Ferromagnetic Single-electron Transistors Research Articles

A diagrammatic approach to single-electron spintronics and a new analytical model for ferromagnetic single-electron transistors

In this paper, we propose a diagrammatic approach to single-electron spintronics and develop a new analytical model for ferromagnetic single electron transistors (FSETs) using the proposed approach. Before this, we have reported an analytical model for FSET which was the only analytical model for FSETs introduced. It was a zero temperature one and was based on orthodox theory by solving several long equations simultaneously such that if one deals with a large system which includes several devices, number of complex equations is increased significantly. Here, the new proposed analytical model uses a much simpler diagrammatic approach and less calculation compared to the existing analytical model. We have used the model for two types of island material based on that spin splitting be negligible or not. This model provides a clear physical insight into single-electron spintronics and has been verified against the existing analytical model and numerical simulations. A good agreement has been shown and the model validity has been established.

Time-dependent equivalent circuit modeling of ferromagnetic single electron transistors

In this paper, a physics-based time-dependent circuit model is proposed for ferromagnetic single electron transistors (FSETs). This model is based on a modified version of the single electronics orthodox theory and obtained by simultaneously solving the governing equations. The introduced model is valid for single or multi gate, symmetric or asymmetric, and magnetic or nonmagnetic island FSETs. The model describes accurately FSET characteristics for a wide range of temperatures and drain to source voltages and also includes the spin relaxation time effect. The proposed model is implemented in a commercial circuit simulator HSPICE for use in circuit simulation. Two series of SPICE simulations are then successfully carried out. In the first simulations, different DC characteristics of a nonmagnetic island FSET are produced and verified against the existing numerical and analytical results with good agreements. In the second simulations, the transient behavior of a nonmagnetic island FSET is analyzed by considering the effects of temperature and spin relaxation time. It is shown that there are two different time scales in the transient response; the shorter one originates from the discrete coulomb charging of the island and the longer one from the spin relaxation effect. As an application example of the model at the circuit level, a magnetic island FSET-based inverter is simulated. These results are verified against Monte Carlo simulation results with excellent agreement. Then, the transient behavior of the inverter is investigated using the model for the first time.

The effects of changing the electrodes temperature on the tunnel magnetoresistance in the ferromagnetic single electron transistor

Ferromagnetic single electron transistor with electrodes having different temperatures is investigated and the effects of changing electrodes temperature on TMR of system are studied. A modified orthodox theory is used to study the system and to calculate the electron tunneling transition rate. The results show that the temperature of electrodes can be an effective tool to control and tune the tunnel magnetoresistance of FM-SET. Also, the effects of parameters such as resistance ratio of junctions, magnetic polarization and spin relaxation time on the behaviour of the system are studied.

Physics-based analytical model for ferromagnetic single electron transistor

A physically based compact analytical model is proposed for a ferromagnetic single electron transistor (FSET). This model is based on the orthodox theory and solves the master equation, spin conservation equation, and charge neutrality equation simultaneously. The model can be applied to both symmetric and asymmetric devices and does not introduce any limitation on the applied bias voltages. This feature makes the model suitable for both analog and digital applications. To verify the accuracy of the model, its results regarding a typical FSET in both low and high voltage regimes are compared with the existing numerical results. Moreover, the model's results of a parallel configuration FSET, where no spin accumulation exists in the island, are compared with the results obtained from a Monte Carlo simulation using SIMON. These two comparisons show that our model is valid and accurate. As another comparison, the model is compared analytically with an existing model for a double barrier ferromagnetic junction (having no gate). This also verifies the accuracy of the model.

Correlation between polarity of magnetoresistance ratio and tunnel resistance in ferromagnetic single-electron transistor with superconductive island

We report on the correlation between the polarity of magnetoresitance ratios and the tunnel resistance observed in ferromagnetic single-electron transistors with a superconductive island (FM–SC–FM SETs). Negative magnetoresistance ratios are observed at approximately the superconductive gap voltages, which indicates that an excessive number of spin-polarized quasiparticles accumulated in a superconductive island suppress the superconductive gaps. Since the spin polarization in a superconductor decays with time, the spin injection rate should be high enough to observe the suppression of superconductive gaps. The spin injection rate at a certain bias voltage is inversely proportional to the tunnel resistance; hence, the polarity of magnetoresistance ratio should correlate with the tunnel resistance. We fabricated 26 FM–SC–FM SETs. Samples having tunnel resistances lower than 100 kΩ exhibited negative magnetoresistance ratios, while samples having tunnel resistances higher than 600 kΩ exhibited positive magnetoresistance ratios.

Magnetic polaron formation in graphene-based single-electron transistor

We theoretically study the magnetic polaron (MP) formation in a ferromagnetic graphene single-electron transistor (SET), which consists of a graphene quantum dot (QD) between two insulating layers, i.e., a ferromagnetic insulator EuO and a nonmagnetic substrate such as SiC. In the lateral direction, the QD is electrically coupled to source, drain and gate electrodes, so that the number of electrons can be controlled by the gate voltage. Due to a proximity effect at the EuO/graphene interface, i.e., the exchange interaction between the charge carriers in graphene and the localized magnetic electrons in EuO, there is a magnetic coupling between the graphene QD and EuO. Using Green's function technique an expression for the total free energy of the SET is derived, which is then minimized at the given temperature and gate voltage. This leads to the MP formation and a consequent local enhancement of the ferromagnetic properties of EuO at the EuO/graphene interface. The MP formation is enforced by the large Coulomb interaction between the carriers in graphene. The spin polarization at the graphene/EuO interface in the QD area can be controlled by the gate voltage of the SET.

Reduced Master Equation for Modeling of Ferromagnetic Single-Electron Transistor

In this paper, the reduced master equation which is a fast simulation method of spin dependent transport in ferromagnetic single electron transistors is presented, for first time. This simulation method follows steady state master equation in which all charge states of the system are considered, whereas charge states are decreased in reduced master equation. This method is based on two degrees of electron freedom which are charge and spin. This is applied in the condition that orthodox tunneling theory is applicable to calculate the tunneling rate of electrons through barriers. The comparison between the I-V characteristics of a ferromagnetic single-electron transistor by following the reduced and full master equation methods for different main parameters of these transistors show that the results are exactly the same at low bias voltages. Consequently, the reduced master equation method is not only more simplified and improves the speed of numerical simulation, but also the modeling results are as accurate as the results of the full maser equation method at low bias conditions.

Reduced Master Equation as a Novel and Fast Method for Modeling of Spin Transport in Ferromagnetic Single Electron Transistors

In this paper, we formulate and investigate the reduced master equation as a novel and fast simulation method of spin dependent transport in ferromagnetic single electron transistors (FMSET) which so far this method for modeling of FMSET has not been mentioned in no paper. This simulation method follows the steady state master equation in which all charge states of the system are considered, whereas the charge states decrease in reduced master equation. This method is based on two degrees of electron freedom which are charge and spin. This is applied in the condition that the orthodox tunneling theory is applicable to calculate the tunneling rate of electrons through barriers. A comparison between current-bias voltage and current-gate voltage characteristics of different ferromagnetic single electron transistors following the reduced and full master equation methods shows that the results at low bias voltages are the same. Consequently, the reduced master equation method for simulation of current-bias/gate voltage of FMSETs is more simplified and improves the speed of numerical simulation, and also the modeling results are as accurate as the results of the full master equation method at low bias conditions in current scale.

The Effects of Cotunneling and Spin Flip on the Spin Polarized Transport in a Ferromagnetic Single Electron Transistor

We present a theoretical study of spin polarized transport in a single-electron tunneling transistor with ferromagnetic source and drain electrodes. The sequential tunneling and cotunneling currents are analyzed as a function of the intrinsic spin polarization of the electrodes, and spin flip effects within the central island electrode, for the case of collinear magnetization configuration. It was found that an antiparallel alignment of the electrode magnetization leads to a suppression of both the sequential tunneling and cotunneling currents, with the degree of suppression being greater for the higher order cotunneling current. For the sequential case, the suppression can be reduced by introducing finite spin flip within the island, but this has virtually no effect on the cotunneling current.

Current-induced magnetic switching and dynamics in spin valves

Spin torque and current-induced magnetic switching (dynamics) in spin valve nanopillars is considered theoretically in the diffusive transport regime. Basic characteristics of the precessional states are discussed. Current-induced switching in other spin valves is analyzed, particularly in ferromagnetic single-electron transistors based on magnetic molecules.

Assembling ferromagnetic single-electron transistors by atomic force microscopy

We demonstrate the assembly of nanoscale ferromagnetic single-electron transistors usingatomic force microscopy for imaging as well as for nanoscale manipulation. A single 30 nmAu disc, forming the central island of the transistor, is manipulated with angstromprecision into the gap between a plasma-oxidized Ni source and drain electrodes. Thetunnel resistances can be tuned in real time during the device fabrication by repositioningthe Au disc. Transport measurements reveal long-term stable single-electron transistorcharacteristics at 4.2 K. The well-controlled devices with very small central islands facilitatefuture in-depth studies of the interplay between Coulomb blockade, spin-dependenttunnelling and spin accumulation in ferromagnetic single-electron transistors at elevatedtemperatures.

AFM lithography for fabrication of magnetic nanostructures and devices

Nanostructures of oxide were fabricated on ferromagnetic thin films by a nano-oxidation technique using an atomic force microscope. Electrical and magnetic properties in the magnetic nanostructures were directly modified by the nano-oxidation. A ferromagnetic single electron transistor exhibited a single electron tunneling due to the Coulomb blockade effect. A direct modification of magnetic domain structures was also achieved by this nano-lithography technique.

Torque induced by spin‐polarized current in ferromagnetic single‐electron transistors

AbstractWe present theoretical analysis of the current‐induced torque exerted on the magnetic moment of the central electrode (island) in a ferromagnetic single electron transistor with non‐collinear magnetic moments of the electrodes. The considerations are restricted to the sequential tunneling regime, and the charge and spin currents are calculated within the master equation approach. The torque is calculated from the net spin current absorbed by the island. The calculations are carried out in the limit of fast spin relaxation processes, when no nonequilibrium magnetic moment can build up on the island. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Quantum criticality in ferromagnetic single-electron transistors.

Considerable evidence exists for the failure of the traditional theory of quantum critical points, pointing to the need to incorporate novel excitations. The destruction of Kondo entanglement and the concomitant critical Kondo effect may underlie these emergent excitations in heavy fermion metals (a prototype system for quantum criticality), but the effect remains poorly understood. Here, we show how ferromagnetic single-electron transistors can be used to study this effect. We theoretically demonstrate a gate-voltage-induced quantum phase transition. The critical Kondo effect is manifested in a fractional-power-law dependence of the conductance on temperature (T). The AC conductance and thermal noise spectrum have related power-law dependences on frequency (omega) and, in addition, show an omega/T scaling. Our results imply that the ferromagnetic nanostructure constitutes a realistic model system to elucidate magnetic quantum criticality that is central to the heavy fermions and other bulk materials with non-Fermi liquid behavior.

Spin transfer and current-induced switching in a ferromagnetic single-electron transistor

We propose a theoretical model of current-induced magnetization (CIMS) switching in a ferromagnetic single electron tunneling (FM-SET) transistor. The CIMS effect arises from the transfer of spin angular momentum from the net spin accumulation $\ensuremath{\Delta}S$ on the island electrode to the local magnetic moments via $s\text{\ensuremath{-}}d$ exchange coupling. Based on the single-domain model, we derive an analytical expression for the critical spin accumulation $\ensuremath{\Delta}{S}_{\mathrm{sw}}$ on the island for CIMS, and calculate the $M\text{\ensuremath{-}}\ensuremath{\Delta}S$ hysteresis curves which represent the effect of $\ensuremath{\Delta}S$ on the island moments. This magnetization response is then related to the charge and spin transport model in the SET transistor. We extend the Korotkov scheme spin-dependent ``orthodox'' theory of single charge tunneling, by linking the transport $I\text{\ensuremath{-}}V$ and $\ensuremath{\Delta}S\text{\ensuremath{-}}V$ characteristics to the $M\text{\ensuremath{-}}\ensuremath{\Delta}S$ hysteresis. We thus determine $\ensuremath{\Delta}S$ as a function of external bias or current and hence obtain the switching current density ${j}_{\mathit{sw}}$ for CIMS. For a typical spin polarization $P=60%$ of the source electrode, ${j}_{\mathit{sw}}$ is calculated to be of the order of ${10}^{5}\phantom{\rule{0.3em}{0ex}}\mathrm{A}∕{\mathrm{cm}}^{2}$, and this falls to just $\ensuremath{\sim}3\ifmmode\times\else\texttimes\fi{}{10}^{4}\phantom{\rule{0.3em}{0ex}}\mathrm{A}∕{\mathrm{cm}}^{2}$ when a near half-metal $(P=90%)$ is used. This value is several orders of magnitude smaller than ${j}_{\mathit{sw}}$ observed in multilayer and magnetic tunnel junction structures. The SET transistor is an ideal device for the CIMS effect since (i) a small amount of moments (on the island) need to be switched to generate a large change in conduction and (ii) the island electrode being isolated from the rest of the circuit by spin-dependent tunnel barriers effectively confines the spin accumulation $\ensuremath{\Delta}S$ in the vicinity of these moments.

Single- and double-island ferromagnetic single-electron transistors

Electronic transport in a ferromagnetic single-electron transistor has been considered theoretically in the sequential tunneling regime. The device consists of two external leads and one or two islands as the central part, connected to the leads by tunneling barriers. External gates are additionally attached to the islands. Generally, the two external electrodes and the islands can be ferromagnetic with arbitrary orientation of the corresponding magnetic moments. We have carried out detailed theoretical analysis of the current–voltage characteristics and spin-valve magnetoresistance in the limit of fast spin relaxation on the islands. Asymmetry in tunneling probabilities of spin-majority and spin-minority electrons leads to interesting features in the transport characteristics, like for instance magnetoresistance oscillations with the bias and gate voltages, negative differential resistance, and others.

Spin dependent transport in ferromagnet/superconductor/ferromagnet single electron transistor

Ferromagnetic single electron transistors with Al islands and orthogonal ferromagnetic leads (Co) are fabricated using e-beam lithography followed by shadow evaporation techniques. I–V characteristics exhibit typical single electron tunneling effects. Transport measurements performed in external magnetic field show that, when the two ferromagnetic leads are in antiparallel configuration, spin imbalance leads to a suppression of superconductivity.

Ferromagnetic Ultra-Small Tunnel Junction Devices Fabricated by Scanning Probe Microscope (SPM) Local Oxidation

A novel lithography technique for fabricating ferromagnetic metal/insulator/ferromagnetic metal (FM/I/FM)-based nanoscale devices was investigated using a scanning probe microscope (SPM) local oxidation process. This technique was applied to the surface modification of Ni thin films. Planar-type Ni/Ni oxide/Ni-based diodes and ferromagnetic single-electron transistor (FMSET) structures were fabricated by SPM local oxidation. Ni-based diodes clearly showed nonlinear current-voltage (I-V) characteristics, and capacitively coupled FMSET structures with a Ni-based double ferromagnetic tunnel junction exhibited Coulomb blockade effects.

Coherent and stochastic charge tunneling in ferromagnetic single electron transistors

We present a model of tunneling magnetotransport across a ferromagnetic single electron transistor (FM-SET). The model applies the “orthodox” theory and the Master equation method to describe the stochastic nature of separate tunneling events. The coherent transport of an individual charge through a tunnel barrier is modeled by a free-electron Hamiltonian through a trapezoidal barrier, and a two-band model within the FM electrodes. Single electron charging effect is incorporated into both stochastic and coherent parts of the model. The calculated tunneling resistance Rt is dependent on the thickness and voltage-dependent profile of the tunnel barriers. A bias modulation of the tunneling magnetoresistance (TMR) is obtained with the same period as the Coulomb staircase pattern. This modulation is present even for “homogeneous” FM-SETs, where each junction is of the same material composition. By contrast, previous studies based on the Julliere model predict total suppression of TMR modulation for such FM-SETs. The TMR modulation is found to be highly dependent on barrier thickness and the material composition of the junctions, implying further adjustable parameters for optimal TMR ratio. Finally, the bias modulation of TMR persists at high temperatures, even though the Coulomb staircase steps have been virtually smeared out.

Fabrication and characteristics of ferromagnetic single electron transistors

A method for fabricating ferromagnetic single electron transistors with similar or different ferromagnetic electrodes is presented. In this method, the coercive fields of the electrodes can be easily distinguished. Calculations have been performed to optimize the device design and fabrication. Small values of island length, junction resistance and junction area are crucial for observing non-equilibrium spin accumulation in the island.