At the first stage, the characteristics of the direct ME effect in the described heterostructure were measured using the method of harmonic magnetic field modulation [36]. Figure 2a shows the dependence of the ME voltage on the frequency of the excitation field u (f) at h = 4.8 Oe and H = 12.8 Oe. It can be seen a peak near the frequency f₀ ≈ 78 kHz with the amplitude u_m ≈ 600 mV and a quality factor Q = f₀/Δf ≈ 29, where Δf is a resonance width at the level of 0.707u_m. The peak corresponds to the excitation of the fundamental longitudinal acoustic oscillations in the heterostructure, when the magnitude of deformations and the amplitude of ME voltage increase sharply. Figure 2b shows the dependence of the resonance peak height on a constant field u_m(H), measured at h = 4.8 Oe. The maximum peak voltage is observed at the field H_m ≈ 12.8 Oe, at which the maximum linear piezomagnetic coefficient of the FM layer is achieved q = λ⁽¹⁾(H) = ∂λ/∂H|_H, where λ(H) is the dependence of the magnetostriction of the FM layer on the magnetic field H.

The ME interaction in the heterostructure under study is explained by the theory of the low-frequency linear ME effect in planar FM-PE heterostructures [37]. The magnitude of the ME voltage generated by the heterostructure at its own resonance frequency is determined by the simplified formula

$u(H)\approx AQ\frac{d_{31}q}{\epsilon }h$,

where A is a coefficient that depends only on the geometric dimensions and mechanical characteristics of the FM and PE layers; Q is the quality factor; d₃₁ and ε are the piezoelectric modulus and dielectric constant of the PE layer, respectively; q is piezomagnetic coefficient; h is the amplitude of the excitation magnetic field.

Figure 2c shows the dependence of the ME voltage at the resonance frequency f₀ on the excitation field u_m(h), measured at the field H_m. In the amplitude range h < 1.4 Oe, the dependence is linear; however, as the field increases, the voltage u_m tends to saturation, which is associated with the increase in contribution of nonlinear harmonic generation at large amplitudes of the excitation field [38].

Let us estimate the frequency of the longitudinal acoustic resonance of the heterostructure using the formula for the fundamental oscillations of a free rod

$f_{\mathrm{c}\mathrm{a}\mathrm{l}}=\frac{1}{2L}\sqrt{\frac{Y}{\rho }}$,

where L is the length of the structure Y = (Y_ma_m + Y_pa_p)/(a_m + a_p) and ρ = (ρ_ma_m + ρ_pa_p)/(a_m + a_p) are the effective Young’s modulus and the effective density of the heterostructure, respectively [39]. The indices “m” and “p” correspond to the FM and PE layers. Substituting the material parameters into the formula: Y_p = 5.9·10¹⁰ N/m², Y_m = 18.6·10¹⁰ N/m², ρ_p = 7.4·10³ kg/m³, ρ_m = 8.2·10³ kg/m³, a_p = 250 µm, a_m = 25 µm we obtain a resonant frequency f_cal ≈ 81 kHz, which agrees well with the measured one. Using the data in Fig. 2, we can find the value of the ME coefficient at the resonance frequency α_E = u_m/(a_p·h) ≈ 5.2 V/(Oe∙cm). The resulting resonant ME coefficient is typical for heterostructures with layers of PZT and Metglas and is ~2 orders of magnitude higher than the ME coefficient in the non-resonant mode [38]. The value of the ME coefficient outside the resonance can be estimated using the formula α_E/Q = 5.2/29 ≈ 0.18 V/(Oe∙cm), where Q is the resonance quality factor.

Figure 2.

(a) Frequency response of the PZT-Metglas heterostructure at h = 4.8 Oe and H = H_m = 12.8 Oe; (b) dependence of the ME voltage u_m on the constant field H at f = f₀ = 78 kHz and h = 4.8 Oe; (c) dependence of the ME voltage u_m on the excitation field h at f = f₀ and H = H_m

At the next stage, the influence of single electric field pulses on the characteristics of the ME effect was studied. To do this, single electric field pulses of different polarity with amplitude E = 16 kV/cm and duration τ = 5 s were applied to the heterostructure. Then the output ME voltage was measured at the resonance frequency f₀ at a constant field H_m = 12.8 Oe and h = 4.8 Oe. The choice of field strength E = 16 kV/cm was justified by a compromise between the maximum possible value of residual polarization P_r and the dielectric strength of the PZT, since electrical breakdown was observed at E ≥ 20 kV/cm.

Figure 3a shows the time dependences of the ME voltage u_m and ME coefficient α_E after applying electric field pulses.

Figure 3.

Switching between 2 nonvolatile stable states after applying electric field pulses of different polarities and a fixed amplitude E = 16 kV/cm to the ME heterostructure (a) and time dependences of the ME voltage u_m and the excitation magnetic field h, demonstrating a phase shift by π at opposite directions of the polarization P of piezoceramics (b)

The graph shows a clear switching of the ME voltage amplitude and the ME coefficient value between 2 nonvolatile stable states with u_m = ±624 mV and α_E = ±5.2 V/(Oe·cm). The states have mutually opposite directions of the polarization P and correspond to a phase shift of ME voltage u_m of π (Fig. 3b). After applying each electric field pulse, the measurement of u_m was carried out for t = 70 s to demonstrate the stability of the switched state over time.

The dynamic range α_E is determined by the remnant polarization P_r of the piezoceramics, both positive and negative. Within this range, it is possible to create lot of nonvolatile stable states with different P_r values, which determines the number of possible values of α_E and, thus, the weight bit-width of a synaptic device based on an ME heterostructure [40]. The mechanism for controlling the value of the α_E due to changes in the remnant polarization P_r is shown in Fig. 4, which shows the dependence of the polarization P of a ferroelectric material on the applied electric field E. The application of electric field pulses E changes the value of P_r due to movement along the major and minor hysteresis loops. Electric field pulses of the same polarity and growing amplitude increase the value of P_r. The maximum value of P_r is determined by the saturation field E_s and movement along the major hysteresis loop. A decrease in P_r and a change in its sign occur due to applying electric field pulses of opposite polarity with growing amplitude. After applying the electric field pulse and returning to the state E = 0, the piezoelectric modulus of piezoceramics changes as d = ∂S/∂E|_E=0, where S is the strain. Minor hysteresis loops have different slopes at E = 0 and, consequently, different values of the piezoelectric modulus d, which directly affect the ME voltage u_m.

Figure 4.

Dependence of polarization P of a ferroelectric material on the applied electric field E

In biology, the main characteristic of a synapse is a synaptic weight – a parameter that determines the effectiveness of the action potential of a presynaptic neuron (pre-neuron) on changing the membrane potential and the probability of generating its own action potential by a postsynaptic neuron (post-neuron). The action potential of a neuron (spike) is considered to be a sharp, abrupt surge in the membrane potential of the cell when the threshold value of about –10 mV is exceeded. The process of spike transmission between neurons is schematically presented in Fig. 5a. The synaptic weight is determined by the amount of neurotransmitter molecules released into the synaptic cleft by the pre-neuron and captured by the receptors of the post-neuron upon the generation of one pre-spike [41]. Depending on the type of neurotransmitter, the membrane potential of the post-neuron may increase or decrease. In the first case, it is dealing with excitation of the post-neuron and an increase in the membrane potential by the value of the excitatory postsynaptic potential (EPSP). In the other case, it is inhibition by the value of the inhibitory postsynaptic potential (IPSP). The EPSP potential increases the probability of a neuron generating a spike, while the IPSP reduces this probability (Fig. 5b).

Figure 5.

Schematic view of the spike transmission between neurons (a) and diagram of changing the neuron membrane potential (b)

In the case of excitation, the greater the synaptic weight, the more neurotransmitter is released into the synaptic cleft and the greater the number of post-neuron receptors that receive it. This increases the membrane potential of the post-neuron by a larger EPSP value, so that the probability of generating a spike increases. When the post-neuron is inhibited, a larger synaptic weight leads to a decrease in the membrane potential of the post-neuron by a larger IPSP value, which reduces the probability of spike generation. The new value of the post-neuron membrane potential remains for a long time, thereby exhibiting long-term potentiation (LTP) or long-term depression (LTD). The membrane potential of the post-neuron is “reset” to the resting value of –70 mV only after generating its own spike.

For a ME heterostructure, from the point of view of neuromorphic behavior, the incoming electric field pulse can be considered as the action potential. The ME coefficient α_E is an analogue of the synaptic weight, and the ME voltage u_m generated by the ME heterostructure plays the role of a postsynaptic potential – excitatory (EPSP) or inhibitory (IPSP). Maintaining a stable value of α_E after applying electric field pulses resulting in an increase or decrease in the output voltage u_m, represents LTP and LTD, respectively.

To simulate the neuromorphic behavior in the PZT-Metglas heterostructure, electric field pulses of different polarity and gradually increasing amplitude were applied to the PE layer, followed by measuring the ME characteristics of the heterostructure. Fig. 6 shows how the first positive electric field pulse E with an amplitude of 16 kV/cm polarizes the PE layer so that the heterostructure generates a voltage with an amplitude u_m ≈ 620 mV. Subsequent negative electric field pulses with increasing amplitude from 6 kV/cm to 16 kV/cm lead to a decrease in the amplitude of the generated ME voltage and then to a change in the phase of the voltage by π. After applying the 7th pulse to the structure at a time of ~500 s, u_m reaches an amplitude of 620 mV and stops growing until the application of a pulse with a field strength of 16 kV/cm. This moment indicates saturation of the PE layer. Subsequent application of positive electric pulses with an amplitude from 6 kV/cm to 16 kV/cm leads to a decrease in the u_m to zero, a phase change by π, a subsequent increase in amplitude to 620 mV and saturation of the PE layer. Similarly, applying electric field pulses to the PE layer leads to a change in the magnitude and sign of the ME coefficient α_E. When the field E increased from 8 to 16 kV/cm, no change in α_E was observed, which indicates that the remnant polarization of the PE layer P_r was close to saturation. Due to the slight increase in α_E, pulses within the range E = 8–16 kV/cm are not shown in the graph.

From Fig. 6 it follows that the application of positive pulses leads to an increase in α_E and u_m, while negative pulses reduce these values. Thus, an increase in u_m is equivalent to the appearance of the EPSP, and a decrease in u_m represents the IPSP.

Figure 7 shows the change in the ME coefficient α_E depending on the polarity of the applied electric field pulses. Taking the value α_E = 1 V/(Oe·cm) as the initial stable state, we can increase it to α_E = 3.6 V/(Oe·cm) when applying a positive pulse, demonstrating EPSP, or reduce it to α_E = –1.6 V/(Oe·cm) due to a negative pulse, showing IPSP. New stable states remain for a long time, which is equivalent to the simulation of LTP and LTD.

Figure 8 shows the dependence of the ME coefficient α_E on the electric field strength E of applied pulses of different polarity at a fixed pulse duration τ = 5 s. The dependence has the form of a hysteresis loop with clearly distinguishable thresholds E_th1 – E_th4. When applying field pulses with an amplitude of E_th1 < E < E_th2 or E_th3 < E < E_th4, the change in α_E is maximum, while outside the indicated areas α_E changes slightly. Within these thresholds, the change in the ME coefficient was Δα_E ≈ 9 V/(Oe·cm). Outside the thresholds, at E < –7.2 kV/cm and E > 7.2 kV/cm, the α_E varied only about Δα_E ≈ 0.5 V/(Oe·cm).

Applying the pulse with amplitude E = E_c ~ 6.5 kV/cm, corresponding to the coercive field of the piezoceramics, the values of u_m and α_E are close to zero. Further increase in the field amplitude changes the sign of u_m and α_E, which indicates a change in the direction of the polarization P to the opposite and a change in the phase of the u_m by π. This behavior of α_E is directly related to the ferroelectric hysteresis loop of the PE material (see Fig. 4).

Figure 6.

Time dependences of the generated voltage u_m and ME coefficient α_E when applying electric field pulses E of different amplitudes and polarities. The change in the sign of u_m and α_E corresponds to a change in the phase of the u_m by π

Figure 7.

Change in the initial state of the ME coefficient α_E when applying electric field pulses of different polarities, demonstrating LTP and LTD

Figure 8.

Dependence of the ME coefficient α_E on the amplitude of electric field pulses in the range E = ±16 kV/cm. Red dotted lines are the range of fields where the change in α_E is maximum

In the nervous system, neurons transmit electrical and chemical signals to other neurons through synapses. One of the most important qualities of a synapse is synaptic plasticity, which is the ability to change the synaptic weight in response to external impact. Among the types of synaptic plasticity, it is worth highlighting spike-timing-dependent plasticity (STDP), which is believed to play a key role in brain learning and memory processes [42].

STDP plasticity in the nervous system can be represented in the form of strengthening or weakening of synaptic connections (increasing or decreasing the weight of individual synapses). This phenomenon manifests, in particular, in a change in the number of receptors that capture neurotransmitter molecules in the post-synapse [43, 44], due to the difference in the time between the generation of pre- and post-spikes in the corresponding neurons. The arrival of a pre-spike to the synapse before the generation of a post-spike (time delay Δt > 0) leads to excitation - an increase in synaptic weight and a greater contribution to the increase in the membrane potential of the post-neuron. Thereby, this condition increases the probability of post-spike generation (LTP). In this case, a cause-and-effect relationship between spikes can be observed. Otherwise, when the pre-spike arrives later than the post-spike (time delay Δt < 0), the synaptic connection is weakened, which leads to depression. In this case, the membrane potential does not grow, and the probability of generating a post-spike diminishes (LTD) because the post-spike cannot occur on its own [45].

In the case of the PZT-Metglas heterostructure under study, the presence of clear thresholds associated with a coercive field E_c in the PZT layer allows for the simulation of STDP plasticity [41, 46].

In an artificial synaptic device based on an ME heterostructure, the ME coefficient α_E, acting as the synaptic weight, can be adjusted by superposition of voltage pulses corresponding to pre- and post-spikes applied to both ends of an artificial synapse (Fig. 9) [6, 31–33].

Thus, the change in the weight will be determined by the voltage drop U_pre – U_post on the ME structure and the corresponding field strength difference E_pre – E_post. The weight change reaches its maximum when a maximum overlap of pre- and post-spike pulses occurs. It is also important to select the amplitude and polarity of the pulses for the effective implementation of the STDP rule. A spike, corresponding to the waveforms generated by pre- and post-neurons, can be described as a sequence of electric field pulses of different polarities. In this work, STDP was examined using the above mentioned thresholds of electric field strength (E_th1 – E_th4).

In the absence of time correlation between spikes, the polarization of the ME structure remains almost unchanged, since a single spike cannot exceed the threshold values of the E_th. In this regard, the remnant polarization P_r, and thereby α_E and u_m, should change significantly only when the pre- and post-spikes overlap. For this reason, the change in polarization caused by a single spike should be minimized. On the other hand, the change caused by the overlap of pre- and post-spikes should be maximum and take place within the E_th1–E_th2 and E_th3–E_th4 thresholds. In this work, the maximum amplitude of a single spike was reduced so that only the resulting pulse with the amplitude E_pre – E_post could exceed thresholds.

Time dependences of pulse sequences corresponding to the pre-spike E_pre, the post-spike E_post and the resulting sequence E_pre – E_post applied to the ME heterostructure for the case of LTD (post-spike precedes pre-spike) and LTP (pre-spike precedes post-spike) are presented in Fig. 10a and Fig. 10b, respectively.

The graphs show that individually, the maximum amplitudes of E_pre and E_post are significantly lower than the threshold values E_th1 = –7.2 kV/cm, E_th2 = –6 kV/cm, E_th3 = 6 kV/cm, E_th4 = 7.2 kV/cm. However, the amplitude of the resulting pulse E_pre – E_post is within the thresholds E_th1 < E < E_th2 and E_th3 < E < E_th4, which results in LTD and LTP, respectively. An important parameter is the time window Δt, which determines the relative arrival time of pre- and post-spikes. In our case, the smaller Δt, the greater the amplitude of the resulting pulse. Figure 10a and Figure 10b show the cases for Δt = –6 s and Δt = 6 s, respectively. To effectively change α_E, before applying the resulting pulse E_pre – E_post for each Δt, the piezoceramics was polarized by a single electric field pulse with an amplitude of E = 16 kV/cm (for LTD observation) and E = –16 kV/cm (for LTP observation), respectively.

Figure 11 shows the dependences of the absolute Δα_E and relative Δα_E/α_Ei changes in the ME coefficient α_E according to the STDP rule on the time window Δt. The data was obtained by applying the resulting pulses E_pre – E_post to the ME heterostructure. The pulses shifted relative to each other by Δt = – 54 – 54 s with a step of 6 s. The calculation of the absolute change in α_E was carried out using the formula Δα_E = α_Ef – α_Ei, where α_Ei and α_Ef are the values of the ME coefficient before and after applying the resulting pulse.

As seen from the graphs, the highest value of Δα_E was observed at Δt = 6 s due to the largest amplitude of the E_pre – E_post. However, with a further increase in Δt, the value of Δα_E decreases exponentially. The decrease in Δα_E is explained by less overlap of the E_pre and the E_post pulses and, accordingly, a smaller resulting amplitude of the E_pre – E_post.

With a further increase in Δt, the value Δα_E ~ 0, which indicates that the E_pre and the E_post pulses do not overlap and so that α_E does not changed significantly. The STDP behavior shown in Fig. 11 can be approximated by the STDP rule learning function described in [47]

$\frac{\mathrm{\Delta }{\alpha }_E}{{\alpha }_{Ei}}(\mathrm{\Delta }t)=\{\begin{array}{l}{k}^{+}{e}^{-\frac{\mathrm{\Delta }t}{t^{+}}},\mathrm{\Delta }t>0\\ k^{-}{e}^{\frac{\mathrm{\Delta }t}{t^{-}}},\mathrm{\Delta }t<0\end{array}$.

In our case, the k⁺ = 294, k – = –294, t⁺ = 9, t – = –9.

It follows from the graphs that the magnitude of the change in the ME coefficient Δα_E depends on the arrival time of pre- and post-spikes.

Thus, it is shown that ME heterostructures have the potential for the development of artificial synaptic devices for the creation of neuromorphic computing systems. It is also worth noting the possibilities for improving the characteristics of the described ME heterostructure and further development prospects. The reproducibility of characteristics of ME heterostructures can be improved by more technologically advanced fabrication methods, such as vacuum and electrolytic deposition of FM layers on a PE substrate. The amplitude of the output ME voltage can be increased by optimizing the sample mounting during the measurement. The number of nonvolatile stable states corresponding to different values of α_E can be controlled with higher precision by applying electric field pulses with smaller steps. The shape of the STDP dependences Δα_E (Δt) can be controlled in an arbitrary manner by applying pulses of different shapes, amplitudes and polarities, corresponding to pre- and post-spikes. To increase performance, reduce energy consumption, and reliably simulate synaptic behavior, the duration of the applied electric field pulses must be comparable to the duration of the spike in biological systems (a few to tens of milliseconds). The size of the heterostructures themselves requires miniaturization. Moreover, the addition of FM layers with coercive field H_c ~ 10–100 Oe, such as Ni, will make it possible to observe the ME interaction without a bias constant magnetic field H.

Figure 9.

The mechanism for changing the ME coefficient α_E due to the superposition of voltage pulses U_pre – U_post, corresponding to pre- and post-spikes

Figure 10.

Time dependences of the pre-spike E_pre, the post-spike E_post and the resulting pulse E_pre – E_post at Δt = –6 s for LTD case (a) and Δt = 6 s for LTP case (b)

Figure 11.

Dependences of the absolute Δα_E and relative Δα_E/α_Ei changes in the ME coefficient α_E according to the STDP rule on the time window Δt (solid line – exponential approximation by the STDP learning function)