for translation-invariant quantum spin chains, more specifically, that these are gapped with a positive probability if the interaction is of small rank. This is in line with a previous analysis of the spin-$1/2$ case by Bravyi and Gosset [S. Bravyi and D. Gosset, J. Math. Phys. 56, 061902 (2015)]. The Hamiltonians are constructed by selecting a single projection of sufficiently small rank at random and then translating it across the entire chain. By the rank assumption, the resulting Hamiltonians are automatically frustration-free and this fact plays a key role in our analysis.