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PHYSICAL REVIEW B 114, 084405 (2026)
Fei Zou , 1 Long Zhang , 1 and Guoying Gao 1,2,* 1 School of Physics, Hubei Fundamental Research Center for Physics, Huazhong University of Science and Technology,
Wuhan 430074, People’s Republic of China 2 Wuhan National High Magnetic Field Center, Huazhong University of Science and Technology, Wuhan 430074, People’s Republic of China (Received 1 June 2026; revised 15 July 2026; accepted 15 July 2026; published 7 August 2026)
Altermagnets, characterized by vanishing net magnetization and momentum-dependent spin-splitting, offer a unique platform for high-performance spintronic devices. Here, we propose a double-barrier altermagnetic tunneling junction, and investigate the spin transport properties of RuO 2 /TiO 2 /RuO 2 /TiO 2 /RuO 2 by using first-principles calculations combined with the nonequilibrium Green’s function method. A giant tunneling magnetoresistance (TMR) of up to 75 094% is achieved at optimal geometry, which is much higher than that of 200−500 % for the single-barrier altermagnetic tunneling junction of RuO 2 /TiO 2 /RuO 2 . The transport is governed by momentum-selective resonant tunneling through quantum-well (QW) states formed in the altermagnetic RuO 2 spacer. Due to the intrinsic k-dependent spin splitting of RuO 2 , the resonance condition is satisfied at distinct k || points for different spin channels, giving rise to localized transmission hot spots near the Brillouin-zone corners. In the parallel configuration, these QW states align with the Fermi level and support near-unity transmission, whereas reversing the Néel vector disrupts the resonance condition and suppresses transmission across the Brillouin zone, leading to the large TMR. By analyzing the dependence on QW thickness and barrier thickness, we show that the transport is controlled by the interplay of quantum confinement, total broadening, and coupling symmetry. High transmission is achieved when the QW states are properly aligned and the coupling to the electrodes is both strong and symmetric. These results provide a microscopic understanding of altermagnetism-driven resonant tunneling and offer a route to enhancing TMR through momentum-selective transport.
DOI: 10.1103/h13n-whcx
Tunneling magnetoresistance (TMR) is a central phenomenon in spintronics and underlies a wide range of applications in magnetic memory and spin-based logic devices [1–3]. Conventional magnetic tunnel junctions (MTJs) rely on the spin polarization of ferromagnetic electrodes to produce conductance variations between different magnetic configurations, with the resulting TMR governed by the spin-dependent electronic structure of the electrodes and the tunneling characteristics of the barrier [4,5]. A prototypical example is the Fe/MgO/Fe junction, where the large TMR originates from symmetry-selective tunneling: the slowly decaying 1 evanescent state in the MgO barrier couples efficiently to the 1 majority-spin Bloch states of Fe [6,7]. Despite these successes, ferromagnet-based devices face intrinsic limitations, including stray fields that hinder high-density integration and relatively slow magnetization dynamics that constrain device speed [8–10].
Against this background, the recent emergence of altermagnetism (AM) offers a different route for spin-dependent transport [11–17]. Altermagnets carry no net magnetization, similar to antiferromagnets, yet exhibit pronounced * Contact author: [email protected] 2469-9950/2026/114(8)/084405(12)
momentum-dependent spin splitting governed by magnetic space-group symmetry, which lifts spin degeneracy even in the absence of spin-orbit coupling [18,19]. This distinctive band structure enables the generation of highly spin-polarized currents without stray fields, making AMs a promising platform for next-generation spintronic devices. As a representative example, RuO 2 has been identified as a prototypical altermagnet, exhibiting spin splitting up to ∼1.4 eV near the Fermi level with strong anisotropy across the Brillouin zone, as well as a Néel temperature exceeding room temperature [20,21]. The Néel vector of RuO 2 can be reversibly switched by current-induced spin-orbit torque, as demonstrated experimentally in epitaxial RuO 2 thin films and verified by electrical transport and x-ray magnetic linear dichroism (XMLD) measurements [22]. Therefore, the parallel and antiparallel magnetic configurations considered in RuO 2 -based MTJs are expected to be experimentally achievable through electrical control of the RuO 2 Néel vectors. These properties of RuO 2 have motivated increasing efforts to explore spin-dependent transport in AM-based junctions [11,12,17,23–25]. For example, theoretical studies have predicted TMR values on the order of 500% in RuO 2 /TiO 2 /RuO 2 (001) single-barrier MTJs, arising from momentum-dependent matching of spinpolarized conduction channels between the electrodes [11]. Experimentally, RuO 2 /TiO 2 /CoFeB junctions have demonstrated that the TMR depends sensitively on the Néel vector 084405-1 ©2026 American Physical Society FEI ZOU, LONG ZHANG, AND GUOYING GAO PHYSICAL REVIEW B 114, 084405 (2026)
orientation and can even change sign upon its reversal [25]. Nevertheless, the transport in these RuO 2 -based single-barrier MTJs remains largely dominated by states near the point, indicating that the underlying mechanism is still closely related to conventional symmetry-filtered tunneling. As a result, such systems remain constrained by the exponential attenuation of evanescent states within a single insulating barrier.
An alternative strategy is provided by resonant tunneling in double-barrier structures, where quantum-well (QW) states can significantly enhance transmission [26–30]. By inserting a semiconducting or metallic layer between two insulating barriers, discrete quasibound states are formed within the well region [26,31–33]. When the energy and in-plane momentum of incident electrons match these states, resonant tunneling can lead to near-unity transmission [27]. The introduction of QW states thus adds an additional degree of control over tunneling transport [34,35]. In the context of altermagnets, the symmetry-governed spin texture further implies that the QW states can be sublattice polarized and strongly momentumdependent, distinguishing them from those in conventional ferromagnetic or antiferromagnetic systems. However, most existing studies of resonant tunneling have focused on ferromagnetic junctions, and a systematic understanding of how QW resonances couple to momentum-selective spin transport in altermagnetic systems is still lacking.
It should be noted that the magnetic ground state of RuO 2 remains under active debate. While several theoretical and experimental studies have reported evidence consistent with altermagnetic order, recent works have questioned whether the reported signatures uniquely demonstrate intrinsic altermagnetism [36,37]. Therefore, the existence and microscopic origin of magnetic order in RuO 2 have not yet reached a consensus and remain under active investigation. In this work, we adopt the altermagnetic RuO 2 model widely used in recent first-principles studies and investigate a doublebarrier altermagnetic tunnel junction (DBAMTJ) with the
first-principles calculations with the nonequilibrium Green’s function (NEGF) method. We show that the transport is governed by momentum-selective resonant tunneling through QW states formed in the altermagnetic spacer. Due to the intrinsic k-dependent spin splitting of RuO 2 , the resonance condition is satisfied at distinct k || points for different spin channels, leading to highly localized transmission hot spots near the Brillouin-zone corners. We demonstrate that the strong contrast between parallel and antiparallel configurations originates from the sensitivity of these QW states to the Néel vector orientation, yielding a tunneling magnetoresistance of up to 75 094%. By analyzing the dependence on QW and barrier thickness, we further demonstrate that the transport is controlled by the interplay of quantum confinement, total broadening, and coupling symmetry. These findings provide a microscopic understanding of altermagnetism-driven resonant tunneling and offer a route to enhancing TMR through momentum-selective transport.
Vienna ab initio Simulation Package (VASP) [38]. The pseudopotentials were described by the projector-augmentedwave (PAW) method, and the exchange-correlation effects were treated within the generalized gradient approximation (GGA) in the Perdew-Burke-Ernzerhof (PBE) form [39]. A plane-wave cutoff energy of 500 eV and a k-point mesh of 16 × 16 × 20 were adopted. The calculations were continued until the total energy difference and the maximum ionic forces converged to below 10 −6 eV and 0.001 eV/Å, respectively. To better describe the correlated d electrons, the GGA+U approach was employed [40], with effective Hubbard parameters (U eff ) of 2.0 eV for Ru 4d states and 5.0 eV for Ti 3d states. For all tunnel junction models, a vacuum layer of 15 Å was introduced along the transport direction to avoid interactions between periodic images. The in-plane lattice constants were fixed to those of bulk RuO 2 (a = b = 4.522 Å). Structural relaxations of the DBAMTJs were performed using a 10 × 10 × 1 k-point mesh, with an energy convergence threshold of 10 −5 eV, and atomic positions were optimized until all forces were smaller than 0.01 eV/Å.
Transport properties were evaluated by combining DFT with the nonequilibrium Green’s function (NEGF) formalism, as implemented in QuantumATK [41]. All computational parameters followed those used in previous studies of the RuO 2 /TiO 2 /RuO 2 MTJ [11]. The exchange-correlation potential was treated within spin-polarized GGA+U using the PBE functional [39,42], together with a single-zeta-polarized basis set. The U eff values were set to 2.3 eV for Ru 4d orbitals and 5.0 eV for Ti 3d orbitals. A cutoff energy of 75 Ha and a 11 × 11 × 101 k-point mesh were used for the DBAMTJs. Transmission functions were calculated using a 401 × 401 k-point mesh in the two-dimensional Brillouin zone of the devices.
Figures were plotted using VESTA [43], and M ATPLOTLIB [44].
The essential physics of the proposed RuO 2 /TiO 2 / RuO 2 /TiO 2 /RuO 2 (001) DBAMTJ is illustrated in Fig. 1. Spin-dependent transport is governed by resonant tunneling through QW states formed in the altermagnetic spacer. In the parallel (P) configuration, the altermagnetic order in RuO 2 induces a momentum-dependent spin splitting of the conduction bands, leading to distinct spin-resolved Fermi surfaces in the two-dimensional Brillouin zone (2DBZ). As a result, the spectral weight for opposite spins is concentrated at different transverse momenta k ↑ and k ↓ . For a subset of these momentum regions, the quantized QW levels E r ( k || ) become aligned with the Fermi level, satisfying the resonance condition E r ( k || ) = E F [45] and producing spin-selective transmission hot spots. The total spin-summed transmission is dominated
First-principles calculations were carried out within the framework of density functional theory (DFT) using the where the BZ normalization factor is omitted, σ denotes the spin index (σ = ↑, ↓), and T σ P ( k || ) ≈ 1 at the resonant hot 084405-2 GIANT TUNNELING MAGNETORESISTANCE DRIVEN BY … PHYSICAL REVIEW B 114, 084405 (2026)
spots, indicating that resonant transmission can arise from either spin channel at different momentum regions, thereby enhancing the total T P [46,47].
In the antiparallel (AP) configuration, the Néel vector in the right electrode is reversed relative to that in the left electrode. Consequently, the altermagnetic spin splittings of the two electrodes have opposite signs in momentum space, preventing the simultaneous satisfaction of the spin-selective resonance condition for either spin channel at any k || . Accordingly, no resonant state aligns with the Fermi level, and T σ AP ( k || ) are suppressed to the off-resonant background across
The resulting TMR ratio, expressed in terms of the integrated transmission as TMR = (T P − T AP )/T AP × 100%, can become exceptionally large because the conductance contrast is amplified by the resonant enhancement of T P , rather than being determined solely by the spin-dependent electronic structure of the electrodes and the tunneling characteristics of the barrier, as in conventional single-barrier MTJs. This physical picture indicates that the TMR in RuO 2 -based junctions is highly sensitive to both the relative Néel vector orientation and the alignment of the QW levels, which can be further tuned by the spacer thickness. These predictions are systematically examined in the following analyses.
To clarify the origin of the tunneling features, we first examine the electronic properties of rutile RuO 2 electrodes and the TiO 2 barrier. As shown in Fig. 2, bulk RuO 2 is a collinear altermagnet, in which the magnetic moments on the two Ru sublattices are oppositely aligned, resulting in a vanishing net magnetization but a pronounced momentum-dependent spin splitting [20]. This behavior is dictated by the magnetic space group P4 2 /mnm , and the calculated magnetic moment at the Ru site is ±1.17 μ B . This altermagnetic character is reflected in the calculated spin-resolved band structure [Fig. 2(b)]. Along high-symmetry directions such as M- and A-Z, clear spin splitting is observed, whereas degeneracies persist along other symmetry-protected paths. This band structure gives rise to distinct spin-dependent conduction channels in the 2DBZ, 084405-3 FEI ZOU, LONG ZHANG, AND GUOYING GAO PHYSICAL REVIEW B 114, 084405 (2026)
as shown in Fig. 2(c). Both spin channels reach their maximum density (N = 2) at the and H points; however, their distributions in momentum space are staggered, reflecting the underlying altermagnetic symmetry. The insulating nature of the TiO 2 barrier is summarized in Fig. S1 [48]. Although the point exhibits the weakest evanescent-state decay and the H point also possesses a relatively low decay rate in the TiO 2 barrier, the actual transmission is ultimately governed by whether QW states are formed in the central RuO 2 layer and can mediate resonant tunneling across the double-barrier junction (see Sec. III D).
With this electronic structure in mind, we now turn to the transport properties of the junction. The interplay of electrode channels, barrier filtering, and QW resonances is reflected in the k || -resolved transmission spectra (Fig. 3). Enhanced transmission emerges near the Brillouin-zone corners in the P configuration but is suppressed in the AP configuration. To further quantify their contribution, we analyze the k || -resolved → transmission difference [T ( k || )], as shown in Fig. 4. The TMR is determined by the difference in total transmission
For the AP-I (right electrode reversed) case [Fig. 4(a)], the positive T( k || ) shows pronounced hot spots near the Brillouin-zone corners (arclike features). These hot spots form symmetry-related patterns and dominate the overall transport. To quantify the relative importance of different k points, we analyze the cumulative contribution to T. As shown in Fig. 4(b), the positive contributions are highly localized: about 90% of the total originates from only 0.28% of the k points, indicating that transport is dominated by a small number of hot-spot channels. In contrast, regions with negative T ( k || ) [i.e., T AP ( k || ) > T P ( k || ) ] are sparse and of much smaller magnitude [Fig. 4(a)], resulting in a negligible cumulative contribution [Fig. 4(b)]. Consistently, the total transmission coefficients are T P = 6.62 × 10 −4 and T AP−I = 2.84 × 10 −6 , differing by more than two orders of magnitude. This large contrast confirms that the TMR is governed by 084405-4 GIANT TUNNELING MAGNETORESISTANCE DRIVEN BY … PHYSICAL REVIEW B 114, 084405 (2026)
constructive transmission channels, with minimal contribution from negative T. A similar behavior is found for the alternative AP-II (central QW layer reversed) configuration (Fig. S2 [48]), where the hot-spot distribution remains essentially unchanged and negative contributions are likewise negligible. In this case, the top 0.29% of k points account for about 90% of the total T, further supporting the robustness of the momentum-selective transport.
In the P configuration [Figs. 3(b)–3(e)], the QW resonance condition is satisfied at specific k points for the given barrier and well thicknesses, giving rise to the arclike hot-spot features. In contrast to a reference single-barrier MTJ, where transport is dominated by nonresonant tunneling near the point (Fig. S4 [48]), the DBAMTJ exhibits much stronger momentum localization and enhanced transmission due to QW states. To clarify the microscopic origin of these features, we consider the H, H , and points as representative cases. At H (a primary resonance center), the transmission is dominated by the spin-down channel with T ↓ ≈ 1, while H acts as a secondary hot spot with T ↑ ≈ 0.5. This strong spin selectivity at specific k points arises from the altermagnetic symmetry of RuO 2 . In contrast, the point—despite having the lowest evanescent decay rate (κ min ) in the TiO 2 barrier—shows negligible transmission (3.4 × 10 −4 ) for both spin channels. This indicates that transport is governed by momentum-selective resonant tunneling rather than simple barrier transparency. When the device is switched to the AP-I or AP-II configurations, the resonance-driven transparency is strongly suppressed. In the AP-I state [Figs. 3(f)–3(i)], the resonance peaks are reduced and shifted away from the Fermi level. In the AP-II state [Figs. 3(j)–3(m)], the transmission across the 2DBZ is nearly extinguished. This behavior indicates that reversing the magnetic moment of the central altermagnetic QW provides a more effective modulation of the quantum states, leading to a near-complete suppression of tunneling and giving rise to the giant TMR ratios shown in Fig. 5.
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We quantify the device performance through the energydependent transport properties shown in Fig. 5. The total transmission T(E) [Fig. 5(a)], obtained by integration over the 2DBZ, exhibits a pronounced resonance at the Fermi level in the P configuration. In contrast, for both AP-I and AP-II configurations, T(E) is suppressed by several orders of magnitude within the energy window from –0.03 to 0.03 eV. This suppression reflects the shift of the hot-spot states away from the resonant condition upon breaking the magnetic symmetry. The corresponding TMR ratios are shown in Fig. 5(b). At the Fermi level, the DBAMTJ reaches TMR values of 23 222% (TMR-I) and 75 094% (TMR-II). The larger TMR in the AP-II case is consistent with the statistical analysis, which shows that the transport is dominated by a very small fraction of k points (∼0.29%) (Fig. S2 [48]). The energyresolved spin components (Fig. S3 [48]) show that the giant TMR is confined to a narrow energy window around E F , consistent with resonant tunneling. For comparison, replacing the central RuO 2 quantum well with two additional TiO 2 unit cells yields a single-barrier junction with nearly the same total barrier thickness but a TMR of only ∼130% (see Sec. S4 of the Supplemental Material [48]), demonstrating that the giant TMR in the DBAMTJ originates from the QW effect (see Sec. III D). Together with the comparison to the previously reported RuO 2 /TiO 2 /RuO 2 single-barrier MTJ containing a four-unit-cell TiO 2 barrier [11], these results demonstrate that the proposed DBAMTJ substantially enhances the TMR through momentum-selective resonant tunneling enabled by the central RuO 2 quantum well. Compared with conventional ferromagnetic double-barrier MTJs, where the TMR enhancement mainly originates from spin-dependent QW resonances in the middle ferromagnetic layer, the present RuO 2 -based
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DBAMTJ further exploits the momentum-dependent spin splitting characteristic of altermagnetic RuO 2 . The synergy between resonant tunneling and altermagnetic spin splitting makes the resonant transmission highly sensitive to the Néel vector configuration, yielding TMR values substantially larger than the ∼10 3 % typically reported for conventional counterparts [49–52].
To further substantiate the resonant tunneling mechanism, we examine the energy-resolved transmission and the local device density of states (LDOS) at representative k || points in the P configuration (Fig. 6). The LDOS, integrated over the central RuO 2 quantum well, directly reflects the quasibound states in the double-barrier structure. As shown in Fig. 6(b), both the H and H points exhibit pronounced LDOS peaks near the Fermi level, indicating well-defined QW states. At the H point, a spin-down LDOS peak aligns closely with E F , consistent with the near-unity transmission (T ↓ ≈ 1) in Fig. 6(a). Similarly, at the H point, a spin-up QW state gives rise to the secondary transmission hot spot. The correspondence between the LDOS peaks and the transmission maxima indicates that transport is governed by QW statemediated resonant tunneling, consistent with Fabry-Pérot-like interference within the QW. In contrast, the point shows a featureless LDOS and vanishing transmission over the entire energy range, indicating the absence of QW states at the zone center. This alignment (or misalignment) of QW states with the Fermi level determines the contrast between the P and AP configurations and underlies the large TMR.
We calculate the coordinate-resolved LDOS along the transport direction at the Fermi level to provide a real-space view of the resonant tunneling hot spots (Fig. 7). This analysis distinguishes the contributions from the left and right electrodes and reveals their coupling within the QW. At the primary resonance point H, the spin-down channel [Figs. 7(b) and 7(c)] shows strong penetration of the LDOS from both electrodes through the TiO 2 barriers. The resulting LDOS exhibits a pronounced standing-wave pattern throughout the QW, reflecting the formation of QW states. This behavior reflects constructive interference and strong spatial overlap of states from opposite electrodes, characteristic of Fabry-Pérot resonances. A similar but weaker pattern is observed for the spin-up channel at the H point [Figs. 7(d) and 7(f)], consistent with its role as a secondary hot spot. In contrast, transport at the point is evanescent. As shown in Figs. 7(g)–7(i), the LDOS from the left electrode decays exponentially across the barrier and remains negligible within the QW. No appreciable overlap between left- and right-originating states is observed, and the LDOS in the QW is several orders of magnitude smaller than at the H point. The logarithmic plots further highlight the contrast between resonant enhancement at H and H and monotonic decay at . These results show that the high transmission at the hot spots is sustained by quasibound states that span the two barriers, whereas such states are absent at the Brillouin-zone center. Importantly, the resonant LDOS is spatially extended across the central RuO 2 quantum well, with only weak contributions near the RuO 2 /TiO 2 interfaces. This spatial distribution indicates that the transmission resonances are mediated by QW states rather than interface resonance states.
The transmission eigenchannels and corresponding eigenstates at the Fermi energy (Fig. 8) provide further insight into the microscopic origin of the resonant transport. At the hot spot H, the leading eigenchannel has an eigenvalue close to unity, indicating nearly perfect transmission. The corresponding eigenstate is primarily confined within the central RuO 2 layer, forming a well-defined QW state. This confinement indicates that transport proceeds via a quasibound state that couples to the electrodes and enables coherent tunneling across the double barrier. A notable feature at H point is the sublattice selectivity of the eigenstate. This indicates that the QW state is not only momentum selective but also governed by the internal symmetry and orbital character of the RuO 2 layer, such that only specific orbital components effectively hybridize with the electrode states. At the secondary hot spot H , a similar QW-confined state is observed, but with a 084405-7 FEI ZOU, LONG ZHANG, AND GUOYING GAO PHYSICAL REVIEW B 114, 084405 (2026)
reduced eigenvalue (∼0.49), indicating weaker coupling to the electrodes and hence lower transmission. In contrast, at the point, the eigenstate is localized near the injecting electrode and decays rapidly into the barrier, with negligible weight in the central region. The absence of a QW-confined state indicates that no resonant condition is established at this k || , resulting in a vanishing transmission eigenvalue.
Combined with the k || -resolved transmission and LDOS analyses, these results support a consistent picture in which transport is governed by momentum-selective, spin-dependent resonant tunneling mediated by QW states that are spatially confined and symmetry selective. High transmission occurs when these conditions are satisfied, giving rise to the observed hot spots.
To assess the stability of the momentum-selective resonant tunneling mechanism, we examine the dependence of the TMR on the junction geometry, in particular the thickness of the altermagnetic QW and the tunneling barrier (Fig. 9) (see the Supplemental Material for details on thickness-dependent resonant transport [48]). The TMR exhibits a nonmonotonic dependence on the number of RuO 2 QW layers N [Fig. 9(a)], reaching a maximum at N = 2 (23 222% for TMR-I and 75 094% for TMR-II), corresponding to the structure discussed above. This behavior contrasts with the monotonic trends typically reported in previous studies [24,53]. A phase analysis based on FFT-extracted k z shows that the resonance condition 2k z L ≈ 2π n is satisfied for N = 2, 3, and 4, 084405-8 GIANT TUNNELING MAGNETORESISTANCE DRIVEN BY … PHYSICAL REVIEW B 114, 084405 (2026)
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TMR. Instead, the transport is governed by the relative transmission in the P and AP configurations. For N = 4, additional resonant channels emerge in the AP configuration as extra QW levels enter the Fermi window, enhancing T AP by several orders of magnitude and thereby reducing the ratio T P /T AP and suppressing the TMR (see details in Section S5 of the Supplemental Material [48]).
Notably, the transmission coefficient T P at N = 3 is lower than that at N = 2 and 4, with the maximum at N = 4, indicating a nonmonotonic behavior [Fig. S15(a) [48]]. Although the resonance condition is satisfied for N ⩾ 2, the transmission is not determined by the phase condition alone but is strongly influenced by the coupling between the QW states and the electrodes. This can be understood within a resonant tunneling
(3)
where L and R denote the coupling to the left and right electrodes, = L + R is the total level broadening, and E n is the energy of the quasibound state. The peak transmission is maximized for symmetric coupling, 4 L R /( L + R ) 2 , while the resonance width is set by . The evolution of L / R and with junction thickness is summarized in Fig. S16 [48]. For the variation with N [Figs. S16(a) and S16(c) [48]], the transmission follows a nonmonotonic trend that correlates directly with . While L / R remains of order unity, indicating relatively balanced coupling, the total broadening varies significantly. In particular, reaches a minimum at N = 3 (∼10 −4 eV), corresponding to an extremely narrow resonance that is highly sensitive to energy alignment and results in a reduced transmission (T P ≈ 1.5 × 10 −4 ). In contrast, for N = 4, increases by nearly two orders of magnitude (∼10 −3 eV), leading to a broader resonance and enhanced transmission (T P ≈ 8.5 × 10 −3 ), despite comparable coupling symmetry. This trend is consistent with the energy-dependent transmission spectra in Figs. 6 and S8 [48], confirming the direct correspondence between and the spectral broadening.
Figure 9(b) shows the dependence of the TMR on the right TiO 2 barrier thickness L. The TMR first increases with L, reaching a maximum at L = 4 (N = 2), and then decreases for thicker barriers (L = 5, 6, 7), with the overall trend primarily governed by the variation in T P . Phase analysis indicates that varying L does not alter the resonance condition [Fig. S14(b) [48]], which is primarily determined by the QW thickness. Instead, L modulates the coupling strength. For
transport is dominated by nonresonant tunneling, resulting in lower transmission than for L = 4 and the absence of k || -resolved hot spots. As shown in Figs. S16(b) and S16(d) [48], remains within the same order of magnitude across different L, whereas L / R varies strongly, ranging from highly asymmetric to nearly symmetric. The transmission is therefore maximized at L = 4, where the coupling is closest to symmetric ( L / R ≈ 0.82). For other L, increased asymmetry introduces a bottleneck that suppresses transmission even when QW states are present.
Overall, the total broadening and the coupling asymmetry L / R play distinct but complementary roles: determines the resonance width and its tolerance to energy detuning, while L / R controls the peak transmission. Their interplay governs the nonmonotonic dependence of the transmission on both N and L.
Taken together, the dependences on the QW thickness N and the barrier thickness L can be understood within a consistent resonant tunneling picture. The phase condition determines the existence and energy of the QW states, while N primarily controls the resonance width and L tunes the coupling symmetry. High transmission is achieved when (i) well-defined QW states are aligned with the Fermi level, (ii) the coupling to the electrodes is sufficiently strong, and (iii) the coupling remains nearly symmetric ( L ≈ R ). Deviations from these conditions suppress resonant transport: strong confinement (N = 1) prevents the formation of resonant QW states near the Fermi level, asymmetric coupling (N = 3, L = 3, 5, 6, 7) reduces the peak transmission, and additional resonant channels in the AP configuration (N = 4) enhance T AP and lower the TMR. Variations in L can also modify the dominant evanescent channel and induce spin-channel switching, reflecting the momentum- and spin-selective nature of the altermagnetic band structure. These results provide a consistent understanding of how quantum confinement, total broadening, and coupling symmetry jointly determine the transport characteristics.
Finally, our calculations show that TMR-II is consistently larger than TMR-I for all structures with N ⩾ 2 or L ⩾ 3, despite the shared resonant tunneling mechanism (Fig. 9). This difference originates from the lower transmission in the AP-II configuration. For example, at N = 2, T AP−II = 8.80 × 10 −7 is about three times smaller than T AP−I = 2.84 × 10 −6 , while both remain much smaller than T P . The difference can be traced to the distinct magnetic symmetries of the two antiparallel states. In the AP-I configuration, partial symmetry between the left electrode and the QW is preserved. In contrast, in AP-II the magnetic moment of the central RuO 2 quantum well is reversed, which more strongly perturbs the resonant condition by introducing a mismatch at both interfaces. Because the resonant hot spots are sublattice polarized (Fig. 8), this reversal effectively imposes a “double-filtering” condition, reducing the overlap between the sublattice-resolved states of the left electrode and the QW, as well as between the QW and the right electrode. Consequently, the resonant coupling is less efficient in AP-II than in AP-I. Although resonant tunneling can still occur in AP-II for some QW thicknesses (e.g., N = 4), its transmission remains systematically lower than that of AP-I, leading to a smaller T AP and hence a larger TMR-II throughout the studied range
In conclusion, we demonstrate a giant TMR effect in RuO 2 -based altermagnetic double-barrier junctions, reaching 75 094% at optimal geometry. The transport is governed by momentum-selective resonant tunneling through QW states in the altermagnetic spacer. Due to the intrinsic k-dependent spin splitting of altermagnetic RuO 2 , the resonance condition is satisfied at distinct k || points for different spin channels, giving rise to highly localized transmission hot spots near the Brillouin-zone corners. The strong contrast between the 084405-10 GIANT TUNNELING MAGNETORESISTANCE DRIVEN BY … PHYSICAL REVIEW B 114, 084405 (2026)
P and AP configurations originates from the sensitivity of these QW states to the Néel vector orientation. While the P configuration supports well-aligned QW resonances and nearunity transmission at selected k || , reversing the magnetic order disrupts the resonance condition, suppressing transmission across the Brillouin zone and leading to large TMR ratios. By analyzing the dependence on QW thickness and barrier thickness, we demonstrate that the transport is controlled by the interplay of quantum confinement, total broadening, and coupling symmetry. High transmission is achieved only when the QW states are aligned with the Fermi level, and the coupling to the electrodes remains both strong and symmetric. Deviations from these conditions reduce the transmission or enhance leakage in the AP states, thereby limiting the TMR. These results provide a consistent microscopic understanding of altermagnetism-driven resonant tunneling and demonstrate a route to achieving large TMR through momentum-selective transport.
[1] J. S. Moodera, L. R. Kinder, T. M. Wong, and R. Meservey,
Large magnetoresistance at room temperature in ferromagnetic thin film tunnel junctions, Phys. Rev. Lett. 74, 3273 (1995). [2] S. A. Wolf, D. D. Awschalom, R. A. Buhrman, J. M. Daughton,
S. von Molnár, M. L. Roukes, A. Y. Chtchelkanova, and D. M. Treger, Spintronics: A Spin-based electronics vision for the future, Science 294, 1488 (2001). [3] I. Žutić, J. Fabian, and S. Das Sarma, Spintronics: Fundamen-
tals and applications, Rev. Mod. Phys. 76, 323 (2004). [4] M. Julliere, Tunneling between ferromagnetic films, Phys. Lett.
A 54, 225 (1975). [5] E. Y. Tsymbal, O. N. Mryasov, and P. R. LeClair, Spin-
dependent tunnelling in magnetic tunnel junctions, J. Phys.: Condens. Matter 15, R109 (2003). [6] W. H. Butler, X.-G. Zhang, T. C. Schulthess, and J.
Fe|MgO|Fe sandwiches, Phys. Rev. B 63, 054416 (2001). [7] J. Mathon and A. Umerski, Theory of tunneling magnetoresis-
tance of an epitaxial Fe/MgO/Fe(001) junction, Phys. Rev. B 63, 220403(R) (2001). [8] V. Baltz, A. Manchon, M. Tsoi, T. Moriyama, T. Ono, and Y.
Tserkovnyak, Antiferromagnetic spintronics, Rev. Mod. Phys. 90, 015005 (2018). [9] A. Hirohata, K. Yamada, Y. Nakatani, I.-L. Prejbeanu, B. Diény,
P. Pirro, and B. Hillebrands, Review on spintronics: Principles and device applications, J. Magn. Magn. Mater. 509, 166711 (2020). [10] V. D. Nguyen, S. Rao, K. Wostyn, and S. Couet, Recent
progress in spin-orbit torque magnetic random-access memory, npj Spintronics 2, 48 (2024). [11] D.-F. Shao, S.-H. Zhang, M. Li, C.-B. Eom, and E. Y. Tsymbal,
Spin-neutral currents for spintronics, Nat. Commun. 12, 7061 (2021). [12] Y.-Y. Jiang, Z.-A. Wang, K. Samanta, S.-H. Zhang, R.-C. Xiao,
W. J. Lu, Y. P. Sun, E. Y. Tsymbal, and D.-F. Shao, Prediction of giant tunneling magnetoresistance in RuO 2 /TiO 2 /RuO 2 (110) antiferromagnetic tunnel junctions, Phys. Rev. B 108, 174439 (2023). [13] L. Zhang, G. Ni, J. He, and G. Gao, Above room temperature
multiferroic tunnel junction with the altermagnetic metal CrSb, Phys. Rev. B 112, 064401 (2025).
[14] K. Samanta, D.-F. Shao, and E. Y. Tsymbal, Spin filtering with
insulating altermagnets, Nano Lett. 25, 3150 (2025). [15] X. Yang, S. Fang, Z. Yang, P. Ho, J. Lu, and Y. S. Ang, Al-
termagnetic flatband-driven fermi surface geometry for giant tunneling magnetoresistance, Adv. Funct. Mater. 36, e31921 (2026). [16] Z. Guo, X. Wang, W. Wang, G. Zhang, X. Zhou, and Z. Cheng,
Spin-polarized antiferromagnets for spintronics, Adv. Mater. 37, 2505779 (2025). [17] L. Zhang, G. Ni, X. Wu, and G. Gao, All-altermagnetic tunnel
junction of RuO 2 /NiF 2 /RuO 2 , Chin. Phys. Lett. 43, 040711 (2026). [18] L. Šmejkal, J. Sinova, and T. Jungwirth, Beyond conventional
ferromagnetism and antiferromagnetism: A phase with nonrelativistic spin and crystal rotation symmetry, Phys. Rev. X 12, 031042 (2022). [19] C. Song, H. Bai, Z. Zhou, L. Han, H. Reichlova, J. H. Dil, J. Liu,
materials, Nat. Rev. Mater. 10, 473 (2025). [20] T. Berlijn et al., Itinerant Antiferromagnetism in RuO 2 , Phys.
Rev. Lett. 118, 077201 (2017). [21] R. González-Hernández, L. Šmejkal, K. Výborný, Y. Yahagi, J.
Sinova, T. Jungwirth, and J. Železný, Efficient electrical spin splitter based on nonrelativistic collinear antiferromagnetism, Phys. Rev. Lett. 126, 127701 (2021). [22] Y. Zhang et al., Electrical manipulation of spin splitting torque
in altermagnetic RuO 2 , Nat. Commun. 16, 5646 (2025). [23] K. Samanta, Y.-Y. Jiang, T. R. Paudel, D.-F. Shao, and E.
Y. Tsymbal, Tunneling magnetoresistance in magnetic tunnel junctions with a single ferromagnetic electrode, Phys. Rev. B 109, 174407 (2024). [24] B. Chi, L. Jiang, Y. Zhu, G. Yu, C. Wan, and X. Han,
Anisotropic spin filtering by an altermagnetic barrier in magnetic tunnel junctions, Phys. Rev. Appl. 23, 014013 (2025). [25] S. Noh et al., Tunneling magnetoresistance in altermagnetic
RuO 2 -Based magnetic tunnel junctions, Phys. Rev. Lett. 134, 246703 (2025). [26] L. L. Chang, L. Esaki, and R. Tsu, Resonant tunneling in
semiconductor double barriers, Appl. Phys. Lett. 24, 593 (1974).
ACKNOWLEDGMENTS
G.G. acknowledges support from the National Natural Science Foundation of China (Grant No. 12174127).
DATA AVAILABILITY
The data that support the findings of this article are not publicly available upon publication because it is not technically feasible and/or the cost of preparing, depositing, and hosting the data would be prohibitive within the terms of this research project. The data are available from the authors upon reasonable request.
084405-11 FEI ZOU, LONG ZHANG, AND GUOYING GAO PHYSICAL REVIEW B 114, 084405 (2026)
[27] B. Ricco and M. Ya. Azbel, Physics of resonant tunneling. The
one-dimensional double-barrier case, Phys. Rev. B 29, 1970 (1984). [28] J. A. Gil-Corrales, J. A. Vinasco, M. E. Mora-Ramos, A. L.
Morales, and C. A. Duque, Study of electronic and transport properties in double-barrier resonant tunneling systems, Nanomaterials 12, 1714 (2022). [29] N. Ghobadi, R. Daqiq, and S. A. Hosseini Moradi, Improved
tunnel magnetoresistance by double-barrier magnetic tunnel junctions with a layered antiferromagnet material, Results Phys. 70, 108171 (2025). [30] K. Kinoshita, R. Moriya, M. Onodera, Y. Zhang, K. Watanabe,
T. Taniguchi, T. Sasagawa, and T. Machida, Resonant tunneling in WSe 2 /h-BN/WSe 2 /h-BN/WSe 2 van der waals triple quantum well device, ACS Nano 19, 35592 (2025). [31] T. Nozaki, N. Tezuka, and K. Inomata, Quantum oscillation
of the tunneling conductance in fully epitaxial double barrier magnetic tunnel junctions, Phys. Rev. Lett. 96, 027208 (2006). [32] Y. Wang, Z.-Y. Lu, X.-G. Zhang, and X. F. Han, First-principles
theory of quantum well resonance in double barrier magnetic tunnel junctions, Phys. Rev. Lett. 97, 087210 (2006). [33] D. Herranz, F. G. Aliev, C. Tiusan, M. Hehn, V. K. Dugaev,
and J. Barnaś, Tunneling in double barrier junctions with “hot spots”, Phys. Rev. Lett. 105, 047207 (2010). [34] J. J. Paggel, T. Miller, and T.-C. Chiang, Quantum-well states
as fabry-pérot modes in a thin-film electron interferometer, Science 283, 1709 (1999). [35] D. Cimbri, J. Wang, A. Al-Khalidi, and E. Wasige, Resonant
tunneling diodes high-speed terahertz wireless communications - a review, IEEE Trans. Terahertz Sci. Technol. 12, 226 (2022). [36] J. Liu et al., Absence of altermagnetic spin splitting char-
acter in rutile oxide RuO 2 , Phys. Rev. Lett. 133, 176401 (2024). [37] Y.-X. Li, Y. Chen, L. Pan, S. Li, S.-B. Zhang, and H.-Z. Lu,
Exploration of altermagnetism in RuO 2 , Sci. China Phys. Mech. Astron. 69, 257001 (2026). [38] G. Kresse and J. Furthmüller, Efficient iterative schemes for
ab initio total-energy calculations using a plane-wave basis set, Phys. Rev. B 54, 11169 (1996). [39] J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gra-
dient approximation made simple, Phys. Rev. Lett. 77, 3865 (1996). [40] F. Aryasetiawan, K. Karlsson, O. Jepsen, and U. Schönberger,
Calculations of Hubbard U from first-principles, Phys. Rev. B 74, 125106 (2006).
[41] J. Taylor, H. Guo, and J. Wang, Ab initio modeling of quantum
transport properties of molecular electronic devices, Phys. Rev. B 63, 245407 (2001). [42] S. L. Dudarev, G. A. Botton, S. Y. Savrasov, C. J. Humphreys,
and A. P. Sutton, Electron-energy-loss spectra and the structural stability of nickel oxide: An LSDA+U study, Phys. Rev. B 57, 1505 (1998). [43] K. Momma and F. Izumi, VESTA 3 for three-dimensional visu-
alization of crystal, volumetric and morphology data, J. Appl. Crystallogr. 44, 1272 (2011). [44] J. D. Hunter, M ATPLOTLIB : A 2D graphics environment,
Comput. Sci. Eng. 9, 90 (2007). [45] R. Tsu and L. Esaki, Tunneling in a finite superlattice, Appl.
Phys. Lett. 22, 562 (1973). [46] R. Landauer, Spatial variation of currents and fields due to
localized scatterers in metallic conduction, IBM J. Res. Dev. 1, 223 (1957). [47] M. Büttiker, Y. Imry, R. Landauer, and S. Pinhas, Generalized
many-channel conductance formula with application to small rings, Phys. Rev. B 31, 6207 (1985). [48] See Supplemental Material at http://link.aps.org/supplemental/
10.1103/h13n-whcx for details on the complex band structure of TiO 2 (001), spin-resolved transmission, statistical analysis of transmission differences, comparison with single-barrier junctions, thickness-dependent transport, resonant tunneling conditions, coupling asymmetry and total broadening, and related analyses, which includes Ref. [11]. [49] J. Peralta-Ramos, A. M. Llois, I. Rungger, and S. Sanvito, I–
V Curves of Fe/MgO (001) Single- and double-barrier tunnel junctions, Phys. Rev. B 78, 024430 (2008). [50] A. N. Useinov, J. Kosel, N. Kh. Useinov, and L. R. Tagirov,
Resonant tunnel magnetoresistance in double-barrier planar magnetic tunnel junctions, Phys. Rev. B 84, 085424 (2011). [51] R. S. Liu et al., CoFe alloy as middle layer for strong spin
dependent quantum well resonant tunneling in MgO double barrier magnetic tunnel junctions, Phys. Rev. B 87, 024411 (2013). [52] X. Zheng, S. Yang, Z. Zheng, C.-S. Liu, W. Wang, and L.
Zhang, Double-barrier magnetic tunnel junctions with enhanced tunnel magnetoresistance, Appl. Phys. Lett. 125, 223503 (2024). [53] Z. Yang, X. Yang, J. Wang, Q. Li, R. Peng, C. H. Lee, L. K.
Ang, J. Lu, Y. S. Ang, and S. Fang, Unconventional thickness scaling of coherent tunnel magnetoresistance in altermagnets, Phys. Rev. B 112, 205202 (2025). [54] S. Datta, Electronic Transport in Mesoscopic Systems
(Cambridge University Press, Cambridge, UK, 1997).
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