We present a thorough investigation by magneto-optical imaging of the magnetic flux penetration in Nb thin films with lithographically defined border indentations. We demonstrate that discontinuity lines ($d$ lines), caused by the abrupt bending of current streamlines around the indentations, depart from the expected parabolic trend close to the defect and depend on the shape and size of the indentation as well as on the temperature. These findings are backed up and compared with theoretical results obtained by numerical simulations and analytical calculations highlighting the key role played by demagnetization effects and the creep exponent $n$. In addition, we show that the presence of nearby indentations and submicrometer random roughness of the sample border can severely modify the flux front topology and dynamics. Strikingly, in contrast to what has been repeatedly predicted in the literature, we do not observe that indentations act as nucleation spots for flux avalanches, but they instead help to release the flux pressure and avoid thermomagnetic instabilities.

The motion of ferroelectric domain walls greatly contributes to the macroscopic dielectric and piezoelectric response of ferroelectric materials. The domain-wall motion through the ferroelectric material is, however, hindered by pinning on crystal defects, which substantially reduces these contributions. Here, using thermodynamic models based on the Landau-Ginzburg-Devonshire theory, we find a relation between the microscopic reversible motion of nonferroelastic ${180}^{\circ }$ domain walls interacting with a periodic array of pinning centers and the nonlinear macroscopic permittivity. We show that the reversible motion of domain walls can be split into two basic modes: first, the bending of a domain wall between pinning centers, and, second, the uniform movement of the domain-wall plane. We show that their respective contributions may change when the distribution of pinning centers is rearranged during the material aging. We demonstrate that it is possible to indicate which mechanism of the domain-wall motion is affected during material aging. This allows one to judge whether the defects only homogeneously accumulate at domain walls or prefer to align in certain directions inside the domain-wall plane. We suggest that this information can be obtained using simple macroscopic dielectric measurements and a proper analysis of the nonlinear response. Our results may therefore serve as a simple and useful tool to obtain details on domain-wall pinning in an aging process.

We have investigated the magnetic and magnetoelectric properties of ${\mathrm{CaMnGe}}_2{\mathrm{O}}_6$ by means of powder neutron diffraction, magnetic susceptibility, heat capacity, and electrical polarization measurements. The presence of one-dimensional short-range magnetic correlations within the ${\mathrm{MnO}}_6$ octahedra chains well above long-range antiferromagnetic ordering (15 K) was evidenced. A one-dimensional antiferromagnetic correlation model along the zigzag chains was developed to fit the diffuse magnetic scattering. The linear magnetoelectric effect and pertinent ferrotoroidicity, allowed by the magnetic symmetry ($C{2}^{\prime }/c$), have been verified experimentally and theoretically.

In ultrathin ferromagnetic films with perpendicular anisotropy a spin-reorientation transition from out-of-plane to in-plane orientation of the magnetization vector may occur. The competition of exchange and dipole interaction leads to the formation of stripe domain patterns in the vicinity of the spin reorientation transition. Here we investigate fluctuations of domain patterns in ultrathin epitaxial Ni/Fe films grown on Cu(001) using the technique of threshold photoemission magnetic circular dichroism in combination with photoemission electron microscopy allowing real-time observation of the domain pattern dynamics. The key finding of our experiments is that fluctuations can easily be quantified by calculating thermodynamic susceptibilities from a series of time resolved images. We analyze the strength of fluctuations with respect to temperature and externally applied out-of-plane magnetic fields.

We present measurements of the exchange stiffness $D$ and the exchange constant $A$ of a sputtered 80 nm ${\mathrm{Tb}}_{0.3}{\mathrm{Dy}}_{0.7}{\mathrm{Fe}}_2$ film. Using a broadband ferromagnetic resonance setup in a wide frequency range from 10 to 50 GHz, multiple perpendicular standing spin-wave resonances were observed with the external static magnetic field applied in-plane. The field corresponding to the strongest resonance peak at each frequency is used to determine the effective magnetization, the $g$ factor, and the Gilbert damping. Furthermore, the dependence of spin-wave mode on field position is observed for several frequencies. The analysis of spin-wave resonance spectra at multiple frequencies allows precise determination of the exchange stiffness $D=\left(2.79\pm 0.02\right)\times {10}^{-17}\mathrm{T}{\mathrm{m}}^2$ for an 80 nm thick film. From this value, we calculated the exchange constant $A=(9.1\pm 0.1)\mathrm{pJ}{\mathrm{m}}^{-1}$.

In this paper, we report inelastic neutron scattering measurements of the magnetic excitations of green dioptase ${\mathrm{Cu}}_6\left[{\mathrm{Si}}_6{\mathrm{O}}_{18}\right]·6{\mathrm{H}}_2\mathrm{O}$. The observed spectrum contains two magnetic modes and a prominent spin gap that is consistent with the ordered ground state of Cu moments coupled antiferromagnetically in spiral chains along the $c$ axis and ferromagnetically in $ab$ planes on the hexagonal cell. The data are in excellent agreement with a spin-$\frac{1}{2}$ Hamiltonian that includes antiferromagnetic nearest-neighbor intrachain coupling $J_c=10.6\left(1\right)$ meV, ferromagnetic interchain coupling $J_{ab}=-1.2\left(1\right)$ meV, and exchange anisotropy $\mathrm{\Delta }{J}_c=0.14\left(1\right)$ meV. We calculated the sublattice magnetization to be strongly reduced, $\sim 0.39{\mu }_{\mathrm{B}}$. This appears compatible with a reduced Néel temperature, $T_{\mathrm{N}}=14.5\text{K}\ll J_c$, and can be explained by a presence of quantum spin fluctuations.

We consider an isolated vortex in the two-dimensional proximity-induced superconducting state formed at the interface of a three-dimensional strong topological insulator (TI) and an $s$-wave superconductor. Prior calculations of the bound states of this system famously revealed a zero-energy state that is its own conjugate, a Majorana fermion bound to the vortex core. We calculate, not the bound states, but the scattering states of this system, and ask how the spin-momentum-locked massless Dirac form of the single-particle Hamiltonian, inherited from the TI surface, affects the cross section for scattering Bogoliubov quasiparticles from the vortex. As in the case of an ordinary superconductor, this is a two-channel problem with the vortex mixing particlelike and holelike excitations. As in the ordinary case, the same-channel differential cross section diverges in the forward direction due to the Aharonov-Bohm effect, resulting in an infinite total cross section but finite transport and skew cross sections. We calculate the transport and skew cross sections numerically, via a partial wave analysis, as a function of both quasiparticle excitation energy and chemical potential. Novel effects emerge as particlelike or holelike excitations are tuned through the Dirac point.

Type-II superconductors owe their magnetic and transport properties to vortex pinning, the immobilization of flux quanta through material inhomogeneities or defects. Characterizing the potential energy landscape for vortices, the pinning landscape (or short, pinscape), is of great technological importance. Aside from measurement of the critical current density $j_c$ and of creep rates $S$, the $\text{ac}$ magnetic response provides valuable information on the pinscape which is different from that obtained through $j_c$ or $S$, with the Campbell penetration depth ${\lambda }_{\mathrm{C}}$ defining a characteristic quantity well accessible in an experiment. Here, we derive a microscopic expression for the Campbell penetration depth ${\lambda }_{\mathrm{C}}$ using strong-pinning theory. Our results explain the dependence of ${\lambda }_{\mathrm{C}}$ on the state preparation of the vortex system and the appearance of hysteretic response. Analyzing different pinning models, metallic or insulating inclusions, as well as $\delta T_c$ and $\delta \ell$ pinning, we discuss the behavior of the Campbell length for different vortex-state preparations within the phenomenological $H\text{−}T$ phase diagram and compare our results with recent experiments.

Hexagonal $\mathrm{LuFe}{\mathrm{O}}_3$ has drawn a lot of research attention due to its contentious room-temperature multiferroicity. Due to the instability of hexagonal phase in the bulk form, most experimental studies focused on $\mathrm{LuFe}{\mathrm{O}}_3$ thin films which can be stabilized by strain using proper substrates. Here we report on the hexagonal phase stabilization, magnetism, and magnetoelectric coupling of bulk $\mathrm{LuFe}{\mathrm{O}}_3$ by partial Sc substitution of Lu. First, our first-principles calculations show that the hexagonal structure can be stabilized by partial Sc substitution, while the multiferroic properties, including the noncollinear magnetic order and geometric ferroelectricity, remain robustly unaffected. Therefore, $\mathrm{L}{\mathrm{u}}_{1-x}\mathrm{S}{\mathrm{c}}_x\mathrm{Fe}{\mathrm{O}}_3$ can act as a platform to check the multiferroicity of $\mathrm{LuFe}{\mathrm{O}}_3$ and related materials in the bulk form. Second, the magnetic characterizations on bulk $\mathrm{L}{\mathrm{u}}_{1-x}\mathrm{S}{\mathrm{c}}_x\mathrm{Fe}{\mathrm{O}}_3$ demonstrate a magnetic anomaly (probable antiferromagnetic ordering) above room temperature, ∼425–445 K, followed by magnetic transitions in low temperatures (∼167–172 K). In addition, a magnetoelectric response is observed in the low-temperature region. Our study provides useful information on the multiferroic physics of hexagonal $R\mathrm{Fe}{\mathrm{O}}_3$ and related systems.

We present a theoretical platform for modeling the electronic and magneto-optic properties of magnetically doped core-shell nanoparticles that has, as a central prediction, a mechanism by which the $g$ factors in these nanoparticles can be tuned over a wide range by controlled positioning of magnetic impurities. We illustrate this effect for wide-gap Mn-doped CdS-ZnS core-shell particles and point out several unexpected trends that merit extended experimental investigation. The ability to tune $g$ factors will make core-shell nanostructures viable candidates for spintronic applications, and the comprehensive modeling approach outlined here will be a powerful tool for predicting their properties as well as for optimizing the design of novel spintronic devices.

An exact solution is presented for the time-dependent wave function of an initial ground-state Kramers-doublet qubit that is driven around a quantum ring. We show that the initial qubit may be transformed to an arbitrary point on the Bloch sphere for an integral number of revolutions around the ring. Full coverage of the Bloch sphere is achieved by dividing the total rotation into segments, changing the rotation axis after each segment by an adiabatic shift in the Rashba spin-orbit interaction. Prospects and challenges for possible realizations are discussed for which rings based on InAs quantum wires are promising candidates.

Based on low-temperature resistivity, heat capacity, and magnetization investigations, we show that the unusually strong suppression of superconductivity in ${\mathrm{Lu}}_x{\mathrm{Zr}}_{1-x}{\mathrm{B}}_{12}$ ($x<8\%$) BCS-type superconductors is caused by the emergence of static spin polarization in the vicinity of nonmagnetic lutetium impurities. The analysis of the obtained results points to a formation of static magnetic moments with ${\mu }_{\mathrm{eff}}\approx 6{\mu }_B$ per ${\mathrm{Lu}}^{3+}$ ion (${}^1{S}_0$ ground state, $4f^{14}$ configuration) incorporated in the superconducting ${\mathrm{ZrB}}_{12}$ matrix. The size of these spin-polarized nanodomains was estimated to be about 5 Å.

We study particle-hole instabilities in the framework of the spin-fermion (SF) model. In contrast to previous studies, we assume that adjacent hot spots can overlap due to a shallow dispersion of the electron spectrum in the antinodal region. In addition, we take into account effects of a remnant low energy and momentum Coulomb interaction. We demonstrate that at sufficiently small values $|\varepsilon (\pi ,0)-E_F|\lesssim \mathrm{\Gamma }$, where $E_F$ is the Fermi energy, $\varepsilon \left(\pi ,0\right)$ is the energy in the middle of the Brillouin zone edge, and $\mathrm{\Gamma }$ is a characteristic energy of the fermion-fermion interaction due to the antiferromagnetic fluctuations, the leading particle-hole instability is a $d$-form factor Fermi surface deformation (the Pomeranchuk instability) rather than the charge modulation along the Brillouin zone diagonals predicted within the standard SF model previously. At lower temperatures, we find that the deformed Fermi surface is further unstable to formation of a $d$-form factor charge density wave (CDW) with a wave vector along the Cu-O-Cu bonds (axes of the Brillouin zone). We show that the remnant Coulomb interaction enhances the $d$-form-factor symmetry of the CDW. These findings can explain the robustness of this order in the cuprates. The approximations made in the paper are justified by a small parameter that allows one to implement an Eliashberg-like treatment. Comparison with experiments suggests that in many cuprate compounds the prerequisites for the proposed scenario are indeed fulfilled and the results obtained may explain important features of the charge modulations observed recently.

A large part of the interest in magnets with frustrated antiferromagnetic interactions comes from the many new phases found in applied magnetic field. In this article, we explore some of the new phases which arise in a model with frustrated ferromagnetic interactions, the $J_1\text{−}{J}_2\text{−}{J}_3$ Heisenberg model on a square lattice. Using a combination of classical Monte Carlo simulation and spin-wave theory, we uncover behavior reminiscent of some widely studied frustrated antiferromagnets, but with a number of new twists. We first demonstrate that, for a suitable choice of parameters, the phase diagram as a function of magnetic field and temperature is nearly identical to that of the Heisenberg antiferromagnet on a triangular lattice, including the celebrated $1/3$-magnetization plateau. We then examine how this phase diagram changes when the model is tuned to a point where the classical ground state is highly degenerate. In this case, two new phases emerge: a classical, finite-temperature spin liquid, characterized by a “ring” in the spin structure factor $\mathcal{S}\left(\mathbf{q}\right)$; and a vortex crystal, a multiple-$Q$ state with finite magnetization, which can be viewed as an ordered lattice of magnetic vortices. All of these new phases persist for a wide range of magnetic fields. We discuss the relationship between these results and published studies of frustrated antiferromagnets, together with some of the materials where these new phases might be observed in experiment.

We calculate the orbital magnetic susceptibility ${\chi }_{\mathrm{orb}}$ for an 8-band tight-binding model of gapless and gapped graphene using Green's functions. Analogously, we study ${\chi }_{\mathrm{orb}}$ for a ${\mathrm{MoS}}_2$ 12-band model. For both materials, we unravel the character of the processes involved in the magnetic response by looking at the contribution at each point of the Brillouin zone. By this, a clear distinction between intra- and interband excitations is generally possible and we are able to predict qualitative features of ${\chi }_{\mathrm{orb}}$ only through the knowledge of the band structure. The study is complemented by comparing the magnetic response with that of 2-band lattice Hamiltonians which reduce to the Dirac and Bernevig-Hughes-Zhang models in the continuum limit.

The electronic structure of monolayer ${\mathrm{MoS}}_2$ nanoribbons and quantum dots has been investigated by means of an effective $\mathbf{k}·\mathbf{p}$ two-band model. Both systems with borders exhibit states spatially localized on the edges and with energies lying in the band gap. We show that the conduction- and valence-band curvatures determine the presence/absence of these states the origin of which has been related to the marginal topological properties of the ${\mathrm{MoS}}_2$ single-valley Hamiltonian.

An efficient and stable algorithm for $U\left(1\right)$ symmetric matrix product states (MPS) with periodic boundary conditions (PBCs) is proposed. It is applied to a study of correlation and entanglement properties of the eigenstates of the spin-$\frac{1}{2}$ XXZ model with different spin projections. Convergence properties and accuracy of the algorithm are studied in detail.

We present an analytic study of domain-wall statics and dynamics in ferromagnetic nanotubes with spin-orbit-induced Dzyaloshinskii-Moriya interaction (DMI). Even at the level of statics, dramatic effects arise from the interplay of space curvature and DMI: the domains become chirally twisted, leading to more compact domain walls. The dynamics of these chiral structures exhibits several interesting features. Under weak applied currents, they propagate without distortion. The dynamical response is further enriched by the application of an external magnetic field: the domain-wall velocity becomes chirality dependent and can be significantly increased by varying the DMI. These characteristics allow for enhanced control of domain-wall motion in nanotubes with DMI, increasing their potential as information carriers in future logic and storage devices.

Superconductivity in the noncentrosymmetric compound ${\mathrm{SrAuSi}}_3$ [$\mathrm{BaNiS}{\mathrm{n}}_3$ type, $I4mm,a=4.4024\left(9\right)\AA$, and $c=9.942\left(2\right)\AA$] was studied by electrical resistivity, magnetic susceptibility, and specific heat measurements using single-phase polycrystalline samples, and ab initio band calculation. These measurements of the physical properties confirmed that the ${\mathrm{SrAuSi}}_3$ phase shows bulk superconductivity with a critical temperature of $T_{\mathrm{C}}\sim 1.6\mathrm{K}$ and an upper critical field of $H_{\mathrm{C}2}\sim 1.8\mathrm{kOe}$. In the superconducting state, the electronic specific heat exhibits a thermal-activation-type temperature dependence and the Sommerfeld constant γ linearly responds to magnetic fields for low-energy excitation. These results clearly indicate that ${\mathrm{SrAuSi}}_3$ is a full-gap $s$-wave superconductor without a gap node in the superconducting order parameter. The density functional theory ab initio band calculation revealed that the electron system is composed of three kinds of Fermi surface: a cylindrical shape, a dumbbell shape, and a peculiar-shaped hole pocket. Fermi-surface splitting due to spin-orbit coupling exists only along limited directions in the Brillouin zone. Overall, the splitting energy size is small, insufficient to realize unconventional anisotropic superconductivity attributed to space-inversion symmetry breaking.