The domain wall depinning from a notch in a Permalloy nanostrip on top of a ${\rm SiO_2/Si}$ substrate is studied theoretically under application of static magnetic fields and the injection of short current pulses. The influence of Joule heating on current-induced domain wall depinning is explored self-consistently by coupling the magnetization dynamics in the ferromagnetic strip to the heat transport throughout the system. Our results indicate that Joule heating plays a remarkable role in these processes, resulting in a reduction in the critical depinning field and/or in a temporary destruction of the ferromagnetic order for typically injected current pulses. In agreement with experimental observations, similar pinning-depinning phase diagrams can be deduced for both current polarities when the Joule heating is taken into account. These observations, which are incompatible with the sole contribution of spin transfer torques, provide a deeper understanding of the physics underlying these processes and establish the real scope of the spin transfer torque. They are also relevant for technological applications based on current-induced domain-wall motion along soft strips.
The temperature distribution in nanowires due to Joule heating is studied analytically using a continuum model and a Green's function approach. We show that the temperatures reached in nanowires can be much lower than that predicted by bulk models of Joule heating, due to heat loss at the nanowire surface that is important at nanoscopic dimensions, even when the thermal conductivity of the environment is relatively low. In addition, we find that the maximum temperature in the nanowire scales weakly with length, in contrast to the bulk system. A simple criterion is presented to assess the impor…
We investigate the formation of nanogaps in gold wires due to electromigration. We show that the breaking process will not start until a local temperature of typically 400 K is reached by Joule heating. This value is rather independent of the temperature of the sample environment (4.2-295 K). Furthermore, we demonstrate that the breaking dynamics can be controlled by minimizing the total series resistance of the system. In this way, the local temperature rise just before break down is limited and melting effects are prevented. Hence, electrodes with gaps < 2 nm are easily made, without the nee…
Using full-band electron and phonon dispersion relation, we investigate the temperature dependence of Joule heating in Zigzag Graphene Nanoribbons under high-field. At different temperatures of 300 K, 600 K, and 900 K, the Joule heating always increases linearly with time or the power is a constant. Although the scattering rates at 900 K and 600 K are 113 and 55 times higher than that of 300 K, the Joule heating power of 900 K and 600 K are just 12.6 and 6.7 timers higher than that of 300 K.
We use simulations to examine current saturation in sub-micron graphene transistors on SiO2/Si. We find self-heating is partly responsible for current saturation (lower output conductance), but degrades current densities >1 mA/um by up to 15%. Heating effects are reduced if the supporting insulator is thinned, or in shorter channel devices by partial heat sinking at the contacts. The transient behavior of such devices has thermal time constants of ~30-300 ns, dominated by the thickness of the supporting insulator and that of device capping layers (a behavior also expected in ultrathin body SOI…
We consider the electrical current through a magnetic point contact in the limit of a strong inelastic scattering of electrons. In this limit local Joule heating of the contact region plays a decisive role in determining the transport properties of the point contact. We show that if an applied constant bias voltage exceeds a critical value, the stationary state of the system is unstable, and that periodic, non-harmonic oscillations in time of both the electrical current through the contact and the local temperature in the contact region develop spontaneously. Our estimations show that the nece…
The Joule heating effect on graphene electronic properties is investigated by using full-band Monte Carlo electron dynamics and three-dimensional heat transfer simulations self-consistently. A number of technologically important substrate materials are examined: SiO2, SiC, hexagonal BN, and diamond. The results illustrate that the choice of substrate has a major impact via the heat conduction and surface polar phonon scattering. Particularly, it is found that the poor thermal conductivity of SiO2 leads to significant Joule heating and saturation velocity degradation in graphene (characterized …
The theoretical formula for the entropy production rate in the presence of spin current is derived using the spin-dependent transport equation and thermodynamics. This theory is applicable regardless of the source of the spin current, for example, an electric field, a temperature gradient, or the Hall effect. It reproduces the result in a previous work on the dissipation formula when the relaxation time approximation is applied to the spin relaxation rate. By using the developed theory, it is found that the dissipation in spin Hall geometry has a contribution proportional to the square of the …
We theoretically study the spin-polarized current flowing through a Josephson junction (JJ) in a spin injection device. When the spin-polarized current is injected from a ferromagnet (FM) in a superconductor (SC), the charge current is carried by the superconducting condensate (Cooper pairs), while the spin-up and spin-down currents flow in the equal magnitude but in the opposite direction in SC, because of no quasiparticle charge current in SC. This indicates that not only the Josephson current but also the spin current flow across JJ at zero bias voltage, thereby generating Joule heating by …
A programmable micromechanical resonator based on a VO2 thin film is reported. Multiple mechanical eigenfrequency states are programmed using Joule heating as local power source, gradually driving the phase transition of VO2 around its Metal-Insulator transition temperature. Phase coexistence of domains is used to tune the stiffness of the device via local control of internal stresses and mechanical properties. This study opens perspectives for developing mechanically configurable nanostructure arrays.
Nonlinear devices, such as transistors, enable contemporary computing technologies. We theoretically investigate nonlinear effects, bearing a high fundamental scientific and technical relevance, in magnonics with emphasis on superconductor-ferromagnet hybrids. Accounting for finite magnon chemical potential, we theoretically demonstrate magnonic spin-Joule heating, the spin analogue of conventional electronic Joule heating. Besides suggesting a key contribution to magnonic heat transport in a broad range of devices, it provides insights into the thermal physics of non-conserved bosonic excitat…
This work investigates nanosecond superparamagnetic switching in 50 nm diameter in-plane magnetized magnetic tunnel junctions (MTJs). Due to the small in-plane uniaxial anisotropy, dwell times below 10 ns and auto-correlation times down to 5 ns are measured for circular superparamagnetic tunnel junctions (SMTJs). SMTJs exhibit probabilistic switching of the magnetic free layer, which can be used for the generation of true random numbers. The quality of random bitstreams, generated by our SMTJ, is evaluated with a statistical test suite (NIST STS, sp 800-22) and shows true randomness after thre…
The features of the $IV$ characteristics of metallic carbon nanotubes (m-NTs) in different experimental setups are studied using semi-classical Boltzmann transport equation together with the heat dissipation equation to account for significant thermal effects at high electric bias. Our model predicts that the shape of the m-NT characteristics is basically controlled by heat removal mechanisms. In particular we show that the onset of negative differential resistance in free standing nanotubes finds its origins in strong transport nonlinearities associated with poor heat removal unlike in substr…
Pulsed domain wall movement is studied here in Ni80Fe20 nanowires on SiO2, using a fully integrated electrostatic, thermoelectric, and micromagnetics solver based on the Landau-Lifshitz-Bloch equation, including Joule heating, anisotropic magneto-resistance, and Oersted field contributions. During the applied pulse the anisotropic magneto-resistance of the domain wall generates a dynamic heat gradient which increases the current-driven velocity by up to 15%. Using a temperature-dependent conductivity significant differences are found between the constant voltage-pulsed and constant current-pul…
Manipulating materials at the nanometer scale is challenging, particularly if alignment with nanoscale electrodes is desired. Here we describe a lithography-free, self-aligned nanotrench ablation (SANTA) technique to create nanoscale trenches in a polymer like poly(methyl) methacrylate (PMMA). The nanotrenches are self-aligned with carbon nanotube (CNT) and graphene ribbon electrodes through a simple Joule heating process. Using simulations and experiments we investigate how the Joule power, ambient temperature, PMMA thickness, and substrate properties can improve the spatial resolution of thi…
Graphene oxide (GO) is reduced by Joule heating using in-situ transmission electron microscopy (TEM). The approach allows the simultaneous study of GO conductivity by electrical measurements and of its composition and structural properties throughout the reduction process by TEM, electron diffraction and electron energy-loss spectroscopy. The small changes of GO properties observed at low applied electric currents are attributed to the promotion of diffusion processes. The actual reduction process starts from an applied power density of about 2 1014 Wm-3 and occurs in a highly uniform and loca…
We show that Joule heating causes current-controlled negative differential resistance (CC-NDR) in TiO2 by constructing an analytical model of the voltage-current V(I) characteristic based on polaronic transport for Ohm's Law and Newton's Law of Cooling, and fitting this model to experimental data. This threshold switching is the 'soft breakdown' observed during electroforming of TiO2 and other transition-metal-oxide based memristors, as well as a precursor to 'ON' or 'SET' switching of unipolar memristors from their high to their low resistance states. The shape of the V(I) curve is a sensitiv…
We consider the heat equation for monolayer two-dimensional materials in the presence of heat flow into a substrate and Joule heating due to electrical current. We compare devices including a nanowire of constant width and a bow tie (or wedge) constriction of varying width, and we derive approximate one-dimensional heat equations for them; a bow tie constriction is described by the modified Bessel equation of zero order. We compare steady state analytic solutions of the approximate equations with numerical results obtained by a finite element method solution of the two-dimensional equation. Us…
Joule heating and electronic Gurzhi effect in hydrodynamic differential transport in an electron liquid
State Key Laboratory of Semiconductor Physics and Chip Technologies, Institute of Semiconductors, Chinese Academy of Science（中国科学院半导体研究所半导体物理与芯片技术国家重点实验室）；College of Material Science and Opto-Electronic Technology, University of Chinese Academy of Sciences（中国科学院大学物质科学与光电技术学院）；Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所北京凝聚态物理国家研究中心）；Center for Quantum Matters, School of Physics, Zhejiang University（浙江大学物理学院量子物质中心）；CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences（中国科学院大学拓扑量子计算卓越创新中心）
We study the effect of Joule heating from electric currents flowing through ferromagnetic nanowires on the temperature of the nanowires and on the temperature of the substrate on which the nanowires are grown. The spatial current density distribution, the associated heat generation, and diffusion of heat is simulated within the nanowire and the substrate. We study several different nanowire and constriction geometries as well as different substrates: (thin) silicon nitride membranes, (thick) silicon wafers, and (thick) diamond wafers. The spatially resolved increase in temperature as a functio…
We study deterministic magnetic reversal of a perpendicularly magnetized Co layer in a Co/MgO/Ta nano-square driven by spin Hall torque from an in-plane current flowing in an underlying Pt layer. The rate-limiting step of the switching process is domain-wall (DW) depinning by spin Hall torque via a thermally-assisted mechanism that eventually produces full reversal by domain expansion. An in-plane applied magnetic field collinear with the current is required, with the necessary field scale set by the need to overcome DW chirality imposed by the Dzyaloshinskii-Moriya interaction. Once Joule hea…
Recently the memristive electrical transport properties in NbO$_2$ have attracted much attention for their promising application to the neuromorphic computation. At the center of debates is whether the metal-to-insulator transition (MIT) originates from the structural distortion (Peierls) or the electron correlation (Mott). With inputs from experiments and first principles calculations, we develop a thermodynamical model rooted in the scenario of the MIT driven by a $2^{nd}$ order Peierls instability. We find that the temperature dependence of the electrical conductivity can be accurately fit …
In many transition metal oxides the electrical resistance is observed to undergo dramatic changes induced by large biases. In magnetite, Fe$_3$O$_4$, below the Verwey temperature, an electric field driven transition to a state of lower resistance was recently found, with hysteretic current-voltage response. We report the results of pulsed electrical conduction measurements in epitaxial magnetite thin films. We show that while the high- to low-resistance transition is driven by electric field, the hysteresis observed in $I-V$ curves results from Joule heating in the low resistance state. The sh…
We provide an experimental demonstration that the focusing of ionic currents in a micron size hole connecting two chambers can produce local temperature increases of up to $100^\circ$ C with gradients as large as $1^\circ$ K$μm^{-1}$. We find a good agreement between the measured temperature profiles and a finite elements-based numerical calculation. We show how the thermal gradients can be used to measure the full melting profile of DNA duplexes within a region of 40 $μ$m. The possibility to produce even larger gradients using sub-micron pores is discussed.
During the standard ac lock-in measurement of the resistance of a two-dimensional electron gas (2DEG) applying an ac current $I = \sqrt{2} I_0 \sin(ωt)$, the electron temperature $T_e$ oscillates with the angular frequency $2 ω$ due to the Joule heating $\propto I^2$. We have shown that the highest ($T_\mathrm{H}$) and the lowest ($T_\mathrm{L}$) temperatures during a cycle of the oscillations can be deduced, at cryogenic temperatures, exploiting the third-harmonic (3$ω$) component of the voltage drop generated by the ac current $I$ and employing the amplitude of the Shubnikov-de Haas oscillat…
We study, both theoretically and experimentally, the features on the current-voltage characteristic of a highly transparent Josephson junction caused by transition of the superconducting leads to the normal state. These features appear due to the suppression of the Andreev excess current. We show that by tracing the dependence of the voltage, at which the transition occurs, on the bath temperature and by analyzing the suppression of the excess current by the bias voltage one can recover the temperature dependence of the heat flow out of the junction. We verify theory predictions by fabricating…
We present measurements of the Joule heating of a 2D hole gas (2DHG) formed in a 30nm GaAs quantum well. The hole density is in the range (4.6-18.9)*10^9cm^-2 and exhibits an apparent metal-to-insulator transition (MIT) with a critical density 6*10^9 cm^-2. In the limit of zero heating power density P, the GaAs lattice is within 2 mK of the 6 mK base temperature of our dilution refrigerator determined by He-3 melting curve thermometry. Throughout the range of heating power densities used (1 to 10^6 fW/cm^2), the temperature rise of the lattice is estimated to be negligible compared to the temp…
We present a time-resolved study of the DC-current driven magnetization dynamics in a microstructured Cr/Heusler/Pt waveguide by means of Brillouin light scattering. A reduction of the effective spin-wave damping via the spin-transfer-torque effect leads to a strong increase in the magnon density. This is accompanied by a decrease of the spin-wave frequencies. By evaluating the time scales of these effects, the origin of this frequency shift can be identified. However, recently, we found that the experimental setup partially influences the decay of the spin-wave intensity after the current pul…
Efficient control of magnetism with electric means is a central issue of current spintronics research, which opens an opportunity to design integrated spintronic devices. However, recent well-studied methods are mostly based on electric-current injection, and they are inevitably accompanied by considerable energy losses through Joule heating. Here we theoretically propose a way to exert spin torques into magnetic bilayer systems by application of electric voltages through taking advantage of the Rashba spin-orbit interaction. The torques resemble the well-known electric-current-induced torques…
We have studied spin orbit torque in heavy metal (HM)/ferromagnetic metal (FM) bilayers using magneto-optical Kerr effect. A double modulation technique is developed to separate signals from spin orbit torque and Joule heating. At a current density of ~1x10$^{10}$ A/m$^2$, we observe optical signals that scale linearly and quadratically with the current density, both in similar magnitude. The spin orbit torque estimated using this technique is consistent with that evaluated using spin transport measurements. We find that changes in the refractive index of the film with temperature is the main …
We consider losses in monolayer graphene nanoresonator connected with Joule dissipation (heating) caused by valley currents stipulated by synthetic electric fields . These synthetic electric fields arise in graphene membrane due to periodic in time gauge fields generated there by external periodic electromotive force. This mechanism accounts for essential part (about 40 percents) of losses in graphene nanoresonator and is specific just for graphene. The ways of the minimization of these Joule dissipation (increase of the quality-factor of the electromechanical system) are discussed. It is expl…
Motivated by recent experiments [Lee et al. Nature 498, 209 (2013)], we present here a detailed theoretical analysis of the Joule heating in current-carrying single-molecule junctions. By combining the Landauer approach for quantum transport with ab initio calculations, we show how the heating in the electrodes of a molecular junction is determined by its electronic structure. In particular, we show that in general the heat is not equally dissipated in both electrodes of the junction and it depends on the bias polarity (or equivalently on the current direction). These heating asymmetries are i…
We demonstrate by experiments and numerical simulations that the low-temperature current-voltage characteristics in diffusive bilayer graphene (BLG) exhibit a strong superlinearity at finite bias voltages. The superlinearity is weakly dependent on doping and on the length of the graphene sample. This effect can be understood as a result of Joule heating. It is stronger in BLG than in monolayer graphene (MLG), since the conductivity of BLG is more sensitive to temperature due to the higher density of electronic states at the Dirac point.
Based on spin-dependent transport theory and thermodynamics, we develop a generalized theory of the Joule heating in the presence of a spin current. Along with the conventional Joule heating consisting of an electric current and electrochemical potential, it is found that the spin current and spin accumulation give an additional dissipation because the spin-dependent scatterings inside bulk and ferromagnetic/nonmagnetic interface lead to a change of entropy. The theory is applied to investigate the dissipation due to pure spin-current generated by spin pumping across a ferromagnetic/nonmagneti…
In the presence of Joule heating, the electronic temperature in a metallic resistor placed at sub-Kelvin temperatures can significantly exceed the phonon temperature. Electron cooling proceeds mainly through two processes: electronic diffusion to and from the connecting wires and electron-phonon coupling. The goal of this paper is to present a general solution of the problem, in a form that can easily be used in practical situations. As an application, we compute two quantities that depend on the electronic temperature profile: the second and the third cumulant of the current noise at zero fre…
The spin-transfer torque is a fundamental physical quantity to operate the spintronics devices such as racetrack memory. We theoretically study the spin-transfer torque and analyze the dynamics of the magnetic domain walls in magnetic Weyl semimetals. Owing to the strong spin-orbit coupling in Weyl semimetals, the spin-transfer torque can be significantly enhanced, because of which they can provide a more efficient means of controlling magnetic textures. We derive the analytical expression of the spin-transfer torque and find that the velocity of the domain wall is one order of magnitude great…
We derive and employ a semi-classical Langevin equation obtained from path-integrals to describe the ionic dynamics of a molecular junction in the presence of electrical current. The electronic environment serves as an effective non-equilibrium bath. The bath results in random forces describing Joule heating,current-induced forces including the non-conservative wind force,dissipative frictional forces, and an effective Lorentz-like force due to the Berry phase of the non-equilibrium electrons. Using a generic two-level molecular model, we highlight the importance of both current-induced forces…
The temporal evolution of quantal Joule heating of 2D electrons in GaAs quantum well placed in quantizing magnetic fields is studied using a difference frequency method. The method is based on measurements of the electron conductivity oscillating at the beat frequency $f=f_1-f_2$ between two microwaves applied to 2D system at frequencies $f_1$ and $f_2$. The method provides $direct$ access to the dynamical characteristics of the heating and yields the inelastic scattering time $τ_{in}$ of 2D electrons. The obtained $τ_{in}$ is strongly temperature dependent, varying from 0.13 ns at 5.5K to 1 n…
We discuss the mechanisms behind the electrically driven insulator-metal transition in single crystalline VO$_2$ nanobeams. Our DC and AC transport measurements and the versatile harmonic analysis method employed show that non-uniform Joule heating causes phase inhomogeneities to develop within the nanobeam and is responsible for driving the transition in VO$_{2}$. A Poole-Frenkel like purely electric field induced transition is found to be absent and the role of percolation near and away from the electrically driven transition in VO$_{2}$ is also identified. The results and the harmonic analy…
We calculate the phonons in a graphene nanoconstriction(GNC) in the presence of a high current density. The Joule-heating, current-induced forces, and coupling to electrode phonons is evaluated using first principles nonequilibrium DFT-NEGF calculations. Close to a resonance in the electronic structure we observe a strongly nonlinear heating with bias and breakdown of the harmonic approximation. This behavior results from negatively damped phonons driven by the current. The effect may limit the stability and capacity of graphene nanoconstrictions to carry high currents.
