Electron optics exploits the analogies between rays in geometrical optics and electron trajectories, leading to interesting insights and potential applications. Graphene, with its two dimensionality and photon-like behavior of its charge carriers, is the perfect candidate for the exploitation of electron optics. We show that a circular gate- or doping-controlled region in the presence of Rashba spin-orbit interaction in graphene may indeed behave as a Veselago electronic lens but with two different indices of refraction. We demonstrate that this birefringence results in complex caustics patterns for a circular gate, selective focusing of different spins, and the possible direct measurement of the Rashba coupling strength in scanning-probe experiments.

We demonstrate that a scanning tunneling microscope tip can be used to manipulate the tightly bound core ($d$-electron) state of single Fe ions embedded in GaAs. Increasing tip-sample voltage removes one $d$ electron from the core of a single Fe, changing the dopant from the (Fe${}^{2+}$)${}^{-}$ ionized acceptor state to the (Fe${}^{3+}$)${}^0$ isoelectronic state, which alters the spin moment and dramatically modifies the measured local electronic contrast in topographic maps of the surface. Evidence of internal transitions among the $d$ states of the Fe core is also seen in topographic maps where dark anisotropic features emerge from the interference between two paths: the direct tip-sample tunneling and tunneling which excites a $d$-state core exciton of the Fe dopant.

The odd-parity, spin-triplet superconductor Sr${}_2$RuO${}_4$ has been found to feature exotic vortex physics including half-flux quanta trapped in a doubly connected sample and the formation of vortex lattices at low fields. The consequences of these vortex states on the low-temperature magnetoresistive behavior of mesoscopic samples of Sr${}_2$RuO${}_4$ were investigated by using a ring device fabricated on mechanically exfoliated single crystals of Sr${}_2$RuO${}_4$ by photolithography and a focused ion beam. With the magnetic field applied perpendicular to the in-plane direction, thin-wall rings of Sr${}_2$RuO${}_4$ were found to exhibit pronounced quantum oscillations with a conventional period of the full-flux quantum even though the unexpectedly large amplitude and the number of oscillations suggest the observation of vortex-flow-dominated magnetoresistance oscillations rather than a conventional Little-Parks effect. For rings with a thick wall, two distinct periods of quantum oscillations were found in high- and low-field regimes, respectively, which we argue to be associated with the “lock-in” of a vortex lattice in these thick-wall rings. No evidence for half-flux-quantum resistance oscillations were identified in any sample measured so far without the presence of an in-plane field.

We present results of nonlocal and three-terminal (3T) spin precession measurements on spin injection devices fabricated on epitaxial graphene on SiC. The measurements were performed before and after an annealing step at 150 ${}^{\circ }$C for 15 minutes in vacuum. The values of spin relaxation length $L_s$ and spin relaxation time ${\tau }_s$ obtained after annealing are reduced by a factor 2 and 4, respectively, compared to those before annealing. An apparent discrepancy between spin diffusion constant $D_s$ and charge diffusion constant $D_c$ can be resolved by investigating the temperature dependence of the $g$ factor, which is consistent with a model for paramagnetic magnetic moments.

The quasi-one-dimensional (Q1D) molecular conductors (DIETSe)${}_2$$M$Cl${}_4$ [$M=\text{Fe}$, Ga] undergo a spin density wave (SDW) transition below 12 K. The SDW ground state is suppressed by applying high pressure, recovering the Q1D Fermi surface which is confirmed by the appearance of Lebed resonance in the angle-dependent magnetoresistance (MR). Above the critical pressure of SDW, MR shows kink structures at high magnetic fields, reminiscent of field-induced spin density wave (FISDW) transition in both salts. The $\pi$-$d$ hybrid (DIETSe)${}_2$FeCl${}_4$ also exhibits an antiferromagnetic (AF) transition of $d$-electron spins at 2.5 K, below which the spin-flop-induced positive large MR are observed. The change in the interlayer MR reaches 130$\%$ at 10.5 kbar. The resistance anomalies associated with spin flop are also observed in the angle-dependent MR at low magnetic fields below 5 T, associated with clear hysteresis. A polar plot of these anomalies reveals the presence of hidden spin canting. Two magnetic easy axes of $d$-electron spins are found to be tilted $\pm$16 degrees from the $b$ axis towards the $c$ axis. The interplay between the SDW instability of Q1D $\pi$ electrons and the local moments of AF $d$-electron spins is considered as the origin of the anomalous transport behaviors.

We have performed angle- and spin-resolved photoemission measurements on Fe${}_3$O${}_4$(0 0 1)/MgO(0 0 1). Despite intrinsic electron-lattice (polaron) interaction a Fe $t_{2g}$ band dispersion is observed, as well as a Fermi surface. The states close to the Fermi level show a spin polarization up to $-72$$\%$ as measured with a 4.65 eV laser light. All the data can be simulated starting from GGA+U bulk band-structure calculations and taking into account the polaron and initial-state lifetime broadening involved in the photoemission process. This conciliates the electronic structure of Fe${}_3$O${}_4$ with a band model and confirms the half-metallic nature of Fe${}_3$O${}_4$.

We study electrons in a tight-binding lattice driven by a dc electric field with their energy dissipated through on-site fermionic thermostats. Due to the translational invariance in the transport direction, the problem can be block diagonalized. We solve this time-dependent quadratic problem and demonstrate that the problem has a well-defined steady state. The steady-state occupation number shows that the Fermi surface shifts at small fields by the drift velocity, in agreement with the Boltzmann transport theory, but it then deviates significantly at high fields due to strong nonlinear effect. Despite the lack of momentum scattering, the conductivity takes the same form as the semiclassical Ohmic expression from the relaxation-time approximation.

Cleavage induced rows of linear vacancy structures on $p$-doped ZnTe (110) surface are studied at room temperature by using cross-sectional scanning tunneling microscopy (X-STM). The oscillating contrast superimposed on the Te-driven occupied states neighboring to the vacancy cores are characterized at the atomic scale in order to determine the type of the missing component on the ZnTe surface matrix. We identify three major intensity distributions associated with different vacancy states. The X-STM images of three possible configurations comprising Zn only, Te only, and ZnTe binary vacancy structures on the ZnTe surface are modeled by using ab initio density functional theory calculations. The comparison of the X-STM measurements of each individual vacancy state to the corresponding theoretical simulation showed that unlike the Te vacancy, which leads to a local depression, the absence of Zn only or ZnTe binary gives rise to hillock features on the neighboring Te states of the ZnTe (110) cleaved surface. The theoretical STM images calculated for an undoped ZnTe crystal imply that possible doping-related effects on vacancy-induced features can be disregarded for interpreting the experimentally observed vacancy structures in our samples.

We study the connection between the spin-heat and spin-charge response in a disordered Fermi gas with spin-orbit coupling. It is shown that the ratio between the above responses can be expressed as the thermopower $S=-{\left(\pi k_B\right)}^{2}T{\sigma }^{\prime }/3e\sigma$ times a number $R_s$ which depends on the strength and type of the spin-orbit couplings considered. The general results are illustrated by examining different two-dimensional electron or hole systems with different and competing spin-orbit mechanisms, and we conclude that a metallic system could prove much more efficient as a heat-to-spin than as a heat-to-charge converter.

It is known that the near-field spectrum of the local density of states of the electromagnetic field above a SiC-air interface displays an intense narrow peak due to the presence of a surface polariton. It has been recently shown that this surface wave can be strongly coupled with the sheet plasmon of graphene in graphene-SiC heterosystems. Here, we explore the interplay between these two phenomena and demonstrate that the spectrum of the electromagnetic local density of states in these systems presents two peaks whose positions depend dramatically both on the distance to the interface and on the chemical potential of graphene. This paves the way toward active control of the local density of states.

Dislocations and dislocation networks act as sinks for irradiation-induced point defects such as vacancies and interstitials, or impurities such as helium. Recently, it has been found that the intersection points of the screw dislocation network formed at twist grain boundaries in Au (experimental) and Cu (simulations) act as nucleation sites for He bubbles, which form an array at the interface [J. Hetherly, E. Martinez, Z. F. Di, M. Nastasi, and A. Caro, Scr. Mater. 66, 17 (2012)]. The modeling part of that study was based on Monte Carlo algorithms. Here, using molecular dynamics simulations, we have performed shear deformation simulations of small-angle twist grain boundaries in α-iron. We report on the mechanical properties of this interface in pure as well as He-segregated samples. We find that this particular dislocation array in pure Fe is extremely mobile, with a Peierls stress ten times smaller than the value for a single straight screw dislocation, and that He bubbles induce a colossal increase (>50 times) in Peierls stress with respect to the pristine network. We interpret the results in terms of preexisting kinks and no shear transmission across the He bubbles.

BaCo${}_2$V${}_2$O${}_8$ is a nice example of a quasi-one-dimensional quantum spin system that can be described in terms of Tomonaga-Luttinger liquid physics. This is explored in the present study where the magnetic field-temperature phase diagram is thoroughly established up to 12 T using single-crystal neutron diffraction. The transition from the Néel phase to the incommensurate longitudinal spin density wave (LSDW) phase through a first-order transition, as well as the critical exponents associated with the paramagnetic-Néel phase transition, and the magnetic order both in the Néel and in the LSDW phase are determined, thus providing a stringent test for the theory.

We investigate the phonon-induced relaxation dynamics in the Fe${}_7$ magnetic molecule, which is made of two Fe${}^{3+}$ triangles bridged together by a central Fe${}^{3+}$ ion. The competition between different antiferromagnetic exchange interactions leads to a low-spin ground state multiplet with a complex pattern of low-lying excited levels. We theoretically investigate the decay of the time correlation function of molecular observables, such as the cluster magnetization, due to the spin-phonon interaction. We find that more than one time contributes to the decay of the molecular magnetization. The relaxation dynamics is probed by measurements of the nuclear spin-lattice relaxation rate $1/T_1$. The interpretation of these measurements allows the determination of the magnetoelastic coupling strength and to set the scale factor of the relaxation dynamics time scales. In our theoretical interpretation of $1/T_1$ data we also take into account the wipeout effect at low temperatures.

Multiferroic nanomaterials bear the potential for assembling a manifold of novel and smart devices. For room temperature (RT) applications, however, only the BiFeO${}_3$ single-phase perovskites are potential candidates to date. Nevertheless, vertical heterostructures separating magnetic and ferroelectric functionality into different layers are now widely proposed to circumvent this lack in materials’ availability. We show here that the second approach is very profitable as illustrated by the strain-mediated coupling between such two layers, i.e., a ferroelectric barium titanate single-crystal (BTO) and a magnetostrictive nickel (Ni) thin film. Applying an electric field across the BTO substrate forces the magnetic easy axis in the Ni film to rotate by 90${}^{\circ }$, resulting in a magnetic anisotropy in the range of $-1.2$ to $-33$ kJ/m${}^3$. We show that local switching proceeds through the nucleation and growth of straight Néel-domain walls at a cost of zigzag walls. The process is fully reversible and continuously tunable as investigated with magnetooptical Kerr microscopy and magnetic force microscopy probing the local in-plane and out-of-plane magnetizations, respectively. Moreover, the degree of anisotropy can be pre-engineered by depositing the Ni film either at RT, above the Curie temperature $T_c$ of BTO, or at an intermediate temperature. Our findings give evidence for using the reported coupling in modern devices, such as magnetoresistive random access memories, spin valves, spin-polarized electron emission, but equally for the bottom-up assembling of magnetizable molecular nanostructures through magnetic domain wall engineering.

Dielectric and magnetic properties have been studied in polycrystalline samples of quasi-one-dimensional frustrated spin-1/2 system Rb${}_2$(Cu${}_{1-x}$$M_x$)${}_2$Mo${}_3$O${}_{12}$ ($M$ = Ni and Zn) that does not exhibit a three-dimensional magnetic transition due to quantum spin fluctuation and low dimensionality. A broad peak in the magnetic susceptibility-temperature curves originating from a short-range helical ordering at low temperature is suppressed by the Ni and Zn substitution for Cu sites. The capacitance is found to anomalously increase with decreasing $T$ below ∼50 K, which is also suppressed by the impurity doping. The behavior of the anomalous capacitance component is found to be strongly connected with that of the magnetic susceptibility for Rb${}_2$(Cu${}_{1-x}$$M_x$)${}_2$Mo${}_3$O${}_{12}$, which indicates that the low-temperature dielectric response is driven by the magnetism.

We calculate the temperature dependence of the correlation length $\xi$ and the uniform susceptibility ${\chi }_0$ of the frustrated $J_1$–$J_2$ square-lattice Heisenberg ferromagnet in the collinear stripe phase using the Green-function technique. The height ${\chi }_{\max }$ and the position $T\left({\chi }_{\max }\right)$ of the maximum in the ${\chi }_0\left(T\right)$ curve exhibit a characteristic dependence on the frustration parameter $J_2/\left|J_1\right|$, which is well described, for $J_2>0.7\left|J_1\right|$, by the relations ${\chi }_{\max }=a{(J_2-J_2^c)}^{-\nu }$ and $T\left({\chi }_{\max }\right)=b(J_2-J_2^c)$, where $J_2^c=0.4\left|J_1\right|$ and $\nu$ is of the order of unity. The correlation length diverges at low temperatures as $\xi \propto e^{A/T}$, where $A$ increases with growing $J_2/\left|J_1\right|$. We also compare our results with recent measurements on layered oxovanadates and find reasonable agreement.

We study the proposed plaquette resonating valence bond (pRVB) state in the honeycomb lattice $J_1-J_2$ model with frustration arising from next-nearest-neighbor interactions. Starting with the limit of decoupled hexagons, we develop a plaquette operator approach to describe the pRVB state and its low-energy excitations. Our calculation clarifies that the putative pRVB state necessarily has $f$-wave symmetry: the plaquette wave function is an antisymmetric combination of the Kekulé structures. We estimate the plaquette ordering amplitude, ground-state energy, and spin gap as a function of $J_2/J_1$. The pRVB state is most stable around $J_2/J_1\sim 0.25$. We identify the wave vectors of the lowest triplet excitations, which can be verified using exact diagonalization or density-matrix renormalization group (DMRG) studies. When $J_2$ is reduced, we can have either a deconfined quantum phase transition (QPT) or a first-order transition into a Néel state. When $J_2$ is increased, we surmise that the system will undergo a first-order phase transition into a state which breaks lattice rotational symmetry.

In topologically protected quantum computation, quantum gates can be carried out by adiabatically braiding two-dimensional quasiparticles, reminiscent of entangled world lines. Bonesteel et al. [Phys. Rev. Lett. 95, 140503 (2005)], as well as Leijnse and Flensberg [Phys. Rev. B 86, 104511 (2012)], recently provided schemes for computing quantum gates from quasiparticle braids. Mathematically, the problem of executing a gate becomes that of finding a product of the generators (matrices) in that set that approximates the gate best, up to an error. To date, efficient methods to compute these gates only strive to optimize for accuracy. We explore the possibility of using a generic approach applicable to a variety of braiding problems based on evolutionary (genetic) algorithms. The method efficiently finds optimal braids while allowing the user to optimize for the relative utilities of accuracy and/or length. Furthermore, when optimizing for error only, the method can quickly produce efficient braids.