The tri-layer magnetic tunnel junction (MTJ) has surfaced as a building block for engineering next-generation integrated circuits while combining the attributes of non-volatility and meager energy consumption. Nevertheless, the perceptible switching energy (2050 fJ/bit) and sub-optimal tunnelmagnetoresistance (TMR) (200%300%) have acted as major hindrances, concealing its potential to supersede the capabilities of static and dynamic random access memories. In this work, we introduce a novel device that features a minimalistic non-uniform heterostructure/superlattice instead of the oxide layer in a conventional MTJ and analyze it in the premise of the self-consistent coupling of the Non-Equilibrium-Green’s Function (NEGF) and the Landau-Liftshitz-Gilbert-Slonczewski (LLGS) equation. We ascertain that the coupling of the electrodes to the proposed heterostructure renders a highly spin-selective broadband transmittance, thereby enabling a towering TMR (%) of 3.7 × 104% along with a significant reduction in the spin transfer torque (STT) switching energy (≈1.96 fJ). Furthermore, the sizable slonczewski term (Is) originating from the heterostructure facilitates a swift STT-switching within the scale of a few hundred picoseconds (≈400 ps).

Spintronic devices have recently emerged as the pinnacle of storage technology, providing a harmonious blend of speed and energy efficacy. Owing to the union of CMOS integrability, high packing density, and non-volatility, magnetic tunnel junctions (MTJs) have lit up the horizon of spintronics with numerous possibilities ranging from magnetoresistive random access memories (MRAMs),1 biomedical studies,2 spin transfer torque nano oscillators (STNOs)3 and wireless technology4 to a wide range of sensors.5 

A canonical MTJ is realized by a nanopillar that constitutes a free and a pinned ferromagnet (FM) parted by an insulating material (e.g., MgO) as depicted in Fig. 1(a). The spin-dependent quantum transport through the device is gauged by the tunnel magnetoresistance (TMR), given by TMR (%) = (RPC − RAPC)/RPC × 100% where RAPC and RPC represents the resistances in anti-parallel (APC) and parallel (PC) configurations, respectively. The dynamics of the free FM can be modulated by either spin transfer torque (STT) or spin–orbit torque (SOT), facilitating writing operations via exclusively electrical currents.6 Perpendicular magnetic anisotropy (PMA) enables the magnetization of the pinned and the free layer to stand vertically against the plane of the film. A standard PMA-MTJ (p-MTJ) achieves swift switching within the time frame of nanoseconds, coupled with reduced energy consumption and enhanced thermal stability in comparison to in-plane MTJs.7 Given that contemporary volatile memories such as SRAM and DRAM have the capability to achieve switching down to the fJ limit,8–10 enhancement in the TMR (200%300%) and reduction of the switching energy (2050 fJ/bit) of a conventional MTJ, constrained by the principles of single barrier tunneling, are at the nexus of contemporary research.1,11–13

FIG. 1.

Schematic of (a) conventional MTJ and (b) a non-uniform heterostructure/superlattice-based MTJ (NHMTJ).

FIG. 1.

Schematic of (a) conventional MTJ and (b) a non-uniform heterostructure/superlattice-based MTJ (NHMTJ).

Close modal
In this work, we introduce a non-uniform heterostructure/superlattice-based MTJ (NHMTJ) with four barriers, conceived to markedly amplify the TMR (%) while concurrently resulting in a significant reduction in power consumption. To systematically compare the switching bias of the NHMTJ against the standard MTJ, we instantiate a performance metric, designated as the suppression in the switching bias (SSB), defined by the following equation:
SSB=|SBPCAPCMTJ|+|SBAPC→PCMTJ||SBPCAPCNHMTJ|+|SBAPC→PCNHMTJ|
(1)
where APC(PC) symbolizes the anti-parallel(parallel) configuration, SBPCAPCMTJ(NHMTJ) and SBAPC→PCMTJ(NHMTJ) represent the switching biases applied to the conventional MTJ (NHMTJ) for the transformations from PC to APC and vice versa, with SB denoting the switching bias.
To probe the intricacies of quantum transport within MTJs, we leverage the non-equilibrium Green’s function (NEGF) formalism to compute the spin current (IS) through the device while using the equation formulated below:
ISi=q Real [Trace(σiÎop)]dE
(2)
where σi denotes the Pauli spin-matrices along x̂, ŷ, ẑ directions and Îop13,14 is given by
Iop,N1,N=iHN1,NGN,N1n(HN1,NGN,N1n)
(3)
where HN−1,N represents the N − 1th row, Nth column element of the device Hamiltonian and GN,N1n represents the N − 1th row, Nth column element of the Green’s function matrix.1 The dynamics of the free layer under the influence of spin current and an imposed magnetic field are modeled through a synergistic conjunction of the NEGF formalism with the Landau–Lifshitz–Gilbert–Slonczewski (LLGS) equation described by:15 
1+α2m̂t=γm̂×Heffγαm̂×(m̂×Heff)γ2qMSV(m̂×(m̂×IS))α(m̂×IS)
(4)

In this equation, m̂ denotes the magnetization of the free FM, γ stands for the gyromagnetic ratio associated to electrons with α being the Gilbert damping parameter. Here Ms stands for the saturation magnetization, and V is the volume of the CoFeB contacts. The effective magnetic field, Heff, is formulated as Heff=Happlied+Hkmzẑ, with Happlied representing the applied field, assumed zero in this work, and Hkmz symbolizing the uniaxial magnetic anisotropy of the FM contacts with Perpendicular Magnetic Anisotropy (PMA). Besides, the spin current is bifurcated into three constituents so that IS=Is,M̂+Is,mm̂+Is,M̂×m̂ with M̂ and m̂ being the unit vectors along the magnetization of the pinned and free FM, respectively while the Is and Is denotes the field like and the Slonczewski term.

The threshold current needed for switching is given by Is,t=2qMsVαHeff with Heff being HK + Hd/2, where Hd and HK denotes the demagnetizing field and the in-plane anisotropy, respectively.13,16 Given the fact that Is loses its requisite influence when superposed with Is, it doesn’t impact the threshold current required for switching13 the free FM. It is pertinent to observe that Hd customarily exhibits a value that is one order of magnitude higher than HK, culminating in a considerable uptick in power consumption. The adverse effects of Hd can be alleviated by the adoption of FMs with PMA,17 which aligns the magnetization perpendicularly to the thin film’s plane,18 with the threshold current being calculated as Is,t=2qMsVαHK13 with HK being the perpendicular anisotropy.

In this study, we utilized CoFeB13 as ferromagnetic (FM) contacts, characterized by a Fermi level Ef = 2.25 eV and ferromagnetic exchange splitting of Δ = 2.15 eV.19 We assumed the effective masses in MgO barriers, NM quantum wells (Ru, Cu, Ti etc.13), and FM contacts to be mox = 0.18me, mnm = 0.9me, and mfm = 0.8me,20 respectively, where me signifies the free-electron mass. The barrier height from CoFeB toward MgO was marked at UB = 0.76 eV higher than the Fermi level,13 with the conduction band offset between the FM and NM layers being UBW = 0.5 eV.

We meticulously kept the thickness of the NM q-wells to W = 0.35 nm in adherence to fabrication constraints.21 Further, we considered a minimum oxide width of 0.6 nm, which relies comfortably within the reliable deposition limit of MgO.22 We keep the width of the free FM at 1.3 nm23 and establish the diameter of the CoFeB contacts at 30 nm, enabling the depiction of the free FM’s magnetization dynamics via a macro-spin model.24 We accounted for the saturation magnetization at MS = 1150 emu/cc and consider the perpendicular uni-axial magnetic anisotropy at Hk = 3.3 kOe.25 The thermal stability factor is calculated as ΔB=HKMsV2kBT42. Finally, we took the values for the gyromagnetic ratio and damping parameter as γ = 17.6 MHz/Oe and α = 0.01, respectively. Post evaluating all the parameters in the expression of the threshold current given by Is,t=2qMsVαHk, we obtain an Is‖,t of 0.0106 mA. For seamless switching, we adjust the bias to get the Is, 20% higher than the Is‖,t.13 

We commence this section by first describing the attributes of a conventional MTJ depicted in Fig. 1(a), in conjunction with the STT-based switching of the free layer. The MTJ features a MgO barrier of thickness 1 nm sandwiched between the FM layers. The band diagram of the device is illustrated in Fig. 2(a) and the I–V characteristics for the PC and the APC is showcased in Fig. 3(a). The conventional MTJ delivers a peak TMR of 240%, as depicted in Fig. 3(b). Figures 6(a) and 6(b) describes the STT-facilitated switching of the free FM from the PC to APC along with the APC to PC at switching biases −74 and 60 mV, respectively. The discrepancy in magnitude of the SBPCAPC and SBAPCPC emanates from the asymmetrical IsV characteristics of the MTJ presented in Fig. 5(a).

FIG. 2.

Schematic of band diagram in a (a) conventional MTJ and the (b) NHMTJ.

FIG. 2.

Schematic of band diagram in a (a) conventional MTJ and the (b) NHMTJ.

Close modal
FIG. 3.

(a) I–V characteristics and (b) TMR of the MTJ, (c) I–V characteristics and (d) TMR of the NHMTJ in the PC(IP) and APC(IAP).

FIG. 3.

(a) I–V characteristics and (b) TMR of the MTJ, (c) I–V characteristics and (d) TMR of the NHMTJ in the PC(IP) and APC(IAP).

Close modal

The spin current and TMR of the conventional MTJ can be discerned from the spin selective transmittance of the PC and APC, underpinned by single barrier tunneling.13 

In the next step, we design the NHMTJ [see Fig. 1(b)] with terminal barriers, q-wells, and the central barriers of thickness of 0.6, 0.35 and 0.9 nm respectively [see Fig. 2(b)]. We depict the I–V characteristics, and TMR of the device in Figs. 3(c) and 3(d). Leveraging the highly spin-selective nature of the box-cart-shaped transmittance see Fig. 4, the NHMTJ engenders a pronounced Is. Consequently, the free FM goes through the magnetization reversal [see Figs. 6(c) and 6(d)] at a nominal bias of 7.3 mV leading to an appreciable SSB of 9.17. Unlike the MTJ, the NHMTJ shows a symmetric Is-V characteristics yielding commensurate SBPCAPC and SBAPCPC. Apart from that, the APC exhibits negligible transmittance while obstructing any conceivable flow of electrons (see Fig. 4). This precipitates a towering TMR of 3.7 × 104%. Concurrently, owing to a maximum value of nearly 0.26 mA [see Fig. 5(b)], the Is expedites a swift switching within mere 400 ps, which is at par with the proficiency of typical spin-orbit-torque (SOT) assisted STT switching6 and yet provides a leeway to bypass complexity associated with SOT.

FIG. 4.

Transmittance profile: (a) Upspin and (b) downspin transmittance of the NHMTJ in the PC, (c) upspin and (d) downspin transmittance of the NHMTJ in the APC at 10 mV for various transverse modes.

FIG. 4.

Transmittance profile: (a) Upspin and (b) downspin transmittance of the NHMTJ in the PC, (c) upspin and (d) downspin transmittance of the NHMTJ in the APC at 10 mV for various transverse modes.

Close modal
FIG. 5.

(a) Is of the MTJ and the (b) NHSLTJ with the applied voltage (at θ = 90°). Inset: IsV characteristics at higher voltage.

FIG. 5.

(a) Is of the MTJ and the (b) NHSLTJ with the applied voltage (at θ = 90°). Inset: IsV characteristics at higher voltage.

Close modal

Given the fact that the MTJ falls short in yielding adequate Slonczewski (Is) at a lower voltage, it was imperative to provide an elevated bias to achieve the stipulated Is for the switching presented in Figs. 6(c) and 6(d). This incurred an average switching energy for the alterations between the PC to APC and APC to PC of 30 fJ.

FIG. 6.

(a) STT-facilitated switching of the conentional MTJ from the APC to PC(V = 60 mV) and (b) PC to APC(V = −74 mV). STT-based switching of the NHMTJ from the (c) APC to PC(V = 7.3 mV) and the (d) PC to APC(V = −7.3 mV).

FIG. 6.

(a) STT-facilitated switching of the conentional MTJ from the APC to PC(V = 60 mV) and (b) PC to APC(V = −74 mV). STT-based switching of the NHMTJ from the (c) APC to PC(V = 7.3 mV) and the (d) PC to APC(V = −7.3 mV).

Close modal

Conversely, the NHMTJ offered an average switching energy of a meager 1.96 fJ under analogous conditions. In Fig. 7 we have shown the dependence of the MTJ and the NHMTJ with variations in the thickness of the insulating layers. In the case of the MTJ, we see that reducing the insulator thickness reduces both the TMR and the spin current. Whereas in the NHMTJ increasing the thickness of two central barriers reduces the transmission and hence decreases the spin current but improves the spin selectivity thereby improving the TMR. Apart from that, the opposite behavior of the TMR and the Is of the NHMTJ with the increase in the thickness of the central barriers renders the designer a provision to modulate the performance matrices according to his need. These results also provide us with an estimate of how errors in fabricating the thickness of the NHMTJ shall impact its performance.

FIG. 7.

Variation of TMR and Is of the (a) conventional-MTJ with thickness of the insulating layer and the (b) NHMTJ with thickness of the central barriers while keeping the terminal barriers intact at 10 mV.

FIG. 7.

Variation of TMR and Is of the (a) conventional-MTJ with thickness of the insulating layer and the (b) NHMTJ with thickness of the central barriers while keeping the terminal barriers intact at 10 mV.

Close modal

Along with the insufficient TMR (%), the non-optimal switching energy13 continues to remain the major hurdle hindering the opportunity for a conventional MTJ to become a premier substitute of sate-of-the-art storage devices such as SRAMs and DRAMs.8,9 In this study, we explore the broad-band spin filtering in a minimalistic NHMTJ that displays a sizable proliferation in the TMR (3.7 × 104%) with a noteworthy reduction in the switching energy (≈1.96 fJ). Since the NHMTJ facilitates a swift STT-based-switching in the time frame of a few hundred picoseconds, it adeptly counteract the deficiencies of unpredictable switching observed in SOT-based MTJs, maintaining synchrony with the speed.6,13 Furthermore, it is anticipated that the recent advancements in double metallic quantum well-based MTJs21 will intensify the exploration of heterostructure-based memory devices. We hope that a seminal breakthrough in the periphery of non-volatile memories by the likes of energy-efficient MTJs as exemplified in this study might torch the avenues of the future with a scintillating prospectus in the beyond the Moore era.

The author A.S. acknowledges the support by the Science and Engineering Research Board (SERB), Government of India, Grant No. SRG/2023/001327.

The authors have no conflicts to disclose.

Sabarna Chakraborti: Conceptualization (lead); Data curation (lead); Formal analysis (lead); Funding acquisition (lead); Investigation (lead); Methodology (supporting); Project administration (supporting); Resources (supporting); Software (supporting); Supervision (supporting); Validation (lead); Visualization (lead); Writing – original draft (lead); Writing – review & editing (lead). Korra Vamshi Krishna: Conceptualization (supporting); Data curation (supporting); Formal analysis (supporting); Funding acquisition (supporting); Investigation (supporting); Methodology (supporting); Project administration (supporting); Resources (supporting); Software (supporting); Supervision (supporting); Validation (supporting); Visualization (supporting); Writing – original draft (supporting); Writing – review & editing (supporting). Virendra Singh: Software (supporting); Supervision (supporting); Validation (supporting); Visualization (supporting). Abhishek Sharma: Conceptualization (lead); Data curation (supporting); Formal analysis (supporting); Funding acquisition (lead); Investigation (supporting); Methodology (lead); Project administration (lead); Resources (lead); Software (lead); Supervision (lead); Validation (supporting); Visualization (supporting); Writing – original draft (supporting); Writing – review & editing (supporting).

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

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