Exploiting random phenomena in magnetic materials for data security, logics, and neuromorphic computing: Challenges and prospects Cite as: APL Mater. 9, 070903 (2021); https://doi.org/10.1063/5.0055400 Submitted: 28 April 2021 • Accepted: 10 June 2021 • Published Online: 08 July 2021 C. Navau and J. Sort COLLECTIONS This paper was selected as Featured This paper was selected as Scilight ARTICLES YOU MAY BE INTERESTED IN Neuromorphic computing with antiferromagnetic spintronics Journal of Applied Physics 128, 010902 (2020); https://doi.org/10.1063/5.0009482 The design and verification of MuMax3 AIP Advances 4, 107133 (2014); https://doi.org/10.1063/1.4899186 Advances in magneto-ionic materials and perspectives for their application APL Materials 9, 030903 (2021); https://doi.org/10.1063/5.0042544 APL Mater. 9, 070903 (2021); https://doi.org/10.1063/5.0055400 9, 070903 © 2021 Author(s). APL Materials PERSPECTIVE scitation.org/journal/apm Exploiting random phenomena in magnetic materials for data security, logics, and neuromorphic computing: Challenges and prospects Cite as: APL Mater. 9, 070903 (2021); doi: 10.1063/5.0055400 Submitted: 28 April 2021 • Accepted: 10 June 2021 • Published Online: 8 July 2021 C. Navau1,a) and J. Sort1,2,a) AFFILIATIONS 1 Departament de Física, Universitat Autònoma de Barcelona, E-08193 Cerdanyola Del Vallès, Spain 2 Institució Catalana de Recerca i Estudis Avançats (ICREA), Pg. Lluís Companys 23, E-08010 Barcelona, Spain a) Authors to whom correspondence should be addressed: Carles.Navau@uab.cat and jordi.sort@uab.cat ABSTRACT Random phenomena are ubiquitous in magnetism. They include, for example: the random orientation of magnetization in an assembly of non-interacting isotropic magnets; arbitrary maze domain patterns in magnetic multilayers with out-of-plane anisotropy, random polar- ization, and chirality of an array of magnetic vortices; or Brownian skyrmion motion, among others. Usually, for memory applications, randomness needs to be avoided to reduce noise and enhance stability and endurance. However, these uncontrolled magnetic effects, espe- cially when incorporated in magnetic random-access memories, offer a wide range of new opportunities in, e.g., stochastic computing, the generation of true random numbers, or physical unclonable functions for data security. Partial control of randomness leads to tunable prob- abilistic bits, which are of interest for neuromorphic computing and for new logic paradigms, as a first step toward quantum computing. In this Perspective, we present and analyze typical materials that exhibit stochastic magnetic phenomena and we show some examples of emerging applications. The current challenges in terms of material development, as well as new strategies to tune stochasticity, enhance energy efficiency, and improve operation speeds are discussed, aiming to provide new prospects and opportunities in this compelling research field. © 2021 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). https://doi.org/10.1063/5.0055400 I. INTRODUCTION and structural defects) can find applications in logics and in neuro- morphic computing. Probabilistic bits (i.e., bits with a probability to Magnetic materials exhibit a plethora of stochastic (or random) occur higher or lower than fully random 50%) are considered a first effects. Such randomness occurs in the magnetic orientation of small step toward quantum q-bits.5 Figure 1 illustrates the main concepts magnetic nanoparticles over time,1 in the Brownian trajectories of related to stochasticity in magnetic phenomena and the prospective skyrmion quasiparticles,2 or in the polarity and chirality of magnetic applications. The goal of this Perspective is to analyze the state of vortices generated in micrometer-sized soft-magnetic disks,3 among the art of materials and phenomena related to magnetic random- others. For some applications (e.g., conventional memory devices), ness, with emphasis on the current challenges (control of random- randomness is highly undesirable (since it can generate noise and ness, energy efficiency, CMOS integration, or operation speed) and loss of information), and strategies have been put forward to avoid future opportunities in different technological fields, encompassing it. However, randomness can be used to generate true random num- data security, probabilistic computing, or neuromorphic computing bers at hardware level or in new computing paradigms,4 as will be (see Fig. 1). The reported effects can be of interest to deal with data described in this Perspective. Partial control of randomness with in which uncertainty is inherently present. It has been long recog- external stimuli (voltage, current, particle/dot shape modifications, nized that probabilistic algorithms can tackle some specific problems APL Mater. 9, 070903 (2021); doi: 10.1063/5.0055400 9, 070903-1 © Author(s) 2021 APL Materials PERSPECTIVE scitation.org/journal/apm the energy barrier can be expressed as ΔE = 1/2 MS VHK , where MS is the saturation magnetization, V is volume, and HK is the effec- tive anisotropy field. While τ is of the order of years in non-volatile memories, the time can be engineered to be much shorter (sub- second) using suitable nanomaterials (with low HK , MS , and V val- ues). When the size of a magnet is sufficiently small (approaching the superparamagnetic limit), its orientation will spontaneously fluctu- ate with time between two binary states due to thermal agitation. The readout from such tiny magnets, once the magnetic signal is trans- duced into a voltage or current, will result in telegraphic noise,1 and this can be considered as a simplified version of a stochastic device. This concept has been applied to magnetic tunnel junctions (MTJs) comprising a free layer with small in-plane magnetic anisotropy (superparamagnetic MTJs), where thermal activation effects induce FIG. 1. Illustration of the main phenomena that lead to magnetic random effects and the prospective applications in different research domains. PMA stands for stochastic fluctuations in the magnetoresistance values at time scales “perpendicular magnetic anisotropy.” below 5 ns.8 In magnetic objects of larger dimensions, the magnetization reversal mode can be tailored to arbitrarily fluctuate between dif- much more efficiently than classical algorithms using a deterministic ferent mechanisms. In a previous work, we adjusted the thickness computer.6 While the areal density of information in magnetic stor- and diameter of circular magnetic disks to critical values close to age media has been drastically increasing over the years, new chal- the boundaries between single-domain and vortex states so that the lenges posed by artificial intelligence and the need to tackle big data disks could reverse their magnetization arbitrarily either by coherent require changes in the computing paradigms, in which stochasticity rotation or through vortex formation. This is illustrated in Fig. 2(c), can play a key role. which shows the element-specific polarized x-ray photoemission electron microscopy (XPEEM) image at the Fe L-edge, in the absence of magnetic field applied, of an array of Ni80 Fe20 (6 nm)/Ir20 Mn80 II. STOCHASTIC EFFECTS IN MAGNETIC MATERIALS (5 nm) disks (2 μm in diameter) deposited onto a naturally oxidized It is well known that the magnetic dipoles of an assembly Si wafer. Disks 1 and 4 form vortex states at remanence, while disks of small magnets will orient at random in the as-prepared state 2 and 3 are single domains.9 or when cooled through the Curie temperature if they are not Remarkably, even when all disks in an array form vortex states affected by dipolar interactions. As an example, Fig. 2(b) shows the (e.g., in 100 nm-thick Ni80 Fe20 disks with 1 μm diameter), the chi- magnetic-force microscopy (MFM) image of random “up” (white) rality of the vortex and polarity of the vortex core are random if and “down” (black) single-domain states of an array of Ni pillars no symmetry-breaking geometrical constraints are applied to the with out-of-plane magnetization grown by electrodeposition.7 disk shape (see Fig. 3). The white and black spots at the cen- A single-domain nanomagnet can be characterized by an ter of the disks, imaged using full-field magnetic transmission soft energy barrier (ΔE) that separates two possible states, each of them x-ray microscopy (MTXM) [see Fig. 3(b)], reveal positive and nega- with the magnetic moment oriented in opposite directions. When tive polarity of the vortex core, respectively.3 The chirality is deter- the magnet is placed in one of these two states, it stays there for mined from the in-plane magnetic component [Fig. 3(a)], taking a certain amount time, called “retention time” (τ), which is given into account the vortex core polarity. Another example is con- by τ = τ 0 exp(ΔE/kB T), where τ 0 is a material constant, kB is the tinuous multilayers with perpendicular effective anisotropy, which Boltzmann constant, and T is temperature. In a first approximation, exhibit magnetic domains that form random maze patterns each time the system is demagnetized, provided that there are no struc- tural defects (e.g., grain boundaries) that influence the labyrinthic paths. There are many other examples of random phenomena in mag- netic materials. Steels and other types of ferromagnets exhibit the Barkhausen effect, which is related to noise in the magnetic output signal when the material is subject to an applied magnetic field and the size of the domains fluctuates with time in discrete steps due to structural defects in the crystal lattice.10 Concerning magnetic FIG. 2. (a) Scanning electron microscopy (SEM) image and (b) magnetic-force “moving entities,” stochastic domain wall pinning has been pre- microscopy (MFM) micrographs of an array of Ni pillars (90 nm diameter, 220 nm height), showing random “single-domain” behavior with out-of-plane magnetiza- dicted11 in magnetic nanowire devices due to the influence of ther- tion. Reproduced from Ross et al., J. Appl. Phys. 91, 6848 (2002) with the mal perturbations on the domain walls’ dynamics. Random ther- permission of AIP Publishing. (c) Magnetic contrast image acquired by x-ray mally driven effects also manifest in the trajectories of magnetic photoemission electron microscopy (XPEEM) at the Fe L-edge of an array of skyrmions in unconstrained, defect-free, ultra-thin magnetic films Ni80 Fe20 /Ir20 Mn80 disks (showing dissimilar magnetic configurations) in the frame- (see Fig. 4).12,13 Skyrmions are spin swirling quasiparticles that have work of an exchange bias investigation. Reproduced from Salazar-Alvarez et al., generated great expectations in recent years due to their potential to Appl. Phys. Lett. 95, 012510 (2009) with the permission of AIP Publishing. act as small information carriers.14 APL Mater. 9, 070903 (2021); doi: 10.1063/5.0055400 9, 070903-2 © Author(s) 2021 APL Materials PERSPECTIVE scitation.org/journal/apm applications. For example, the retention time in low energy bar- rier nanomagnets, τ, can be manipulated with current or voltage. By doing so, one can generate probabilistic p-bits, which have a prob- ability of being “1” or “0” different than 50% (which would be the fully stochastic case). These p-bits are considered as an intermediate between classical bits (with deterministic “0” and “1” orientations) and quantum q-bits (with coherent superpositions of “0” and “1”).1 Another example is the control of double-shifted loops in [Pt/Co]n multilayers with out-of-plane magnetization that we could achieve using the coupling with an adjacent antiferromagnetic (AFM) Ir20 Mn80 layer (exchange bias effect).15 This is illustrated in Fig. 5. Configuration (a) is the typical maze domain patterns with random shapes obtained after demagnetizing the [Pt/Co]n mul- tilayer. An equal proportion of white and dark stripes (indicat- ing regions with “up” and “down” magnetization, respectively) is observed by MFM. When this pattern is coupled to the adjacent AFM layer, a double-shifted loop (50% shifted to the right and 50% FIG. 3. Full-field magnetic transmission soft x-ray microscopy (MTXM) images of shifted to the left) is obtained. By annealing the system close to the the in-plane (a) and out-of-plane (b) magnetic components taken at remanence in an array of 100-nm-thick Ni80 Fe20 disks (1 μm diameter). The sense of rota- exchange bias blocking temperature and subsequently cooling under tion of the in-plane magnetization (i.e., vortex chirality) is indicated with the white different magnetic fields, the degree of randomness is decreased. arrows in (a). The black and white spots at the center of the disks are upward and For larger magnetic fields, the amount of “white” regions progres- downward vortex cores (positive and negative polarity), respectively (b). The vor- sively increases [configuration (b)] while the magnetization ampli- tex configuration of each disk is illustrated in (c). Reproduced with permission from tude of the left-shifted hysteresis loop also increases. If the system is Im et al., Nat. Commun. 3, 983 (2012). Copyright 2012, Nature Publishing Group. cooled with a sufficiently high magnetic field, an almost determinis- tic single-domain state is generated [configuration (c)] and the loop shape approaches that of a single-shifted hysteresis loop. During the last few years, we have also proposed strategies to manipulate and control the chirality and polarity of magnetic vor- tices by incorporating asymmetrical variations in the thickness of FIG. 4. Non-deterministic trajectories, determined by Kerr microscopy imaging, of selected skyrmions formed at 296 K in Ta (5 nm)/Co20 Fe60 B20 (1 nm)/Ta (0.08 nm)/MgO (2 nm)/Ta (5 nm) stacks. All the skyrmions were set to start at position (0, 0). The timescale of the observation was in the range of seconds to minutes. The inset shows the time-averaged mean squared displacement (MSD) (black line) and the linear fit of the data (red dashed line). Reproduced with per- mission from Zázvorka et al., Nat. Nanotechnol. 14, 658 (2019) Copyright 2019, FIG. 5. (Left) Magnetic-hysteresis loops measured along the perpendicular to the Nature Publishing Group. plane of a [Pt/Co]n multilayer coupled to IrMn, after field cooling from T = 520 K using different magnetic field values (HFC ). The various loops show the progressive tuning of the vertical magnetization amplitude depending on HFC . (Right) Depen- dence of the normalized magnetization amplitude of the sub-loop shifted toward III. IS IT POSSIBLE TO CONTROL RANDOMNESS the negative fields, ΔM, vs the squareness ratio (Mr /Ms ). The insets show the cor- IN MAGNETIC MATERIALS? responding magnetic-force microscopy images for (a) Mr /Ms = 0, (b) Mr /Ms = 0.43, While fully random magnetic effects are appealing for stochas- and (c) Mr /Ms = 0.93. Note that each image has a side length of 20 μm. Repro- tic computing or true random number generators (RNGs) (see duced with permission from Brück et al., Adv. Mater. 17, 2978 (2005). Copyright 2005, Wiley. Sec. IV), partial control of randomness can yield other interesting APL Mater. 9, 070903 (2021); doi: 10.1063/5.0055400 9, 070903-3 © Author(s) 2021 APL Materials PERSPECTIVE scitation.org/journal/apm the dots.16 A similar approach consists in breaking the circular rota- STT-magnetoresistive random-acces memories (MRAMs)).28,29 In tional symmetry by, e.g., asymmetrical notches.17 Although experi- the following, the basic idea of STT-MRAM, in which a pulse gen- mental realization of these effects requires the use of advanced litho- erator utilizes the stochastic nature of spin-torque switching in an graphic procedures, these procedures are now quite manageable, and MTJ to generate true random numbers,28 is illustrated (Fig. 6). therefore, a variety of works demonstrating geometrical control of An MTJ consists of two nanoscale ferromagnetic (FM) layers the vortex state have been reported.18–22 separated by a spacer layer (typically MgO). While the magneti- Very recently, we have also used micromagnetic simulations to zation of one of the layers (“reference” layer) is pinned in a par- study the dynamics of skyrmions in the presence of defects (pinning ticular direction (usually through the coupling with an antiferro- sites) or borders. The probability that a skyrmion becomes trapped magnet), the magnetization of the other layer (free layer) can be in a pinning center or the probability of its survival along a race- switched by external stimuli, such as a magnetic field or a spin cur- track can be calculated as a function of temperature and the length rent. Depending on the relative orientation of the two FM layers, of the track.23 Indeed, inherent or artificially created defects in the the device exhibits two resistance states: “high” (when the two lay- crystallographic structure of the films can modify the trajectory of ers are antiparallel to each other) or “low” (when the two layers show skyrmions in a partly deterministic manner. parallel orientation of their magnetization). These two states are sep- In spite of the previous examples, a number of different chal- arated by an energy barrier that is determined by the anisotropy lenges, in terms of materials properties and technological advances, and volume of the FM layers.30 As mentioned in Sec. II, thermal need to be overcome for a successful accomplishment of fully agitation in nanomagnets brings about a distribution of switching stochastic magnetic effects and the probabilistic (i.e., partial) con- fields. A similar effect occurs when these nanomagnets constitute the trol of this randomness. Namely, superparamagnetic MTJs require free layer of an MTJ. The switching current of a STT-MTJ nanopil- the use of very thin amorphous soft-magnetic layers with very low lar also has a distribution due to thermal agitation. The switching anisotropy. So far, almost all examples are based on CoFeB. Con- probability between the two resistance states depends on the cur- versely, for the coupling between FM and AFM domains, a rela- rent amplitude and pulse width. Both parameters can be adjusted tively high uniaxial magnetic anisotropy is required in the ferro- so that the switching probability of a given MTJ is close to 0.5. In magnet, while the anisotropy in the antiferromagnet and the size this way, these switching events are the source of true random num- of AFM domains should be small or at least commensurate to bers.4,31–33 The main challenge of this approach is the Joule heating the domain size in the ferromagnet. This needs to be accompa- power dissipation, which is not negligible and hinders large scale nied with a relatively high interfacial exchange constant so that the integration of these types of devices. As will be described in detail strength of the coupling is sufficient to overcome the magnetostatic in Sec. V, the energy efficiency challenge can be tackled by the devel- energy in the ferromagnet. Finally, formation of skyrmions at room opment of voltage-controlled (i.e., magnetoelectric) MRAMs, where temperature only occurs in a limited number of systems, such as voltage could be used (instead of current) to tailor the anisotropy Ta/Co40 Fe40 B20 /TaOx ,24,25 in asymmetric Co nanodot arrays with of the free layer and the magnetic easy axis direction. Implemen- the in-plane magnetic easy axis grown on Co/Pd underlayers with tation of voltage-controlled MRAMs requires precise control of the perpendicular anisotropy,22 or in Pt/Co/Ta and Pt/CoFeB/MgO thickness and microstructure of the magnetic free layer so that its stacks with ultrathin Co and CoFeB layers,26 among others.27 The properties can be sensitive to an applied electric field. Another chal- control of structural defects (e.g., periodic pinning sites) in these lenge is that the STT-MTJ share the same access path for the read layers, with the aim of guiding skyrmions motion, again requires and write operations, thereby causing interference problems and dedicated lithography procedures and is not always straightforward. some lack of reliability. This has been overcome using the spin–orbit torque (SOT) effect, instead of STT, which utilizes three terminals IV. HIGHLIGHTS OF EMERGING APPLICATIONS BASED instead of two (read/write paths are thus separated).34 In this case, ON MAGNETIC STOCHASTIC EFFECTS the switching between parallel and antiparallel states is induced by A. Exploiting magnetic randomness for true random number generators Random numbers play a crucial role in the encryption of secure data for communication and storage purposes. Taxonomically, ran- dom number generators (RNGs) can be classified into two large cat- egories: pseudo-RNGs, which use deterministic software algorithms to generate a sequence of random numbers (and are thus vulnerable to hacking cyberattacks), and true-RNGs, which are implemented at the hardware level and generate sequences of random numbers using non-deterministic, uncontrollable physical events (thus being cryp- tographically more secure).4 From a physical viewpoint, true-RNGs FIG. 6. Schematic diagram of STT-MRAM “spin dice.” Current pulses are injected can benefit from two types of randomness sources: fluctuations into a MTJ with perpendicular anisotropy to switch the magnetization in the free (e.g., thermal noise, shot current noise, and chaotic fluctuation of layer by spin-transfer-torque (STT).28 Highly reliable random bits can be obtained a semiconductor laser) and stochastic switching events (radioactive by comparing resistance values of an array of MTJs comprised in the STT-MRAM. decay intervals, magnetization switching in nanomagnets, switching This is sometimes referred to as “differential concept.”4 Reproduced with permis- events in resistive-random-acces memories (RAMs), and current- sion from Fukushima et al., Appl. Phys. Express 7, 083001 (2014). Copyright 2014, The Japan Society of Applied Physics. triggered random transitions in spintronic spin-transfer-torque APL Mater. 9, 070903 (2021); doi: 10.1063/5.0055400 9, 070903-4 © Author(s) 2021 APL Materials PERSPECTIVE scitation.org/journal/apm an in-plane current that flows along a heavy metal (Pt, Ta, W, and STT-MRAM cells (typically in crossbar geometry) is needed and Ir) grown underneath the free layer.35,36 In spite of a better robust- each MTJ is set to be in a random configuration of high and low ness, energy loss due to heating effects continues to be a challenge in resistance states when a critical switching current is applied.33,46–50 SOT-RAM true-RNGs. Generally speaking, PUF architectures utilizing non-volatile Randomness in the trajectories of skyrmions (Fig. 4) can memories are quite new, mostly developed during the last five years. also be used to generate random numbers or random sequences. These include, for example, PUFs based on resistive switching mate- A particular design combined the stochastic dynamics of syn- rials (RE-RAM PUFs), phase change materials (PCM-PUFs), ferro- thetic AFM skyrmions, driven by spin-polarized currents, with electric oxides (FE-RAM PUFs), toggle magnetoresistance (MRAM the racetrack memory concept using a topologically bifurcated PUFs), or STT-MRAM PUFs. The advantages and disadvantages of path with one input branch and two output branches.37 The each type of these data security primitives depend on the proper- authors demonstrated that under the steady action of current, ties of the constituent materials and the involved switching mecha- skyrmions starting from a continuous nucleation in the input branch nisms. STT-RAM PUFs are among the most energy efficient (with were stochastically divided into the two output branches of the 10−2 pJ/bit), orders of magnitude more efficient than PCM-PUFs device. (10 pJ/bit), RE-RAM PUFs, or toggle-MRAM PUFs (10−1 pJ/bit). Access speed in STT-RAM PUFs (1–10 ns) is also faster than in FE-RAM PUFs (10–100 ns) or flash PUFs (>103 ns) and comparable B. Exploiting magnetic randomness for physical to RE-RAM PUFs or toggle MRAM-PUFs.39,40,51–59 Thus, magnetic unclonable functions (data security) materials exhibiting stochastic transitions can indeed offer unique Traditionally, protection of confidential information has relied opportunities in the exciting field of data security. on the use of passwords generated either by the user or by encryp- tion software. This type of protection is often vulnerable to cyber- C. Exploiting magnetic randomness for logics attacks (phishing, malware, ransomware, and eavesdropping). To and probabilistic computing minimize security breaches, a new concept was proposed in 2002 Probabilistic computing is emerging as an intermediate com- when the utilization of the so-called “physical unclonable functions” putation paradigm that lies between classical digital computing and (PUFs) was first suggested as a hardware alternative to conven- quantum computing. At present, quantum computing suffers from tional algorithmic “passwords” or encryption procedures.38 A PUF some important challenges, such as low-temperature operation and is defined as a collection of robust, singular, unclonable, and unpre- the limited number of many-body interactions that can be imple- dictable physical properties of a device, which make it unique mented. These challenges can be tackled to some extent through (i.e., “device fingerprint”).39,40 Such properties can be the result probabilistic computing. The basic computation units are the prob- of non-controllable manufacturing imperfections or can originate abilistic p-bits, which are classical entities spontaneously fluctuating from stochastic physical phenomena that occur during device oper- in time between “1” and “0” states.1,5,34,60 The full potential of p-bits ation. These features can be used to generate a series of queries can be realized only when the probability of occurrence of the two and device responses technically called “challenge-response pairs” possible states can be modulated by an external input.34 Figure 7 (CRPs). Authentication is based on the physical verification of these shows a schematic comparison between the large energy barrier in CRPs. There are many variables that can be used to generate PUFs: the MTJ of a conventional MRAM memory (which would lead to local variations of the capacitance across a film containing ran- retention times of the order of years) and that of a p-bit based using dom assemblies of dielectric particles (“coating PUF”), stochastic MTJs with a thinner free layer (leading to retention times of the switching of superparamagnetic MRAMs with time, and variations order of ms).5 of the magnetoresistance state (high/low) in the memory units of STT-MRAMs. Some recent PUF schemes have even taken advan- tage of carbon nanotubes41 or plasmonic particles and quantum materials.42 PUFs can be implemented with small hardware invest- ment, and they are more energy efficient than tamper-proof security packages existing in the market. First magnetic PUF designs date back to 1994.43 They were engineered to make unique magnetic swipe cards, such as credit and identity cards, by blending FM particles with random sizes and shapes on a receptor layer. The PUF principle was thus based on the manufacturing variability. More sophisticated mag- netic PUFs include an MTJ operating using the toggle principle (where switching is induced by applied magnetic fields44 or the STT-MRAMs).45 Toggle-MRAM-PUFs take advantage of geomet- ric variations between different MTJ cells, which are used as a digital signature of the device.44 Usually, the free layer is affected by thermal FIG. 7. Illustration of the energy profiles between the parallel and antiparallel states agitation. In the case of superparamagnetic MRAM-PUFs, random of the free and pinned magnetization orientations in (a) a MTJ for typical MRAM switching occurs with time in each cell (Sec. II). The working princi- technology (with a large energy barrier) and (b) a probabilistic bit (with much lower ple of STT-MRAM PUFs is similar to the one described in Sec. IV A energy barrier and retention times in the order of ms). Adapted from Borders et al., Nature 573, 390 (2019). Copyright 2019, Nature Publishing Group. for true-RNGs. However, to establish the set of CRPs, an array of APL Mater. 9, 070903 (2021); doi: 10.1063/5.0055400 9, 070903-5 © Author(s) 2021 APL Materials PERSPECTIVE scitation.org/journal/apm The energy barrier of the p-bit can be tuned by adjust- ing the thickness, saturation magnetization, and effective mag- netic anisotropy of the free layer in the MTJs. The occurrence of dipolar interactions between the free and pinned layers can lead to not completely random parallel and antiparallel (i.e., non- fully isotropic) configurations, resulting in some probabilities for each of the two states that can be modulated to values differ- ent than 0.5.60 In STT-MRAMs, such switching probability can be tuned by proper adjustment of the spin-torque currents. In some other cases, the anisotropy of the free layer can be controlled with voltage (by magnetoelectric effects). This offers a wide range of opportunities to use magnetic materials for the implementation of p-bits. In particular, different types of operations (e.g., factoriza- tion, invertible logic, Bayesian inference, and combinatorial opti- mization) can be performed using matrices of correlated MTJ- FIG. 8. Reshuffler operation with skyrmion nucleation by a direct current. (a) The based p-bit networks that can be read by, e.g., precharge sense input signal is constructed as a time frame in which the skyrmion crosses the amplifiers.61,62 blue threshold line. The output is produced on crossing the orange line. (b) The Similarly, by tailoring the design of stochastic nanomagnets corresponding input signal is depicted in blue (top), and the resulting output signal (e.g., tuning the effective magnetic anisotropy of Co60 Fe20 B20 circu- is depicted in orange (bottom). The radius of the reshuffling chamber is 40 μm. The Pearson correlation factor between the input and the output was evaluated as lar disks or combining pairs of coupled nanomagnets with in-plane 0.11 ± 0.14. Reproduced with permission from Zázvorka et al., Nat. Nanotechnol. and perpendicular-to-plane anisotropies), the use of probabilistic 14, 658 (2019). Copyright 2019, Nature Publishing Group. computing for spin logic operations has been proposed and, to some extent, experimentally demonstrated.63–66 Within the field of stochastic computing, a promising route using skyrmions is the ability to process random bit-streams, instead of individual bits. A bit-stream formed by N bits with “1” or “0” is of using finite nanotracks as probabilistic selectors of skyrmionic bits characterized by the stochastic number p, which is the probability of or bit-streams, as well as for designing stochastic logic gates. observing a “1” in the stream. In this sense, a perfect control of indi- Thus, defects, either engineered or naturally occurring, can vidual skyrmions is not critical, and the system would be highly tol- have strong interaction with the skyrmions. Recent works stud- erant to soft errors: a collapse of a single skyrmion would not modify ied the dynamics of skyrmions considering random distribution significantly the overall p value.67,68 When two bit-streams are com- of defects72 or randomly distributed granularity.73 Moreover, the puted in an AND logic gate (as example), the p value for the output dynamics of skyrmions (or other skyrmionic-like structures) in the bit-stream is the multiplication of the “p” values of the input bit- presence of defects is highly non-linear, which yields the possibility streams. The use of skyrmions allows for very energy efficient and of having critical points (attractors, repeller, and/or saddle points) fast processing, thus being promising candidates for massive parallel depending on the input parameters.74 This could result in interest- computing.69 However, to ensure this multiplication property, it is ing chaotic scenarios.75 These systems are at an early stage of their necessary that the input bit-streams are uncorrelated. The thermal- development but could be also envisaged to randomize or shuffle driven randomness in the skyrmion movement has been proposed information. as the mechanism for reshuffling one bit-stream, before entering the computation gate, in order to avoid the undesired correlations while D. Exploiting magnetic randomness maintaining the p value.68 In Fig. 8, we show a very recent experi- for neuromorphic computing mental validation of the skyrmionic reshuffling using a continuous Neuromorphic computing imitates the physical structure of a single layer stack of Ta(5)/Co20 Fe60 B20 (1)/Ta(0.08)/MgO(2)/Ta(5) human brain to perform computational operations. The possible (in parentheses, the thickness of the layers in nm).12 This reshuf- utilization of magnetic randomness for neuromorphic computing fling is an off-chip system, although recent developments on in- applications is still in its infancy.30,36,76–80 Yet, stochastic effects are chip creation, manipulation, and detection of skyrmions70 point of primary importance in artificial neural networks that are intended to the in-chip integration of skyrmionic systems for stochastic to mimic the brain capability to do “pattern recognition” (i.e., object computing. identification by resemblance). It has been proposed that arrays of Another possibility for taking advantage of randomness in interconnected magnetic nanowires could trigger further develop- skyrmion movement is to consider the interaction with specially ments in the field of neuromorphic computing.81 Artificial synapses designed defects. Recently, by considering this interaction, we have should possess sufficiently high fault tolerance in order to be able to shown that, due to thermal diffusion, the probability that a skyrmion identify a given object even if there are some errors or differences avoids the defect or is being trapped in it can change continuously between the input signal as the pre-recorded pattern (similar to how from 0 to 1 by varying the position where the skyrmion is generated, the brain works). as shown in Fig. 9.23 Moreover, we also calculated the probability In recent years, there is growing evidence from the neurologists’ of survival of a skyrmion along a nanotrack, which depends on the community that the brain performs probabilistic computation based driving current and the interaction with the borders of the track. on partially random operations of neurons, synapses, and dendrites. This, together with evaluation of thermal collapse,71 opens the path This effect should be emulated in artificial intelligence systems, APL Mater. 9, 070903 (2021); doi: 10.1063/5.0055400 9, 070903-6 © Author(s) 2021 APL Materials PERSPECTIVE scitation.org/journal/apm FIG. 9. Snapshots of the probability density (color bar in units of 10−3 nm−2 ) of the presence of a skyrmion as time runs (from left to right, time t in ns). v h is proportional to the driving spin-current density. This probability can be tuned from 0 to 1 by changing the initial position of the skyrmion and the temperature (bottom). The circle corresponds to the snapshots shown. The two lobules in the last snapshot show clearly that there is a probability (around 0.45 in this case) of being trapped and a probability of scaping (around 0.55). Reproduced with permission from Castell-Queralt et al., Phys. Rev. B 101, 140404(R) (2020). Copyright 2020, American Physical Society. particularly for deep learning approaches. The field of magnetoelec- disks under application of negative and positive voltage long-term tricity (voltage control of magnetism) has brought some compelling pulses.84 While there is a general trend for M to always increase results into this direction.30,79 It has been theoretically proposed that, (or decrease) for negative (or positive) voltages, respectively, dif- by using voltage to manipulate the relative orientation of the pinned ferences in the exact M values among dots (and samples) were also and free layers in MTJs, such structures can lead to low-power spik- encountered. Namely, due to microstructural differences among the ing neurons. Magnetoelectric neurons would be encoded through patterned dots, the exact O2− ion diffusion channels generated in dif- the control of externally applied voltage signals in each individual ferent dots were different. Consequently, stochastic magneto-ionic MTJ.30 The idea is that by applying appropriately shaped voltage responses were observed. Further randomness can be induced by pulses, the MTJs can be switched in a probabilistic (rather than fully interconnecting the dots in several paths and applying different stochastic) manner. In this way, a probabilistic output stream is gen- voltage pulses in each of the electrical contacts [Fig. 10(c)]. erated with a probability that depends on the magnitude of the input A further development toward neuromorphic computing using stimuli.76 magnetic materials is displayed in Fig. 10(d).85,86 The basic structure The well-known spike timing-dependent plasticity behavior consists of an elongated ferromagnet/heavy metal heterostructure has also been accomplished recently by means of magneto-ionics.80 able to stabilize domain walls, which can be moved with the elec- This refers to a particular class of magnetoelectric actuation in tric current using a three-terminal device (spin-Hall effect). The FM which an applied voltage triggers the motion of ions from (or layer in contact with the heavy metal is actually the free layer of toward) a target magnetic material, depending on the voltage polar- a MTJ where multi-level resistive states can be generated through ity, in order to modify its magnetic properties in a non-volatile the motion of the domain wall in the free layer. That is, depend- (permanent) manner. So far, spike timing-dependent plasticity ing on the position of the domain wall, the fraction of the free layer and other neuromorphic features have been studied in detail in parallel or antiparallel to the pinned layer varies in an analog man- Co/GdOx bilayers, where GdOx is an ionic conductor able to provide ner, as required for neuromorphic computing. Simulations on the O2− ions to Co (to reduce its magnetization, emulating forgetting operation principle of this device suggest that it has the potential to processes, or synaptic depression) or to remove O2− ions from achieve energy consumption as low as 2 pJ per synaptic event, which CoO (to increase the magnetization, emulating learning processes, is comparable to the energy consumption in biological synapses. or synaptic potentiation). Non-linear voltage-driven magnetization Skyrmionic systems have also been proposed for neuromor- (M) vs time potentiation/depression curves have been observed in phic computing.87 Again, the tunable current-driven dynamics of a number of other electrolyte-gated magnetoelectric materials.82,83 skyrmions allows designing systems mimicking the biological neu- As an example, Fig. 10(b) shows potentiation–depression mag- rons, where “skyrmionic synapses” can reproduce the synaptic plas- netic transitions that we measured in mesoporous FeOx patterned ticity and a gradient of perpendicular magnetic anisotropy along APL Mater. 9, 070903 (2021); doi: 10.1063/5.0055400 9, 070903-7 © Author(s) 2021 APL Materials PERSPECTIVE scitation.org/journal/apm FIG. 10. (a) Scanning electron microscopy image of an array of magnetoelectrically actuated mesoporous FeOx disks.84 (b) Variation of the normalized magnetization with time for FeOx during two consecutive cycles, first applying ΔV = −10 V (to induce synaptic potentiation) and then ΔV = +10 V (to induce synaptic depression). (c) A solid- state magnetoelectric device that consists of an ordered array of micro-/nano-scale FeOx interconnected dots, each of them in direct contact with an oxygen getter/donor layer (e.g., Gd, which will become GdOx upon voltage application). The dots can be electrically connected in a combinatorial fashion, i.e., using different paths, therefore, forming a number of possible circuits. (d) Design of a device able to encode multilevel resistive states through the position of the domain wall in the FM free layer due to the passage of a charge current of appropriate magnitude between terminals T2 and T3. The device state can be “read” between terminals T1 and T3 using the tunneling junction. Note that PL, TB, FL, and HM denote the pinned layer, tunnel barrier, free layer, and heavy metal layer, respectively. Reproduced from Roy et al., J. Appl. Phys. 123, 210901 (2018) with the permission of AIP Publishing. a track can be tuned to simulate the leaky-integrate-fire function enhanced energy efficiency (bearing in mind that 20% of the global of a neuron.88,89 Experimental versions of such artificial synapses energy will be spent in information technologies by 203090 ), (iii) fur- have been built using skyrmions on [Pt (3 nm)/Gd24 Fe66.6 Co9.4 ther compatibility with existing CMOS technologies, (iv) enhanced (9 nm)/MgO (1 nm)]20 ferrimagnetic multilayer stacks, while sim- endurance (cyclability) to increase the lifetime of devices, or (v) ulations showed an 89% accuracy in pattern recognition using faster operation speed (ideally toward sub-μs), among others. all-electric skyrmionic artificial synapses.87 Many of newly proposed stochastic magnetic devices are based on STT-MRAMs. The endurance of STT-MRAM PUF systems is sometimes compromised by the dielectric breakdown of the insu- V. FUTURE OUTLOOK lating barrier layer resulting from repeated applied electric pulses, The utilization of random phenomena in magnetic materials which cause stress and degradation. Similar to true-RNGs, the offers formidable challenges for future implementation of innova- use of (SOT)-PUFs has been recently suggested as an alternative tive technologies, such as new data security primitives, probabilis- to overcome this limitation.35,91 Interestingly, new strategies are tic logics (with prospects toward quantum computing), or artificial being proposed to enhance tamper resistance (ability to detect a neural networks. Some of the described materials and proposed lay- cyberattack) by means of new STT- and SOT-MRAM PUF archi- outs are compatible with CMOS architectures, and many of them tectures,47 thereby surpassing the functionalities of other types of can be readily developed at the chip level (e.g., crossbar arrays for non-magnetic PUFs. Recently, STT magnetic tunnel junction archi- STT-RAMs, arrays of nanomagnets for stochastic computing and tectures have also been proposed for their use as spintronic nano- logics, and room-temperature skyrmions). However, the current oscillators, which allow for new neuromorphic functionalities at state of the art in these fields faces several challenges, such as (i) high frequencies, such as pattern recognition.92,93 However, this need for improved control of randomness for probabilistic com- technology (STT-MRAMs or SOT-MRAMs) utilizes spin-polarized puting (beyond the approaches described in Sec. III), (ii) need for currents, which still involves a significant power dissipation in the APL Mater. 9, 070903 (2021); doi: 10.1063/5.0055400 9, 070903-8 © Author(s) 2021 APL Materials PERSPECTIVE scitation.org/journal/apm form of Joule heating effect. In recent years, voltage-driven switch- metamaterial in which a large number of nanoscale magnetic ing of nanomagnets has gained interest as an alternative to STT elements are coupled together to render controllable random effects. By using voltage instead of current to control the mag- responses (i.e., tunable probability distributions) based on stochas- netic properties of materials, important energy savings are expected. ticity in magnetic domain wall motion (domain wall sinks) at the Switching energies as low as 10−6 pJ/bit have been theoretically pre- nanoscale.105 It has been claimed that such types of materials can be dicted for optimized strain-mediated magnetoelectric materials.55 exploited to perform complex computational tasks, beyond conven- So far, switching energies of the order of 10−3 pJ/bit have been tional Von Neumann computing paradigms. experimentally reported in both multiferroic heterostructures and magneto-ionic systems.55,94 Yet, the implementation of stochastic ACKNOWLEDGMENTS devices based on the use of magnetoelectric materials is still at the This project received funding from the European Research early stages.29,95,96 Aspects such as clamping effects with the sub- Council (MAGIC-SWITCH 2019-Proof of Concept Grant No. strate (in the case of strain-mediated ferroelectric/magnetostrictive 875018), the Agencia Estatal de Investigación of the Spanish bilayers), reduction of the needed threshold voltages to induce the Government (Grant Nos. MAT2017-86357-C3-1-R and PID2019- desired effects, or full reversibility upon successive application of 104670GB-I00 and associated FEDER), and the Generalitat de repeated voltage pulses still require further optimization and new Catalunya (Grant Nos. 2017-SGR-292 and 2017-SGR-105). We materials engineering. In turn, magneto-ionic materials based on would like to thank Dr. C. Navarro-Senent, Dr. A. Nicolenco, and J. O2− ion migration often suffer from limited cyclability (endurance) Castell-Queralt for assisting us with the preparation of some layouts (sometimes not exceeding 100 cycles), and the rates at which ions for the figures. diffuse can be rather slow (∼seconds or, in some cases, ms). These switching rates are too slow for memory applications but can still DATA AVAILABILITY be convenient for neuromorphic applications. Progress at the mate- rial level has been accomplished by replacing materials based on The data that support the findings of this study are available O2− ion motion by others governed by different ion species, such as from the corresponding authors upon reasonable request. N3− or H+ , which have been shown to diffuse faster.97,98 Remarkably, it has been proposed that the proton-based magneto-ionic approach REFERENCES can also induce new functionalities, such as Dzyaloshinskii–Moriya 1 K. Y. Camsari, P. Debashis, V. Ostwal, A. Z. Pervaiz, T. Shen, Z. Chen, S. Datta, interactions.99 Further materials engineering could boost magneto- and J. Appenzeller, Proc. IEEE 108, 1322–1337 (2020). ionics. In particular, control of structural defects [e.g., vacancies) 2 L. Zhao, Z. Wang, X. Zhang, X. Liang, J. Xia, K. Wu, H.-A. Zhou, Y. Dong, G. Yu, and grain boundaries (which often act as fast diffusion paths100 ) K. L. Wang, X. Liu, Y. Zhou, and W. Jiang, Phys. Rev. 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