We develop an efficient and general method for optimizing the microwave field that achieves magnetization switching with a smaller static field. This method is based on optimal control and renders an exact solution for the 3D microwave field that triggers the switching of a nanomagnet with a given anisotropy and in an oblique static field. Applying this technique to the particular case of uniaxial anisotropy, we show that the optimal microwave field, that achieves switching with minimal absorbed energy, is modulated both in frequency and in magnitude. Its role is to drive the magnetization from the metastable equilibrium position towards the saddle point and then damping induces the relaxation to the stable equilibrium position. For the pumping to be efficient, the microwave field frequency must match at the early stage of the switching process the proper precession frequency of the magnetization, which depends on the magnitude and direction of the static field. We investigate the effect of the static field (in amplitude and direction) and of damping on the characteristics of the microwave field. We have computed the switching curves in the presence of the optimal microwave field. The results are in qualitative agreement with micro-SQUID experiments on isolated nanoclusters. The strong dependence of the microwave field and that of the switching curve on the damping parameter may be useful in probing damping in various nanoclusters.
We measure the temperature, magnetic-field, and current dependence for the switching of nanomagnets by a spin-polarized current. Depending on current bias, switching can occur between either two static magnetic states or a static state and a current-driven precessional mode. In both cases, the switching is thermally activated and governed by the sample temperature, not a higher effective magnetic temperature. The activation barriers for switching between static states depend linearly on current, with a weaker dependence for dynamic to static switching.
Using soft x-ray spectromicroscopy, we investigate the magnetic domain structure in embedded nanomagnets defined in La$_{0.7}$Sr$_{0.3}$MnO$_3$ thin films and LaFeO$_3$/La$_{0.7}$Sr$_{0.3}$MnO$_3$ bilayers. We find that shape-controlled antiferromagnetic domain states give rise to a significant reduction of the switching field of the rectangular nanomagnets. This is discussed in the framework of competition between an intrinsic spin-flop coupling and shape anisotropy. The data demonstrates that shape effects in antiferromagnets may be used to control the magnetic properties in nanomagnets.
We present an ultrafast route for a controlled, toggle switching of magnetic vortex cores with ultrashort unipolar magnetic field pulses. The switching process is found to be largely insensitive to extrinsic parameters, like sample size and shape, and it is faster than any field-driven magnetization reversal process previously known from micromagnetic theory. Micromagnetic simulations demonstrate that the vortex core reversal is mediated by a rapid sequence of vortex-antivortex pair-creation and annihilation sub-processes. Specific combinations of field pulse strength and duration are required…
Reversible straintronic switching of a nanomagnet's magnetization between two stable or metastable states promises ultra-energy-efficient non-volatile memory. Here, we report strain-induced magnetization switching in ~300 nm sized FeGa nanomagnets delineated on a piezoelectric PMN-PT substrate. Voltage of one polarity applied across the substrate generates compressive strain in a nanomagnet and switches its magnetization to one state, while voltage of the opposite polarity generates tensile strain and switches the magnetization back to the original state, resulting in "non-toggle" switching. T…
Electric-field control of magnetism without electric currents potentially revolutionizes spintronics towards ultralow power. Here by using mechanically coupled phase field simulations, we computationally demonstrate the application of the strain-mediated magnetoelectric effect for the electric-field control of magnetic states in heterostructure. In the model heterostructure constituted of the soft nanomagnet Co and the piezoelectric substrate PMN-PT, both the volatility of magnetic states and the magnetization switching dynamics excited by the electric field are explored. It is found that an e…
We report manipulation of the magnetic states of elliptical cobalt magnetostrictive nanomagnets (of nominal dimensions ~ 340 nm x 270 nm x 12 nm) delineated on bulk 128° Y-cut lithium niobate with Surface Acoustic Waves (SAWs) launched from interdigitated electrodes. Isolated nanomagnets that are initially magnetized to a single domain state with magnetization pointing along the major axis of the ellipse are driven into a vortex state by surface acoustic waves that modulate the stress anisotropy of these nanomagnets. The nanomagnets remain in the vortex state until they are reset by a strong m…
We have explored the electric field controlled magnetization in the nanodot CoFe2O4/SrRuO3/PMN-PT heterostructures. Ordered ferromagnetic CFO nanodots (~300 nm lateral dimension) are developed on the PMN-PT substrate (ferroelectric as well as piezoelectric) using a nanostencil-mask pattering method during pulsed laser deposition. The nanostructures reveal electric field induced magnetization reversal in the single domain CFO nanodots through transfer of piezostrains from the piezoelectric PMN-PT substrate to the CFO. Further, electric field modulated spin structure of CFO nanomagnets is analys…
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…
Features of thermally-activated magnetization switching have been studied in a FeCoB nanomagnet using the Néel model. A method of a high-precision measurement of the coercive field, retention time, Δ and the size of the switching nucleation domain has been proposed and experimentally demonstrated using a Hall-probe setup. A high measurement precision, repeatability and reliability are the features of the proposed method. The dependency of the parameters of thermally-activated magnetization switching on the gate voltage and the bias current were studied.
Spin orbit torque (SOT) provides an efficient way of generating spin current that promises to significantly reduce the current required for switching nanomagnets. However, an in-plane current generated SOT cannot deterministically switch a perpendicularly polarized magnet due to symmetry reasons. On the other hand, perpendicularly polarized magnets are preferred over in-plane magnets for high-density data storage applications due to their significantly larger thermal stability in ultra-scaled dimensions. Here we show that it is possible switch a perpendicularly polarized magnet by SOT without …
We report the possibility of achieving an order of magnitude reduction in the energy dissipation needed to write bits in perpendicular magnetic tunnel junctions (p-MTJs) by simulating the magnetization dynamics under a combination of resonant surface acoustic waves (r-SAW) and spin-transfer-torque (STT). The magnetization dynamics were simulated using the Landau-Lifshitz-Gilbert equation under macrospin assumption with the inclusion of thermal noise. The resonant magnetization dynamics in the magnetostrictive nanomagnet build over few 10s of cycles of SAW application that drives the magnetizat…
The asymptotic behavior of switching time as a function of current for a uniaxial macrospin under the effects of both spin-torque and thermal noise is explored analytically by focusing on its diffusive energy space dynamics. The scaling dependence ($I\rightarrow 0$, $<τ\propto\exp(-ξ(1-I)^2)$) is shown to confirm recent literature results. The analysis shows the mean switching time to be functionally independent of the angle between the spin current and magnet's uniaxial axes. These results have important implications for modeling the energetics of thermally assisted magnetization reversal of …
We study the magnetization dynamics of thin-film magnetic elements with in-plane magnetization subject to a spin-current flowing perpendicular to the film plane. We derive a reduced partial differential equation for the in-plane magnetization angle in a weakly damped regime. We then apply this model to study the experimentally relevant problem of switching of an elliptical element when the spin-polarization has a component perpendicular to the film plane, restricting the reduced model to a macrospin approximation. The macrospin ordinary differential equation is treated analytically as a weakly…
We consider the general Landau-Lifshitz-Gilbert (LLG) dynamical theory underlying the magnetization switching rates of a thin film uniaxial magnet subject to spin-torque effects and thermal fluctuations (thermal noise). After discussing the various dynamical regimes governing the switching phenomena, we present analytical results for the mean switching time behavior. Our approach, based on explicitly solving the first passage time problem, allows for a straightforward analysis of the thermally assisted, low spin-torque, switching asymptotics of thin film magnets. To verify our theory, we have …
Detailed understanding of spin dynamics in magnetic nanomaterials is necessary for developing ultrafast, low-energy and high-density spintronic logic and memory. Here, we develop micromagnetic models and analytical solutions to elucidate the effect of increasing damping and uniaxial anisotropy on magnetic field pulse-assisted switching time, energy and field requirements of nanowires with perpendicular magnetic anisotropy and yttrium iron garnet-like spin transport properties. A nanowire is initially magnetized using an external magnetic field pulse (write) and self-relaxation. Next, magnetic …
In this letter, we show that Giant Spin Hall Effect (GSHE) MRAM can enable better energy- delay and voltage performance than traditional MTJ based spin torque devices at scaled nanomagnet dimensions (10-30 nm). Firstly, we derive the effect of dimensional scaling on spin injection efficiency, voltage-delay and energy-delay of spin torque switching using MTJs and GSHE and identify the optimum electrode geometry for low operating voltage (<0.1 V), high speed (>10 GHz) operation. We show that effective spin injection efficiency >100 % can be obtained using optimum spin hall electrode thickness fo…
Numerical integration of the Landau-Lifshitz-Gilbert equation with thermal fluctuations is used to study the dynamic response of single-domain nanomagnets to rapid changes in the applied magnetic field. The simulation can resolve magnetization patterns within nanomagnets and uses the Fast Multipole method to calculate dipole-dipole interactions efficiently. The thermal fluctuations play an essential part in the reversal process whenever the applied field is less than the zero-temperature coercive field. In this situation pillar-shaped nanomagnets are found to reverse through a local curling mo…
Rotating the magnetization of a magnetostrictive nanomagnet with electrically generated mechanical strain dissipates miniscule amount of energy compared to any other rotation method and would have been the ideal method to write bits in nonvolatile magnetic memory, except strain cannot ordinarily rotate the magnetization of magnet by more than 90 degrees and "flip" it. Here, we describe a scheme to achieve complete 180 degree rotation of the magnetization of a nanomagnet with strain that will enable writing of binary bits in non-volatile magnetic memory implemented with magneto-tunneling juncti…
We present a comprehensive investigation of the size-dependent switching characteristics and spin wave modes of FePt nanoelements. Curved nanomagnets ("caps") are compared to flat disks of identical diameter and volume over a size range of 100 to 300nm. Quasi-static magnetization reversal analysis using first-order reversal curves (FORC) shows that spherical caps have lower vortex nucleation and annihilation fields than the flat disks. As the element diameter decreases, the reversal mechanism in the caps crosses over sooner to coherent rotation than in the disks. The magnetization dynamics are…
Through the hysteresis loop and magnetization spatial distribution we study and compare two models for surface anisotropy in nanomagnets: a model with transverse anisotropy axes and Néel's model. While surface anisotropy in the transverse model induces several jumps in the hysteresis loop because of the cluster-wise switching of spins, in the Néel model the jumps correspond to successive {\it coherent partial rotations} of the whole bunch of spins. These calculations together with experimental results suggest that Néel's model for surface anisotropy is more appropriate.
We show that dipole-field induced antiferromagnetic coupling, or RKKY ferromagnetic coupling, between Co layers can strongly affect the low magnetic field switching behavior of Co/Cu/Co nanopillars. Whereas current-assisted switching at low fields in uncoupled nanopillars is always hysteretic, strong coupling of either kind can change the switching to non-hysteretic (reversible). These differences can be understood with a simple picture of current-assisted thermal activation over a barrier.
Concepts for memories based on the manipulation of giant magnetostrictive nanomagnets by stress pulses have garnered recent attention due to their potential for ultra-low energy operation in the high storage density limit. Here we discuss the feasibility of making such memories in light of the fact that the Gilbert damping of such materials is typically quite high. We report the results of numerical simulations for several classes of toggle precessional and non-toggle dissipative magnetoelastic switching modes. Material candidates for each of the several classes are analyzed and forms for the …
Perpendicular MgO-based Magnetic Tunnel Junctions are optimal candidates as building block of Spin Transfer Torque (STT) magnetoresistive memories. However, up to now, the only STT is not enough to achieve switching current density below 106 A/cm2. A recent work [Wang et al., Nature Mater., vol. 11, pp 64-68, Jan. 2012] has experimentally demonstrated the possibility to perform magnetization switching assisted by an electric-field at ultra-low current density. Theoretically, this switching has been studied by using a macrospin approach only. Here, we show a full micromagnetic study. We found t…
Segmented magnetic nanowires are a promising route for the development of three dimensional data storage techniques. Such devices require a control of the coercive field and the coupling mechanisms between individual magnetic elements. In our study, we investigate electrodeposited nanomagnets within host templates using vibrating sample magnetometry and observe a strong dependence between nanowire length and coercive field (25 nm to 5 $μ$m) and diameter (25 nm to 45 nm). A transition from a magnetization reversal through coherent rotation to domain wall propagation is observed at an aspect rat…
The progress of magnetization reversal of weakly packed ferromagnetic Ni80Fe20 nanowire arrays of different diameters (40, 50, 70 and 100 nm) electrodeposited in polycarbonate membranes was studied by magnetic force microscopy (MFM). For such a low packing density of nanomagnets, the dipolar interactions between neighbouring wires can be neglected. The intrinsic switching field distribution has been extracted from in situ MFM images and its width was found to be considerably smaller than for densely packed nanowire arrays.
The microwave assisted magnetisation reversal is modelled in a permalloy micron-sized magnetic ellipsoid. Our simulations confirm that this process requires less field than magnetisation reversal under a static field. This is due to a different reversal mode which in case of the microwave-assisted process is always a ripple structure. During the magnetisation reversal two stages: nucleation and relaxation are distinguished. The nucleation process is governed by spinwave instabilities. The relaxation process is related to the domain expansion through domain wall propagation determined by the pr…
Crossover between intrinsic and temperature-assisted regimes in spin-orbit torque switching of antiferromagnetic order
The University of Tokyo（东京大学）；The Johns Hopkins University（约翰斯·霍普金斯大学）；Japan Science and Technology Agency（日本科学技术振兴机构）；Institute for Solid State Physics, The University of Tokyo（东京大学固体物理研究所）；Osaka University（大阪大学）；RIKEN（理化学研究所）；Trans-scale Quantum Science Institute, The University of Tokyo（东京大学跨尺度量子科学研究所）；Canadian Institute for Advanced Research（加拿大高级研究院）
Using numerical and analytical micromagnetics we calculated the switching fields and energy barriers of the composite (exchange spring) magnetic recording media, which consist of layers with high and low magnetocrystalline anisotropy. We demonstrate that the ultimate potential of the composite media is realized if the interfacial domain wall fits inside the layers. The switching occurs via domain wall nucleation, compression in the applied field, de-pinning and propagation through the hard/soft interface. This domain wall assisted switching results in a significant reduction of the switching f…
Voltage-driven 180$^\circ$ magnetization switching without electric current provides the possibility for revolutionizing the spintronics. We demonstrated the voltage-driven charge-mediated 180$^\circ$ magnetization switching at room temperature by combining first-principles calculations and temperature-dependent magnetization dynamics simulation. The electric field ($E$) induced interface charge is found to allow a giant modulation of the magnetic anisotropy ($K$) of the nanomagnet. Particularly $K$ is revealed to vary linearly with respect to $E$ and the epitaxial strain. Magnetization dynami…
Within the framework of the Landau-Lifshitz-Gilbert equation, using permalloy parameters, we study the statics and dynamics of flat circular magnetic nano-structures with an in-plane magnetic vortex configuration, putting particular emphasis on the (planar) vorticity of the magnetic state and on the (perpendicular) polarisation of the vortex center (which may be shifted with respect to the center of the circle). These binary degrees of freedom can in principle be used to manipulate two independent bits of information. Studying switching processes induced by in-plane and out-of plane field puls…
Here, we describe the prototype for precisely scaled temperature assisted magnetic recording scheme utilizing the characteristics of thermo-remnant magnetization (TRM) in bulk SmCrO$_3$ as a memory media. The TRM response can be exploited in completely reversible bipolar switching performances either by tuning the temperature only across a sharp thermal window $ΔT_w$ = 10 K, or annealing isothermally with a single pulse of field $\ge$ 0.1 T by flipping the direction of magnetization from 0$^o$ to 180$^o$. The microscopic mechanism of TRM in SmCrO$_3$ is explored by means of diffuse scattering …
We have proposed the use of surface plasmon resonances at the interface of hybrid magneto-photonic heterostructures [Opt. Mat. Exp., 7, 4316 (2017)] for all-optical control of the macroscopic spin orientation in nanostructures in fs time scales. This requires strong spin-photon coupling for the resonant enhancement of opto-magnetic fields, generated through the inverse Faraday effect, in magnetic nanostructures with perpendicular anisotropy. Here we report on the development of nm thick interlayers to control the growth orientation of hcp-Co alloys grown on refractory plasmonic materials to al…
We systematically investigated the spin wave-assisted magnetization switching (SWAS) of a L10-FePt / Ni81Fe19 (Permalloy; Py) exchange-coupled bilayer using a pulse-like rf field (hrf) and mapped the switching events in the magnetic field (H) - hrf frequency (f) plane to reveal the switching conditions. The switching occurred only in a limited region following the dispersion relationship of the perpendicular standing spin wave (PSSW) modes in Py. The results indicate that SWAS is a resonant magnetization switching process, which is different from the conventional microwave assisted switching, …
Microwave assisted magnetization reversal has been investigated in a bilayer system of Pt/ferromagnet by detecting a change in the polarity of the spin pumping signal. The reversal process is studied in two material systems, Pt/CoFeB and Pt/NiFe, for different aspect ratios. The onset of the switching behavior is indicated by a sharp transition in the spin pumping voltage. At a threshold value of the external field, the switching process changes from partial to full reversal with increasing microwave power. The proposed method provides a simple way to detect microwave assisted magnetization re…
Photoresponse of bimetallic Au-Ag nanoparticle embedded soda glass (Au-Ag@SG) substrate is reported for surface plasmon assisted optical switching using 808 nm excitation. Au-Ag@SG system is made by an ion beam technique where Ag^+ is introduced first in the soda glass matrix by ion exchange technique. Subsequently 400 keV Au^+ is implanted in the sample for different fluences which is followed by an ion beam annealing process using 1 MeV Si^+ at a fixed fluence of 2E16 ions.cm^{-2}. Characteristic surface plasmon resonance (SPR) peaks around 400 and 550 nm provided evidence for the presence o…
We studied the microwave assisted magnetic reversal of 65 nm by 71 nm elliptical Ni80Fe20 nanomagnets. Hysteresis curves were measured by magneto-optical Kerr effect for a range of microwave frequencies and amplitudes. The coercive field Hc was reduced by 26% for an rf field of 0.08Hc when the microwave frequency coincided with the minimum of the experimentally determined ferromagnetic resonance frequency with varying dc field. The experimental results for the fractional reduction in Hc with rf field amplitude are in good agreement with numerical simulations for an array of interacting macrosp…
We study the combined effects of spin transfer torque, voltage modulation of interlayer exchange coupling and magnetic anisotropy on the switching behavior of perpendicular magnetic tunnel junctions (p-MTJs). In asymmetric p-MTJs, a linear-in-voltage dependence of interlayer exchange coupling enables the effective perpendicular anisotropy barrier to be lowered for both voltage polarities. This mechanism is shown to reduce the critical switching current and effective activation energy. Finally, we analyze the possibility of having switching via interlayer exchange coupling only.
Growing demands for the voltage-driven spintronic applications with ultralow-power consumption have led to new interest in exploring the voltage-induced magnetization switching in ferromagnetic metals. In this study, we observed a large perpendicular magnetic anisotropy change in Au(001) / ultrathin Fe80Co20(001) / MgO(001) / Polyimide / ITO junctions, and succeeded in realizing a clear switching of magnetic easy axis between in-plane and perpendicular directions. Furthermore, employing a perpendicularly magnetized film, voltage-induced magnetization switching in the perpendicular direction un…
The results of large-scale simulations investigating the dynamics of magnetization reversal in arrays of single-domain nanomagnets after a rapid reversal of the applied field at nonzero temperature are presented. The numerical micromagnetic approach uses the Landau-Lifshitz-Gilbert equation including contributions from thermal fluctuations and long-range dipole-dipole demagnetizing effects implemented using a fast-multipole expansion. The individual model nanomagnets are 9 nm x 9 nm x 150 nm iron pillars similar to those fabricated on a surface with STM-assisted chemical vapor deposition [S. W…
It is assumed that heat-assisted magnetic recording (HAMR) is the recording technique of the future. For pure hard magnetic grains in high density media with an average diameter of $5$nm and a height of $10$nm the switching probability is not sufficiently high for the use in bit-patterned media. Using a bilayer structure with 50$\%$ hard magnetic material with low Curie temperature and 50$\%$ soft magnetic material with high Curie temperature to obtain more than 99.2$\%$ switching probability, leads to very large jitter. We propose an optimized material composition to reach a switching probabi…
We describe time-domain measurements which provide new information about the large-angle nonlinear dynamics of nanomagnets excited by spin-transfer torque from a spin-polarized current. Sampling-oscilloscope measurements, which average over thousands of experimental time traces, show that the mean reversal time for spin-transfer-driven magnetic switching has a step-like dependence on magnetic field, because an integer number of precession cycles is required for reversal. Storage-oscilloscope measurements of individual experimental traces reveal non-periodic large-amplitude resistance variation…
Spin-orbit torques (SOT) allow the electrical control of magnetic states. Current-induced SOT switching of the perpendicular magnetization is of particular technological importance. The SOT consists of damping-like and field-like torques so that the efficient SOT switching requires to understand combined effects of the two torque-components. Previous quasi-static measurements have reported an increased switching probability with the width of current pulses, as predicted with considering the damping-like torque only. Here we report a decreased switching probability at longer pulse-widths, based…
We have investigated Surface Acoustic Wave (SAW) induced ferromagnetic resonance (FMR) assisted Spin Transfer Torque (STT) switching of perpendicular MTJ (p-MTJ) with inhomogeneities using micromagnetic simulations that include the effect of thermal noise. With suitable frequency excitation, the SAW can induce ferromagnetic resonance in magnetostrictive materials, and the magnetization can precesses in a cone with high deflection from the perpendicular direction. With incorporation of inhomogeneity via lateral anisotropy variation as well as room temperature thermal noise, the magnetization pr…
Numerical solutions of the Landau-Lifshitz-Gilbert micromagnetic model incorporating thermal fluctuations and dipole-dipole interactions (calculated by the Fast Multipole Method) are presented for systems composed of nanoscale iron pillars of dimension 9 nm x 9 nm x 150 nm. Hysteresis loops generated under sinusoidally varying fields are obtained, while the coercive field is estimated to be 1979 $\pm$ 14 Oe using linear field sweeps at T=0 K. Thermal effects are essential to the relaxation of magnetization trapped in a metastable orientation, such as happens after a rapid reversal of an extern…
We investigate fast-pulse switching of in-plane-magnetized magnetic tunnel junctions (MTJs) within 3-terminal devices in which spin-transfer torque is applied to the MTJ by the giant spin Hall effect. We measure reliable switching, with write error rates down to $10^{-5}$, using current pulses as short as just 2 ns in duration. This represents the fastest reliable switching reported to date for any spin-torque-driven magnetic memory geometry, and corresponds to a characteristic time scale that is significantly shorter than predicted possible within a macrospin model for in-plane MTJs subject t…
We show that the spin-orbit torque induced magnetization switching in nanomagnets presenting Dzyaloshinskii-Moriya (DMI) interaction is governed by a chiral domain nucleation at the edges. The nucleation is induced by the DMI and the applied in-plane magnetic field followed by domain wall propagation. Our micromagnetic simulations show that the DC switching current can be defined as the edge nucleation current, which decreases strongly with increasing amplitude of the DMI. This description allows us to build a simple analytical model to quantitatively predict the switching current. We find tha…
Spin Hall effect (SHE) induced reversal of perpendicular magnetization has attracted significant interest, due to its potential to lead to low power memory and logic devices. However, the switching requires an assisted in-plane magnetic field, which hampers its practical applications. Here, we introduce a novel approach for external-field-free spin Hall switching of a perpendicular nanomagnet by utilizing a local dipolar field arising from an adjacent in-plane magnetic layer. Robust switching of perpendicular CoFeB nanopillars in a dipole-coupled composite stack is experimentally demonstrated …
Ta/CoFeB/MgO trilayers with perpendicular magnetic anisotropy are expected to play a key role in the next generation of current and electric field switched memory and logic devices. In this study we use Kerr microscopy alongside electrical transport measurement to gain insight into the underlying switching mechanisms of such devices. We find switching to be a stochastic, domain wall driven process, the speed of which is strongly dependent on the switching current. Kerr imaging shows domain nucleation at the edge of the device which modelling reveals is likely assisted by the perpendicular comp…
Combination of local heating and biasing at the tip-surface junction in temperature-assisted piezoresponse force microscopy (tPFM) opens the pathway for probing local temperature induced phase transitions in ferroics, exploring the temperature dependence of polarization dynamics in ferroelectrics, and potentially discovering coupled phenomena driven by strong temperature- and electric field gradients. Here, we analyze the signal formation mechanism in tPFM and explore the interplay between thermal- and bias-induced switching in model ferroelectric materials. We further explore the contribution…
