Multiferroic neuromorphic computation devices Open Access

Neuromorphic devices are based on memristive ionic conductivity,¹ where the electronic analog of a biological synapse is a memristor, proposed in 1971² and first demonstrated in 2008.³ A memristor resistance can be continuously tuned with strong history dependence. In this configuration, high conductivity indicates a strong synaptic connection, whereas in a low conduction state, the connection becomes weak. The learning and processing abilities of our brain are linked to the strength of the synaptic connection that varies as the information flow between neurons,^4–7 and several inorganic materials have been proposed as memristors for neuromorphic computation.^8–15 

Ferroelastic materials are particularly adapted for such devices because they contain two useful domain patterns, which increase the efficiency of the memristor switching. The first are needle domains that progress and retract under external electric fields and stresses.^16–18 The second nanostructure that dominates ferroelastic materials are domain wall junctions,¹⁹ namely, intersections between polar domain walls. Changing temperature or fields will change these nanostructures, which is the topic of this paper. As an example, perovskite materials, such as WO₃,²⁰ are particularly promising for such device applications because the ionic mobility of dopants, such as sodium or oxygen, is very high and conductivity change can, for some temperature intervals,²¹ be as large as a factor of 30 during the metal–insulator phase transition.²² A structural phase transition between the β and γ phase of WO₃ occurs near room temperature.²³ During this transition, the nano-structure of WO₃ changes dramatically, which is a secondary effect that we explore in this paper. These nano-structures are important because they channel ionic diffusion.^24–26 The switching of the transport path mainly depends on the regions between domains, namely, domain walls.²⁷ These domain walls are typically polar and have similar crystal structures to ferroelectric materials.^28–34 The domains in ferroelastic materials remain non-polar and do not contribute to the sample polarization. Wall-related switches occur typically over extremely short time scales³⁵ and involve reorientations of local polarity. Such changes necessarily induce displacement currents.^36–38 These magnetic fields extend to some μT.³⁹ In this scenario, ultrafast wall switching is a feature of fast memristive switching and is expected to occur in neuromorphic devices. The characteristic structural element during the switches, which generates magnetism, is the polarization vortex. If this happens, weak but measurable magnetic signals during neuromorphic operation are expected. In addition to WO₃, similar effects were seen in Pb₃(PO₄)₂^40–43 and cryogenic SrTiO₃.^44–50 

To quantify the ferroelastic domain structures and the emitted magnetism, we simulate the structural changes using a two-dimensional Landau-type potential with different interatomic interactions, as schematically shown in Fig. 1. The model consists of two sublattices carrying positive (green atoms) and negative (violet atoms) charges. The interactions are divided into short-range interatomic interactions and long-range Coulombic interactions. The pairwise short-range interactions for anion sublattices contain four terms: the harmonic first nearest atomic interactions $Ur=20r−12$ (black springs), the anharmonic second-nearest Landau-type interaction $Ur=−10r−22+8000r−22$ (gray sticks) along the diagonals in the lattice unit, the fourth-order third-nearest interaction $Ur=8r−24$⁠, and the anharmonic fourth-nearest Landau-type interaction $Ur=−10r−52+5100r−52$ along diagonals in the lattice unit, where r is the distance between atoms. The interactions for cation atoms are purely harmonic with first-nearest interaction $Ur=20r−12$ (green springs) and second-nearest interaction $Ur=1.5r−22$ along the diagonals. The harmonic springs are related to the elastic interactions and constitute the elastic background in ferroelastic materials. The second-nearest Landau-type interactions are constructed to maintain an equilibrium shear angle of 2°, which was inspired by the typical ferroelastic phase transition of SrTiO₃ at 105 K.⁵¹ An additional Landau-type spring is added to obtain a reasonable domain wall thickness and stability.^52,53 The interaction between the anion and cation is a harmonic spring $Ur=1.5r−2/22$ (red springs) to avoid the collapse of the cation sublattice onto the anion sublattice. The interactions were chosen to be purely harmonic to exclude any polar instabilities inside the bulk. The symmetry properties of the model were discussed in detail in Ref..54. The domain walls are polar due to the flexoelectric effect^55–57 and a biquadratic coupling between deformation parameters^58,59 near the domain walls. Experimentally, wall dipoles are related to displacements of 6 pm as observed in CaTiO₃.²⁸ All the simulations are performed by using the LAMMPS code.⁶⁰ The domain structures are visualized by using OVITO software.⁶¹ 

The dominant microstructure in ferroelastic materials is the comb pattern, which consists of needle arrays with various distances between the needles. The simulated stress-driven propagation of comb patterns consists of 5 vertical thin needles with 3 atomic layers for each [Fig. 2(a)]. By controlling the external stress, vertical needles were stabilized at the same distance from the surface with equal needle distances of 0.7 nm. A shear deformation drives the propagation of the comb pattern with a strain rate 2.7 × 10⁸ s⁻¹. All the vertical needles were activated at the same time with a gradual increase in speed before reaching a steady state at a velocity of 0.24 km/s [Fig. 2(d)]. They finally slow down when moving close to the lower surface or interface. Two atomic configurations with a time interval Δt = 3.0 ps during the steady state motion were chosen to calculate the local current density and the corresponding magnetic moment. Relative displacements between cations and anions [Fig. 2(b)] and the inducing displacement current vortex array [Fig. 2(c)] are observed between the vertical needles. The total magnetic moment is 0.000 73 µ_B, where μ_B = 9.274 × 10⁻²⁴ JT⁻¹ is the magnetic moment of an electron. The magnetic field density for this current vortex array is 6.2 × 10⁻⁷ T.

We now add temperature as a second variable. Many potential memristors possess structural phase transitions near room temperature. We simulate the effect of a para-elastic to ferroelastic transition on the domain structure. Starting from the single domain state (symmetry breaking strain in our simulation is ɛ_xy = 0.035), we first increase the temperature with low heating rate through the phase transition temperature T_tr. Then, we repeatedly heat and cool the structure with sequences of domain nucleation and migration and annihilation of the polar domain walls. The evolution of the potential energy and temperature as function of time is shown in Fig. 3(a). Starting from the high temperature paraelastic phase [“A” in Fig. 3(b)], the structure is cooled down below T_tr with the formation of typical stripe ferroelastic domains [“B” in Fig. 3(b)]. As the temperature decreases further, ferroelastic domains evolve with the migrations of the domain walls [“C” in Fig. 3(b)]. Under the second cooling and heating cycle, more complex domains with vertical and horizontal domain walls and domain wall junctions occur at low temperature [“F” in Fig. 3(b)].

These complex domain structures are expected to form close to the injection points of the memristor. The domain walls act as fast diffusion paths, which show that the low temperature phase is the most effective memristor. The needle domains will generate magnetic signals during their propagation. In addition, when needle domains of orthogonal orientations intersect and form wall junctions, they generate displacement current vortices [Fig. 4(b)].

In summary, we have shown that macroscopic, transient magnetism can be emitted from neuromorphic devices for two reasons. The nucleation and progression of the typical needle domains generate displacement currents on either side of a micro-structural needle domain (Fig. 2). The second mechanism is the nucleation of domain junctions⁶² where each junction is decorated by a vortex (Fig. 4). These vortices carry displacement currents, which, in turn, generate magnetism of some 10⁻⁷ T. Given these results, it is now possible that the readout from neuromorphic devices can be extended to magnetic signals in addition to the electric signals used previously. This technology has potentially tremendous advantages as it allows a second channel for the information transfer between artificial neurons. Preliminary squid observations has indeed shown magnetic signals in low temperature SrTiO₃, but much more research is needed to develop neuromorphic devices based on this idea.

Conversely, in complex biological systems, magnetic brain signals are well known to exist during brain activities .⁶³ While most can be related to known biochemical processes, others seem to be unknown for its physical origin. In particular, transcranial magnetic stimulation (TMS) has evolved from an almost magical curiosity and a simple tool for neurophysiologists to a mainstay of non-invasive neuromodulation, gaining acceptance as a candidate treatment in psychiatry, neurology, and, perhaps, other clinical specialties.⁶⁴ Our simple simulations can, at this stage, not clarify any of these biological issues, but it remains a tantalizing possibility that weak magnetism is possibly related to artificial neurons, as in neuromorphic computation or even in biological systems.

We thank Beena Kaliski and Shai Rabkin (Bar Illan University, Israel) and Gustau Catalan (ICN2 Oxide Nanophysics Group, Catalonia) for their help in the first attempts to develop device applications. Guangming Lu acknowledges the financial support by the National Natural Science Foundation of China (Grant No. 12304130) and the Doctoral Starting Fund of Yantai University (Grant No. 1115-2222006). EKHS acknowledges the EPSRC (Grant No. EP/P024904/1) and EU Marie Sklodowska-Curie 2020 program (Grant No. 861153).

The authors have no conflicts to disclose.

Guangming Lu: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Funding acquisition (lead); Investigation (equal); Writing – original draft (equal); Writing – review & editing (equal). Ekhard K. H. Salje: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Investigation (equal); Writing – original draft (equal); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding authors upon reasonable request.