Magnetic tunnel junctions (MTJs), which comprise two ferromagnetic (FM) layers separated by a thin insulating layer, serve as the core building blocks for magnetic random access memory (MRAM), spin logic devices, and brain-inspired computing systems^[1-6]. Electron tunneling between two FM electrodes can be effectively controlled by switching the relative magnetization orientation between parallel (P) and antiparallel (AP) states. This effect is known as tunneling magnetoresistance (TMR) [Figure 1A]^[7-9]. However, the miniaturization of MTJ devices remains a critical challenge in spintronics, owing to stray fields generated within ferromagnetic layers [Figure 1B]^[10,11]. Moreover, the intrinsic slow spin dynamics of ferromagnets limit the operational speed of arithmetic devices^[12]. Antiferromagnets (AFM) have become potential candidates for spintronic applications owing to their strong magnetic stability, zero stray fields and ultrafast dynamic responses [Figure 1B]^[13,14]. An antiferromagnetic tunnel junction (AFMTJ) consists of two AFM electrodes, and the P or AP alignment of their Néel vectors gives rise to the TMR effect [Figure 1A]^[7,8]. Antiferromagnets exhibit zero net magnetization, which greatly complicates the achievement of TMR in AFMTJs. To overcome these bottlenecks, ferrimagnets stand out as a promising candidate that combines the merits of ferromagnets and antiferromagnets simultaneously. Consisting of two sublattices with antiparallel but unequal magnetic moments, ferrimagnets produce tunable and detectable net magnetization and ultrafast spin dynamics. Owing to the limited net magnetization, ferrimagnets feature drastically suppressed stray fields relative to conventional ferromagnets, effectively mitigating edge-induced perturbations in scaled-down spintronic devices [Figure 1B]^[15-18]. As a result, perpendicular ferrimagnetic tunnel junctions possess great potential to boost the integration density of MTJ units and promote arithmetic frequency and operating speed.

Research studies on ferrimagnetic tunnel junctions have primarily focused on compensated ferrimagnets, composing Rare-earth (RE) and transition metals (RE-TM)^[19-21]. Such materials exhibit a unique antiferromagnetic coupling between the non-equivalent magnetic moments of the RE and TM sublattices^[22-24]. At a specific magnetization compensation temperature (T_M), the magnetic moments of the two sublattices become equivalent and opposite. Below and above T_M, the net magnetization is dominated by the RE and TM sublattices, respectively. By changing the temperature, the dominant sublattice responsible for the net magnetic moment can be switched^[25,26]. Significant progress has been made in realizing TMR (~33% to 58%) and giant magnetoresistance (GMR) (~0.5%), particularly in CoFe/MgO/CoGd or CoFeB/MgO/CoFeB/CoTb tunnel junctions and CoFe/Cu/CoGd spin valves^[27-29]. Despite these achievements, the presence of in-plane magnetic anisotropy and the ferromagnetic layer (CoFe) in the devices restrict further performance optimization. As a result, the development of perpendicular all-ferrimagnetic magnetic junctions remains highly desirable [Figure 1A].

In this work, we demonstrate a novel type of perpendicular compensated ferrimagnetic tunnel junctions, in which the compensated ferrimagnet Co_100-xGd_x and the ferrimagnetic metal oxide NiCo₂O₄ (NCO) are separated by an MgAl₂O₄ (MAO) insulating barrier. As a ferrimagnet, NCO exhibits robust perpendicular magnetic anisotropy (PMA) together with an extremely high spin polarization (theoretically up to 100%), rendering it an ideal candidate for our ferrimagnetic tunnel junctions^[30]. Intriguingly, we observe a sign transition of TMR (from +72% to -22%) as the temperature increases across the T_M point. This sign transition arises from the reversible switching of magnetic dominance between Co and Gd sublattices in the CoGd layer. Furthermore, the proposed ferrimagnetic devices can realize temperature-dependent non-volatile multilevel resistance states.

First, the NCO (16 nm)/MAO (3 nm) bilayers with flat surface morphology were deposited on (100)-oriented MAO single-crystal substrates using a KrF excimer laser [Figure 2A]. Subsequently, Co₈₂Gd₁₈ (5 nm)/Pt (50 nm) bilayers were prepared by co-sputtering Co and Gd targets (see Experimental Section). The X-ray diffraction (XRD) patterns of NCO (16 nm), MAO (12 nm), and the NCO (16 nm)/MAO (3 nm) bilayers verify that all the crystallographic planes of these films are parallel to the (00l) planes of MAO [Figure 2B]^[38,39]. To evaluate the substrate-induced strain, reciprocal space mapping (RSM) was performed around the asymmetric (408) reflections [Figure 2C]. The almost identical in-plane scattering vectors Q_x indicate that the bilayer stack is epitaxially grown and fully strained^[40]. High-resolution transmission electron microscopy (HRTEM) imaging of the cross section along the [100] zone axis was performed to further elucidate the interfacial features. The locally magnified atomic-resolution high-angle annular dark-field (HAADF) scanning transmission electron microscopy (STEM) image clearly reveals the stack of inverse spinel structures in NCO [Figure 2D]^[41]. The tetrahedral (T_d) sites are populated by the Co atoms, while the octahedral (O_h) sites are evenly occupied by the Ni and Co atoms^[42,43]. In addition, the annular bright-field (ABF) STEM image and its corresponding energy-dispersive X-ray spectroscopy (EDS) indicate the high structural quality of our films and interfaces [Supplementary Figure 2].

We further investigate the spin-dependent transport properties of the ferrimagnetic layers: Co₈₂Gd₁₈ and NCO (see Experimental Section). Regarding the Co₈₂Gd₁₈ layer, the square-shaped AHE loops of the Co₈₂Gd₁₈/Pt confirm the presence of PMA [Figure 2E and F]^[44,45]. The temperature-induced reversal of hysteresis loop chirality is attributed to the reversible magnetic dominance between the Co and Gd sublattices [Supplementary Figure 3A]^[46,47]. The sign of the anomalous Hall coefficient tracks the dominant sublattice magnetization, reversing when the net moment switches from Gd-dominated to Co-dominated. Meanwhile, the coercivity H_C increases steeply as the temperature approaches T_M from both sides [Supplementary Figure 3B-D], which arises from the enhanced Zeeman energy to switch the weakened magnetization^[15]. Regarding the NCO layer, square AHE hysteresis loops indicate its intrinsic PMA behavior [Figure 2G], which is further validated by the temperature-dependent magnetization along the out-of-plane and in-plane directions [Supplementary Figure 4]. The magnetic moment of NCO primarily originates from the T_d-site Co atoms and the O_h-site Ni atoms, which exhibit antiparallel magnetic alignment^[41]. The net magnetization and the PMA are dominated by the Co_Td atoms, while the electrical transport behavior is dominated by the Ni_Oh atoms^[48]. Moreover, theoretical calculations verify that the majority spin state below the Fermi level dominantly originates from Co, while the minority spin state near the Fermi level dominantly originates from Ni^[41]. This unique half-metallic band structure with a spin polarization of -100% endows NCO with great potential for spintronic devices such as MTJs^[30]. The out-of-plane magnetic hysteresis loop of the NCO/MAO/Co₈₂Gd₁₈ multilayers at 10 K is presented in Figure 2H. The distinct two-step switching corresponding to the coercivity of the NCO and CoGd layers respectively, guarantees the functional feasibility of the designed perpendicular ferrimagnetic tunnel junction^[49,50].

Furthermore, we systematically investigate the TMR performance of the ferrimagnetic tunnel junction (junction size: Dia~2 μm, A ~3.1 μm²) under out-of-plane magnetic fields (see Experimental Section). Notably, the TMR undergoes a clear sign transition from positive to negative as the temperature rises across the T_M of Co₈₂Gd₁₈ (~27 K) [Figure 3A]. In the TMR hysteresis loops, one switching occurs at a low magnetic field (around 600 Oe), corresponding to the magnetization reversal of NCO. The second switching at a higher magnetic field is tunable from 2,500 Oe to 12,000 Oe and back to 1,600 Oe with increasing temperature from 10 K to 40 K, which is consistent with the changing coercivity of the Co₈₂Gd₁₈ layer. The TMR value is defined as $$ \text { TMR } =\frac{R_{A P}-R_{P}}{R_{P}} \times 100 \% $$, where R_AP and R_P denote the resistances for the AP and P magnetization alignments of the two ferrimagnetic layers^[51]. As illustrated in Figure 3B, a positive TMR ~26% is obtained below T_M, while a negative TMR of approximately -18% is observed above T_M (the reference curve is obtained from the junction with the highest signal-to-noise ratio. Error bars are defined as the signal deviation of the other two junctions within the same device array relative to this benchmark, and the error bars for all subsequent data share the same source). Our results are opposite to those of the in-plane ferrimagnetic TMR reported by Kaiser et al.^[27], where the TMR sign reversal occurred from negative to positive^[29]. This distinct behavior in our work originates from the Co_Td dominance in magnetization and Ni_Oh dominance in transport in the NCO layer, with the two coupled antiparallelly^[48]. Moreover, at temperatures both below (15 K) and above (35 K) the T_M of Co₈₂Gd₁₈, the positive and negative TMR values decrease significantly as the magnetic field orientation approaches the in-plane direction [Figure 3C and D], verifying the perpendicular nature of our tunnel junction^[39,52]. The angular-dependent TMR loops exhibit a pronounced increase in the coercivity for both NCO and Co₈₂Gd₁₈ [Supplementary Figure 5], which is attributed to the reduced out-of-plane component of the applied magnetic field^[53,54]. It is consistent with the angular dependence of the AHE response for both NCO and Co₈₂Gd₁₈ films [Supplementary Figure 6].

In addition, the nonlinear I-V curves of the junction were measured across a temperature range of 100-200 K, demonstrating the high quality of the MAO barrier [Figure 3E]^[30]. The conductance (G = dI/dV) exhibits an approximately parabolic dependence on the bias voltage within the low-bias region, signifying a direct tunneling process^[32,33], which can be fitted using the BDR model [Figure 3E, inset]. Notably, the TMR exhibits strong dependence on device dimension. The pronounced TMR improvement upon device downsizing primarily originates from suppressed parasitic leakage current [Figure 3F]. The optimized device yields maximum TMR values of approximately +72% at 2 K and -22% at 50 K [Supplementary Figure 7]. However, further device miniaturization leads to a degraded signal-to-noise ratio due to the inherent experimental limitations. According to the Jullière model, i.e., $$ \text { TMR } =\frac{2 P_{1} P_{2}}{1-P_{1} P_{2}} $$, assuming the spin polarization of NCO is -100%^[30], the nominal spin polarization of our Co₈₂Gd₁₈ layer is estimated to be -26.5% below T_M (2 K) and +12.4% above T_M (50 K).

To elucidate the spin-dependent transport behavior in our perpendicular ferrimagnetic tunnel junctions, density functional theory (DFT) calculations of the NCO oxide and the CoGd alloy were performed (the structural models of CoGd and NCO are displayed in Figure 4A and 4B, respectively). For simplified modeling and reduced computational cost of DFT calculations, we adopted the Co₇₅Gd₂₅ model with an integer atomic stoichiometric ratio. In the calculated density of states (DOS), the majority of the occupied f states of Gd are located at ~4.5 eV below the Fermi energy level and contribute to the magnetic moment of Gd [Figure 4C]. For the CoGd alloy, the calculated average magnetic moments are ~+7.29 µ_B and ~-1.51 µ_B for each Gd and Co atom, respectively [Supplementary Table 1], suggesting the antiferromagnetic coupling between Gd and Co. The Hall conductance can be described as

(2) $$ \sigma_{H}^{x y}=\frac{-e^{3} \tau^{2}}{(2 \pi)^{3} \hbar} \int d^{3} \boldsymbol{k} \mathrm{v}_{x}\left[(\mathbf{v} \times \boldsymbol{B}) \cdot \nabla_{\boldsymbol{k}}\right] \mathrm{v}_{y}\left(\frac{\partial f_{0}}{\partial \varepsilon}\right) $$

where τ is the momentum relaxation time, e is the electron charge, v is the velocity, B = (0, 0, B_z) is the magnetic field along the z-direction, ε is the energy, ħ is the Planck constant, and f₀ is the Fermi distribution function^[55]. According to the key term $$ \frac{\partial f_{0}}{\partial \varepsilon} $$, the Hall conductance is dominated by the carriers at the Fermi level. The state occupation at the Fermi level in CoGd is dominated by the spin-down state of the d electrons in Co [Figure 4C], confirming that the spin-dependent transport is dominated by the Co sublattice. For the NCO, the magnetization is dominated by the d electrons of the Co_Td and Ni_Oh atoms, and the magnetic moments of the Co_Td and Ni_Oh atoms are estimated to be ~+2.41 µ_B and ~-0.55 µ_B, respectively [Supplementary Table 2]. As shown in Figure 4D, there are almost only spin-down occupied states at the Fermi energy level, confirming the half-metallic nature with a spin polarization of -100%^[30,56]. Furthermore, according to the band structures near the Fermi energy level of Ni and Co [Figure 4E and F], the electrical transport of NCO is dominated by spin-down Ni_Oh. Combining the theoretical calculations, the magnetization and transport of the CoGd alloy are dominated by the Gd and Co sublattices, respectively. Besides, in NCO, the magnetization and transport are dominated by Co_Td and Ni_Oh atoms, respectively. Figure 4G presents the physical schematic of the sign-reversible TMR effect in our perpendicular compensated ferrimagnetic tunnel junctions. At temperatures below T_M, the applied magnetic field aligns the Co_Td moments in NCO parallel to the dominating Gd moments in CoGd. Tunneling occurs between the Co moments in CoGd and the Ni_Oh moments in NCO, which are aligned in parallel (oriented opposite to the magnetic field), giving rise to a positive TMR. At temperatures above T_M, the magnetic field aligns the Co_Td moments in NCO parallel to the dominating Co moments in CoGd. In this case, the Ni_Oh moments in NCO are aligned antiparallel to the Co moments in CoGd, thereby producing a negative TMR.

Benefiting from the temperature-dependent behavior inherent in our ferrimagnetic tunnel junction, the tunneling magnetoresistance states exhibit tunability to temperature modulation, enabling the realization of temperature-dependent non-volatile multilevel resistance states. The tunneling resistance states “0” and “1” at 20 K can be tuned through a heating-up and cooling-down process between 20 K and 40 K, assisted by a fixed magnetic field of 0.3 T [Figure 5A]. During the thermal cycling, the magnetic dominance between Co and Gd sublattices is switched, and the magnetic field fixes the net moment direction when the temperature crosses T_M. Once the resistance state is written, it remains non-volatile as the temperature returns to 20 K. Conversely, the resistance state can be reset to the “0” level through a cooling and warming cycle between 20 K and 10 K [Figure 5B]. The Co₈₂Gd₁₈ layer undergoes a reduction in the coercivity, and the fixed magnetic field becomes sufficient to accomplish the magnetization reversal^[45]. Based on the above mechanisms, temperature-dependent non-volatile multilevel resistance states operating across T_M have been demonstrated. With the assistance of a fixed magnetic field of 0.3 T, the tunneling resistance states can be repeatedly rewritten between “0” or “1” through temperature modulation, delivering reliable non-volatile state manipulation [Figure 5C and D]. However, when the fixed magnetic field falls outside the appropriate range, volatile resistance variations are observed by varying the temperature [Supplementary Figures 8 and 9].

In summary, we have successfully demonstrated the perpendicular compensated ferrimagnetic tunnel junction based on the NCO/MAO/Co₈₂Gd₁₈ heterostructures, which exhibits reversible TMR sign switching (from +72% to -22%) as the temperature increases across the magnetization compensation point of Co₈₂Gd₁₈. The TMR sign switching is attributed to the thermally reversible magnetic compensation in Co₈₂Gd₁₈. Furthermore, we have applied this device to demonstrate temperature-dependent non-volatile multilevel resistance states. Unlike conventional MTJs, our ferrimagnetic tunnel junctions feature stray-field-free operation, temperature-tunable TMR polarity, and non-volatile multilevel resistance states. Utilizing our perpendicular compensated ferrimagnetic tunnel junctions, higher unit density, faster operating speed, and enhanced device controllability are foreseeable for future spintronic applications. Our findings offer a promising route for the design and development of ferrimagnet-based spintronic devices.