Spin-flip Model Research Articles

Local Excitation of Kagome Spin Ice Magnetism Seen by Scanning Tunneling Microscopy.

The kagome spin ice can host frustrated magnetic excitations by flipping its local spin. Under an inelastic tunneling condition, the tip in a scanning tunneling microscope can flip the local spin, and we apply this technique to kagome metal HoAgGe with a long-range ordered spin ice ground state. Away from defects, we discover a pair of pronounced dips in the local tunneling spectrum at symmetrical bias voltages with negative intensity values, serving as a striking inelastic tunneling signal. This signal disappears above the spin ice formation temperature and has a dependence on the magnetic fields, demonstrating its intimate relation with the spin ice magnetism. We provide a two-level spin-flip model to explain the tunneling dips considering the spin ice magnetism under spin-orbit coupling. Our results uncover a local emergent excitation of spin ice magnetism in a kagome metal, suggesting that local electrical field induced spin flip climbs over a barrier caused by spin-orbital locking.

Spin vertical-cavity surface-emitting lasers with linear gain anisotropy: Prediction of exceptional points and nontrivial dynamical regimes

It is shown that when the linear gain anisotropy is properly accounted for, spin-injected vertical-cavity surface-emitting lasers (spin-VCSELs) offer interesting functionalities. Using the extended spin-flip model (SFM), we predict the existence of exceptional points (EPs) in spin-VCSELs and two interesting phenomena which accompany EPs, namely, (i) the polarization switching manifesting as induced change of field helicity sign and (ii) frequency comb generation without the need of external injection locking. Both effects have tremendous technological potential such as fast on-chip polarization switching, and most importantly, their concepts are not limited only to spin-VCSEL technology. We discuss the concept of anisotropy-engineered non-Hermitian microlasers and we provide a theoretical background to study their polarization dynamics near EPs.

Broad Tunable and High-Purity Photonic Microwave Generation Based on an Optically Pumped QD Spin-VCSEL with Optical Feedback

Spin-polarized vertical-cavity surface-emitting lasers (spin-VCSELs) with birefringence-induced polarization oscillations have been proposed to generate desired photonic microwave signals. Here, we numerically investigate the generation of photonic microwave signals in an optically pumped quantum dot (QD) spin-VCSEL. First, the influence of intrinsic key parameters on period-one (P1) oscillations and microwave properties is discussed. Second, the difference between microwave generation based on the quantum well (QW) and QD spin-VCSELs is analyzed by controlling the carrier capture rate that is described in the spin-flip model. The QD spin-VCSEL shows superior microwave quality in the low-frequency range (e.g., 10 GHz~20 GHz) compared with the QW spin-VCSEL. Finally, to boost the performance of the generated photonic microwave signal, optical feedback is introduced. The results show that dual-loop feedback can simultaneously narrow the microwave linewidth and suppress the side modes that are derived from the external cavity mode.

Liquid-Crystal Spin-VCSEL with Electro-Optically Controllable Birefringence

We suggest a new construction of spin-VCSEL with an embedded nematic liquid crystal (LC) in a second cavity. We design such a coupled-cavity LC-VCSEL and develop a procedure for calculating its LC-voltage dependent polarization resolved resonant longitudinal modes and their quantum-well confinement factors. Using these characteristics, we are able to slightly modify the spin-flip VCSEL model to include the voltage dependent birefringence and anisotropy. Then, we show that such an LC-VCSEL can reach small signal modulation response with a 3dB cut off frequency of several hundreds of GHz.

Excited-state exchange interaction in NiO determined by high-resolution resonant inelastic x-ray scattering at the Ni M2,3 edges

The electronic and magnetic excitations of bulk NiO have been determined using the ${}^{3}{A}_{2g}$ to ${}^{3}{T}_{2g}$ crystal-field transition at the Ni ${M}_{2,3}$ edges with resonant inelastic x-ray scattering at 66.3- and 67.9-eV photon energies and 33-meV spectral resolution. Unambiguous assignment of the high-energy side of this state to a spin-flip satellite is achieved. We extract an effective exchange field of $89\ifmmode\pm\else\textpm\fi{}4$ meV in the ${}^{3}{T}_{2g}$ excited final state from empirical two-peak spin-flip model. The experimental data is found consistent with crystal-field model calculations using exchange fields of 60--100 meV. Full agreement with crystal-field multiplet calculations is achieved for the incident photon energy dependence of line shapes. The lower exchange parameter in the excited state as compared to the ground-state value of 120 meV is discussed in terms of the modification of the orbital occupancy (electronic effects) and of the structural dynamics: (A) With pure electronic effects, the lower exchange energy is attributed to the reduction in effective hopping integral. (B) With no electronic effects, we use the $S=1$ Heisenberg model of antiferromagnetism to derive a second-nearest-neighbor exchange constant ${J}_{2}$ = $14.8\ifmmode\pm\else\textpm\fi{}0.6$ meV. Based on the linear correlation between ${J}_{2}$ and the lattice parameter from pressure-dependent experiments, an upper limit of 2% local Ni-O bond elongation during the femtosecond scattering duration is derived.

Three-Variable Reduction of the Spin-Flip Model for Spin-VCSELs

Recent increased interest in spin-polarised vertical-cavity surface-emitting lasers (spin-VCSELs) as potential high-speed sources has spurred research into the analysis of their dynamics. This has often been explored by combining the spin-flip model (SFM) with numerical methods. However, numerical simulation does not readily expose key dependencies and to date there is a lack of accessible closed-form analytical results for the steady-state solutions and dynamic stability boundaries. Thus in the present contribution we address this and show that, for zero dichroism, the five rate equations of the SFM can be reduced to a set of three. These can be solved in the steady-state in terms of the intensity and polarisation of the pump (optical or electrical), and the ellipticity of the output. Additionally, a small-signal analysis leads to analytic results for the boundaries between stable and unstable operation in the plane of pump ellipticity versus pump intensity. Comparison of the results from these expressions with those from numerical bifurcation and continuation methods shows very good agreement. The accuracy of the reduced set of equations is confirmed by comparing the results with those from the full set of SFM equations. In the limiting case of very high birefringence, as would be required for a potential THz source, a simple algebraic relation is derived for the spin relaxation rate in terms of other parameters. Hence we find that the range of spin relaxation rates to achieve THz oscillations is very limited. The relative simplicity of the present approach thus offers a rapid, intuitive and convenient route to study the dynamics of spin-VCSELs.

Modelling the statics and the dynamics of fluctuations in the ordering alloy AuAgZn2

The ordering alloy AuAgZn2 has a Heusser second-order transition at Tc ≃ 336.4°C. Static measurements of the critical scattering were carried out at the BM02 beamline of the European Synchrotron Radiation Facility (ESRF). These results are compared with Monte-Carlo simulations of the Ising model and show that the model with a simple interaction between two neighbouring atoms of the simple cubic Au/Ag lattice fully explains the X-ray diffuse scattering. Dynamic measurements obtained from X-ray scattering below Tc and the observation of X-ray photon correlations at the ESRF ID10 beamline are compared with dynamic simulations. It is shown that this system follows the predictions of “model A” [P.C. Hohenberg, B.I. Halperin, Rev. Mod. Phys. 49, 436 (1977)] for a transition with non-conserved order parameter. The dynamics of ordering with nearest neighbour exchange of atoms in the simple cubic lattice is shown to be equivalent to the usual Ising spin flip model, but with a different time scale. A comparison between the kinetics of ordering and the dynamics of the observed speckles arising from critical fluctuations shows some discrepancy suggesting the need for further experiments.

Spin-Flip Pair-Density Functional Theory: A Practical Approach To Treat Static and Dynamical Correlations in Large Molecules

We present a practical approach to treat static and dynamical correlation accurately in large multiconfigurational systems. The static correlation is taken into account by using the spin-flip approach, which is well-known for capturing static correlation accurately at low-computational expense. Unlike previous approaches to add dynamical correlation to spin-flip models which use perturbation theory or coupled-cluster theory, we explore the ability to use the on-top pair-density functional theory approaches recently developed by Gagliardi and co-workers (J. Comput. Theor. Chem., 2014, 10, 3669). External relaxations are performed in the spin-flip calculations through a restricted active space framework for which a truncation scheme for the orbitals used in the external excitation is presented. The performance of the approach is demonstrated by computing energy gaps between ground and excited states for diradicals, triradicals, and linear polyacene chains ranging from naphthalene to dodecacene. Accurate results are obtained using the new approach for these challenging open-shell molecular systems.

The Overlap Factor Model of Spin-Polarised Coupled Lasers

A general model for the dynamics of arrays of coupled spin-polarised lasers is derived. The general model is able to deal with waveguides of any geometry with any number of supported normal modes. A unique feature of the model is that it allows for independent polarisation of the pumping in each laser. The particular geometry is shown to be introduced via ’overlap factors’, which are a generalisation of the optical confinement factor. These factors play an important role in determining the laser dynamics. The model is specialised to the case of a general double-guided structure, which is shown to reduce to both the spin flip model in a single cavity and the coupled mode model for a pair of guides in the appropriate limit. This is applied to the particular case of a circular-guide laser pair, which is analysed and simulated numerically. It is found that increasing the ellipticity of the pumping tends to reduce the region of instability in the plane of pumping strength versus guide separation.

Spin-VCSELs with Local Optical Anisotropies: Toward Terahertz Polarization Modulation

Putting a different spin on photonics: Spin-injected vertical-cavity surface-emitting lasers (Spin-VCSELs) with strong anisotropies are important in particular for ultrafast and terahertz applications, but the field is being held back in part because of lack of sufficiently predictive physical models. This study uses temporal coupled-mode theory with the transfer-matrix formalism to make progress by extending the spin-flip model. Additionally, the authors propose a spin-VCSEL with an anisotropic intracavity grating. This approach points to engineering solutions for ultrafast optical communication and compact terahertz sources.

Numerical Analysis of Nonlinear Dynamics Based on Spin-VCSELs with Optical Feedback

In this paper, the nonlinear dynamics of a novel model based on optically pumped spin-polarized vertical-cavity surface-emitting lasers (spin-VCSELs) with optical feedback is investigated numerically. Due to optical feedback being the external disturbance component, the complex nonlinear dynamical behaviors can be enhanced and the regions of different nonlinear dynamics in size can be extended with appropriate parameters of spin-VCSELs. According to the equations of the modified spin-flip model (SFM), the comparison of bifurcation diagrams is first presented for the clear presentation of different routes to chaos. Meanwhile, numerous bifurcation diagrams in color are illustrated to demonstrate the rich dynamical regimes intuitively, and the crucial effects of optical feedback strength, feedback delay, linewidth enhancement factor, and spin-flip relaxation rate on the region evolvement of complex dynamics of the proposed model are revealed to investigate the dependence of dynamical behaviors on external and internal parameters when the optical feedback scheme is introduced. These parameters play a remarkable role in enhancing the mechanism of complex dynamic oscillations. Furthermore, utilizing combination with time series, power spectra, and phase portraits, the various dynamical behaviors observed in the bifurcation diagram are simulated numerically. Correspondingly, the powerful measure 0–1 test is employed to distinguish between chaos and non-chaos.

Training a Multi-Layer Photonic Spiking Neural Network With Modified Supervised Learning Algorithm Based on Photonic STDP

We propose a framework for hardware architecture and learning algorithm co-design of multi-layer photonic spiking neural network (SNN). The vertical-cavity surface-emitting laser with an embedded saturable absorber (VCSEL-SA) which contains two polarization-resolved modes is employed as a spiking neuron. The connection between two identical polarization modes is considered as the excitatory synapse, whereas the connection between two orthogonal polarization modes is regarded as the inhibitory synapse. The physical model of the photonic spiking neuron is derived based on the combination of spin-flip model and Yamada model. The photonic spike timing dependent plasticity (STDP) is applied to design a hardware-friendly biologically plausible supervised learning algorithm for a multi-layer photonic SNN. Thanks to the polarization mode competition effect in the VCSEL-SA, the proposed neuromorphic network is capable of solving the classical XOR problem. The effect of physical parameters of photonic neuron on the training convergence is also considered. We further extend the multi-layer photonic SNN to realize other logic learning tasks. To the best of our knowledge, such a modified supervised learning algorithm dedicated for a multi-layer photonic SNN has not yet been reported, which is interesting for spiking learning of neuromorphic photonics.

Photonic Associative Learning Neural Network Based on VCSELs and STDP

In this article, we propose a photonic neural network (PNN) to emulate associative learning and forgetting for the first time. The PNN contains three photonic neurons based on 1550nm long-wavelength vertical-cavity surface-emitting lasers (VCSELs) subject to double polarized optical injection. A computational model of the PNN is derived based on the well-known spin-flip model. According to the learning rule named spike-time-dependent plasticity (STDP), the connection weight between neurons in the PNN is modified by self-learning. The simulation results show that, during the associative learning process, an association of feeding food and bell ringing is established within the Long-term synaptic potentiation window of the STDP; while, the association is forgotten within the Long-term depression window of the STDP in the forgetting process. Moreover, the effects of time interval between two pre-synaptic spikes on the speed of associative learning and forgetting are considered in detail. Finally, we further realize pattern recall based on the photonic associative learning, which shows promises for emerging applications of a large-scale energy-efficient PNN.

Real-time optical spike-timing dependent plasticity in a single VCSEL with dual-polarized pulsed optical injection

We propose and numerically realize an optical spike-timing dependent plasticity (STDP) scheme by using a single vertical-cavity surface-emitting laser (VCSEL). In the scheme, the VCSEL is subjected to an orthogonally-polarized continuous-wave optical injection (OPCWOI) and dual-polarized pulsed optical injections (DPPOI). Based on the widely used spin-flip model, the response spiking dynamics of VCSEL is numerically studied, and then the optical STDP in a single VCSEL is explored. The roles of bias current, the strength of OPCWOI and DPPOI, and the frequency detuning on the optical STDP curve are numerically analyzed. It is found that, by simultaneously utilizing the response spiking dynamics in two orthogonal polarization modes, an optical STDP could be achieved by using a single VCSEL. Furthermore, the weight update of STDP curve can be calculated in real-time. Additionally, the STDP curves can also be controlled by adjusting some controllable parameters. The real-time optical STDP based on a single VCSEL is numerically realized for the first time, which paves the way towards fully VCSELs-based photonic neuromorphic systems with low power consumption.

Dynamics of Laterally-Coupled Pairs of Spin-VCSELs

A newly-developed normal mode model of laser dynamics in a generalised array of waveguides is applied to extend the spin-flip model (SFM) to pairs of evanescently-coupled spin-VCSELS. The effect of high birefringence is explored, revealing new dynamics and regions of bistability. It is shown that optical switching of the polarisation states of the lasers may be controlled through the optical pump and that, under certain conditions, the polarisation of one laser may be switched by controlling the intensity and polarisation in the other.

Local and mean-field approaches for modeling semiconductor spin-lasers

Electrically and optically pumped spin-polarized vertical-cavity surface-emitting lasers (spin-VCSELs) seem to attain improved performance compared to their conventional counterparts. Their dynamical properties are studied mostly in the framework of effective rate equations containing parameters that are difficult to directly relate with fundamental material properties. Consequently, such approaches are not suitable for the precise design and optimization of future spin-lasers with desirable dynamical properties. We propose a method for extraction of dynamics-related parameters for the spin-flip model, which is widely used for the description of spin-laser dynamics. This method is based on the correspondence between robust local computational tools and effective models. A general matrix formalism based on S-matrices and generalized Maxwell–Bloch equations is used to determine approximate values of parameters such as cavity decay rate or birefringence rate. This would allow us to tune laser properties by changing the optical properties of the laser cavities and active media according to our needs. The method is demonstrated on realistic anisotropic spin-VCSEL structures containing a 12-quantum-well InGaAs/GaAsP active region. The potential limitations of already existing effective models are discussed.

All-optical neuromorphic XOR operation with inhibitory dynamics of a single photonic spiking neuron based on a VCSEL-SA.

We propose a simple hardware architecture for solving exclusive OR (XOR) tasks in a single step by using a single photonic spiking neuron based on vertical-cavity surface-emitting lasers with an embedded saturable absorber (VCSEL-SA) subject to dual-polarized pulsed optical injection. We model the inhibitory photonic spiking neuron by extending the Yamada model and spin-flip model to incorporate the two polarization-resolved modes and the saturable absorber. It is shown that, by carefully adjusting the temporal difference according to the inhibitory window, the XOR operation can be realized in a single photonic spiking neuron, which is interesting and valuable for the photonic neuromorphic computing and information processing.

Orthogonally polarized frequency combs in a mode-locked VECSEL

We introduce a spin–flip model for a vertical-external-cavity surface-emitting laser (VECSEL) with a saturable absorber. We demonstrate the possibility, due to the spin–flip dynamics, to generate two orthogonally linearly polarized frequency combs in the mode-locked regime. The two combs are shifted in wavelength due to the birefringence in the VECSEL gain and/or saturable absorption mirror. We show that the polarization degree of freedom may also lead to several pulses being generated per roundtrip in the two orthogonal linear polarizations and to more complicated dynamics with both linear polarizations excited.

Polarization Responses of a Solitary and Optically Injected Vertical Cavity Spin Laser

The polarisation properties of a quantum well spin – vertical cavity surface emitting laser (spin – VCSEL), both without injection and with variable polarisation optical injection, are investigated experimentally and compared with the spin flip model (SFM). Without injection, we demonstrate two distinct types of VCSEL-pump response depending on the signs of the linewidth enhancement factor, birefringence and dichroism: firstly where the pump and VCSEL have the same sign of the ellipticity, and secondly where the VCSEL ellipticity, accompanied by the linear polarisation, switches sign. We show that by controlling the injected power, ellipticity or linear angle, near circular polarisation can be obtained. These responses both give insight into the electro-optical injected spin-VCSEL system, and have practical implications for the use of spin VCSELs in unique applications exploiting the ellipticity degree of freedom.

All-optical majority gate based on an injection-locked laser

An all-optical computer has remained an elusive concept. To construct a practical computing primitive equivalent to an electronic Boolean logic, one should utilize nonlinearity that overcomes weaknesses that plague many optical processing schemes. An advantageous nonlinearity provides a complete set of logic operations and allows cascaded operations without changes in wavelength or in signal encoding format. Here we demonstrate an all-optical majority gate based on a vertical-cavity surface-emitting laser (VCSEL). Using emulated signal coupling, the arrangement provides Bit Error Ratio (BER) of 10−6 at the rate of 1 GHz without changes in the wavelength or in the signal encoding format. Cascaded operation of the injection-locked laser majority gate is simulated on a full adder and a 3-bit ripple-carry adder circuits. Finally, utilizing the spin-flip model semiconductor laser rate equations, we prove that injection-locked lasers may perform normalization operations in the steady-state with an arbitrary linear state of polarization.