Recent scattering experiments in the 3D Kitaev magnet $\beta \text{−}{\mathrm{Li}}_2{\mathrm{IrO}}_3$ have shown that a relatively weak magnetic field along the crystallographic $\mathbf{b}$ axis drives the system from its incommensurate counter-rotating order to a correlated magnet, with a significant uniform ‘zigzag’ component superimposing the magnetization along the field. Here it is shown that the zigzag order is not emerging from its linear coupling to the field (via a staggered, off-diagonal element of the $\mathbf{g}$ tensor) but from its intertwining with the incommensurate order and the longitudinal magnetization. The emerging picture explains all qualitative experimental findings at zero and finite fields, including the rapid decline of the incommensurate order with field and the so-called intensity sum rule. The latter are shown to be independent signatures of the smallness of the Heisenberg exchange $J$, compared to the Kitaev coupling $K$ and the off-diagonal anisotropy $\mathrm{\Gamma }$. Remarkably, in the regime of interest, the field $H^{*}$ at which the incommensurate component vanishes, depends essentially only on $J$, which allows us to extract an estimate of $J\simeq 4$ K from reported measurements of $H^{*}$. We also comment on recent experiments in pressurized $\beta \text{−}{\mathrm{Li}}_2{\mathrm{IrO}}_3$ and conclude that $J$ decreases with pressure.

Polarized neutron reflectometry is used to determine the sequence of magnetic switching in interlayer exchange coupled Fe/MgO(001) superlattices in an applied magnetic field. For 19.6 Å thick MgO layers we obtain a ${90}^{\circ }$ periodic magnetic alignment between adjacent Fe layers at remanence. In an increasing applied field the top layer switches first followed by its second-nearest neighbor. For 16.4 Å MgO layers, a ${180}^{\circ }$ periodic alignment is obtained at remanence and with increasing applied field the layer switching starts from the two outermost layers and proceeds inwards. This sequential tuneable switching opens up the possibility of designing three-dimensional magnetic structures with a predefined discrete switching sequence.

The search for problems where quantum adiabatic optimization might excel over classical optimization techniques has sparked a recent interest in inducing a finite-temperature spin-glass transition in quasiplanar topologies. We have performed large-scale finite-temperature Monte Carlo simulations of a two-dimensional square-lattice bimodal spin glass with next-nearest ferromagnetic interactions claimed to exhibit a finite-temperature spin-glass state for a particular relative strength of the next-nearest to nearest interactions [Phys. Rev. Lett. 76, 4616 (1996)]. Our results show that the system is in a paramagnetic state in the thermodynamic limit, despite zero-temperature simulations [Phys. Rev. B 63, 094423 (2001)] suggesting the existence of a finite-temperature spin-glass transition. Therefore, deducing the finite-temperature behavior from zero-temperature simulations can be dangerous when corrections to scaling are large.

We use spin-polarized scanning tunneling microscopy and density functional theory (DFT) to study domain walls (DWs) and the Dzyaloshinskii-Moriya interaction (DMI) in epitaxial films of Co/Ir(111) and Pt/Co/Ir(111). Our measurements reveal DWs with fixed rotational sense for one monolayer of Co on Ir, with a wall width around 2.7 nm. With Pt islands on top, we observe that the DWs occur mostly in the uncovered Co/Ir areas, suggesting that the wall energy density is higher in Pt/Co/Ir(111). From DFT we find an interfacial DMI that stabilizes Néel-type DWs with clockwise rotational sense. The calculated DW widths are in good agreement with the experimental observations. The calculated total DMI nearly doubles from Co/Ir(111) to Pt/Co/Ir(111); however, in the latter case the DMI is almost entirely due to the Pt with only a minor Ir contribution. Therefore a simple additive effect, in which both interfaces contribute significantly to the total DMI, is not observed for one atomic Co layer sandwiched between Ir and Pt.

Exchange magnetic coupling interactions between $L{1}_0\text{-MnGa}$ and ultrathin Co (Fe) films were studied by first-principles calculations. An unexpected oscillation of magnetic coupling was observed by varying the thickness of Co or Fe layer. Moreover, the coupling types are different for Co and Fe with $L{1}_0\text{-MnGa}$. The magnetic coupling maintains the ferromagnetic interaction for $L{1}_0\text{-MnGa}$/Fe, even if the thickness of Fe layer varies. Interestingly, a change from ferromagnetic to antiferromagnetic couplings appears alternately for $L{1}_0\text{-MnGa}$/Co till Co thickness is up to 11 atomic layers. The coupling oscillations were attributed to the quantum well states formed in the Co (Fe) films. The orbital characters of the quantum well states were analyzed. Our results are useful to further understand the magnetic coupling interactions and design new magnetic nanostructures.

We calculate the superconducting $T_c$ for a system which experiences Rashba spin-orbit interactions. Contrary to the usual case where the electron-electron interaction is assumed to be wave vector independent, where superconductivity is suppressed by the spin-orbit interaction (except for a small region at low electron or hole densities), we find an enhancement of the superconducting transition temperature when we include a correlated hopping interaction between electrons. This interaction originates in the expansion of atomic orbitals due to electron-electron repulsion and gives rise to superconductivity only at high electron (low hole) densities. When superconductivity results from this interaction it is enhanced by spin-orbit coupling, in spite of a suppression of the density of states. The degree of electron-hole asymmetry about the Fermi surface is also enhanced.

We present results of specific heat, electrical resistance, and magnetoresistivity measurements on single crystals of the heavy-fermion superconducting alloy ${\mathrm{Ce}}_{0.91}{\mathrm{Yb}}_{0.09}{\mathrm{CoIn}}_5$. Non-Fermi-liquid to Fermi-liquid crossovers are clearly observed in the temperature dependence of the Sommerfeld coefficient $\gamma$ and resistivity data. Furthermore, we show that the Yb-doped sample with $x=0.09$ exhibits universality due to an underlying quantum phase transition without an applied magnetic field by utilizing the scaling analysis of $\gamma$. Fitting of the heat capacity and resistivity data based on existing theoretical models indicates that the zero-field quantum critical point is of antiferromagnetic origin. Finally, we found that at zero magnetic field the system undergoes a third-order phase transition at the temperature $T_{c3}\approx 7$ K.

We propose a general edge index definition for two-dimensional Floquet topological phases based on a switch-function formalism. When the Floquet operator has a spectral gap, the index covers both clean and disordered phases, anomalous or not, and does not require the bulk to be fully localized. It is interpreted as a nonadiabatic charge pumping that is quantized when the sample is placed next to an effective vacuum. This vacuum is gap-dependent and obtained from a Floquet Hamiltonian. The choice of a vacuum provides a simple and alternative gap-selection mechanism. Inspired by the model from Rudner et al. we then illustrate these concepts on Floquet disordered phases. Switch-function formalism is usually restricted to infinite samples in the thermodynamic limit. Here we circumvent this issue and propose a numerical implementation of the edge index that could be adapted to any bulk or edge index expressed in terms of switch functions, already existing for many topological phases.

Finite topologically nontrivial systems are characterized, among many other unique properties, by the presence of bound states at their physical edges. These topological edge modes can be distinguished from usual Shockley waves energetically, as their energies remain finite and in gap even when the boundaries of the system represent an effectively infinite and sharp energetic barrier. Theoretically, the existence of topological edge modes can be shown by means of the bulk-edge correspondence and topological invariants. On a clean one-dimensional lattice and reducible two-dimensional models, in either the commensurate or semi-infinite case, the edge modes can be essentially obtained analytically, as shown previously [Y. Hatsugai, Phys. Rev. Lett. 71, 3697 (1993); D. Hügel and B. Paredes, Phys. Rev. A 89, 023619 (2014)]. In this work, we put forward a method for obtaining the spectrum and wave functions of topological edge modes for arbitrary finite lattices, including the incommensurate case. A small number of parameters are easily determined numerically, with the form of the eigenstates remaining fully analytical. We also obtain the bulk modes in the finite system analytically and their associated eigenenergies, which lie within the infinite-size limit continuum. Our method is general and can be easily applied to obtain the properties of nontopological models and/or extended to include impurities. As an example, we consider a relevant case of an impurity located next to one edge of a one-dimensional system, equivalent to a softened boundary in a separable two-dimensional model. We show that a localized impurity can have a drastic effect on the original topological edge modes of the system. Using the periodic Harper and Hofstadter models to illustrate our method, we find that, on increasing the impurity strength, edge states can enter or exit the continuum, and a trivial Shockley state bound to the impurity may appear. The fate of the topological edge modes in the presence of impurities can be addressed by quenching the impurity strength. We find that at certain critical impurity strengths, the transition probability for a particle initially prepared in an edge mode to decay into the bulk exhibits discontinuities that mark the entry and exit points of edge modes from and into the bulk spectrum.

We present a method for reconstructing the phonon relaxation-time function ${\tau }_{\omega }=\tau \left(\omega \right)$ (including polarization) and associated phonon free-path distribution from thermal spectroscopy data for systems featuring interfaces with unknown properties. Our method does not rely on the effective thermal-conductivity approximation or a particular physical model of the interface behavior. The reconstruction is formulated as an optimization problem in which the relaxation times are determined as functions of frequency by minimizing the discrepancy between the experimentally measured temperature profiles and solutions of the Boltzmann transport equation for the same system. Interface properties such as transmissivities are included as unknowns in the optimization; however, because for the thermal spectroscopy problems considered here the reconstruction is not very sensitive to the interface properties, the transmissivities are only approximately reconstructed and can be considered as byproducts of the calculation whose primary objective is the accurate determination of the relaxation times. The proposed method is validated using synthetic experimental data obtained from Monte Carlo solutions of the Boltzmann transport equation. The method is shown to remain robust in the presence of uncertainty (noise) in the measurement.

Here, we report an extremely large positive magnetoresistance (XMR) in a single-crystal sample of ${\mathrm{MoSi}}_2$, approaching almost ${10}^7\%$ at 2 K in a 14-T magnetic field without appreciable saturation. Hall resistivity data reveal an uncompensated nature of ${\mathrm{MoSi}}_2$ with an electron-hole compensation level sufficient enough to expect strong saturation of magnetoresistance in the high-field regime. Magnetotransport and the complementary de Haas–van Alphen (dHvA) oscillations results, however, suggest that strong Zeeman effect causes a magnetic field-induced modulation of the Fermi pockets and drives the system towards perfect electron-hole compensation condition in the high-field regime. Thus, the nonsaturating XMR of this semimetal arises under the unconventional situation of Zeeman effect-driven electron-hole compensation, whereas its huge magnitude is decided solely by the ultralarge value of the carrier mobility. Intrinsic ultralarge carrier mobility, strong suppression of backward scattering of the charge carriers, and nontrivial Berry phase in dHvA oscillations attest to the topological character of ${\mathrm{MoSi}}_2$. Therefore, this semimetal represents another material hosting combination of topological and conventional electronic phases.

Type-II Weyl semimetals are characterized by the tilted linear dispersion in the low-energy excitations, mimicking Weyl fermions but with manifest violation of the Lorentz invariance, which has intriguing quantum transport properties. The magnetoconductivity of type-II Weyl semimetals is investigated numerically based on lattice models in parallel electric and magnetic field. We show that in the high-field regime, the sign of the magnetoconductivity of an inversion-symmetry-breaking type-II Weyl semimetal depends on the direction of the magnetic field, whereas in the weak field regime, positive magnetoconductivity is always obtained regardless of magnetic field direction. We find that the weak localization is sensitive to the spatial extent of impurity potential. In time-reversal symmetry-breaking type-II Weyl semimetals, the system displays either positive or negative magnetoconductivity along the direction of band tilting, owing to the associated effect of group velocity, Berry curvature, and the magnetic field.

We have demonstrated size-dependent radiative coupling in a ${\mathrm{Cu}}_2\mathrm{O}$ mesoscopic film, where the spatial matching between the center-of-mass exciton motion and light waves plays an essential role. The observed quadratic increase and oscillation of the photoluminescence intensity with varying film thicknesses (16–1000 nm) indicate a nonlocal response that is unique to mesoscopic systems. Optimally, a ${10}^4$-fold enhanced radiative rate was found compared with bulk ${\mathrm{Cu}}_2\mathrm{O}$. A new degree of freedom in the light-matter interaction is presented, which differs from the mode volume control in cavity quantum electrodynamics.

It is a crucial issue to study interactions among water molecules and hydrophobic interfacial water at the nanoscale. Here we succeed in measuring the nuclear magnetic resonance spectrum of a diamond-water interfacial ice with a detection volume of about $2.2\times {10}^{-22}$ L. More importantly, the magnetic dipolar coupling between the two protons of a water molecule is resolved by measuring the signal contributed from about 7000 water molecules at the nanoscale. The resolved intramolecule magnetic dipolar interactions are about 15 and 33 kHz with spectral resolution of 5 kHz. This work provides a platform for hydrophobic interfacial water study under ambient conditions, with further applications in more general nanoscale structural analysis.

We compare different methods to measure the anisotropy of the spin lifetime in graphene. In addition to out-of-plane rotation of the ferromagnetic electrodes and oblique spin precession, we present a Hanle experiment where the electron spins precess around either a magnetic field perpendicular to the graphene plane or around an in-plane field. In the latter case, electrons are subject to both in-plane and out-of-plane spin relaxation. To fit the data, we use a numerical simulation that can calculate precession with anisotropies in the spin lifetimes under magnetic fields in any direction. Our data show a small, but distinct anisotropy that can be explained by the combined action of isotropic mechanisms, such as relaxation by the contacts and resonant scattering by magnetic impurities, and an anisotropic Rashba spin-orbit based mechanism. We also assess potential sources of error in all three types of experiment and conclude that the in-plane/out-of-plane Hanle method is most reliable.

Effects of temperature ${\displaystyle T}$ (6–18 K) and variable in situ static disorder on dissipative resistance of two-dimensional electrons are investigated in GaAs quantum wells placed in a perpendicular magnetic-field ${\displaystyle B_{\perp }}$. Quantum contributions to the magnetoresistance, leading to quantum positive magnetoresistance (QPMR), are separated by application of an in-plane magnetic field. QPMR decreases considerably with both the temperature and the static disorder and is in good quantitative agreement with theory. The remaining resistance ${\displaystyle R}$ decreases with the magnetic field exhibiting an anomalous polynomial dependence on ${\displaystyle B_{\perp }\text{:}[R\left(B_{\perp }\right)-R\left(0\right)]=A(T,{\tau }_q)B_{\perp }^{\eta }}$ where the power is ${\displaystyle \eta \approx 1.5\pm 0.1}$ in a broad range of temperatures and disorder. The disorder is characterized by electron quantum lifetime ${\displaystyle {\tau }_q}$. The scaling factor ${\displaystyle A(T,{\tau }_q)\sim {[\kappa \left({\tau }_q\right)+\beta \left({\tau }_q\right)T^2]}^{-1}}$ depends significantly on both ${\displaystyle {\tau }_q}$ and ${\displaystyle T}$ where the first term ${\displaystyle \kappa \sim {\tau }_q^{-1/2}}$ decreases with ${\displaystyle {\tau }_q}$. The second term is proportional to the square of the temperature and diverges with increasing static disorder. Above a critical disorder the anomalous magnetoresistance is absent, and only a positive magnetoresistance, exhibiting no distinct polynomial behavior with the magnetic field, is observed. The presented model accounts memory effects and yields ${\displaystyle \eta =3/2}$.

Series expansion methods are used to study the quantum critical behavior of the bicubic spin-1/2 antiferromagnet. Excitation energies are computed throughout the Brillouin zone, for both the Néel and dimer phases. We compute the energy of the amplitude/Higgs mode and show that it becomes degenerate with the magnon modes at the quantum critical point, as expected on general symmetry grounds.

A monopole liquid is a spin system with a high density of magnetic charges but no magnetic-charge order. We study such a liquid over an Ising pyrochlore lattice, where a single topological charge or monopole sits in each tetrahedron. Restricting the study to the case with no magnetic field applied we show that, in spite of the liquidlike correlations between charges imposed by construction constraints, the spins are uncorrelated like in a perfect paramagnet. We calculate a massive residual entropy for this phase ($ln\left(2\right)/2$, a result which is exact in the thermodynamic limit), implying a free Ising-like variable per tetrahedron. After defining a simple model Hamiltonian for this system (the balanced monopole liquid) we study its thermodynamics. Surprisingly, this monopole liquid remains a perfect paramagnet at all temperatures. Thermal disorder can then be simply and quantitatively interpreted as single charge dilution, by the excitation of neutral sites and double monopoles. The addition of the usual nearest neighbors interactions favoring neutral ‘2in-2out’ excitations as a perturbation maintains the same ground state but induces short-range (topological) order by thermal disorder. While it decreases charge-charge correlations, pair spin correlations—resembling those in spin ice—appear on increasing temperature. This helps us to see in another light the dipolarlike correlations present in spin ices at unexpectedly high temperatures. On the other side, favoring double excitations strengthens the charges short range order and its associated spin correlations. Finally, we discuss how the monopole liquid can be related to other systems and materials where different phases of monopole matter have been observed.

We report a ${}^{75}\mathrm{As}$ nuclear magnetic resonance study in LaFeAsO single crystals, which undergoes nematic and antiferromagnetic transitions at $T_{\text{nem}}\sim 156$ K and $T_N\sim 138$ K, respectively. Below $T_{\text{nem}}$, the ${}^{75}\mathrm{As}$ spectrum splits sharply into two for an external magnetic field parallel to the orthorhombic $a$ or $b$ axis in the FeAs planes. Our analysis of the data demonstrates that the NMR line splitting arises from an electronically driven rotational symmetry breaking. The ${}^{75}\mathrm{As}$ spin-lattice relaxation rate as a function of temperature shows that spin fluctuations are strongly enhanced just below $T_{\text{nem}}$. These NMR findings indicate that nematic order promotes spin fluctuations in magnetically ordered LaFeAsO, as observed in nonmagnetic and superconducting FeSe. We conclude that the origin of nematicity is identical in both FeSe and LaFeAsO regardless of whether or not a long-range magnetic order develops in the nematic state.