Interfacial giant tunnel magnetoresistance and bulk-induced large perpendicular magnetic anisotropy in (111)-oriented junctions with fcc ferromagnetic alloys: A first-principles study

We study the tunnel magnetoresistance (TMR) effect and magnetocrystalline anisotropy in a series of magnetic tunnel junctions (MTJs) with fcc $L1_1$ ferromagnetic alloys and MgO barrier along the [111] direction. Considering the (111)-oriented MTJs with different $L1_1$ alloys, we calculate their TMR ratios and magnetocrystalline anisotropies on the basis of the first-principles calculations. The analysis shows that the MTJs with Co-based alloys (CoNi, CoPt, and CoPd) have high TMR ratios over 2000$\%$. These MTJs have energetically favored Co-O interfaces where interfacial antibonding between Co $d$ and O $p$ states is formed around the Fermi level. We find that the resonant tunneling of the antibonding states, called the interface resonant tunneling, is the origin of the obtained high TMR ratios. Our calculation of the magnetocrystalline anisotropy shows that many $L1_1$ alloys have large perpendicular magnetic anisotropy (PMA). In particular, CoPt has the largest value of anisotropy energy $K_{\rm u} \approx 10\,{\rm MJ/m^3}$. We further conduct a perturbation analysis of the PMA with respect to the spin-orbit interaction and reveal that the large PMA in CoPt and CoNi mainly originates from spin-conserving perturbation processes around the Fermi level.

We study the tunnel magnetoresistance (TMR) effect and magnetocrystalline anisotropy in a series of magnetic tunnel junctions (MTJs) with fcc L11 ferromagnetic alloys and MgO barrier along the [111] direction. Considering the (111)-oriented MTJs with different L11 alloys, we calculate their TMR ratios and magnetocrystalline anisotropies on the basis of the first-principles calculations. The analysis shows that the MTJs with Co-based alloys (CoNi, CoPt, and CoPd) have high TMR ratios over 2000%. These MTJs have energetically favored Co-O interfaces where interfacial antibonding between Co d and O p states is formed around the Fermi level. We find that the resonant tunneling of the antibonding states, called the interface resonant tunneling, is the origin of the obtained high TMR ratios. Such a mechanism is similar to that found in our recent work on the simple Co/MgO/Co(111) MTJ [Masuda et al., Phys. Rev. B 101, 144404 (2020)]. In contrast, different systems have different spin channels where the interface resonant tunneling occurs; for example, the tunneling mainly occurs in the majority-spin channel in the CoNi-based MTJ while it occurs in the minority-spin channel in the CoPt-based MTJ. This means that even though the mechanism is similar, different spin channels contribute dominantly to the high TMR ratio in different systems. Such a difference is attributed to the different exchange splittings in the particular Co d states contributing to the tunneling though the antibonding with O p states. Our calculation of the magnetocrystalline anisotropy shows that many L11 alloys have large perpendicular magnetic anisotropy (PMA). In particular, CoPt has the largest value of anisotropy energy Ku ≈ 10 MJ/m 3 . We further conduct a perturbation analysis of the PMA with respect to the spin-orbit interaction and reveal that the large PMA in CoPt and CoNi mainly originates from spin-conserving perturbation processes around the Fermi level.

I. INTRODUCTION
Magnetic tunnel junctions (MTJs), in which an insulating tunnel barrier is sandwiched between ferromagnetic electrodes, have attracted considerable attention not only from the viewpoint of fundamental physics but also from their potential applications to various devices. In particular, for the application to nonvolatile magnetic random access memories (MRAMs), they need to have perpendicular magnetic anisotropy (PMA) as well as high tunnel magnetoresistance (TMR) ratios. The PMA is more beneficial than in-plane magnetic anisotropy for achieving high thermal stability when device sizes are scaled down in ultrahigh-density MRAMs [1]. The PMA is also preferred for the different types of magnetization switching in MRAMs; the critical current for the switching in spin-transfer-torque MRAMs (STT-MRAMs) [1] can be reduced and the write error rate in voltagecontrolled MRAMs [2] can be decreased.
To obtain both large PMA and high TMR ratios in MTJs, two types of approaches have been employed. One approach is to utilize ferromagnets with strong bulk magnetocrystalline anisotropy as electrodes of MTJs.
The ordered alloys, L1 0 FePt [3,4], D0 22 Mn 3 Ga(Ge) [5][6][7][8], and L1 0 MnGa [6], are ferromagnets with such strong magnetic anisotropy along the [001] direction, using which one can achieve large PMA in the (001)oriented MTJs. However, unfortunately, these MTJs did not show high TMR ratios even if one of the ferromagnetic electrodes was replaced by CoFe(B) or Fe [9][10][11][12][13]. The other approach is to combine the interface-induced PMA and the established technology for high TMR ratios in Fe(Co)/MgO/Fe(Co)(001) MTJs [14,15]. Actually, experiments on CoFeB/MgO/CoFeB MTJs [16] have demonstrated relatively large interfacial PMA (∼ 1.3 mJ/m 2 ) and high TMR ratios (> 120% at room temperature). However, such interfacial PMA is sensitive to the interfacial oxidation condition [17,18] and the thickness of the ferromagnetic layers [16]. Thus, large PMA due to bulk magnetocrystalline anisotropy is attractive for storage layers of MRAMs. It should also be remarked that large bulk PMA is beneficial for the pinned layers in the synthetic antiferromagnetic structures in MRAM cells [19]. In this study, we theoretically demonstrate such large bulk-induced PMA and high TMR ratios in unconventional MTJs and discuss their physical under-  Fig. 1(c)]. It is natural to consider such (111)-oriented MTJs for fcc materials, since the (111) plane is the closepacked plane of the fcc lattice and has the lowest surface energy [20]. However, most previous studies have addressed (001)-oriented MTJs with bcc materials because of the initial success in Fe/MgO/Fe(001) [14,15,21,22]. Recently, three of the present authors theoretically investigated the TMR effect in two simple (111)-oriented MTJs, Co/MgO/Co(111) and Ni/MgO/Ni(111), and obtained a high TMR ratio (∼ 2100%) in the Co-based MTJ [23]. This result motivates us to study other (111)oriented MTJs for obtaining high TMR ratios.
Another important merit of (111)-oriented MTJs is that several magnetic superlattices and L1 1 alloys can be used as ferromagnetic electrodes for large PMA. For example, Seki et al. [24] recently observed large PMA with uniaxial magnetic anisotropic energy (K u ) of ∼ 0.5 MJ/m 3 in epitaxial Co/Ni(111) multilayers, consistent with previous experiments [25]. In another experimental study [26], Sato et al. grew L1 1 CoPt films on an MgO(111) substrate and showed large PMA (K u ∼ 3.7 MJ/m 3 ). Furthermore, Yakushiji et al. [27] obtained PMA (K u ∼ 0.5 MJ/m 3 ) in Co/Pt(111) and Co/Pd(111) multilayers that have similar structures as L1 1 films. All these studies indicate the potential of (111)-oriented MTJs with L1 1 alloys for large PMA; however, such MTJs have not been investigated both theoretically and experimentally in previous studies.
In this work, we present a systematic theoretical study of the TMR effect and magnetocrystalline anisotropy in (111)-oriented MTJs with L1 1 alloys. We consider various possible MTJs consisting of L1 1 alloys and the MgO tunnel barrier and calculate their TMR ratios and magnetocrystalline anisotropies by means of the firstprinciples calculations. It is shown that the MTJs with Co-based alloys (CoNi, CoPt, and CoPd) have high TMR ratios over 2000%. The detailed analysis of the electronic structures and conductances clarifies that all the obtained high TMR ratios originate from the resonant tunneling of the interfacial d-p antibonding states called the interface resonant tunneling [23], which is clearly different from the conventional coherent tunneling mechanism of the high TMR ratio in Fe/MgO/Fe(001) [21,22]. The interface resonant tunneling mainly occurs in the majority-and minority-spin channels in the CoNi-and CoPt-based MTJs, respectively. Namely, the high TMR ratios in different systems come from the tunneling in different spin channels. In the calculation of the magnetocrystalline anisotropy, we obtain large PMA in many L1 1 alloys. Among them, CoPt has the largest K u of ≈ 10 MJ/m 3 . A second-order perturbation analysis of the PMA with respect to the spin-orbit interaction clarifies that the large PMA in CoPt and CoNi originates from the spin-conserving perturbation processes around the Fermi level.

A. Structure optimization
Since the L1 1 phase can exist only in multilayer films owing to its metastable nature, it is hard to obtain the experimental lattice constants of the L1 1 alloys. This forces us to conduct the structure optimization to theoretically determine the optimal lattice constants. In the present study, we considered eight different L1 1 alloys (Table I) and prepared their unit cells with the z axis along the [111] direction of the original fcc cell [ Fig. 1(a)]. We optimized the value of a fcc in each L1 1 alloy by means of the density-functional theory (DFT) implemented in the Vienna ab initio simulation program (VASP) [28]. Here, we adopted the generalized gradient approximation (GGA) [29] for the exchange-correlation energy and used the projected augmented wave (PAW) pseudopotential [30,31] to treat the effect of core electrons properly. A cutoff energy of 337 eV was employed and the Brillouin-zone integration was performed with 23 × 13 × 5 k points. The convergence criteria for energy and force were set to 10 −5 eV and 10 −4 eV/Å, respectively. The obtained values of a fcc are shown in Table I.
By combining the unit cell of each L1 1 alloy [ Fig. 1

(a)]
and that of the (111)-oriented MgO [ Fig. 1(b)], we built the supercell of the corresponding (111)-oriented MTJ [ Fig. 1(c)]. The x-and y-axis lengths of the supercell were fixed to a fcc / √ 2 and √ 3 a fcc / √ 2 in each supercell where the optimized a fcc of each alloy was used. The atomic positions along the z direction in the supercells were relaxed using the DFT with the aid of the VASP code. In these calculations for supercells, 23 × 13 × 1 k points were used, and the other calculation conditions were the same as the structure optimizations of the L1 1 alloys. More technical details of structure optimizations of supercells are given in our previous work [32]. In each supercell, we compared energies for all interfacial atomic configurations and determined the energetically favored configuration. For example, in CoNi/MgO/CoNi(111), there are four atomic configurations at the interface: Co-O, Ni-O, Co-Mg, and Ni-Mg. By comparing formation energies for these cases, we found that the Co-O interface has the lowest energy. In Table I, each L1 1 -ordered alloy is denoted as XY (X = Co and Y = Ni for CoNi). We confirmed that X-O interface was energetically favored in each supercell. Such supercells with energetically favored interfaces were used in the transport calculation explained below.

B. Calculation method of TMR ratios
The TMR ratio of each (111)-oriented MTJ was calculated using the DFT and Landauer formula with the help of the PWCOND code [33] in the QUANTUM ESPRESSO package [34]. We first constructed the quantum open system by attaching the left and right semi-infinite electrodes of each L1 1 alloy to the supercell. The application of the DFT to the quantum open system provided the self-consistent potential, which was used to derive the scattering equation mentioned below. In the DFT calculation, the exchange-correlation energy was treated within the GGA, and the ultrasoft pseudopotentials were used. The cutoff energies were set to 45 and 450 Ry for the wave function and the charge density, respectively. The number of k points was taken to be 23×13×1 and the convergence criterion was set to 10 −6 Ry. Since our system has translational symmetry in the xy-plane, the scattering states can be classified by an in-plane wave vector k = (k x , k y ). For each k and spin index, we solved the scattering equation derived under the condition that the wave function and its derivative of the supercell are connected to those of the electrodes [33,35]. These calculations gave the kresolved transmittances from which the k -resolved conductances were obtained through the Landauer formula: G P,↑ (k ), G P,↓ (k ), G AP,↑ (k ), and G AP,↓ (k ). Here, P (AP) refers to the parallel (antiparallel) magnetization state of the electrodes and ↑ (↓) indicates the majorityspin (minority-spin) channel. We averaged each conductance over k as, e.g., G P,↑ = k G P,↑ (k )/N , where N is the sampling number of k points. In the present analysis, N was set to 2500 ensuring good convergence for the conductance. For each MTJ, we calculated the TMR ratio following its optimistic definition: where G P(AP) = G P(AP),↑ + G P(AP),↓ . In these transport calculations, the spin-orbit interaction (SOI) was neglected since the SOI usually provides only a small contribution to the TMR effect.

C. Estimation of magnetocrystalline anisotropy
We calculated the uniaxial magnetic anisotropy energy K u of each L1 1 alloy on the basis of the DFT calculation including the spin-orbit interaction. We adopted the expression by the well-known force theorem [36,37]: where E (E ⊥ ) is the sum of the eigenvalues of the unit cell [ Fig. 1(a)] with the magnetization along the x (z) direction, and V is the volume of the unit cell. Here, we used the optimized lattice constant mentioned above for each L1 1 alloy. From the definition in Eq. (2), a positive (negative) K u indicates a tendency toward PMA (inplane magnetic anisotropy). The VASP code was used for the DFT calculation including the spin-orbit interaction, where we adopted the GGA for the exchange-correlation energy, the PAW pseudopotential, and a cutoff energy of 337 eV. Since the energy scale of K u is much smaller than that of the total energy of system, the large number of k points is required to estimate K u accurately. We thus used 51 × 27 × 11 k points after confirming the convergence of K u with respect to the number of k points. In addition to these calculations, we also conducted a second-order perturbation analysis of the magnetocrystalline anisotropy [38] to understand the origin of the PMA. By treating the spin-orbit interaction H SO as a perturbation term, the second-order perturbation energy is given by where (0) knσ is the energy of an unperturbed state |knσ with wave vector k, band index n, and spin σ. The index "occ" ("unocc") on the summation in Eq. (3) means that the sum is over occupied (unoccupied) states of all atoms in the unit cell. In the spin-orbit interaction H SO , ξ i is its coupling constant at an atomic site i, and L i (S i ) is the single-electron angular (spin) momentum operator. Wave functions and eigenenergies obtained in our DFT calculations were used as unperturbed states and energies in Eq. (3). The magnetocrystalline anisotropy  energy within the second-order perturbation was calculated as E ⊥ ) is the energy calculated by Eq. (3) for the magnetization along the x (z) direction of the unit cell. We can decompose E MCA into four types of terms coming from different perturbation processes at each atomic site: Here, E i MCA is the magnetocrystalline anisotropy energy at each atomic site i. The term ∆E i ↑⇒↑ (∆E i ↓⇒↓ ) is the contribution from spin-conserving perturbation processes in the majority-spin (minority-spin) channel. The last two terms are the contributions from spin-flip perturbation processes: ∆E i ↑⇒↓ (∆E i ↓⇒↑ ) comes from electron transition processes from majority-to minority-spin (minority-to majority-spin) channel. This decomposition provides us with information on the origin of the PMA.

III. RESULTS AND DISCUSSION
A. High TMR ratios and their possible origin Table I shows the obtained TMR ratios in the (111)oriented MTJs. The MTJs, including the Co-based alloys, have high TMR ratios over 2000%. In contrast, the Fe-and Ni-based alloys give much lower TMR ratios (< 1000%). To understand the origin of the high TMR ratios, the bulk band structures of the electrodes and the barrier were first analyzed because the high TMR ratio in the well-known Fe/MgO/Fe(001) MTJ [14,15] has been explained by the bulk band structures of Fe and MgO on the basis of the coherent tunneling mechanism [21,22]. If a similar mechanism holds for the present MTJs, the bulk band structures along the Λ line in the Brillouin zone corresponding to the [111] direction should explain the high TMR ratios. Figure 2(a) shows the imaginary part of k z , referred to as the complex band, of the (111)-oriented MgO [ Fig.  1(b)] as a function of k x . The smallest value of Im(k z ) is located at (k x , k y ) = (0, 0) = Γ. This means that the Λ states, i.e., the wave function in the Λ line (0, 0, k z ), has the slowest decay and can provide the dominant contribution to the electron transport. In Fig. 2(b), we show the complex and real bands at the Λ line. We find that the smallest Im(k z ) at E F comes from the Λ 1 state consisting of s and p z orbitals. Therefore, the Λ 1 state decays most slowly in the barrier and the selective transport of this state can occur.
To study whether the L1 1 alloys have half-metallicity in the Λ 1 state, bulk band structures of CoNi and CoPt, which provide the two highest TMR ratios, were analyzed. As shown in Figs. 3(a) and 3(b), both majorityand minority-spin bands from the d 3z 2 −r 2 state (belonging to the Λ 1 state) cross the Fermi level in both alloys; namely, these alloys do not have half-metallicity in the Λ 1 state, which is in sharp contrast to the half-metallicity in the ∆ 1 state of Fe in Fe/MgO/Fe(001) [21,22]. All these results indicate that we cannot explain the present high TMR ratios from the bulk band structures based on the coherent tunneling mechanism as in Fe/MgO/Fe(001).
Another possible way to understand the present high TMR ratios is to focus on interfacial effects. In our previous study [23], we clarified that the interface resonant tunneling provides a high TMR ratio in a simple (111)-oriented MTJ, Co/MgO/Co(111). To examine a similar possibility, we calculated the local density of states (LDOSs) at interfacial Co and O atoms of CoNi/MgO/CoNi(111) shown in Figs. 4(a) and 4(b). We can find a clear similarity in the energy dependence of the LDOS between the Co d zx (d yz ) and O p x (p y ) states in the majority-spin channel due to the formation of the interfacial antibonding between these states. At the Fermi level, such O p x and p y states have large LDOSs and can provide interfacial resonant tunneling between the left and right interfaces. Figure 4(c) shows the k -resolved conductance G P,↑ (k ), which contributes dominantly to the high TMR ratio. The conductance has only a small value at k = Γ, and their large values distribute around the Γ point, which is a characteristic in the conductance originating from interfacial effects. We also analyzed the k -resolved LDOSs of the interfacial O p x and p y majority-spin states as shown in Figs. 4(d) and 4(e). The distribution of k points with large LDOS is similar to that with large conductance in Fig. 4(c), indicating that the interfacial O p x and p y states play the dominant role in the high TMR ratio through the interfacial resonant tunneling. We also studied the interfacial LDOSs and k -resolved conductance of CoPt/MgO/CoPt(111) with the second highest TMR ratio [Figs. 5(a)-5(e)]. In this case, the interfacial antibonding related to the high TMR ratio is formed in the minority-spin state, not the majority-spin state. As shown in Fig. 5(b), O p x and p y minority-spin states have large LDOSs at the Fermi level owing to the antibonding with Co d zx and d yz states. These interfacial states provide a high TMR ratio through the interface resonant tunneling. Actually, the conductance with the largest contribution to the high TMR ratio is that in the minority-spin state G P,↓ (k ) [Fig. 5(c)], whose k dependence can be reproduced by that of the LDOSs in the interfacial O p x and p y minority-spin states [Figs.

5(d) and 5(e)].
Such a difference in the spin channel contributing to the high TMR ratio between the CoNi-and CoPt-based MTJs comes from different exchange splittings in the interfacial Co d zx and d yz states. By comparing Figs. 4(a) and 5(a), we can easily see that the exchange splitting in the d zx and d yz states in the CoNi-based MTJ is clearly smaller than that in the CoPt-based MTJ. In fact, the magnetic moment projected onto each d orbital in the interfacial Co atom was estimated in both MTJs. We obtained 0.96 µ B in the d zx and d yz orbitals for the CoNibased MTJ and 1.10 µ B for the CoPt-based MTJ. In the other d orbitals, the difference in the projected magnetic moment was found to be quite small. Therefore, in the CoNi-based MTJ, the d zx and d yz majority-spin states have finite majority-spin LDOSs at the Fermi level, leading to the large O p x and p y majority-spin LDOSs through the interfacial antibonding [ Fig. 4(b)]. In contrast, the CoPt-based MTJ has negligibly small d zx and d yz majority-spin LDOSs at the Fermi level owing to the larger exchange splitting [ Fig. 5(a)], which provides the dominance of the minority-spin LDOSs in the interfacial O p states [ Fig. 5(b)].
Although not shown here, we confirmed that the high TMR ratio in the CoPd-based MTJ (2172%) can also be explained by the interface resonant tunneling of the interfacial O p x and p y minority-spin states. Our present study revealed that not only the Co/MgO/Co(111) MTJ [23] but also several (111)-oriented MTJs with Co-based L1 1 alloys exhibit high TMR ratios due to the interface resonant tunneling. This fact allows us to expect that such a mechanism may be universal for high TMR ratios in (111)-oriented MTJs.

B. Large PMA and its correlation with perturbation processes
We listed the obtained values of K u in Table I. All the alloys except NiPt have positive K u indicating a tendency toward PMA. Among them, CoPt possesses the largest value close to 10 MJ/m 3 . In this section, we discuss the origin of K u in CoNi and CoPt as representatives based on the second-order perturbation analysis of the magnetocrystalline anisotropy. Here, we used ξ Co = 69.4 meV, ξ Ni = 87.2 meV, and ξ Pt = 523.8 meV as the coupling constants of the spin-orbit interaction ξ i . We also set the Wigner-Seitz radius of each atom to r Co = 1.302Å, r Ni = 1.286Å, and r Pt = 1.455Å for obtaining projected wave functions used in the calculation. All these values are those in the pseudopotential files in the VASP code. Figure 6(a) shows the results of the second-order perturbation analysis of K u in CoNi. We see that Ni has a much larger positive E i MCA than Co and contributes dominantly to the PMA. In the Co atom, ∆E i ↓⇒↓ and ∆E i ↑⇒↓ have large values but with opposite signs, leading to a small ∆E i MCA . In contrast, in the Ni atom, the spinconserving term ∆E i ↓⇒↓ in the minority-spin channel is positive and much larger than the other terms, giving a large positive E i MCA . This is consistent with LDOSs of Ni shown in Fig. 6(c), where the minority-spin state has large values around E F , while the majority-spin state has only small values. It is known that the expression of ∆E i ↓⇒↓ within the second-order perturbation theory is analytically given by where L i α (α = x, z) is the local angular momentum operator at an atomic site i, and |o σ (|u σ ) is a local occupied (unoccupied) state with spin σ and energy oσ ( uσ ) [39]. This expression indicates that the matrix element of L i z gives a positive contribution to ∆E i ↓⇒↓ while that of L i x gives a negative contribution. Actually, we confirmed that d x 2 −y 2 , ↓ |L i z |d xy , ↓ and d xy , ↓ |L i z |d x 2 −y 2 , ↓ have large values in our perturbation calculation, which is consistent with large minority-spin LDOSs in the d x 2 −y 2 and d xy states shown in Fig. 6(c). Figure 7 presents the results for CoPt. From the perturbation analysis [ Fig. 7(a)], we find that in all spintransition processes Pt has much larger anisotropy energy than Co, meaning that the PMA in CoPt mainly comes from the anisotropy in Pt. In the Pt atom, a large positive anisotropy ∆E i ↑⇒↓ is found in the ↑⇒↓ spin-flip process, but this is canceled out by ∆E i ↓⇒↑ in the other spin-flip process. Thus, the dominant contribution to the large positive anisotropy in Pt is given by ∆E i ↑⇒↑ in the ↑⇒↑ spin-conserving process. Similar to Eq. (7), the analytical expression of ∆E i ↑⇒↑ is given as follows [39]: from which the matrix element of L z is found to give a positive contribution to ∆E i ↑⇒↑ . As clearly seen in Fig.  7(c), the d x 2 −y 2 and d xy states have much larger LDOSs than the other d states around E F in the majority-spin channel. Such LDOSs yield large values of d x 2 −y 2 , ↑ |L i z |d xy , ↑ and d xy , ↑ |L i z |d x 2 −y 2 , ↑ , leading to a large positive ∆E i ↑⇒↑ . The importance of the ↑⇒↑ term is also found in Pt of L1 0 FePt with large PMA [44] and is a feature in ordered alloys with Pt atoms.
Conventionally, PMA has been explained with the help of the Bruno theory [45], which states that PMA mainly comes from the anisotropy of the orbital magnetic moment, namely, the spin-conserving term ∆E i ↓⇒↓ in Eq. (6). This theory is applicable to typical ferromagnets with large exchange splittings, since such ferromagnets have almost occupied majority-spin states, and only minority-spin states are located close to the Fermi level. In contrast, many recent studies on PMA have focused on its unconventional mechanism due to the spin-flip terms ∆E i ↑⇒↓ and ∆E i ↓⇒↑ in Eq. (6). These terms can be interpreted in terms of the quadrupole moment and provide novel physical insight into PMA. Up to now, it has been shown that the spin-flip terms play a significant role for PMA in various systems including ferromagnet/MgO interfaces and ferromagnetic multilayers [24,44,[46][47][48][49][50]. In the present study, we obtained large values of spin-flip terms in L1 1 CoNi and CoPt. However, as mentioned above, ∆E i ↑⇒↓ is canceled by ∆E i ↓⇒↓ in CoNi and two types of spin-flip terms are canceled with each other in CoPt. Therefore, the unconventional physical picture is not suitable to explain PMA in the present CoNi and CoPt. A similar cancellation of the spin-flip terms has also been reported recently in an FeIr/MgO system [51].

IV. SUMMARY
We theoretically investigated the TMR effect and magnetocrystalline anisotropy in (111)-oriented MTJs with L1 1 alloys based on the first-principles calculations. Our transport calculation showed that the MTJs with Cobased alloys (CoNi, CoPt, and CoPd) have high TMR ratios over 2000%, which are attributed to the interface resonant tunneling. We also found that the tunneling mainly occurs in the majority-spin channel in the CoNibased MTJ while it occurs in the minority-spin channel in the CoPt-based MTJ, meaning that different spin channels provide dominant contributions to the high TMR ratios in different systems. This can be understood from the different exchange splittings in the d zx and d yz states of interfacial Co atoms contributing to the TMR effect through antibonding with O p x and p y states. The analysis of the magnetocrystalline anisotropy revealed that many L1 1 alloys have large PMA and CoPt has the largest value of K u ≈ 10 MJ/m 3 . Through a detailed second-order perturbation calculation, we clarified that the large PMA in CoPt and CoNi is attributed to the spin-conserving perturbation processes around the Fermi level. All these findings would be useful for understanding experimental results in (111)-oriented MTJs, which will be obtained in future studies.