We study the behavior of the out-of-time-ordered correlator (OTOC) in a non-Hermitian quantum Ising system. We show that the OTOC can diagnose not only the exceptional point in the states with lowest real parts of Hamiltonian spectra (LRHS), which host the Yang-Lee edge singularity, but also the exceptional point in states with higher real parts of Hamiltonian spectra (HRHS). We find that the evolution of the OTOC in the parity-time symmetric phase can be divided into two stages: In the short-time stage, the OTOC oscillates periodically, and when the parameter is near the exceptional point of the LRHS, this oscillation behavior can be described by both the scaling theory of the zero-dimensional ($0\mathrm{D}$) quantum Yang-Lee edge singularity and the scaling theory of the $1\mathrm{D}$ quantum Ising model, while in the long-time stage the OTOC increases exponentially, controlled by the exceptional point of the HRHS. Possible experimental realizations are then discussed.

We present a systematic ${}^{57}\mathrm{Fe}$ Mössbauer study on highly diluted Fe centers in ${\mathrm{Li}}_2\left({\mathrm{Li}}_{1-x}{\mathrm{Fe}}_x\right)\mathrm{N}$ single crystals as a function of temperature and magnetic field applied transverse and longitudinal with respect to the single-ion anisotropy axis. Below 30 K, the Fe centers exhibit a giant magnetic hyperfine field of ${\overline{B}}_A=70.25\left(2\right)\mathrm{T}$ parallel to the axis of strongest electric field gradient ${\overline{V}}_{zz}=-154.0\left(1\right)\mathrm{V}/{\AA }^2$. Fluctuations of the magnetic hyperfine field are observed between 50 and 300 K and described by the Blume two-level relaxation model. From the temperature dependence of the fluctuation rate, an Orbach spin-lattice relaxation process is deduced. An Arrhenius analysis yields a single thermal activation barrier of ${\overline{E}}_A=570\left(6\right)\mathrm{K}$ and an attempt frequency ${\overline{\nu }}_0=309\left(10\right)\mathrm{GHz}$. Mössbauer spectroscopy studies with applied transverse magnetic fields up to 5 T reveal a large increase of the fluctuation rate by more than one order of magnitude. In longitudinal magnetic fields, a splitting of the fluctuation rate into two branches is observed consistent with a Zeeman induced modification of the energy levels. The experimental observations are qualitatively reproduced by a single-ion effective spin Hamiltonian analysis assuming a ${\mathrm{Fe}}^{1+}{d}^7$ charge state with the unquenched orbital moment and a $J=7/2$ ground state. It is demonstrated that a weak axial single-ion anisotropy $D$ of the order of a few Kelvin can cause a two orders of magnitude larger energy barrier for longitudinal spin fluctuations.

In this study, Gd ion implantation and annealing were performed at ${900}^{\circ }\mathrm{C}$ for nominally undoped wurtzite GaN grown by metal-organic chemical vapor deposition. Spin-polarized positron annihilation measurements showed that vacancy clusters including at least 12 vacancies per cluster were the major positron-trapping centers and that the electrons in the vacancy clusters were spin-polarized. These observations could be explained by first-principles calculations. The previous speculation about the defect-assisted ferromagnetism of Gd-implanted GaN may be supported if vacancy clusters are considered.

Dzyaloshinskii-Moriya interaction (DMI) is an antisymmetric fundamental magnetic exchange interaction, which is responsible for the formation of exotic topological spin textures in chiral magnets. Here by investigating the DMI-induced energy asymmetry of the magnon dispersion relation, we quantify the atomistic DMI vectors in two atomic layers made of Fe and Co epitaxially grown on W(110). We provide direct experimental evidence that in layered ferromagnets this fundamental interaction can be tailored via quantum engineering of the lattice symmetry, direct intra- and interlayer DMI coupling. We report on a giant DMI in epitaxial Co/Fe bilayers grown on W(110), exhibiting $C_{2v}$ symmetry. Our results pave the way for tailoring DMI on the atomic length scales with the perspective of designing desired topological spin textures.

A stochastic model for the field-driven polarization reversal in rhombohedral ferroelectrics is developed, providing a description of their temporal electromechanical response. Application of the model to simultaneous measurements of polarization and strain kinetics in a rhombohedral $\mathrm{Pb}\left(\mathrm{Zr},\mathrm{Ti}\right){\mathrm{O}}_3$ ceramic over a wide time window allows the identification of preferable switching paths, fractions of individual switching processes, and their activation fields. In conjunction, the phenomenological Landau-Ginzburg-Devonshire theory is used to analyze the impact of an external field and stress on switching barriers, showing that residual mechanical stress may promote the fast switching.

Two-dimensional (2D) van der Waals (vdW) magnets have recently attracted increasing attention, as they provide a novel system for exploring 2D magnetism. However, intrinsic ferromagnetism in 2D systems has almost exclusively been observed at low temperatures, limiting their technological relevance. ${\mathrm{Fe}}_{\mathrm{N}}{\mathrm{Ge}\mathrm{Te}}_2$ ($N=3$, 4, and 5) systems are currently becoming the most attractive 2D vdW materials due to their relatively high Curie temperatures and large saturation magnetization. However, the nature of their complex yet intriguing magnetic behaviors is still unclear, in part due to the multiple inequivalent iron sites and iron vacancies. Here, we show evolution of magnetic ordering transitions in ${\mathrm{Fe}}_{5-x}{\mathrm{Ge}\mathrm{Te}}_2$ with high Curie temperature and a strong saturation magnetization using photoemission electron microscopy and transport measurements. At 275 K, the ferromagnet transitions to a ferrimagnet, and below 110 K transitions to a state with glassy clusters. These are evidenced from temperature-dependent magnetic stripe domain evolution and anisotropic magnetoresistance measurements. Our findings show a clear magnetic ground state of ${\mathrm{Fe}}_{5-x}{\mathrm{Ge}\mathrm{Te}}_2$ at room temperature which signals that ${\mathrm{Fe}}_{5-x}{\mathrm{Ge}\mathrm{Te}}_2$ system is a very promising candidate for spintronic devices and provides a material design pathway to further increase the Curie temperature and saturation moments in vdW ferromagnets.

We study the matrix elements of local operators in the eigenstates of the integrable XXZ chain and of the quantum-chaotic model obtained by locally perturbing the XXZ chain with a magnetic impurity. We show that, at frequencies that are polynomially small in the system size, the behavior of the variances of the off-diagonal matrix elements can be starkly different depending on the operator. In the integrable model we find that, as the frequency $\omega \to 0$, the variances are either nonvanishing (generic behavior) or vanishing (for a special class of operators). In the quantum-chaotic model, on the other hand, we find the variances to be nonvanishing as $\omega \to 0$ and to indicate diffusive dynamics. We highlight which properties of the matrix elements of local operators are different between the integrable and quantum-chaotic models independently of the specific operator selected.

We introduce the concept of a Majorana molecule, a topological bound state appearing in the geometry of a double quantum dot structure flanking a topological superconducting nanowire. We demonstrate that, if the Majorana bound states at opposite edges are probed nonlocally in a two-probe experiment, the spectral density of the system reveals the so-called half-bowtie profiles, while Andreev bound states become resolved into bonding and antibonding molecular configurations. We reveal that this effect is due to the Fano interference between pseudospin superconducting pairing channels, and we propose that it can be captured by a pseudospin resolved scanning tunneling microscope tip.

The nature of the state at low Landau-level filling factors has been a long-standing puzzle in the field of the fractional quantum Hall effect (FQHE). While theoretical calculations suggest that a crystal is favored at filling factors $\nu \lesssim \frac{1}{6}$, experiments show, at somewhat elevated temperatures, minima in the longitudinal resistance that are associated with fractional quantum Hall effect at $\nu =\frac{1}{7}, \frac{2}{11}, \frac{2}{13}, \frac{3}{17}, \frac{3}{19}, \frac{1}{9}, \frac{2}{15}$, and $\frac{2}{17}$, which belong to the standard sequences $\nu =n/(6n\pm 1)$ and $n/(8n\pm 1)$. To address this paradox, we investigate the nature of some of the low-$\nu$ states, specifically $\nu =\frac{1}{7}, \frac{2}{13}$, and $\frac{1}{9}$, by variational Monte Carlo, density matrix renormalization group, and exact diagonalization methods. We conclude that in the thermodynamic limit, these are likely to be incompressible fractional quantum Hall liquids, albeit with strong short-range crystalline correlations. This suggests a natural explanation for the experimentally observed behavior and a rich phase diagram that admits, in the low-disorder limit, a multitude of crystal-FQHE liquid transitions as the filling factor is reduced.

We study the electronic states that are formed due to the tunnel coupling between helical edge states (HESs) and bound states of nonmagnetic point defects in two-dimensional topological insulators in the general case of broken axial spin symmetry. It is found that the coupling of HESs and a single defect leads to the formation of composite HESs composed of the bound states and a set of the conventional HESs. Their spectral density near the defect has a resonance shifted relative to the energy level of the bound state. But of most importance is a long-range perturbation of the HESs around the defect, which is a cloud consisting of both Kramers partners of conventional edge states. Therefore each of the composite HESs contains both the right- and left-moving conventional HESs. The amplitude of this perturbation decreases inversely with the distance from the defect. In a system of many defects, this perturbation leads to a long-range coupling between bound states of different defects mediated by the HESs and causes amazing effects. We study these effects for a two-defect system where the proposed mechanism of indirect coupling leads to a splitting of the resonances of isolated defects even if the distance between them is very large. As a result an asymmetric structure of two-peak resonance arises that very unusually changes with the distance between the defects.

We use the numerical renormalization group theory to investigate the Yu-Shiba-Rusinov (YSR) bound state properties of single magnetic molecules placed on an $s$-wave superconducting substrate. The molecule is modeled as a large core spin and a single orbital, coupled via exchange interaction. The critical Coulomb interaction for the singlet/doublet transition decreases in the presence of this exchange interaction for both ferro- and antiferromagnetic couplings. The number of YSR states also increases to two pairs; however, in the singlet phase, one of the pairs has zero spectral weight. We explore the evolution of the in-gap states using the Anderson model. Away from the particle-hole symmetry point, the results suggest a doublet-singlet-doublet transition as the on-site energy is lowered while keeping the Coulomb interaction fixed. We construct an effective model for the molecule to understand these results, in the limit of the large superconducting order parameter. Qualitatively, the model accounts for the phase transitions and spectral nature of the in-gap states. Finally, we analyze the effects of magnetic anisotropic fields of the core spin on in-gap states. Due to internal degrees of freedom of the spin excited states, a multitude of new states emerges within the gap. Depending on the sign and strength of the uniaxial anisotropic field, the results indicate up to three pairs of YSR states.

We analyze local operator growth in nonintegrable quantum many-body systems. A recently introduced universal operator growth hypothesis proposes that the maximal growth of Lanczos coefficients in the continued fraction expansion of the Green's function reflects chaos of the underlying system. We first show that the continued fraction expansion, and the recursion method in general, should be understood in the context of a completely integrable classical dynamics in Krylov space. In particular, the time-correlation function of a physical observable analytically continued to imaginary time is a tau-function of integrable Toda hierarchy. We use this relation to generalize the universal operator growth hypothesis to include arbitrarily ordered correlation functions. We then proceed to analyze the singularity of the time-correlation function, which is an equivalent sign of chaos to the maximal growth of Lanczos coefficients, and we show that it is due to delocalization in Krylov space. We illustrate the general relation between chaos and delocalization using an explicit example of the Sachdev-Ye-Kietaev model.

In this work we investigate single crystal $\mathrm{Gd}\mathrm{Ti}{\mathrm{O}}_3$, a promising candidate material for Floquet engineering and magnetic control, using ultrafast optical pump-probe reflectivity and magneto-optical Kerr spectroscopy. $\mathrm{Gd}\mathrm{Ti}{\mathrm{O}}_3$ is a Mott-Hubbard insulator with a ferrimagnetic and orbitally ordered ground state ($T_C$ = 32 K). We observe multiple signatures of the magnetic phase transition in the photoinduced reflectivity signal, in response to above band-gap 660-nm excitation. Magnetic dynamics measured via Kerr spectroscopy reveal optical perturbation of the ferrimagnetic order on spin-lattice coupling timescales, highlighting the competition between the ${\mathrm{Gd}}^{3+}$ and ${\mathrm{Ti}}^{3+}$ magnetic sub-lattices. Furthermore, a strong coherent oscillation is present in the reflection and Kerr dynamics, attributable to an acoustic strain wave launched by the pump pulse. The amplitude of this acoustic mode is highly dependent on the magnetic order of the system, growing sharply in magnitude at $T_C$, indicative of strong magneto-elastic coupling. The driving mechanism, involving strain-induced modification of the magnetic exchange interaction, implies an indirect method of coupling light to the magnetic degrees of freedom and emphasizes the potential of $\mathrm{Gd}\mathrm{Ti}{\mathrm{O}}_3$ as a tunable quantum material.

${\mathrm{TaAs}}_2$ and ${\mathrm{NbAs}}_2$ are members of the ${MPn}_2$ family with weak topological invariants of $Z_2$ = [0;111]. Here, we report the tip-induced superconductivity achieved on both materials using the point-contact technique. Although the weak $Z_2$ number leads to strongly crystal-orientation-dependent surface states, we observed a universal relationship between the zero-temperature upper critical field $H_{c2}\left(0\right)$ and the critical temperature $T_c$ for different crystal orientations. Combined with first-principles calculations, the findings here could identify a bulk band, instead of the much speculated surface bands, playing the dominant role in the induced superconductivity. These results predict a great possibility to realize superconductivity in other members of the ${MPn}_2$ family possessing similar band structures and provide clues to understand the mechanism of tip-induced superconductivity.

Half-metallic ferromagnets have been widely investigated by first-principles density-functional theory (DFT) calculations, but extending such studies to investigate spin-polarization at finite temperatures is still challenging due to the difficulty of incorporating temperature effects appropriately. We present DFT calculations, based on a Green's function formulation, which include thermal effects via the disordered local-moment method to address this issue. The calculations are carried out for Heusler ${\mathrm{Co}}_2\mathrm{MnSi}$ alloys in order to investigate the temperature dependence of spin polarization, where atomic-disordering and nonstoichiometric effects are taken into account. Our results show that the spin polarization strongly depends on temperature and that a Co $d$-orbital effect plays a key role in this effect. Furthermore, we find that the temperature-dependent spin polarization of ${\mathrm{Co}}_2\mathrm{MnSi}$ can be improved by reducing the Co content and incorporating extra Mn.

Electrical manipulation of magnetism via spin-orbit torques (SOTs) promises efficient spintronic devices. In systems comprising magnetic insulators and heavy metals, SOTs have started to be investigated only recently, especially in systems with interfacial Dzyaloshinskii-Moriya interaction (iDMI). Here, we quantitatively study the SOT efficiency and iDMI in a series of gadolinium gallium garnet (GGG)/thulium iron garnet (TmIG)/platinum (Pt) heterostructures with varying TmIG and Pt thicknesses. We find that the nonmonotonic SOT efficiency as a function of the magnetic layer thickness is not consistent with the 1/thickness dependence expected from a simple interfacial SOT mechanism. Moreover, considering the insulating nature of TmIG, our results cannot be explained by the SOT mechanism established for metallic magnets where the transverse charge spin current can inject and dephase in the magnetic layers. Rather we can explain this nonmonotonic behavior by a model based on the interfacial spin mixing conductance that is affected by the thickness-dependent exchange splitting energy by determining the phase difference of the reflected spin-up and spin-down electrons at the TmIG/Pt interface. By studying the Pt thickness dependence, we find that the effective DMI for GGG/TmIG/Pt does not depend on the Pt thickness, which indicates that the GGG/TmIG interface is the source of the iDMI in this system. Our work demonstrates that SOT and DMI can originate from two different interfaces, which enables independent optimization of DMI and SOT for advanced chiral spintronics with low damping magnetic insulators.

The one-dimensional $p$-wave superconductor proposed by Kitaev has long been a classic example for understanding topological phase transitions through various methods, such as examining the Berry phase, edge states of open chains, and, in particular, aspects from quantum entanglement of ground states. In order to understand the amount of information carried in the entanglement-related quantities, here we study topological phase transitions of the model with emphasis of using the deep learning approach. We feed different quantities, including Majorana correlation matrices (MCMs), entanglement spectra (ES) or entanglement eigenvectors (EE) originating from Block correlation matrices, into the deep neural networks for training, and investigate which one could be the most useful input format in this approach. We find that ES is information that is too compressed compared to MCM or EE. MCM and EE can provide us abundant information to recognize not only the topological phase transitions in the model but also phases of matter with different $U$(1) gauges, which is not reachable by using ES only.

The general concern of this investigation is the extraction of the effective electromagnetic properties of agglomerates of randomly located particles, which are small compared to the wavelength. The focus is on the spectral window ranging from the transverse phonon to the longitudinal phonon frequencies, in which resonances may be excited. In this frequency domain, it is shown that limiting the problem to bare dipole-dipole interactions leads to inaccurate calculations of the electromagnetic fields, resulting in a doubtful extraction of the effective properties. We perform the complete electromagnetic calculation by taking into account the higher multipole orders that are activated when the agglomerates are illuminated. Several results, which are not usually observed outside the frequency range highlighted here, are revealed by means of extensive numerical simulations. In particular, we evidence large deviations compared to the predictions provided by the effective medium theories, while we find that the volume of the microstructures (each one with a different internal geometry) that are used to average the fields must be unusually large to avoid a bias in the determination of the effective properties. Furthermore, the evolution of the incoherent component of the fields between the two optical phonon modes is investigated.

Magnetocrystalline anisotropy is a fundamental property of magnetic materials that determines the dynamics of magnetic precession, the frequency of spin waves, the thermal stability of magnetic domains, and the efficiency of spintronic devices. We combine torque magnetometry and density functional theory calculations to determine the magnetocrystalline anisotropy of the metallic antiferromagnet $\mathrm{F}{\mathrm{e}}_2\mathrm{As}$. $\mathrm{F}{\mathrm{e}}_2\mathrm{As}$ has a tetragonal crystal structure with the Néel vector lying in the (001) plane. We report that the fourfold magnetocrystalline anisotropy in the (001) plane of $\mathrm{F}{\mathrm{e}}_2\mathrm{As}$ is extremely small, $K_{22}=-150\mathrm{J}/{\mathrm{m}}^3$ at $T=4\mathrm{K}$, much smaller than the perpendicular magnetic anisotropy of ferromagnetic structure widely used in spintronic devices. $K_{22}$ is strongly temperature dependent and close to zero at $T>150\mathrm{K}$. The anisotropy $K_1$ in the (010) plane is too large to be measured by torque magnetometry and we determine $K_1=-830\mathrm{kJ}/{\mathrm{m}}^3$ using first-principles density functional theory. Our simulations show that the contribution to the anisotropy from classical magnetic dipole-dipole interactions is comparable to the contribution from spin-orbit coupling. The calculated fourfold anisotropy in the (001) plane $K_{22}$ ranges from $-290$ to $280\mathrm{J}/{\mathrm{m}}^3$, the same order of magnitude as the measured value. We used $K_1$ from theory to predict the frequency and polarization of the lowest frequency antiferromagnetic resonance mode and find that the mode is linearly polarized in the (001) plane with $f=$ 670 GHz.