Electrical control of spins at the nanoscale offers significant architectural advantages in spintronics, because electric fields can be confined over shorter length scales than magnetic fields. Thus, recent demonstrations of electric-field (E-field) sensitivities in molecular spin materials are tantalising, raising the viability of the quantum analogues of macroscopic magneto-electric devices.However, the E-field sensitivities reported so far are rather weak, prompting the question of how to design molecules with stronger spin-electric couplings. Here we show that one path is to identify an energy scale in the spin spectrum that is associated with a structural degree of freedom with a significant electrical polarisability. We study an example of a molecular nanomagnet in which a small structural distortion establishes clock transitions (i.e. transitions whose energy is to first order independent of magnetic field) in the spin spectrum; the fact that this distortion is associated with an electric dipole allows us to control the clock transition energy to an unprecedented degree. We demonstrate coherent electrical control of the quantum spin state and exploit it to manipulate independently the two magnetically-identical but inversion-related molecules in the unit cell of the crystal. Our findings pave the way for the use of molecular spins in quantum technologies and spintronics.
Strain-clocked dipole-coupled nanomagnetic logic is an energy-efficient Boolean logic paradigm whose progress has been stymied by its propensity for high error rates. In an effort to mitigate this problem, we have studied the effect of nanomagnet geometry on error rates, focusing on elliptical and cylindrical geometries. We had previously reported that the out-of-plane excursion of the magnetization vector during switching creates a precessional torque that is responsible for high switching error probability in elliptical nanomagnet geometries. The absence of this torque in cylindrical magnets…
Nanomagnetic memory and logic are currently seen as promising candidates to replace current digital computing architectures due to its superior energy-efficiency, non-volatility and propensity for highly dense and low-power applications. In this work, we investigate the use of shape engineering (concave and diamond shape) to introduce biaxial anisotropy in single domain nanomagnets, giving rise to multiple easy and hard axes. Such nanomagnets, with dimensions of 100 nm x 100 nm, double the logic density of conventional two-state nanomagnetic devices by encoding more information (four binary bi…
A good qubit must have a coherence time long enough for gate operations to be performed. Avoided level crossings allow for clock transitions in which coherence is enhanced by the insensitivity of the transition to fluctuations in external fields. Because of this insensitivity, it is not obvious how to effectively couple qubits together while retaining clock-transition behavior. Here we present a scheme for using a heterodimer of two coupled molecular nanomagnets, each with a clock transition at zero magnetic field, in which all of the gate operations needed to implement one- and two-qubit gate…
A viable qubit must have a long coherence time $T_2$. In molecular nanomagnets $T_2$ is often limited at low temperatures by the presence of dipole and hyperfine interactions, which are often mitigated through sample dilution, chemical engineering and isotope substitution in synthesis. Atomic-clock transitions offer another route to reducing decoherence from environmental fields by reducing the effective susceptibility of the working transition to field fluctuations. The Cr$_7$Mn molecular nanomagnet, a heterometallic ring, features a clock transition at zero field. Both continuous-wave and sp…
Nanomagnetic implementations of Boolean logic [1,2] have garnered attention because of their non-volatility and the potential for unprecedented energy-efficiency. Unfortunately, the large dissipative losses that take place when nanomagnets are switched with a magnetic field [3], or spin-transfer-torque [4] inhibit the promised energy-efficiency. Recently, there have been experimental reports of utilizing the Spin Hall effect for switching magnets [5-7], and theoretical proposals for strain induced switching of single-domain magnetostrictive nanomagnets [8-12], that might reduce the dissipative…
Nanomagnets with biaxial magnetocrystalline anisotropy have four stable magnetization orientations that can encode 4-state logic bits (00), (01), (11) and (10). Recently, a 4-state NOR gate derived from three such nanomagnets, interacting via dipole interaction, was proposed. Here, we devise a Bennett clocking scheme to propagate 4-state logic bits unidirectionally between such gates. The nanomagnets are assumed to be made of 2-phase strain-coupled magnetostrictive/piezoelectric multiferroic elements, such as nickel and lead zirconate titanate (PZT). A small voltage of 200 mV applied across th…
We report observation of a "non-volatile" converse magneto-electric effect in elliptical FeGa nanomagnets delineated on a piezoelectric PMN-PT substrate. The nanomagnets are initially magnetized with a magnetic field directed along their nominal major axis and subsequent application of an electric field across the substrate generates strain in the substrate, which is partially transferred to the nanomagnets and rotates the magnetizations of some of them to metastable orientations. There they remain after the field is removed, resulting in "non-volatility". In isolated nanomagnets, the angular …
We demonstrate a possibility to manipulate the magnetic coupling between two nanomagnets with a help of ac electric field. In the scheme suggested the magnetic coupling in question is mediated by a magnetic particle contacting with both of the nanomagnets through the tunnel barriers. The electric field providing a successive suppression of the barriers leads to pumping of magnetization through the mediating particle. Time dependent dynamics of the particle magnetization allows to to switch between ferro- and antiferromagnetic couplings.
We study a single electron transistor (SET) based upon a II-VI semiconductor quantum dot doped with a single Mn ion. We present evidence that this system behaves like a quantum nanomagnet whose total spin and magnetic anisotropy depend dramatically both on the number of carriers and their orbital nature. Thereby, the magnetic properties of the nanomagnet can be controlled electrically. Conversely, the electrical properties of this SET depend on the quantum state of the Mn spin, giving rise to spin-dependent charging energies and hysteresis in the Coulomb blockade oscillations of the linear con…
On-chip magnets can be used to implement relatively large local magnetic field gradients in na- noelectronic circuits. Such field gradients provide possibilities for all-electrical control of electron spin-qubits where important coupling constants depend crucially on the detailed field distribution. We present a double quantum dot (QD) hybrid device laterally defined in a GaAs / AlGaAs het- erostructure which incorporates two single domain nanomagnets. They have appreciably different coercive fields which allows us to realize four distinct configurations of the local inhomogeneous field distri…
We demonstrate on-chip resonant driving of large cone-angle magnetization precession of an individual nanoscale permalloy element. Strong driving is realized by locating the element in close proximity to the shorted end of a coplanar strip waveguide, which generates a microwave magnetic field. We used a microwave frequency modulation method to accurately measure resonant changes of the dc anisotropic magnetoresistance. Precession cone angles up to $9^{0}$ are determined with better than one degree of resolution. The resonance peak shape is well-described by the Landau-Lifshitz-Gilbert equation…
The stochasticity of domain wall (DW) motion in magnetic nanowires has been probed by measuring slow fluctuations, or noise, in electrical resistance at small magnetic fields. By controlled injection of DWs into isolated cylindrical nanowires of nickel, we have been able to track the motion of the DWs between the electrical leads by discrete steps in the resistance. Closer inspection of the time-dependence of noise reveals a diffusive random walk of the DWs with an universal kinetic exponent. Our experiments outline a method with which electrical resistance is able to detect the kinetic state …
A mechanism of current-induced magnetization reversal based on the parametric resonance is described. The source of the magnetization reversal is a current-induced magnetic field, which is applied perpendicularly to the easy axis of magnetic anisotropy of a ferromagnetic nanomagnet. The current-induced magnetic field was measured in a FeCoB nanomagnet to be 60 Gauss at a current density of 65 mA/um2. Two mechanisms of the magnetization reversal are described and calculated. The first mechanism is the reversal by a RF electrical current, which modulated at a frequency close to the precession fr…
Nanomagnetic logic has emerged as a potential replacement for traditional CMOS-based logic because of superior energy-efficiency. One implementation of nanomagnetic logic employs shape-anisotropic (e.g. elliptical) ferromagnets (with two stable magnetization orientations) as binary switches that rely on dipole-dipole interaction to communicate binary information. Normally, circular nanomagnets are incompatible with this approach since they lack distinct stable in-plane magnetization orientations to encode bits. However, circular magnetoelastic nanomagnets can be made bi-stable with a voltage i…
We show that an unpolarized electric current incident perpendicular to the plane of a thin ferromagnet can excite a spin-wave instability transverse to the current direction if source and drain contacts are not symmetric. The instability, which is driven by the current-induced ``spin-transfer torque'', exists for one current direction only.
A hybrid structure combining the advantages of topological insulator (TI), dielectric ferromagnet (FM), and graphene is investigated to realize the electrically controlled correlation between electronic and magnetic subsystems for low-power, high-functional applications. Two-dimensional Dirac fermion states provide an ideal environment to facilitate strong coupling through the surface interactions with proximate materials. The unique properties of FM-TI and FM-graphene interfaces make it possible for active "manipulation" and "propagation", respectively, of the information state variable based…
Collective dynamics in lithographically-defined artificial spin ices offer profound insights into emergent correlations and phase transitions of geometrically-frustrated Ising spin systems. Their temporal and spatial evolution are often simulated using kinetic Monte Carlo simulations, which rely on the precise knowledge of the switching barriers to obtain predictive results in agreement with experimental observations. In many cases, however, the barriers are derived from simplified assumptions only, and do not take into account the full physical picture of nanomagnetic switching. Here we descr…
Quantum impurity (QI) spins offer promising information processing and sensing applications by harnessing up to room-temperature quantum coherence. Challenged by the requirement of designing local coherent drives and improving sensitivity to various signals for such applications, the search of hybrid systems coupling QI spins with matter excitations have garnered significant recent interest. We propose and theoretically study a hybrid system that couples spin-1 QI with the dynamical excitations of nanomagnets, which are controlled by mechanisms uncovered in classical spintronics. We show that …
Magneto-elastic (or "straintronic") switching has emerged as an extremely energy-efficient mechanism for switching the magnetization of magnetostrictive nanomagnets in magnetic memory, logic and non-Boolean circuits. Here, we investigate the ultrafast magneto-dynamics associated with straintronic switching in a single quasi-elliptical magnetostrictive Co nanomagnet deposited on a piezoelectric PMN-PT substrate using time-resolved magneto-optical Kerr effect (TR-MOKE) measurements. The pulsed laser pump beam in the TR-MOKE plays a dual role: it causes precession of the nanomagnet's magnetizatio…
Influence of the spin-transfer torque on the vortex state magnetic nanodisk is studied numerically via Slonczewski-Berger mechanism. The existence of a critical current is determined for the case of same-directed electrical current, its spin polarization and polarity of the vortex. The critical current separates two regimes: (i) deformed but static vortex state and (ii) essentially dynamic state under which the spatio-temporal periodic structures can appear. The structure is a stable vortex-antivortex lattice. Symmetry of the lattice depends on the applied current value and for high currents (…
Spin transfer torque from spin-polarized electrical current can excite large-amplitude magnetization dynamics in metallic ferromagnets of nanoscale dimensions. Since magnetic anisotropy energies of nanomagnets are comparable to the thermal energy scale, temperature can have a profound effect on the dynamics of a nanomagnet driven by spin transfer torque. Here we report the observation of unusual types of microwave-frequency nonlinear magnetization dynamics co-excited by alternating spin transfer torque and thermal fluctuations. In these dynamics, temperature amplifies the amplitude of GHz-rang…
Enhanced coherence in HoW$_{10}$ molecular spin qubits has been demonstrated by use of Clock Transitions (CTs). More recently it was shown that, while operating at the CTs, it was possible to use an electrical field to selectively address HoW$_{10}$ molecules pointing in a given direction, within a crystal that contains two kinds of identical but inversion-related molecules. Herein we theoretically explore the possibility of employing the electric field to effect entangling two-qubit quantum gates among two neighbouring CT-protected HoW$_{10}$ qubits within a diluted crystal. We estimate the t…
The effect of noise on the process of high-speed remagnetization of vortex state of a pentagonal array of five circular magnetic nanoparticles is studied by means of computer simulation of Landau-Lifshits model. The mean switching time and its standard deviation of the reversal between the counterclockwise and clockwise vorticities have been computed. It has been demonstrated that with the reversal by the pulse with sinusoidal shape, the optimal pulse duration exists, which minimizes both the mean switching time (MST) and the standard deviation (SD). Besides, both MST and SD significantly depe…
It has been recently shown that multiferroic logic - where logic bits are encoded in the magnetization orientation of a nanoscale magnetostrictive layer elastically coupled to a piezoelectric layer - can be Bennett clocked with small electrostatic potentials of few tens of mV applied to the piezoelectric layer. The potential generates stress in the magnetostrictive layer and rotates its magnetization by a large angle to carry out Bennett clocking. This method of clocking is far more energy-efficient than using spin transfer torque. In order to assess if such a clocking scheme can be also reaso…
Parametric mechanism of the magnetization reversal as a low-power recording mechanism for MRAM. Measurement of spin-accumulation-induced in-plane magnetic field in a FeB nanomagnet
The desire to perform information processing, computation, communication, signal generation and related tasks, while dissipating as little energy as possible, has inspired many ideas and paradigms. One of the most powerful among them is the notion of using magnetostrictive nanomagnets as the primitive units of the hardware platforms and manipulating their magnetizations with electrically generated static or time varying mechanical strain to elicit myriad functionalities. This approach has two advantages. First, information can be retained in the devices after powering off since the nanomagnets…
Electric field-induced magnetization switching in multiferroics holds profound promise for ultra-low-energy computing in beyond Moore's law era. Bistable nanomagnets in the multiferroics are usually deemed to be suitable for storing a binary bit of information and switching between the two stable states allows us to process digital information. However, it requires to process continuous analog signals too for seamless integration of nanomagnetic devices in our future information processing systems. Here, we show that it is possible to harness the analog nature in the magnetostrictive nanomagne…
Low barrier nanomagnets have attracted a lot of research interest for their use as sources of high quality true random number generation. More recently, low barrier nanomagnets with tunable output have been shown to be a natural hardware platform for unconventional computing paradigms such as probabilistic spin logic. Efficient generation and tunability of high quality random bits is critical for these novel applications. However, current spintronic random number generators are based on superparamagnetic tunnel junctions (SMTJs) with tunability obtained through spin transfer torque (STT), whic…
Electric field-induced magnetization switching in multiferroics is intriguing for both fundamental studies and potential technological applications. Here, we review the recent developments on electric field-induced magnetization switching in multiferroic heterostructures. Particularly, we study the dynamics of magnetization switching between the two stable states in a shape-anisotropic single-domain nanomagnet using stochastic Landau-Lifshitz-Gilbert (LLG) equation in the presence of thermal fluctuations. For magnetostrictive nanomagnets in strain-coupled multiferroic composites, such study of…
We show that direct current in a tantalum microstrip can induce steady-state magnetic oscillations in an adjacent nanomagnet through spin torque from the spin Hall effect (SHE). The oscillations are detected electrically via a magnetic tunnel junction (MTJ) contacting the nanomagnet. The oscillation frequency can be controlled using the MTJ bias to tune the magnetic anisotropy. In this 3-terminal device the SHE torque and the MTJ bias therefore provide independent controls of the oscillation amplitude and frequency, enabling new approaches for developing tunable spin torque nano-oscillators.
We investigate the interplay between the thermodynamic properties and spin-dependent transport in a mesoscopic device based on a magnetic multilayer (F/f/F), in which two strongly ferromagnetic layers (F) are exchange-coupled through a weakly ferromagnetic spacer (f) with the Curie temperature in the vicinity of room temperature. We show theoretically that the Joule heating produced by the spin-dependent current allows a spin-thermo-electronic control of the ferromagnetic-to-paramagnetic (f/N) transition in the spacer and, thereby, of the relative orientation of the outer F-layers in the devic…
Drift-diffusion theory - which fully describes charge transport in semiconductors - is also universally used to model transport of spin-polarized electrons in the presence of longitudinal electric fields. By transforming spin transit time into spin orientation with precession (a technique called the "Larmor clock") in current-sensing vertical-transport intrinsic Si devices, we show that spin diffusion (and concomitant spin dephasing) can be greatly enhanced with respect to charge diffusion, in direct contrast to predictions of spin Coulomb-drag diffusion suppression.
Spin-based coherent information processing and encoding utilize the precession phase of spins in magnetic materials. However, the detection and manipulation of spin precession phases remain a major challenge for advanced spintronic functionalities. By using simultaneous electrical and optical detection, we demonstrate the direct measurement of the precession phase of Permalloy ferromagnetic resonance driven by the spin-orbit torques from adjacent heavy metals. The spin Hall angle of the heavy metals can be independently determined from concurrent electrical and optical signals. The stroboscopi…
Molecular nanomagnets show clear signatures of coherent behavior and have a wide variety of effective low-energy spin Hamiltonians suitable for encoding qubits and implementing spin-based quantum information processing. At the nanoscale, the preferred mechanism for control of quantum systems is through application of electric fields, which are strong, can be locally applied, and rapidly switched. In this work, we provide the theoretical tools for the search for single molecule magnets suitable for electric control. By group-theoretical symmetry analysis we find that the spin-electric coupling …
Designing and constructing model systems that embody the statistical mechanics of frustration is now possible using nanotechnology. We have arranged nanomagnets on a two-dimensional square lattice to form an artificial spin ice, and studied its fractional excitations, emergent magnetic monopoles, and how they respond to a driving field using X-ray magnetic microscopy. We observe a regime in which the monopole drift velocity is linear in field above a critical field for the onset of motion. The temperature dependence of the critical field can be described by introducing an interaction term into…
Coordination-related, two-dimensional (2D) structural phase transitions are a fascinating and novel facet of two-dimensional materials with structural degeneracies. Nevertheless, a unified theoretical account of these transitions remains absent, and the following points are established through {\em ab-initio} molecular dynamics and 2D discrete clock models here: Group-IV monochalcogenide (GeSe, SnSe, SnTe, ...) monolayers have four degenerate structural ground states, and a 2D phase transition from a three-fold coordinated onto a five-fold coordinated structure takes place at finite temperatur…
