We study the field cooled magnetization of a CuMn spin glass (SG) under temperature perturbations. The $T$-cycling curves are compared with the reference curve without temperature cycling. There is a crossover from the cumulative aging region to noncumulative aging region as the temperature change is increased. The cumulative aging range scales with the chaos length, ${\ell }_{\mathrm{c}}$, becoming comparable to the correlation length, $\xi$, at the crossover boundary. The extracted chaos exponent, $\zeta =1.1$, is in agreement with theoretical predictions. Our results strongly suggest temperature chaos exists in real SG systems.

We investigate spin chains with bilinear-biquadratic (BLBQ) spin interactions as a function of an applied magnetic field $h$. At the Uimin-Lai-Sutherland (ULS) critical point we find a gapless to gapless transition revealed by the dynamical structure factor $S(q,\omega )$ as a function of $h$. At $h=0$, the envelope of the lowest-energy excitations goes soft at two points, $q_1=2\pi /3$ and $q_2=4\pi /3$, dubbed the phase A. With increasing field, the spectral peaks at each of the gapless points bifurcate, making in total four soft modes, and combine to form a new set of excitations that soften at a single point $q=\pi$ at $h_{c1}\approx 0.94$. Beyond $h_{c1}$ the system enters another gapless B phase until the transition at $h_{c2}=4$ to the fully polarized phase. We compare the ULS model results with those for the Affleck-Kennedy-Lieb-Tasaki model as a representative of the gapped Haldane phase. We explain the mechanism of the gapless to gapless transition in the ULS model using its conserved charges and a spinon band picture. We also discuss the universality of central charges of the BLBQ family of models subjected to a magnetic field.

The evolution of magnetic properties of isostructural and isoelectronic solid solutions of the superconducting itinerant $5f$-electron ferromagnet (FM) UCoGe with antiferromagnet (AFM) UIrGe was studied by magnetization, AC susceptibility, specific heat, and electrical resistivity measurements of a series of $\mathrm{U}{\mathrm{Co}}_{1-x}{\mathrm{Ir}}_x\mathrm{Ge}$ compounds in polycrystalline and single-crystalline form at various temperatures and magnetic fields. Both the weak FM and superconductivity in UCoGe were found to have vanished already for very low Ir substitution for Co $(x=0.02)$. The AFM of UIrGe is gradually suppressed. This is documented by a rapid decrease in both Néel temperature and the critical field of the metamagnetic transition with decreasing Ir concentration, which both tend to vanish just above $x=0.8$. The section of the $T\text{−}x$ phase diagram in the range $0.02\le x\le 0.8$ is dominated by a correlated paramagnetic phase (CPM) exhibiting very broad bumps in temperature dependencies of $b$-axis magnetization and specific heat developing with increasing $x$. For $x\ge 0.24$, wide peaks appear in the $c$-axis thermomagnetic curves due to AFM correlations which may eventually lead to frozen incoherent spin configurations at low temperatures. The CPM is also accompanied by specific electrical resistivity anomalies. The $T\text{−}x$ phase diagram determined for the $\mathrm{U}{\mathrm{Co}}_{1-x}{\mathrm{Ir}}_x\mathrm{Ge}$ compounds contrasts with the behavior of the related $\mathrm{U}{\mathrm{Rh}}_{1-x}{\mathrm{Ir}}_x\mathrm{Ge}$ system, which was reported to exhibit an extended concentration range of stable FM in Rh-rich compounds and a discontinuous transformation between the FM and AFM phases at a critical Rh-Ir concentration. The striking difference is tentatively attributed to (a) the instability of tiny U moment in the weak itinerant FM UCoGe induced by substitutional disorder at already very low Ir doping, (b) the rather stable U moment in URhGe formed by much less delocalized $5f$ electrons assisted by weakly varying lattice parameters of $\mathrm{U}{\mathrm{Rh}}_{1-x}{\mathrm{Ir}}_x\mathrm{Ge}$ compounds.

We propose a design of an interlaced wire medium with a quasicrystalline lattice based on fivefold rotation symmetry Penrose tiling. The transport properties of this structure are studied. We distinguish two transport regimes, namely, a propagation regime related to the low-frequency interval and localization regime in the high-frequency interval. While the former is observed in structures both with and without the translation symmetry property, the latter is exclusive for aperiodic structures only. We show that the localization regime is promising for many applications, including the engineering of effective multichannel devices for telecommunication and imaging systems.

Superconductivity, an emergence of a macroscopic quantum state, gives rise to unique electromagnetic responses leading to perfect shielding of magnetic field and zero electrical resistance. In this paper, we propose that superconductors with the space-inversion symmetry breaking host giant nonreciprocal optical phenomena, such as photocurrent generation and second harmonic generation. The nonreciprocal optical responses show divergent behaviors in the low-frequency regime and originate from twofold indicators unique to parity-breaking superconductors, namely, the nonreciprocal superfluid density and the Berry curvature derivative. Furthermore, the mechanism and frequency dependence are closely tied to the preserved temporal symmetry in the superconductor. The relation is useful for probing the space-time structure of the superconducting symmetry. The indicators characterize the low-frequency property of nonreciprocal optical responses and hence quantify the performance of superconductors in nonreciprocal optics.

It has been recently shown how the tensorial nature of real-time path integrals (PIs) involving the Feynman-Vernon influence functional can be utilized with matrix product states, taking advantage of the finite length of the bath-induced memory. Tensor networks (TNs) promise to provide a unified language to express the structure of a PI. Here, a generalized TN specifically incorporating the pairwise interaction structure of the influence functional and its invariance with respect to the average forward-backward position or the sojourn value in the form of the blip representation is derived and implemented. This pairwise connected TNPI (PC-TNPI) is illustrated through applications to typical spin-boson problems and explorations of the differences caused by the exact form of the spectral density. The storage and performance scalings are reported, showing the compactness of the representation and the efficiency of the contraction process. Finally, taking advantage of the compressed representation, the viability of using PC-TNPI for simulating multistate problems is demonstrated. The PC-TNPI structure can be shown to yield other TN algorithms currently in use. Consequently, it should be possible to use it as a starting point for deriving other optimized procedures.

The optical spectra of antiferromagnetic copper metaborate ${\mathrm{CuB}}_2{\mathrm{O}}_4$ are characterized by an exceptionally rich structure of narrow absorption lines due to electronic transitions within the magnetic ${\mathrm{Cu}}^{2+}$ ions, but their unambiguous identification and behavior in magnetic fields have remained far from being fully understood. We study the polarized magnetoabsorption spectra of this tetragonal antiferromagnet with high spectral resolution across the energy range of $1.4055–1.4065$ eV in magnetic fields up to 9.5 T for temperatures from 1.6 up to the Néel temperature $T_N=20$ K. We observe a set of eight absorption lines at $T=1.6$ K in magnetic fields exceeding 1.4 T, which we identify as arising from Frenkel excitons related to the ground and first excited states of the ${\mathrm{Cu}}^{2+}$ ions. The number of these excitons is defined by the presence of the four ${\mathrm{Cu}}^{2+}$ ions with doubly degenerate spin state $S=1/2$ at the $4b$ positions in the crystallographic unit cell. The energies of these excitons are determined by the exchange interaction of 0.5 meV of the ${\mathrm{Cu}}^{2+}$ ions in the excited state with the surrounding ions and by the Davydov splitting of 0.12 meV. In large magnetic field the observed Zeeman splitting is controlled by the anisotropic $g$-factors of both the ground and excited states. We develop a theoretical model of Frenkel excitons in the magnetic field that accounts for specific features of the spin structure and exchange interactions in ${\mathrm{CuB}}_2{\mathrm{O}}_4$. The model is used for fitting the experimental data and evaluation of the Frenkel exciton parameters, such as the Davydov splitting, the molecular exchange energy, and the $g$-factors of the ground and excited states of the ${\mathrm{Cu}}^{2+}$ ions.

We apply the projected Hartree-Fock theory (PHF) for approximating ground states of Heisenberg spin clusters. Spin-rotational, point-group, and complex-conjugation symmetry are variationally restored from a broken-symmetry mean-field reference, where the latter corresponds to a product of local spin states. A fermionic formulation of the Heisenberg model furnishes a conceptual connection to PHF applications in quantum chemistry and detailed equations for a self-consistent field optimization of the reference state are provided. Different PHF variants are benchmarked for ground-state energies and spin-pair correlation functions of antiferromagnetic spin rings and three different polyhedra, with various values of the local spin-quantum number $s$. Although PHF is not suitable to study the thermodynamic limit (where it reduces to the conventional HF results), the low computational cost and the compact wave-function representation make PHF a promising complement to existing approaches for ground states of finite spin clusters, particularly for large local spin $s$ and a moderately large number of sites $N$. The present work may also motivate future explorations of more accurate post-PHF methods for Heisenberg spin clusters.

We propose a three-terminal structure to probe robust signatures of Majorana zero modes. This structure consists of a quantum dot coupled to the normal-metal, $s$-wave superconducting, and Majorana Y-junction leads. The zero-bias differential conductance at zero temperature of the normal-metal lead peaks at $2e^2/h$, which will be deflected after Majorana braiding. This quantized conductance can entirely arise from the Majorana-induced crossed Andreev reflection, protected by the energy gap of the superconducting lead. We find that the effect of thermal broadening is significantly suppressed when the dot is on resonance. In the case in which the energy level of the quantum dot is much larger than the superconducting gap, tunneling processes are dominated by Majorana-induced crossed Andreev reflection. Particularly, a novel kind of crossed Andreev reflection equivalent to the splitting of charge quanta $3e$ occurs after Majorana braiding.

Recent experiments have provided evidence for chiral charge order in kagome superconductors (SCs). This intriguing possibility motivates us to unveil the first pathway to engineer topological superconductivity by harnessing the interplay of charge Chern insulators (CIs) and conventional SCs. We here identify under which conditions a pyramidal SC/CI/SC heterostructure induces an effective one-dimensional spinless $p$-wave SC that allows pinning Majorana zero modes (MZMs) at termination edges and domain walls. As we reveal, such a MZM track is controlled by the phase difference of the two SCs involved and additional magnetic fields, which are required for generating Rashba-type spin-orbit coupling. Further, we show that a SC/CI/SC/CI/SC double-pyramidal hybrid defines a double MZM track, in which braiding occurs by varying the two superconducting phase differences in space and adiabatically in time. Given the geometry of the MZM racetrack, we propose to employ the time-averaged quadrupolar differential conductance to confirm the here-termed MZM track-exchange process which is pivotal for braiding. In addition, we identify experimental knobs which enable the fusion of MZM pairs, and the detection of the underlying non-Abelian topological order and twofold many-body ground-state degeneracy by encoding it in a topological invariant.

Recently, superconductivity has been discovered in rocksalt-structured binary lanthanum monoxide LaO through state-of-the-art oxide thin-film epitaxy. In this work, we reveal that the normal state of superconducting LaO is a ${\mathbb{Z}}_2$ nontrivial topological metal, where the Dirac point protected by the crystal symmetry is located around the Fermi energy. By analyzing the orbital characteristics, we show that the nature of the topological band structure of LaO originates from the intra-atomic transition from the outer shell La $5d$ to the inner shell $4f$ orbitals driven by the strong octahedral crystal field. Furthermore, the appearance of novel surface states unambiguously demonstrates the topological signature of the LaO superconductor. Our theoretical findings not only shed light on the understanding of the exotic quantum behaviors in the LaO superconductor with intimate correlation between $4f$ and $5d$ orbitals in La, but also provide an exciting platform to explore the interplay between nontrivial topology and superconductivity.

We perform nonperturbative calculations of light field induced current in twisted bilayer graphene (tBLG) irradiated by a circularly polarized (CP) few-cycle laser pulse. The strong-field electron dynamics is simulated within a single-particle picture by two complementary approaches, including the velocity-gauge density-matrix equation and the length-gauge time-dependent Schrödinger equation, which both combine a tight-binding model for describing tBLG electronic structures. The two theoretical approaches yield the same result in the context of studying the carrier-envelope phase (CEP) and laser intensity dependent photocurrent. We show that the measured current exhibits a sinusoidal dependence on CEP of CP driving fields, with the sine phase determined by the electrode orientation with respect to the tBLG lattices. Moreover, it has been proven that an important reversal of the photocurrent direction occurs as the driving optical field strength increases to the strong-field regime, which cannot appear in the monolayer or conventional AA- and AB-stacked bilayer graphene. Based on the analysis of the conduction band population, we successfully identify that such current direction reversal in tBLG mainly originates from the interference of multichannel electron transition among two conduction bands and four valence bands closest to the Fermi level. Our results may pave the way toward investigation of nonlinear optical response in layered materials, and might provide insight for the design of future ultrafast optoelectronic devices.

Recently it has been shown that not only GdFeCo alloys exhibit single-pulse helicity-independent all-optical switching, but that this effect is also seen in Co/Gd bilayers. However, there have been no reports on the explicit time dynamics of the switching process in these bilayers as of yet. Furthermore, time-resolved measurements of switching of other materials are typically done with a constant applied field to reset the magnetization between consecutive pulses and thus ensure repeatable behavior. In this paper we experimentally resolve the explicit dynamics of the switching process in Co/Gd, and the influence of applied magnetic fields on the switching process. We observe that after a switch within several picoseconds, the magnetization switches back at a time scale of hundreds of picoseconds. This backswitch includes a strong dependence on the magnetic field strength even at subtesla fields, significantly smaller than the exchange fields that govern the switching dynamics. This surprising behavior is explained by a combination of longitudinal switching (on a picosecond timescale), precessional switching (on a nanosecond time scale), and domain-wall motion (on a timescale of $10\mathrm{n}\mathrm{s}$ and beyond). We discuss these different switching regimes and their relative importance using simple model calculations.

Layered hybrid improper ferroelectrics are very important for multiferroic devices; however, it has been very challenging to obtain multiferroic properties at room temperature. In this study we report that acceptor-donor codoping can be used to realize ferromagnetism in ${\mathrm{Ca}}_3{\mathrm{Mn}}_2{\mathrm{O}}_7$ improper ferroelectric ceramics at room temperature. The transmission electron microscope observation and first-principles calculation revealed that the obtained ferromagnetic properties result from the ${\mathrm{MnO}}_6$ octahedron tilt caused by the large lattice distortion near the acceptor-donor pair. At the same time, an obvious magnetoimpedance effect was observed.

The magnetic $H-T$ phase diagram of a quasi-two-dimensional antiferromagnet $\mathrm{RbFe}{\left({\mathrm{MoO}}_4\right)}_2$ $(S=5/2)$ with an equilateral triangular lattice structure is studied with ${}^{87}\mathrm{Rb}$ NMR and neutron-diffraction techniques. This combination of experimental techniques allows us to determine the ordered components of the magnetic moments on the ${\mathrm{Fe}}^{3+}$ ions within various high-field phases—the Y, UUD, V, and fan structures, stabilized in the compound by the in-plane magnetic field. It is also established that the transition from the V to the fan phase is of first order, whereas the transition from the fan phase to the polarized paramagnetic phase is continuous. An analysis of the NMR spectra shows that the high-field fan phase of $\mathrm{RbFe}{\left({\mathrm{MoO}}_4\right)}_2$ can be successfully described by a periodic commensurate oscillation of the magnetic moments around the field direction in each ${\mathrm{Fe}}^{3+}$ layer combined with an incommensurate modulation of the magnetic structure perpendicular to the layers.

Understanding the damping is an important fundamental problem with widespread implications in magnetic technology. Ferrimagnetic materials offer a rich platform to explore not only the damping of the ferromagnetic mode, but also the damping of the high-frequency exchange mode very promising for ultrafast devices. Here we use time-resolved magneto-optical Kerr effect to investigate the ferromagnetic and exchange resonance modes and their damping in the bismuth-doped gadolinium iron garnet over a broad range of magnetic fields (0–10 T) and temperatures (50–300 K) including the magnetization and angular compensation points. These two resonance modes are excited via the inverse Faraday effect and unambiguously identified by their distinct frequency dependence on temperature and magnetic field. The temperature-dependent measurements in the external magnetic field $H_{\mathrm{ext}}=2\mathrm{T}$ revealed that the intrinsic damping of the ferromagnetic mode is always smaller than the one of the exchange modes and both have a maximum near the angular compensation point. These results are fully consistent with recent predictions of atomistic simulations and a theory based on two-sublattice Landau-Lifshitz-Bloch equation. We also demonstrate that the damping of these modes varies differently as a function of $H_{\mathrm{ext}}$. We explain the observed behaviors by considering the different features of the effective fields defining the precession frequencies of the ferromagnetic and exchange modes.

The magnon-phonon interaction is receiving growing attention due to its key role in spin caloritronics and the emerging field of acoustic spintronics. At resonance, this magnetoelastic interaction forms magnon polarons, which underpin exotic phenomena such as magnonic heat currents and phononic spin, but is mostly investigated using mesoscopic spin-lattice models. Motivated to integrate the magnon-phonon interaction into first-principles many-body electronic structure theory, we set out to derive the exchange contribution, which is subtler than the spin-orbit contribution, using Schwinger functional derivatives. To avoid having to solve the famous Hedin-Baym equations self-consistently, the phonons are treated as perturbations to the electronic structure. A formalism based on imposing a crossing-symmetric electron-electron interaction is developed in order to treat charge and spin on equal footing to respect the Pauli exclusion principle. Due to spin conservation, the magnon-phonon interaction first enters to second order through the magnon-magnon interaction, which renormalizes the magnons. We show by iteration that the magnon-magnon interaction contains a “screened $T$ matrix” term and an arguably more important term which, in the local-spin limit, enables first-principles phonon emission and absorption amplitudes, predicted by phenomenological magnetoelastic models. These terms are, respectively, of first and second order in the screened collective four-point interaction $\mathcal{W}$—a crossing-symmetric analog of Hedin's $W$. Proof-of-principle results are presented at varying temperatures for an isotropic magnon spectrum in three dimensions in the presence of a flat optical phonon branch.

The low-frequency lattice vibrations and relaxations are investigated in single crystals of the four 3D hybrid organolead perovskites, ${\mathrm{MAPbBr}}_3$, ${\mathrm{FAPbBr}}_3$, ${\mathrm{MAPbI}}_3$, and $\alpha \text{−}{\mathrm{FAPbI}}_3$, at the Brillouin zone center using Raman and Brillouin scattering and at the zone boundary using inelastic neutron scattering. The temperature dependence of the ${\mathrm{PbX}}_6$ lattice modes in the four compounds can be renormalized into universal curves, highlighting a common vibrational dynamics at the cubic to tetragonal transition. In particular, no soft vibration is observed excluding a displacive-like transitional dynamics. The reorientational (pseudospin) motions of the molecular cations exhibit a seemingly order-disorder character recalling that of plastic crystals, but attributed to a secondary order parameter. At ultralow frequency, a quasielastic component evidenced by Brillouin scattering and associated to the unresolved central peak observed in neutron scattering, is attributed to center of mass anharmonic motions and rattling of the molecular cations in the perovskite cavities. Its partially unexpressed critical behavior at the transition points toward the general importance of defects in HOPs preventing the net divergence of order parameter correlations at the critical temperatures.

The critical properties and magnetic entropy change of quasi-two-dimensional ${\mathrm{LaCrSb}}_3$ single crystals have been systematically investigated. The ferromagnetic transition is determined to be of a second order. Critical exponents $\beta =0.298\left(7\right)$ with a critical temperature $T_c=132.0\left(2\right)$ K and $\gamma =1.277\left(9\right)$ with $T_c=132.5\left(3\right)$ K are yielded by the modified Arrott plot, whereas $\delta =5.28\left(9\right)$ is deduced by a critical isotherm analysis at $T=132$ K. The critical exponents of quasi-two-dimensional ${\mathrm{LaCrSb}}_3$ exhibit a three-dimensional critical behavior. The magnetic interaction is found to be of a long range and the magnetic exchange distance decays as $J\left(r\right)\approx r^{-4.9}$, which lies between the mean-field model and 3D Heisenberg model. Furthermore, the magnetic entropy change $-\mathrm{\Delta }{S}_M$ features a maximum around $T_c$, i.e., $-\mathrm{\Delta }{S}_M^{\text{max}}\sim 3.4$, 5.9, and $5.8 \mathrm{J} {\mathrm{kg}}^{-1}{\mathrm{K}}^{-1}$ for a field change of 5 T applied the $H//a, b$, and $c$ axes, respectively. The rotating magnetic entropy change $\mathrm{\Delta }{S}_M^R(T,H)$ between the $a$ and $b$ axes (the $a$ and $c$ axes) reaches a maximum value of $2.55 \left(2.49\right) \mathrm{J} {\mathrm{kg}}^{-1}{\mathrm{K}}^{-1}$ around $T_c$, exhibiting strong anisotropic features. However, $\mathrm{\Delta }{S}_M^R(T,H)$ between the $b$ and $c$ axes is $\sim 0 \mathrm{J} {\mathrm{kg}}^{-1}{\mathrm{K}}^{-1}$ at $T>T_c$ displaying a nearly isotropic behavior, and is less than $0.3 \mathrm{J} {\mathrm{kg}}^{-1}{\mathrm{K}}^{-1}$ at $T<T_c$ showing weak anisotropy.

The physical properties of the noncentrosymmetric and quasi-two-dimensional canted antiferromagnetic material ${\mathrm{CoTeMoO}}_6$ (CTMO) are studied. We unravel a spectrum of intriguing phenomena, including a correlated short-range-ordered Griffiths-like phase near $T_G\sim 64\mathrm{K}$, a sharp step-like metamagnetic behavior of isothermal magnetization induced by a spin-flop transition at a critical magnetic field $H_{\mathrm{c}}\sim 1.2\mathrm{T}$, a strong dielectric anomaly, a pronounced magnetodielectric effect, and the associated weak magnetoelectric coupling at its magnetic transition temperature, $T_N\sim 23.4\mathrm{K}$. The crucial roles played by spin canting in CTMO are revealed in the aforementioned strongly entangled behavior of the spin and dipolar order parameters. The observed magnetostriction effect coupled with spin-phonon coupling seems to be a key factor in influencing the observed magnetodielectric effect. In addition, our theoretical first-principles calculations predict an insulating state with a canted antiferromagnetic spin configuration that matches well with the experimental results.