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Over the past decades, there has been a significant development in spin-transfer-torque magneto-resistive random-access memory (STT-MRAM). The development was brought by CoFeB/MgO-based magnetic tunnel junctions (MTJs) with interfacial perpendicular magnetic anisotropy (IPMA) [1]. Because thermal stability factor (&lt;i&gt;Δ&lt;/i&gt;) is proportional to effective PMA constant and the volume of the free layer in a coherent magnetic rotation model [2] and proportional to square root of effective PMA constant and the diameter of the free layer in a domain propagation model [3], &lt;i&gt;Δ&lt;/i&gt; decreases with the decrease of MTJ diameter. To achieve great enough &lt;i&gt;Δ &lt;/i&gt;value in a smaller MTJ, increasing the number of CoFeB/MgO interfaces has been proposed to increase PMA [4-6]. In double interface MTJ with MgO/CoFeB/insertion layer/CoFeB/MgO free layer, thin non-magnetic layer such as Ta, W or Mo was used as the insertion layer to obtain higher PMA and tunnel magnetoresistance (TMR) ratio [4,7].&lt;br/&gt;When the insertion layer is too thick, the two CoFeB layers in the free layer behave magnetically independent, resulting in no benefits on &lt;i&gt;Δ&lt;/i&gt; despite the double interface because effective free-layer volume does not increase. To obtain a benefit of double CoFeB / MgO interfaces on &lt;i&gt;Δ&lt;/i&gt;, a great enough magnetic coupling between the two CoFeB layers is required. It is important to clarify the effect of magnetic coupling (the energy constant of unit area:&lt;i&gt; J&lt;/i&gt;&lt;sub&gt;cpl&lt;/sub&gt;) on &lt;i&gt;Δ&lt;/i&gt;. However, it is not clear how the magnitude of &lt;i&gt;J&lt;/i&gt;&lt;sub&gt;cpl&lt;/sub&gt; affects the increase in &lt;i&gt;Δ&lt;/i&gt;, although we achieved a strong &lt;i&gt;J&lt;/i&gt;&lt;sub&gt;cpl&lt;/sub&gt; in the double interface MTJs [8]. In this study, we propose a method to calculate critical &lt;i&gt;J&lt;/i&gt;&lt;sub&gt;cpl&lt;/sub&gt; value to maximize &lt;i&gt;Δ&lt;/i&gt; for free layers of MgO/CoFeB/insertion layer/CoFeB/MgO in the double interface MTJs with various MTJ diameters.&lt;br/&gt;We introduced magnetic coupling energy between two magnetic layers in the free layer based on magnetic domain propagation model (Model A) and magnetization coherent rotation model (Model B) as shown in Fig.1. When &lt;i&gt;d&lt;/i&gt; was larger than the critical diameter &lt;i&gt;d&lt;/i&gt;&lt;sub&gt;c&lt;/sub&gt; (= 16/π [&lt;i&gt;A&lt;/i&gt;&lt;sub&gt;s&lt;/sub&gt; /&lt;i&gt;K&lt;/i&gt;&lt;sub&gt;eff&lt;/sub&gt; ]&lt;sup&gt;1/2&lt;/sup&gt; ), Model A was applied, in which a blue-colored domain with downward magnetization nucleates from an edge and propagates in each FL1 and FL2. The domain nucleation and propagation behavior from edge region assumed in this model is consistent with the results of micromagnetic simulations of the MTJs with CoFeB / MgO interfaces [9,10]. The nucleated domain area &lt;i&gt;Ω&lt;/i&gt;&lt;sub&gt;1&lt;/sub&gt; in FL1 and &lt;i&gt;Ω&lt;/i&gt;&lt;sub&gt;2&lt;/sub&gt; in FL2 were decided by angles φ&lt;sub&gt;1&lt;/sub&gt; and φ&lt;sub&gt;2&lt;/sub&gt;. A magnetic energy &lt;i&gt;E &lt;/i&gt;(φ&lt;sub&gt;1&lt;/sub&gt;, φ&lt;sub&gt;2&lt;/sub&gt;) in Model A was calculated as follows.&lt;br/&gt;&lt;i&gt;E &lt;/i&gt;(φ&lt;sub&gt;1&lt;/sub&gt;, φ&lt;sub&gt;2&lt;/sub&gt;) = &lt;i&gt;Λ&lt;/i&gt;(φ&lt;sub&gt;1&lt;/sub&gt;)&lt;i&gt; t&lt;/i&gt;&lt;sub&gt;1&lt;/sub&gt; σ&lt;sub&gt;w1&lt;/sub&gt; + &lt;i&gt;Λ&lt;/i&gt;(φ&lt;sub&gt;2&lt;/sub&gt;) &lt;i&gt;t&lt;/i&gt;&lt;sub&gt;2&lt;/sub&gt; &lt;i&gt;σ&lt;/i&gt;&lt;sub&gt;w2&lt;/sub&gt; + 2&lt;i&gt;J&lt;/i&gt;&lt;sub&gt;cpl&lt;/sub&gt; |&lt;i&gt;Ω&lt;/i&gt;(φ&lt;sub&gt;1&lt;/sub&gt;) - &lt;i&gt;Ω&lt;/i&gt;(φ&lt;sub&gt;2&lt;/sub&gt;)|---(1)&lt;br/&gt;&lt;i&gt;σ&lt;/i&gt;&lt;sub&gt;w1&lt;/sub&gt; = 4(&lt;i&gt;A&lt;/i&gt;&lt;sub&gt;s &lt;/sub&gt;&lt;i&gt;K&lt;/i&gt;&lt;sub&gt;eff1&lt;/sub&gt;)&lt;sup&gt;1/2&lt;/sup&gt;, &lt;i&gt;σ&lt;/i&gt;&lt;sub&gt;w2&lt;/sub&gt; = 4(&lt;i&gt;A&lt;/i&gt;&lt;sub&gt;s &lt;/sub&gt;&lt;i&gt;K&lt;/i&gt;&lt;sub&gt;eff2&lt;/sub&gt;)&lt;sup&gt;1/2 &lt;/sup&gt;----(2)&lt;br/&gt;&lt;i&gt;Λ&lt;/i&gt;(φ&lt;sub&gt;i&lt;/sub&gt;) = &lt;i&gt;d&lt;/i&gt; (π/2–φ&lt;sub&gt;i&lt;/sub&gt;) tan φ&lt;sub&gt;i&lt;/sub&gt;, (i = 1, 2)---(3)&lt;br/&gt;&lt;i&gt;Ω&lt;/i&gt;(φ&lt;sub&gt;i&lt;/sub&gt;) = &lt;i&gt;d&lt;/i&gt;&lt;sup&gt;2&lt;/sup&gt; φ&lt;sub&gt;i&lt;/sub&gt;/4 + &lt;i&gt;d&lt;/i&gt;&lt;sup&gt;2&lt;/sup&gt;/4 { (π/2 – φ&lt;sub&gt;i&lt;/sub&gt;）tan&lt;sup&gt;2&lt;/sup&gt;φ&lt;sub&gt;i &lt;/sub&gt;– tanφ&lt;sub&gt;i&lt;/sub&gt; }, (i = 1, 2) ---(4)&lt;br/&gt;The 1&lt;sup&gt;st&lt;/sup&gt; and 2&lt;sup&gt;nd&lt;/sup&gt; terms in the equation (1) express magnetic domain wall energies of FL1 and FL2, respectively. The third term expresses magnetic coupling energy between FL1 and FL2. &lt;i&gt;Λ&lt;/i&gt; is wall length and &lt;i&gt;σ&lt;/i&gt;&lt;sub&gt;w&lt;/sub&gt; is wall energy per unit area. &lt;i&gt;A&lt;/i&gt;&lt;sub&gt;s&lt;/sub&gt; is stiffness constant of the free layer.&lt;br/&gt;When &lt;i&gt;d&lt;/i&gt; is smaller than the critical diameter &lt;i&gt;d&lt;/i&gt;&lt;sub&gt;c&lt;/sub&gt;, coherent rotation model (Model B) was applied, in which &lt;i&gt;E &lt;/i&gt;(φ&lt;sub&gt;1&lt;/sub&gt;, φ&lt;sub&gt;2&lt;/sub&gt;) was calculated as follows. The 1&lt;sup&gt;st&lt;/sup&gt; and 2&lt;sup&gt;nd&lt;/sup&gt; terms in the equation (5) express PMA energies of FL1 and FL2. The third term expresses magnetic coupling energy between FL1 and FL2.&lt;br/&gt;&lt;i&gt;E &lt;/i&gt;(φ&lt;sub&gt;1&lt;/sub&gt;, φ&lt;sub&gt;2&lt;/sub&gt;) =π&lt;i&gt;d&lt;/i&gt;&lt;sup&gt;2&lt;/sup&gt;/4 {&lt;i&gt; K&lt;/i&gt;&lt;sub&gt;eff1&lt;/sub&gt;&lt;i&gt;t&lt;/i&gt;&lt;sub&gt;1 &lt;/sub&gt;(1–cos&lt;sup&gt;2&lt;/sup&gt;φ&lt;sub&gt;1&lt;/sub&gt;) +&lt;i&gt; K&lt;/i&gt;&lt;sub&gt;eff2&lt;/sub&gt;&lt;i&gt;t&lt;/i&gt;&lt;sub&gt;2 &lt;/sub&gt;(1–cos&lt;sup&gt;2&lt;/sup&gt;φ&lt;sub&gt;2&lt;/sub&gt;)+ &lt;i&gt;J&lt;/i&gt;&lt;sub&gt;cpl&lt;/sub&gt; (1–cos(φ&lt;sub&gt;1&lt;/sub&gt;–φ&lt;sub&gt;2&lt;/sub&gt;）} ---(5)&lt;br/&gt;Fig. 2 shows &lt;i&gt;J&lt;/i&gt;&lt;sub&gt;cpl&lt;/sub&gt; dependence on &lt;i&gt;Δ&lt;/i&gt; for the MTJs with various diameters. We used &lt;i&gt;K&lt;/i&gt;&lt;sub&gt;eff1&lt;/sub&gt;=&lt;i&gt;K&lt;/i&gt;&lt;sub&gt;eff2&lt;/sub&gt; = &lt;i&gt;K&lt;/i&gt;&lt;sub&gt;eff_film&lt;/sub&gt; +(1-&lt;i&gt;N&lt;/i&gt;&lt;sub&gt;z-x&lt;/sub&gt;) &lt;i&gt;M&lt;/i&gt;&lt;sub&gt;s&lt;/sub&gt;&lt;sup&gt;2&lt;/sup&gt;/(2&lt;i&gt;μ&lt;/i&gt;&lt;sub&gt;0&lt;/sub&gt;). &lt;i&gt;K&lt;/i&gt;&lt;sub&gt;eff_film&lt;/sub&gt; = 2.25x10&lt;sup&gt;5&lt;/sup&gt; J/m&lt;sup&gt;3&lt;/sup&gt;, &lt;i&gt;t&lt;/i&gt;&lt;sub&gt;1&lt;/sub&gt;=&lt;i&gt;t&lt;/i&gt;&lt;sub&gt;2&lt;/sub&gt;=1.2nm,&lt;i&gt; M&lt;/i&gt;&lt;sub&gt;s &lt;/sub&gt;= 0.97 T and &lt;i&gt;A&lt;/i&gt;&lt;sub&gt;s &lt;/sub&gt;= 5.4 pJ/m, which were experimental values in the double interface MTJ [8]. The calculated critical diameter &lt;i&gt;d&lt;/i&gt;&lt;sub&gt;c&lt;/sub&gt; was 23 nm.&lt;br/&gt;With increasing &lt;i&gt;J&lt;/i&gt;&lt;sub&gt;cpl&lt;/sub&gt;, &lt;i&gt;Δ&lt;/i&gt; increases and saturates over a critical &lt;i&gt;J&lt;/i&gt;&lt;sub&gt;cpl&lt;/sub&gt; value (&lt;i&gt;J&lt;/i&gt;&lt;sub&gt;cpl_c&lt;/sub&gt;). The saturated &lt;i&gt;Δ&lt;/i&gt; is twice as great as that of &lt;i&gt;J&lt;/i&gt;&lt;sub&gt;cpl&lt;/sub&gt; = 0. When &lt;i&gt;J&lt;/i&gt;&lt;sub&gt;cpl&lt;/sub&gt; ≤ &lt;i&gt;J&lt;/i&gt;&lt;sub&gt;cpl_c&lt;/sub&gt;, energy barrier is minimized in the paths where the magnetizations of FL1 (&lt;i&gt;M&lt;/i&gt;&lt;sub&gt;FL1&lt;/sub&gt;) and FL2 (&lt;i&gt;M&lt;/i&gt;&lt;sub&gt;FL2&lt;/sub&gt;) separately reverse (not shown in Figures). On the other hand, when the &lt;i&gt;J&lt;/i&gt;&lt;sub&gt;cpl&lt;/sub&gt; ≥ &lt;i&gt;J&lt;/i&gt;&lt;sub&gt;cpl_c&lt;/sub&gt;, energy barrier is minimized in the path where &lt;i&gt;M&lt;/i&gt;&lt;sub&gt;FL1&lt;/sub&gt; and &lt;i&gt;M&lt;/i&gt;&lt;sub&gt;FL1&lt;/sub&gt; reverse simultaneously, resulting in maximum &lt;i&gt;Δ.&lt;/i&gt;&lt;br/&gt;&lt;i&gt;J&lt;/i&gt;&lt;sub&gt;cpl_c&lt;/sub&gt; value rapidly increases with the decrease of the MTJ diameter in Model A (&lt;i&gt;d&lt;/i&gt; ≥ &lt;i&gt;d&lt;/i&gt;&lt;sub&gt;c&lt;/sub&gt;), and gradually increases in Model B (&lt;i&gt;d&lt;/i&gt; ≤ &lt;i&gt;d&lt;/i&gt;&lt;sub&gt;c&lt;/sub&gt;). &lt;i&gt;J&lt;/i&gt;&lt;sub&gt;cpl_c&lt;/sub&gt; value, which is equivalent with &lt;i&gt;K&lt;/i&gt;&lt;sub&gt;eff1&lt;/sub&gt;&lt;i&gt;t&lt;/i&gt;&lt;sub&gt;1 &lt;/sub&gt;( =&lt;i&gt;K&lt;/i&gt;&lt;sub&gt;eff_film&lt;/sub&gt;&lt;i&gt;t&lt;/i&gt;&lt;sub&gt;1&lt;/sub&gt; +(1-&lt;i&gt;N&lt;/i&gt;&lt;sub&gt;z-x&lt;/sub&gt;) &lt;i&gt;M&lt;/i&gt;&lt;sub&gt;s&lt;/sub&gt;&lt;sup&gt;2&lt;/sup&gt;/(2&lt;i&gt;μ&lt;/i&gt;&lt;sub&gt;0&lt;/sub&gt;)&lt;i&gt;t&lt;/i&gt;&lt;sub&gt;1&lt;/sub&gt;) when &lt;i&gt;d&lt;/i&gt; ≤ &lt;i&gt;d&lt;/i&gt;&lt;sub&gt;c,&lt;/sub&gt; increases with the decrease of the demagnetic field coefficient &lt;i&gt;N&lt;/i&gt;&lt;sub&gt;z-x&lt;/sub&gt;. We have reported that &lt;i&gt;J&lt;/i&gt;&lt;sub&gt;cpl&lt;/sub&gt; of the blanket film of the double interface MTJ with a W insertion layer thickness of 0.2 nm reaches 0.44 mJ/m&lt;sup&gt;2&lt;/sup&gt; [8]. Therefore, all the &lt;i&gt;J&lt;/i&gt;&lt;sub&gt;cpl_c&lt;/sub&gt; values obtained for various diameters based on these models are experimentally achievable.&lt;br/&gt;Consequently, we successfully established a method to predict critical &lt;i&gt;J&lt;/i&gt;&lt;sub&gt;cpl&lt;/sub&gt; values to maximize &lt;i&gt;Δ &lt;/i&gt;for double interface MTJ elements.&lt;br/&gt;This work is supported by CIES’s Industrial Affiliation on STT-MRAM program, CIES Consortium, JST-OPERA, and CAO-SIP.

**References:**

[1] S. Ikeda et al., Nat. Mater. 9, 721 (2010).&lt;br/&gt;[2] M. P. Sharrock, IEEE Trans. Magn. 26, 193 (1990).&lt;br/&gt;[3] G. D. Chaves-O’Flynn et al. Phys. Rev. Applied 4, 024010 (2015).&lt;br/&gt;[4] H. Sato et al. Appl. Phys. Lett. 101, 022414 (2012).&lt;br/&gt;[5] K. Nishioka et al., IEEE Trans. Electron Devices 67, 995 (2020).&lt;br/&gt;[6] S. Miura et al., IEEE Trans. Electron Devices 67, 5368 (2020).&lt;br/&gt;[7] J. H. Kim et al., Sci. Rep. 5, 16903 (2015).&lt;br/&gt;[8] K. Nishioka et al., MMM 2020 conference, O2-06.&lt;br/&gt;[9] I. Volvach et al., MMM 2020 conference, O2-07.&lt;br/&gt;[10] I. Volvach et al., Appl. Phys. Lett. 116, 192408 (2020).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/5ab35ffac43499d4ee18b9ab65311340.jpg)
Fig.1 Models to calculate magnetic energy surfaces of the free layer with double-interface MTJs. Model A is a magnetic domain propagation model and Model B is a magnetic coherent rotation model, introducing magnetic coupling energy between two FLs. &lt;i&gt;K&lt;/i&gt;&lt;sub&gt;eff1&lt;/sub&gt;&lt;i&gt;t&lt;/i&gt;&lt;sub&gt;1&lt;/sub&gt; and &lt;i&gt;K&lt;/i&gt;&lt;sub&gt;eff2&lt;/sub&gt;&lt;i&gt;t&lt;/i&gt;&lt;sub&gt;2&lt;/sub&gt; are effective perpendicular magnetic anisotropy const per unit area which MgO layers give rise to FL1 and FL2, respectively.

![](https://assets.underline.io/uploads/markdown_image/1/image/862f0cc74254d646eefaa20472e314b2.jpg)
Fig.2 &lt;i&gt;J&lt;/i&gt;&lt;sub&gt;cpl&lt;/sub&gt; dependence on &lt;i&gt;Δ&lt;/i&gt; for MTJs with various diameters. &lt;i&gt;J&lt;/i&gt;&lt;sub&gt;cpl_c&lt;/sub&gt; is a &lt;i&gt;J&lt;/i&gt;&lt;sub&gt;cpl&lt;/sub&gt; value which saturates &lt;i&gt;Δ &lt;/i&gt;for a MTJ diameter &lt;i&gt;d&lt;/i&gt;. (a) Model A is applied when &lt;i&gt;d&lt;/i&gt; ≥ &lt;i&gt;d&lt;/i&gt;&lt;sub&gt;c&lt;/sub&gt; = 23 nm. (b) Model B is applied when d &lt; &lt;i&gt;d&lt;/i&gt;&lt;sub&gt;c&lt;/sub&gt; = 23nm.

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 Effect of magnetic coupling between two CoFeB layers on thermal stability in perpendicular magnetic tunnel junctions with MgO/CoFeB/insertion layer/CoFeB/MgO free layer

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Over the past decades, there has been a significant development in spin-transfer-torque magneto-resistive random-access memory (STT-MRAM). The development was brought by CoFeB/MgO-based magnetic tunnel junctions (MTJs) with interfacial perpendicular magnetic anisotropy (IPMA) [1]. Because thermal stability factor (Δ) is proportional to effective PMA constant and the volume of the free layer in a coherent magnetic rotation model [2] and proportional to square root of effective PMA constant and the diameter of the free layer in a domain propagation model [3], Δ decreases with the decrease of MTJ diameter. To achieve great enough Δ value in a smaller MTJ, increasing the number of CoFeB/MgO interfaces has been proposed to increase PMA [4-6]. In double interface MTJ with MgO/CoFeB/insertion layer/CoFeB/MgO free layer, thin non-magnetic layer such as Ta, W or Mo was used as the insertion layer to obtain higher PMA and tunnel magnetoresistance (TMR) ratio [4,7]. When the insertion layer is too thick, the two CoFeB layers in the free layer behave magnetically independent, resulting in no benefits on Δ despite the double interface because effective free-layer volume does not increase. To obtain a benefit of double CoFeB / MgO interfaces on Δ, a great enough magnetic coupling between the two CoFeB layers is required. It is important to clarify the effect of magnetic coupling (the energy constant of unit area: Jcpl) on Δ. However, it is not clear how the magnitude of Jcpl affects the increase in Δ, although we achieved a strong Jcpl in the double interface MTJs [8]. In this study, we propose a method to calculate critical Jcpl value to maximize Δ for free layers of MgO/CoFeB/insertion layer/CoFeB/MgO in the double interface MTJs with various MTJ diameters. We introduced magnetic coupling energy between two magnetic layers in the free layer based on magnetic domain propagation model (Model A) and magnetization coherent rotation model (Model B) as shown in Fig.1. When d was larger than the critical diameter dc (= 16/π [As /Keff ]1/2 ), Model A was applied, in which a blue-colored domain with downward magnetization nucleates from an edge and propagates in each FL1 and FL2. The domain nucleation and propagation behavior from edge region assumed in this model is consistent with the results of micromagnetic simulations of the MTJs with CoFeB / MgO interfaces [9,10]. The nucleated domain area Ω1 in FL1 and Ω2 in FL2 were decided by angles φ1 and φ2. A magnetic energy E (φ1, φ2) in Model A was calculated as follows. E (φ1, φ2) = Λ(φ1) t1 σw1 + Λ(φ2) t2 σw2 + 2Jcpl |Ω(φ1) - Ω(φ2)|---(1) σw1 = 4(As Keff1)1/2, σw2 = 4(As Keff2)1/2 ----(2) Λ(φi) = d (π/2–φi) tan φi, (i = 1, 2)---(3) Ω(φi) = d2 φi/4 + d2/4 { (π/2 – φi）tan2φi – tanφi }, (i = 1, 2) ---(4) The 1st and 2nd terms in the equation (1) express magnetic domain wall energies of FL1 and FL2, respectively. The third term expresses magnetic coupling energy between FL1 and FL2. Λ is wall length and σw is wall energy per unit area. As is stiffness constant of the free layer. When d is smaller than the critical diameter dc, coherent rotation model (Model B) was applied, in which E (φ1, φ2) was calculated as follows. The 1st and 2nd terms in the equation (5) express PMA energies of FL1 and FL2. The third term expresses magnetic coupling energy between FL1 and FL2. E (φ1, φ2) =πd2/4 { Keff1t1 (1–cos2φ1) + Keff2t2 (1–cos2φ2)+ Jcpl (1–cos(φ1–φ2）} ---(5) Fig. 2 shows Jcpl dependence on Δ for the MTJs with various diameters. We used Keff1=Keff2 = Keff_film +(1-Nz-x) Ms2/(2μ0). Keff_film = 2.25x105 J/m3, t1=t2=1.2nm, Ms = 0.97 T and As = 5.4 pJ/m, which were experimental values in the double interface MTJ [8]. The calculated critical diameter dc was 23 nm. With increasing Jcpl, Δ increases and saturates over a critical Jcpl value (Jcpl_c). The saturated Δ is twice as great as that of Jcpl = 0. When Jcpl ≤ Jcpl_c, energy barrier is minimized in the paths where the magnetizations of FL1 (MFL1) and FL2 (MFL2) separately reverse (not shown in Figures). On the other hand, when the Jcpl ≥ Jcpl_c, energy barrier is minimized in the path where MFL1 and MFL1 reverse simultaneously, resulting in maximum Δ. Jcpl_c value rapidly increases with the decrease of the MTJ diameter in Model A (d ≥ dc), and gradually increases in Model B (d ≤ dc). Jcpl_c value, which is equivalent with Keff1t1 ( =Keff_filmt1 +(1-Nz-x) Ms2/(2μ0)t1) when d ≤ dc, increases with the decrease of the demagnetic field coefficient Nz-x. We have reported that Jcpl of the blanket film of the double interface MTJ with a W insertion layer thickness of 0.2 nm reaches 0.44 mJ/m2 [8]. Therefore, all the Jcpl_c values obtained for various diameters based on these models are experimentally achievable. Consequently, we successfully established a method to predict critical Jcpl values to maximize Δ for double interface MTJ elements. This work is supported by CIES’s Industrial Affiliation on STT-MRAM program, CIES Consortium, JST-OPERA, and CAO-SIP.

**References:**

[1] S. Ikeda et al., Nat. Mater. 9, 721 (2010). [2] M. P. Sharrock, IEEE Trans. Magn. 26, 193 (1990). [3] G. D. Chaves-O’Flynn et al. Phys. Rev. Applied 4, 024010 (2015). [4] H. Sato et al. Appl. Phys. Lett. 101, 022414 (2012). [5] K. Nishioka et al., IEEE Trans. Electron Devices 67, 995 (2020). [6] S. Miura et al., IEEE Trans. Electron Devices 67, 5368 (2020). [7] J. H. Kim et al., Sci. Rep. 5, 16903 (2015). [8] K. Nishioka et al., MMM 2020 conference, O2-06. [9] I. Volvach et al., MMM 2020 conference, O2-07. [10] I. Volvach et al., Appl. Phys. Lett. 116, 192408 (2020).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/5ab35ffac43499d4ee18b9ab65311340.jpg)
Fig.1 Models to calculate magnetic energy surfaces of the free layer with double-interface MTJs. Model A is a magnetic domain propagation model and Model B is a magnetic coherent rotation model, introducing magnetic coupling energy between two FLs. Keff1t1 and Keff2t2 are effective perpendicular magnetic anisotropy const per unit area which MgO layers give rise to FL1 and FL2, respectively.

![](https://assets.underline.io/uploads/markdown_image/1/image/862f0cc74254d646eefaa20472e314b2.jpg)
Fig.2 Jcpl dependence on Δ for MTJs with various diameters. Jcpl_c is a Jcpl value which saturates Δ for a MTJ diameter d. (a) Model A is applied when d ≥ dc = 23 nm. (b) Model B is applied when d < dc = 23nm.

technical paper

A promising means for long-distance transport of angular momentum is spin superfluidity [1-4]. In this work, the unsteady nonlinear dynamics of spin transport in an easy-plane, thin-film, one-dimensional ferromagnetic channel is studied analytically. We formulate an initial-boundary value problem (IVBP) for the Landau-Lifshitz equation subject to spin injection into a static, uniformly magnetized nanowire. The long-time steady-state configuration in such channels with zero applied field has been identified as either a dissipative exchange flow (DEF) or a contact soliton DEF (CS-DEF) [5], depending on the strength of the injection. Here, we study the injection-induced highly nonlinear, transient magnetization dynamics that occur prior to the damping-dominated steady-state is reached and include a constant applied field. In particular, we focus on the 1 ns timescale where damping is weak, and the spin dynamics are dominated by spin injection, applied field, exchange interaction, and demagnetizing fields. In our analysis, we recast the Landau-Lifshitz equation into its dispersive hydrodynamic (DH) form [6], in terms of the longitudinal spin density and a magnetic analog of the fluid velocity that is proportional to the spin current. The spin injection is characterized by a nonzero fluid velocity at one end of the channel, hence can be viewed as a spin hydrodynamic “piston”. The DH form captures two important effects in the ferromagnetic system: nonlinearity and dispersion, which are inherited from anisotropy and exchange, respectively. These effects lead to the generation of unsteady nonlinear waves when large gradients occur. A rapid rise in the fluid velocity due to spin injection leads to large gradients that result in a new kind of spin shock wave that is an example of a dispersive shock wave (DSW). DSWs are expanding, highly oscillatory, nonlinear excitations that realize a coherent transition between two states in a variety of dispersive media [7]. Spin wave envelope DSWs have been observed in a Yttrium Iron Garnet feedback ring [8]. We provide a full analytical classification of nonlinear wave solutions to this IVBP in terms of the applied field and injection strength, using the Whitham modulation theory [9]. The solution components are rarefaction waves (RWs), DSWs, and solitons (see Fig. 1). Both RWs and DSWs have been identified as solutions to a pure initial value problem (the Riemann problem) in a two-component Bose-Einstein condensate [10], whose governing equations are equivalent to the DH form of the Landau-Lifshitz equation we study here. In contrast, we show that the injection boundary plays a prominent role in the dynamics. Depending on the interplay between the spin injection intensity and the applied magnetic field magnitude, different types and combinations of RWs, DSWs, and solitons arise. The generation of a soliton is a distinct feature due to the boundary and is identified with an important concept [10]: the magnetic sonic condition. Solitons only occur at the spin injection end and only in the supersonic injection regime. Our analytical solutions are confirmed by micromagnetic simulations.

**References:**

[1] E. Sonin, Spin currents and spin superfluidity, Advances in Physics Vol. 59, p.181 (2010). [2] S. Takei and Y. Tserkovnyak, Superfluid spin transport through easy-plane ferromagnetic insulators, Physical Review Letters Vol. 112, p.227201 (2014). [3] H. Skarsvåg, C. Holmqvist, and A. Brataas, Spin superfluidity and long-range transport in thin-film ferromagnets, Physical Review Letters Vol. 115, p.237201 (2015). [4] M. Evers and U. Nowak, Transport properties of spin superfluids: Comparing easy-plane ferromagnets and antiferromagnets, Physical Review B Vol. 101, p.184415 (2020). [5] E. Iacocca and M. A. Hoefer, Hydrodynamic description of long-distance spin transport through noncollinear magnetization states: Role of dispersion, nonlinearity, and damping, Physical Review B Vol. 99, p.184402 (2019). [6] B. Halperin and P. Hohenberg, Hydrodynamic theory of spin waves, Physical Review Vol. 188, p.898 (1969). [7] G. El and M. Hoefer, Dispersive shock waves and modulation theory, Physica D: Nonlinear Phenomena Vol. 333, p.11 (2016). [8] P. A. P. Janantha et al., Observation of self-cavitating envelope dispersive shock waves in Yttrium Iron Garnet thin films, Physical Review Letters Vol. 119, p.024101 (2017). [9] G. B. Whitham, Linear and nonlinear waves, Vol. 42 (John Wiley & Sons, 2011). [10] S. K. Ivanov et al., Solution of the Riemann problem for polarization waves in a two-component Bose-Einstein condensate, Physical Review E Vol. 96, p.062202 (2017). [11] E. Iacocca, T. Silva, and M. A. Hoefer, Breaking of Galilean Invariance in the Hydrodynamic Formulation of Ferromagnetic Thin Films, Physical Review Letters Vol. 118, p.017203 (2017).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/bc60f7f3bb99d10a60fec8c293fde70d.jpg)
Fig. 1: Example simulations of (top to bottom) the spin density n, the magnetic fluid velocity u, and an in-plane magnetization component mx, at t = 1 ns in (left) the subsonic regime and (right) the supersonic regime.

 Spin-Injection-Generated Shock Waves and Solitons in a Ferromagnetic Nanowire

The transverse electric field generated by anomalous Nernst effect (ANE) in a magnetic material is perpendicular to both the temperature gradient (▽T) and its magnetization (M), different from the parallel relationship between the generated electric field and ▽T emerges from Seebeck effect (SE). This allows different design principles for thermoelectric power generation and heat flux sensing devices, which could be advantageous in creating a simple and flexible device with better integratability and scalability.[1-3] However, the practical application of ANE is hampered by the fact that the thermopower of ANE (SANE) is still orders of magnitude smaller compared to that of SE (SSE), and there has been increasing studies in order to find magnetic materials with large SANE in recent years. SANE can be separated into two components as SANE = ρxxαxy − ρAHEαxx, where ρxx is the longitudinal resistivity, ρAHE is the anomalous Hall resistivity, and αxx and αxy are the diagonal and off-diagonal components of the Peltier tensor, respectively. The first term on the right hand side (ρxxαxy) is considered the intrinsic term of ANE, as αxy directly converts ▽T into a transverse electrical current. The L21-ordered Co2MnGa Heusler alloys have shown large values of αxy originated from their topological band structures, which lead to record high values of SANE.[4-7] The second term on the right hand side (− ρyxαxx) can be rewritten as – SSE × ρAHE / ρxx, indicating it originates from the anomalous Hall effect (AHE) of the longitudinal carrier flow induced by SE. Here, inspired by the second term, we propose a different approach for transverse thermoelectric generation. We considered a hybrid system comprising a thermoelectric material and a magnetic material. The electric field generated by SE of the thermoelectric material was converted to transverse thermoelectric generation by AHE of the magnetic material, which showed a similar symmetry to ANE, but surprisingly, more than one order of magnitude enhancement in thermopower. This is referred to as the Seebeck-driven transverse thermoelectric generation (STTG).[8] To model STTG and derive an expression for its transverse thermopower, we consider a system that consists of a thermoelectric material and a magnetic material electrically connected at both ends along the ▽T direction to form a closed circuit, as shown in Fig. 1. Both materials have a rectangular shape, with LTEx, LTEy, and LTEz (LMx, LMy, and LMz) respectively being the length along x, y, and z directions for the thermoelectric (magnetic) material. The magnetic material has the Seebeck coefficient SM, anomalous Nernst coefficient SANE, resistivity ρM, and anomalous Hall resistivity ρAHE. The thermoelectric material has the Seebeck coefficient STE, and resistivity ρTE. By solving the linear-response transport equations for the hybrid system, we derived the total transverse thermopower as Stoty = (EMy / –▽T) = SANE – ρAHE (STE – SM) / ((ρTE / r) + ρM), where EMy is the transverse electric field along the y direction in the magnetic material and r = (LMx / LTEx) × (LTEyLTEz / LMyLMz) is the size ratio between the thermoelectric and magnetic materials. In addition to ANE from the magnetic material, Stoty includes the contribution from the artificial hybridization of SE of the thermoelectric material through STE and AHE of the magnetic material through ρAHE (the second term on the right hand side), which is STTG. For the proof-of-concept demonstration of STTG, we deposited a 50-nm-thick L21-ordered Co2MnGa thin film on a single-crystalline MgO (100) substrate and used it as the magnetic material. The MgO substrate was then cut into a rectangular shape and bonded onto a rectangular-shaped 0.5-mm-thick Si substrate, which was used as the thermoelectric material. The Co2MnGa film and Si substrate were electrically connected to each other through Ohmic contacts and bonding wires near the ends to form the closed circuit. EMy in the Co2MnGa layer was measured while the magnetic field (H) was swept in the direction perpendicular to the sample plane. The same measurement was also carried out without the Co2MnGa-Si connection. Figure 2 shows the H dependence of EMy divided by ▽T for the samples using whether an n-type Si (STE = −1.3×103 µV K−1) or a p-type Si (STE = 1.3×103 µV K−1) as the thermoelectric material. Without the Co2MnGa-Si connection, only the ANE contribution from the Co2MnGa layer was measured, which showed SANE ~ 6.2 µV K−1, consistent with previous reports.[4-7] With the Co2MnGa-Si connection, however, the total transverse thermopower Stoty increased by one order of magnitude to 82.3 µV K−1 for using n-type Si; while Stoty changed sign to −41.0 µV K−1 for using p-type Si. The experimentally obtained Stoty is consistent with the predicted values made using the equation and the properties of the Co2MnGa and Si, which is 77.2 (−45.3) µV K−1 for Co2MnGa/n(p)-type-Si system. Our result indicates that STTG can make significant enhancement from ANE in the transverse thermopower by optimizing transport properties and dimensions of the materials, which would provide great flexibility for designing future thermoelectric power generation and heat flux sensing devices.

**References:**

[1] K. Uchida, H. Adachi, T. Kikkawa et al., Proc. IEEE, Vol. 104, p.1946 (2016). [2] Y. Sakuraba, Scr. Mater., Vol. 111, p.29 (2016). [3] W. Zhou, and Y. Sakuraba, Appl. Phys. Express, Vol. 13, p.043001 (2020). [4] A. Sakai, Y. P. Mizuta, A. A. Nugroho et al., Nat. Phys., Vol. 14, p.1119 (2018). [5] S. N. Guin, K. Manna, J. Noky et al., NPG Asia Mater., Vol. 11, p.16 (2019). [6] L. Xu, X. Li, L. Ding et al., Phys. Rev. B, Vol. 101, p.180404(R) (2020). [7] K. Sumida, Y. Sakuraba, K. Masuda et al., Commun. Mater., Vol. 1, p.89 (2020). [8] W. Zhou, K. Yamamoto, A. Miura et al., Nat. Mater. (2021), DOI: 10.1038/s41563-020-00884-2.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/af67d3057028ca8c7187a10cb62d178a.jpg)
Schematic illustration of the model system for Seebeck-driven transverse thermoelectric generation.

![](https://assets.underline.io/uploads/markdown_image/1/image/d8560fa996a7031109c92672c1f01103.jpg)
(a) H dependence of the transverse electric field EMy divided by ▽T in the Co2MnGa layer of the Co2MnGa/n-type-Si sample and (b) Co2MnGa/p-type-Si sample with (STTG + ANE) and without (ANE) the Co2MnGa-Si connection.

 Seebeck-driven Colossal Transverse Thermoelectric Generation

Spintronics combining with superconductor electronics is of exciting and challenging subject because of its intriguing and amazing properties. Spin-polarized current injected from the ferromagnetic metal can be carried by quasi-particles in a superconductor. The injected quasiparticles diffusively flow and gradually convert the Cooper pairs within a few micron length scale. Since a conventional Cooper pair consists of a pair of up- and down-spin electrons, the spin-polarized current is expected to take longer time to be transformed to the supercurrent. To investigate the relaxation processes of spin-polarized current in superconductor, we developed a Nb-based multi-terminal device with a ferromagnetic CoFeAl spin injector as schematically shown in Fig. 1. The injected quasiparticles relax with decaying electrochemical potentials. In the probe configuration shown in Fig. 1, the decreasing non-local quasiparticles electrochemical potentials can be detected as non-local resistances. Moreover, by changing the injector from Cu to CoFeAl, we can compare the relaxation lengths for non-polarized and polarized quasiparticles. Figure 2 shows non-local resistances measured with nonmagnetic injectors with changing the distance from 0 to 3000 nm. Non-local resistance depends mainly on a charge imbalance which are a nonequilibrium phenomenon that arises from the conversion of quasiparticle current in the normal metal to supercurrent in the superconductor [1]. From the electrodes-distance dependence of non-local resistances, we estimated the relaxation length of non-polarized quasiparticles is 950 ± 30nm, while that of polarized quasiparticles is 1240 ± 130nm. This difference can be explained by the spin diffusion length at the vicinity of superconducting transition temperature which is longer than that in a normal conducting state.

**References:**

[1] P. Cadden-Zimansky and V. Chandrasekhar, Phys. Rev. Lett. 97, 237003 (2006).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/6a7ff821738fccf3134555c8773ca6f1.jpg)
Fig.1 Multi-electrode mesoscopic device

![](https://assets.underline.io/uploads/markdown_image/1/image/1a92e23000507f88fdf5c54608e252c3.jpg)
Fig. 2 Temperature dependence of non-local resistances with various distances between an injector and detectors (top), and the electrodes-distance dependence of the maximum values of non-local resistances (bottom) for (A) Non spin polarized quasiparticles and (B) Spin polarized quasiparticles.

 Relaxation Process of Spin-polarized Quasiparticles in a Superconducting Nb Wire

We theoretically investigated the four-fold symmetric term of the anisotropic magnetoresistance (AMR) effect in cubic ferromagnetic metals (FMs), which has recently been observed experimentally for certain metals, by using fourth-order perturbation theory with respect to the spin-orbit interaction (SOI). The AMR effect is a magnetoresistance effect specific to magnetic metals in which the charge conductivity changes depending on the direction of magnetization in FMs [1], and attracted much attention in the field of spintronics to apply for evaluation of half-metallicity [2] or spin-orbit torque generation [3]. Usually, in experiments on bulk polycrystalline FMs, the longitudinal conductivity is proportional to the cos(2θ) where θ is the relative angle between the current direction and the magnetization direction, that is, the AMR effect has two-fold symmetry under the magnetization rotation. Theoretically, this two-fold AMR effect is caused by the SOIs and has been successfully explained by Campbell’s model, an s-d impurity scattering model with considering the second-order perturbation in terms of the SOIs [4]. In single-crystal FMs such as Fe4N, however, the AMR measurements exhibited not only the conventional two-fold component but also the unconventional four-fold component proportional to cos(4θ) [5]. While this four-fold AMR effect is expected to stem from the symmetry of the cubic crystal, the microscopic origin is not so straightforward because the magnetization direction dependence of the conduction band is too small to explain this effect. Recently, a possible mechanism of the four-fold AMR effect is theoretically proposed by Kokado [6], wherein the s-d scattering coupled with the SOIs and “tetragonal” symmetric crystal fields is responsible for this effect. This theory is an extension of Campbell’s model in polycrystalline FMs to the single crystal FM model by taking into account the energy level splitting due to the tetragonal crystal fields on the d-states (Fig. 1). Since it is argued that the splitting among d-states is significant for the presence of a four-fold component, this theory requires the extra assumption of existing the tetragonal (uniaxial or planar) distortion to apply to the cubic crystals including the Fe4N. However, the experiment is confronted with the fact that the four-fold component appears even though the sample is almost cubic crystal and has little distortion. The microscopic origin is still controversial; therefore, it is worthwhile to explore a possible mechanism of the four-fold AMR effect in the cubic symmetric single-crystal FMs without tetragonal distortion. In this work, we show the presence of the four-fold AMR effect in cubic single crystal FMs from a microscopic viewpoint [7]. Our main finding is that the higher-order perturbation terms of SOI can also be responsible for the four-fold AMR effect in cubic FMs, instead of the second-order SOI with tetragonal distortion as mentioned in Kokado’s theory. Inspired by the Kokado model, we use the s-d impurity scattering model expressed by an impurity Anderson Hamiltonian with cubic crystal fields and SOI. The conductivity is represented on the basis of the Kubo–Greenwood formula. This approach enables us to consider the non-perturbative role of SOIs on the AMR effects. Firstly, to overlook a physical aspect of this effect, we carried out perturbative analysis with respect to the SOIs. The results indicate that the fourth-order terms of SOI can give rise to the four-fold AMR effect. Furthermore, we extract the two important roles of the SOI: first, to couple the electron’s momentum and magnetization, and second, to induce the orbital splitting among d-states instead of the tetragonal crystal field. Secondly, we performed numerical calculations to evaluate the non-perturbative behavior of the AMR effects. As the results, we successfully obtained both the two-fold and four-fold components of the AMR effect without assuming the tetragonal distortion, which is consistent with the perturbative analysis (Fig. 2). Other parameter dependencies will be presented at the conference.

**References:**

[1] T. McGuire and R. Potter, IEEE Trans. Magn., Vol. 11, p.1018 (1975). [2] S. Kokado, M. Tsunoda, K. Harigaya, and A. Sakuma, J. Phys. Soc. Jpn., Vol. 81, p.024705 (2012). [3] T. Taniguchi, J. Grollier, and M. D. Stiles, Phys. Rev. Applied, Vol. 3, p.044001 (2015). [4] I. A. Campbell, A. Fert, and O. Jaoul, J. Phys. C, Vol. 3, p.S95 (1970). [5] M. Tsunoda, H. Takahashi, S. Kokado, Y. Komasaki, A. Sakuma, and M. Takahashi, Appl. Phys. Express, Vol. 3, p.113003 (2010). [6] S. Kokado and M. Tsunoda, J. Phys. Soc. Jpn., Vol. 84, p.094710 (2015). [7] Yuta Yahagi, Daisuke Miura, and Akimasa Sakuma, J. Phys. Soc. Jpn., Vol. 89, p.044714 (2020)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/8e02bcab2e43d5b25b65902dc8186411.jpg)
Fig.1: Schematics of the energy level of the d-states under (a) a cubic symmetric and (b) a tetragonal symmetric crystal-field, respectively.

![](https://assets.underline.io/uploads/markdown_image/1/image/04a12b54dea732a7b428e0597df7effd.jpg)
Fig.2: Two-fold (c2) and four-fold (c4) components of the AMR ratio.

 Theoretical Study on Four-fold Symmetric Anisotropic Magnetoresistance Effect in Cubic Single-crystal Ferromagnetic Model

In spintronics, Cu is often considered as a passive material which cannot generate spin current by itself due to negligible spin-orbit coupling (SOC). However, recent experiments reported observation of gigantic current-induced spin-orbit torque in surface oxidized Cu/ferromagnet structures [1-5], whose magnitude is comparable to material systems with large SOC such as Co/Pt. These experimental results cannot be explained neither by spin Hall effect nor by Rashba-Edelstein effect since these mechanisms assume strong SOC. On the other hand, electric generation of the orbital angular momentum does not require SOC at all, which can be achieved via orbital Hall effect [6] or orbital Rashba-Edelstein effect [7]. Furthermore, according to a recent theory, injection of orbital angular momentum to a ferromagnet can generate torque on the magnetization, which is called orbital torque (OT) [8]. Thus, it has been proposed that a microscopic mechanism responsible for the torque generation in surface oxidized Cu/ferromagnet is OT, originating in the orbital Rashba effect (ORE) at oxidized region of Cu film. The OT mechanism qualitatively explains anomalous features observed in experiments such as strong suppression of the torque by intermixing of atoms at the interface [3], sign change of the torque for depending on ferromagnets [4], and gigantic enhancement of the torque efficiency by insertion of an ultrathin Pt layer [5]. However, to our best knowledge, there is no direct evidence of the ORE nor theoretical investigation of the electronic structure of Cu film under influence of surface oxidization. In this contribution, we present our recent theoretical results showing that surface oxidization of a Cu film leads to strong enhancement of the ORE [9], which is assessed from first-principles calculations based on density functional theory. We find that microscopic origin of the ORE is the resonant hybridization between O p-orbitals and Cu d-orbitals. We investigate various stacking geometries (fcc hollow, hcp hollow, bridge, on-top structures) and find that the ORE emerges in a robust manner. The ORE leads to a pronounced orbital texture at the Fermi surface (Fig. 1), where the magnitude of the orbital polarization reaches as much as 0.5 \hbar per state. Because of the orbital texture, application of an external electric field leads to a generation of orbital Hall current, which by far exceeds the magnitude of the spin current of heavy elements. This implies that the OT mechanism can be significant in surface oxidized Cu/ferromagnet structures. Our theoretical results also encourage experimental verification of the orbital texture, i.e. by angle-resolved photoesmission spectroscopy or momentum microscopy.

**References:**

[1] An et al. Spin-torque generator engineered by natural oxidization of Cu, Nat. Commun. 7, 13069 (2016). [2] Otano et al. Nonreciprocal Spin Current Generation in Surface-Oxidized Copper Films, Phys. Rev. Lett. 122, 217701 (2019). [3] Kim et al. Non-trivial charge-to-spin conversion in ferromagnetic metal/Cu/Al2O3 by orbital transport, Phys. Rev. B, in press. [4] Tazaki et al. Current-induced torque originating from orbital current, arXiv:2004.09165. [5] Ding et al. Harnessing Orbital-to-Spin Conversion of Interfacial Orbital Currents for Efficient Spin-Orbit Torques, Phys. Rev. Lett. 125, 177201 (2020). [6] D. Go, D. Jo, C. Kim, and H.-W. Lee, Intrinsic Spin and Orbital Hall Effects from Orbital Texture, Phys. Rev. Lett. 121, 086602 (2018). [7] Go et al. Toward surface orbitronics: giant orbital magnetism from the orbital Rashba effect at the surface of sp-metals, Sci. Rep. 7, 46742 (2017). [8] D. Go and H.-W. Lee, Orbital torque: Torque generation by orbital current injection, Phys. Rev. Res. 2, 013177 (2020). [9] Go et al. Orbital Rashba effect in surface oxidized Cu film, arXiv:2011.08601.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/4a85b5b77611539a80e30b149ba500dc.jpg)
Orbital angular momentum texture of the surface oxidized Cu film at the Fermi surface. The colormap represents the magnitude and the arrow indicates direction of the angular momentum at each k-point.

 Strong enhancement of the orbital Rashba effect in Cu film by surface oxidization

Magneto resistive random-access memory (MRAM) holds the potential to be a universal memory with its non-volatility, high speed, robust endurance, and system power savings capability. In the semiconductor memory and storage space, MRAM is poised to deliver the performance of working memory with the persistence of storage. The pioneer generation of MRAM product dubbed Toggle MRAM was first launched in 2006 and was based on magnetic field switching. Driven by continuous demand for lower power and higher density, spin transfer torque MRAM (STT-MRAM) was introduced into the market. In its commercialization, standalone STT-MRAM product saw rapid evolution toward higher density in which the memory density quadrupled every 2 years between 2015-2019 [1]. The successful scaling of STT-MRAM product is attributed to a concerted effort in materials engineering and the use of advanced process technologies. Most recently in 2019-2020, we saw two momentous events in MRAM development: Everspin launched a milestone 1Gb product [2], and 3 major foundries and 2 other companies announced their STT-MRAM product offerings [1]. In this talk, we will review the fundamental aspects of STT-MRAM with a focus on read and write distributions of MRAM arrays. In order to achieve reliable high density STT-MRAM products it is critical to understand the contributions to these distributions and minimize the variation across the array. For instance, minimizing array write error rate (WER) relies much upon reducing the population of extrinsic magnetic tunnel junction (MTJ) bits in an array. A method was developed to quantify the population of extrinsic bits by calculating the switching failure rate upon doing N repeat of read-write sequence, which we call soft fail count. Figure 1(a) shows example of soft fail improvement by combining MTJ film engineering and process improvement. The soft fail count improvement is seen from both the reduction of outlier bits and tightening of main bits population to reach below the desired requirement. Figure 1(b) shows the median soft fail count plotted against wafer radius from center to edge. Such plot further elucidated the distinct contribution from MTJ film and process changes implemented. Detailed analysis shows that the MTJ film improvement reduces the extrinsic population and improved the switching reliability on the die level, while the process improvement extends the die uniformity across the wafer. These approaches were found to be additive when combined. A low operating voltage coupled with reliable switching (measured as distributions) is critical to integrating MTJ bits on silicon. Figure 2 shows the plots of normalized array operating voltage (Vop) and its sigma corresponding to the MTJ film and process improvement shown in Figure 1. Initial MTJ film change from A to B improved the Vop by 14% and significantly reduced the sigma by a factor 2.6x. Switching from process A to B using the improved film B improved the Vop by a further 3.3% with a comparable sigma level to process A. Finally, combining MTJ film C with Process B produced slight improvement in Vop and further reduction in sigma by 20%. This observation corroborated the reduction in bit error soft fail count shown in Figure 1. The improvement in bit-to-bit distribution is critical to enable reliable high density STT-MRAM products. In the talk, we will discuss the impact of these distributions on other key aspects such as data retention, switching pulse widths and endurance.

**References:**

References:: [1] S. Ikegawa, F. B. Mancoff, J. Janesky, and S. Aggarwal, “Magnetoresistive Random Access Memory: Present and Future”, IEEE. Trans. Elec. Dev. 67(4), 1407 (2020); doi: 10.1109/TED.2020.2965403. [2] S. Aggarwal, H. Almasi, M. DeHerrera, B. Hughes, S. Ikegawa, J. Janesky, H. K. Lee, H. Lu, F. B. Mancoff, K. Nagel, G. Shimon, J. J. Sun, T. Andre, and S. M. Alam, "Demonstration of a reliable 1 Gb standalone spin-transfer torque MRAM for industrial applications," in IEDM Tech. Dig., 2019, No. 2.1.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/36c8c73ccf560c4e602b00ef4a3f958c.jpg)
Figure 1. (a) Soft fail count improvement with combinations of MTJ film and process changes, (b) median soft fail count plotted against wafer radius from center to edge showing improvement in bits distribution within die and across wafer uniformity.

![](https://assets.underline.io/uploads/markdown_image/1/image/a88c3d224319675d69acb324487122c0.jpg)
Figure 2. Improvement in operating voltage (Vop) and its sigma with combinations of MTJ film and process changes

 Reliable High Density STT-MRAM Products INVITED

STT-MRAM materials and technology have recently matured to the point of moving from “lab to fab” for 28nm-22nm node standalone and eNVM applications. Prior work has mostly placed MTJ devices above M2 or even higher in the BEOL stack, depending on the application and integration constraints [1-4]. However, optimizing MRAM for mobile or last-level cache applications requires significant improvements in write speed, write current, endurance, and density of both the MRAM cell in addition to the CMOS [5]. In this work, we present the first Embedded Spin-Transfer-Torque MRAM (eMRAM) technology in a 14 nm CMOS node. Using a 2 Mb eMRAM macro, we achieve an integration at tight MTJ pitch (0.0273 um2 cell size), which is aggressively placed between M1 and M2. We demonstrate read and write functionality, including write performance down to 4 ns, and show that the eMRAM process module can be added while obeying the existing CMOS logic BEOL design rules and reliability requirements. Several unit process innovations enabled this integration, including a novel sub-lithographic microstud (μ-stud) bottom electrode (BEL), fine profile control of the MTJ patterning and dielectric films, optimized BEL/MTJ metallization, and optimized post-MTJ low-k planarization across array and logic areas. The result preserves the minimum 3 added mask levels (2 critical for μ-stud and MTJ; 1 non-critical for MTJ alignment marks), without mask-adders for low-k planarization or top electrode (TEL). A shrink patterning process ensures that the μ-stud top CD is always smaller than the MTJ bottom CD, for MTJ sizes down to below 35 nm. This minimizes shunting by eliminating the BEL resputtering onto the MTJ sidewalls during patterning, and increases etch budget. The μ-stud BEL module re-uses current manufacturing processes. Figure 1 shows a TEM cross section of 41nm MTJ devices with a sub-lithographic μ-stud underneath. The alternating MTJ pitch presented a challenge for IBE overetch/cleanup without excessive dielectric gouge. Additional tests were completed showing good device scalability to 35nm, with magnetic property degradation at smaller sizes due to edge damage that could be improved with further etch optimization. Cache applications require writing at high speed with high cycling endurance, but data retention performance can be relaxed (e.g. using ECC and data scrubbing). Figure 2 shows the eMRAM write performance. The array was written to the 1 state, then to the 0 state, versus write pulse voltage and width. The curves show the write voltage for passing median bits vs. write pulse width, from 4 ns - 20 ns. Stack B incorporated materials optimizations to reduce write voltage and time for suitability towards the last level cache. We performed a series of retention bakes at 85°C on arrays of target and smaller sized devices, demonstrating projected fail rates well below 1 ppm for retention times of ≤1 min. at nominal 43 nm CD. Results also include endurance cycling tests on 128 kb arrays up to 5x106 cycles, and single MTJs up to 1010 cycles. No dielectric breakdown or resistance drift was observed in either case. Finally, an early BEOL reliability assessment of electromigration and time-dependent dielectric breakdown supports our eMRAM embeddability for high-performance logic applications.

**References:**

[1] S. Aggarwal, et al., IEEE IEDM, San Francisco, pp. 2.1.1-2.1.4, 2019. [2] K. Lee, et al., IEEE IEDM, San Francisco, pp. 2.1.1-2.1.4, 2019. [3] W. J. Gallagher, et al., Symposium on VLSI Technology, Kyoto, pp. T190-T191, 2019. [4] J. G. Alzate et al., IEEE IEDM, San Francisco, pp. 2.4.1-2.4.4, 2019. [5] S. Sakhare et al., IEEE IEDM, San Francisco, pp. 18.3.1-18.3.4.2018.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/4ca2fc66e4cfa0a482eef090a40fd8bc.jpg)
Figure 1: TEM cross section of 41nm MTJ devices inserted between the 14nm node M1 and M2 levels. The mstud enabled sufficient overetch & cleanup during MTJ patterning.

![](https://assets.underline.io/uploads/markdown_image/1/image/005730caa67f8294cda72db1f933d05e.jpg)
Figure 2: Passing median bit write voltage vs write pulse width for both W0 and W1 operation. Stack B improvements to the free layer enabled higher speed 4ns switching.

 Embedded STT-MRAM for 14nm CMOS Node Cache Applications INVITED

CoFeB–MgO-based magnetic tunnel junctions (MTJs) with perpendicular easy axis have emerged as critical components to develop spin transfer torque magnetoresistance random access memories (STT-MRAMs) [1–6]. To develop a large capacity STT-MRAM, a high tunnel magnetoresistance (TMR) ratio, high thermal stability, and low switching current must simultaneously be realized under a thermal tolerance of 400 °C to ensure CMOS back-end-of-line compatibility. To satisfy these requirements, we have developed high performance MTJ stack structures through physical vapor deposition process development [7–9]. As the size of the MTJs decreases, a more stable reference layer is required to achieve reliable write operations. Furthermore, the magnitude of the stray magnetic field from the reference layer must be minimized. This magnitude significantly increases with a decrease in the MTJ size, resulting in an asymmetrical thermal stability factor between the parallel and antiparallel states [9]. Co/Pt-based synthetic anti-ferro (SyF) magnetically coupled layers with an Ru coupling layer have been widely used as a reference layer to reduce the stray magnetic field. Although the exchange coupling field (Hex) is maximized at a 1st-peak Ru thickness of about 0.4 nm, Hex degrades significantly after 400 °C annealing [10]. Therefore, 0.9 nm-thick Ru (2nd peak) layer is often used in SyF reference layer owing to their high thermal tolerance. Nevertheless, the SyF reference layer with 2nd peak Ru exhibits insufficient stability against the magnetic field and write voltage to realize smaller MTJs. To overcome these issues, we developed a reference layer with four SyF magnetically coupled layers (Quad-SyF). In the Quad-SyF, Hex is determined by the middle SyF layer sandwiched between the top and bottom SyF layers [11]. Moreover, a small stray magnetic field can be realized because each ferromagnetic layer in the Quad-SyF, especially the top layer, can be thinner than those in a conventional SyF. These aspects can help achieve reliable write operations with a high thermal tolerance. We prepared five types of stacks (A－E) as shown in the schematics in Fig. 1 (a) and Fig. 2(a). Stack A corresponds to the MTJ with conventional Co/Pt-based SyF reference layers having a 0.4 nm-thick Ru coupling layer (so-called “2L-1st”), and Stacks B and D correspond to those having a 0.9 nm thick Ru coupling layer (so-called “2L-2nd”). Stack C and E corresponds to an MTJ with Quad-SyF consisting of four anti-ferro magnetically coupled Co/Pt layers and three 0.9 nm-thick Ru coupling layers (so-called “4L-2nd”). All the MTJ stacks were deposited on a 300 mmΦ thermally oxidized Si wafer using a DC/RF magnetron sputtering system. Stack A, B and C were annealed at 300, 350, and 400 °C for 1 h. After annealing at 400 °C for 1 h, Stacks D and E were patterned into the MTJs with diameters ranging from 50–120 nm by using ArF immersion lithography and reactive ion etching techniques. The areal magnetic moment versus magnetic field (m–H) curves and TMR ratio were measured using a vibrating sample magnetometer and CIPT, respectively. Figure 1 (b) shows the out-of-plane major m–H curves for the MTJs after annealing at 400 °C for 1 h. The inset shows the minor m–H curves. In the case of the MTJ with 2L-1st, two magnetic reversals corresponding to the free and reference layers occurred. In the case of the MTJ with 2L-2nd, three magnetic reversals corresponding to the free layer, reference layer, and spin-flop of the SyF were observed. In the MTJ with 4L-2nd, four magnetic reversals corresponding to the free layer, reference layer, and spin-flop of the SyF were observed. Hex of the MTJ with 4L-2nd showed a larger value than those of the MTJs with 2L-1st and 2L-2nd. A distinct magnetization plateau region around zero magnetic field was observed in the 2L-2nd and 4L-2nd, whereas the plateau region was not observed in the 2L-1st because of the degradation of the anti-ferro magnetic coupling of the SyF. Figure 1 (c) shows the dependence of the TMR ratio on the annealing temperature for Stacks A, B, and C. For Stacks B and C, the TMR ratio increased as the annealing temperature increased up to 400 °C. In contrast, for Stack A, the TMR ratio degraded at an annealing temperature of more than 350 °C, as an ideal anti-ferromagnetic configuration could not be realized as mentioned above. Figure 2 shows the MTJ size dependence of the shift magnetic field (Hshift). The error bars indicate the standard deviations. Hshift of the MTJ with 4L-2nd showed a small value of less than 3 mT when the number of repetitions of the top, 2nd, 3rd and bottom Co/Pt layers set 1, 4, 1, and 2, respectively. The variation in Hshift and the MTJ size dependence of Hshift for the MTJ with 4L-2nd were smaller than those for the MTJ with 2L-2nd. The employment of Quad-SyF (4L-2nd) can achieve a large Hex, a small shift magnetic field, and high thermal tolerance of the reference layer. This work was supported by CIES’s Industrial Affiliation on STT-MRAM program, CIES Consortium, JST-OPERA, and CAO-SIP.

**References:**

[1] S. Ikeda et al., Nat. Mater. 9, 721 (2010). [2] H. Sato et al., Appl. Phys. Lett. 101, 022414 (2012). [3] H. Sato et al., IEEE Trans. Magn. 49, 4437 (2013). [4] Y. J. Song et al., IEDM 2018. [5] K. Lee et al., IEDM 2018. [6] Y.-C. Shih et al., VLSI 2018. [7] H. Sato et al., IEDM 2018. [8] H. Honjo et al., VLSI 2015. [9] H. Honjo et al., AIP Adv. 7, 055913 (2017). [10] K. Yakushiji et al., Appl. Phys. Express 8, 083003 (2015). [11] T. Suzuki et al., VLSI Tech. Dig., T188, 2005.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/9eafb6f06ba0533c94a3aab5ab44bc15.jpg)
Fig. 1 (a) Schematic of stack structures of the MTJs. The nominal thickness for each layer in nanometers is represented by the numbers in the parentheses. (b) Out-of-plane major areal magnetic moment versus magnetic field (m-H) curves for the MTJ stacks. Inset is the minor m-H curves. (c) Annealing temperature dependence of TMR ratio.

![](https://assets.underline.io/uploads/markdown_image/1/image/0364a185bacf57f9522a7ed47cf5a2e8.jpg)
Fig. 2 (a) Schematic of the stack structures of the MTJs. (b) MTJ size dependence of the shift field Hshift for the MTJs with 2L-2nd and 4L-2nd reference layers.

 Perpendicular magnetic tunnel junctions with reference layer based on four anti-ferromagnetically coupled Co/Pt layers

Magnetic tunnel junctions (MTJ) with perpendicular magnetic anisotropy (PMA) [1] form the basis of the spin-transfer torque magnetic random-access memory (STT-MRAM), which is non-volatile, fast, dense, and has quasi-infinite write endurance and low power consumption. In the usual CoFeB|MgO-based MTJ, the cell diameter must be kept above ~30 nm [2], otherwise, the bit becomes thermally unstable due to insufficient PMA. Being able to increase the PMA of the storage layer opens a way to further downsize scaling. In magnetic recording media, this is typically done by introducing heavy metals like Pt or Pd [3], which increases the spin-orbit coupling parameter. However, in the context of STT-MRAM, this would increase the storage layer Gilbert damping and therefore the switching current [4]. To avoid this, multilayers exhibiting bulk PMA based on purely 3d metallic elements were developed [5,6] such as (Fe/Ni) or (Co/Ni) based multilayers. However, these structures are intrinsically complex to fabricate to get large PMA and often do not withstand the required annealing temperature ~400°C. Based on density functional theory (DFT) calculations, we propose a rather simple design of MTJ with greatly enhanced PMA up to several mJ/m2 in the form Fe(n)Co(m)Fe(n)|MgO [Fig. 1]. This design leverages the well-known interfacial PMA of Fe|MgO along with a strain-induced bulk PMA discovered within bcc Co [plot in Fig. 1]. This strain in bcc Co is induced by the underlying layer. The storage layer can be several nm thick and still exhibit perpendicular magnetization. We perform DFT calculations of the effective PMA (the sum of magnetocrystalline energy EMCA and demagnetizing energy Edd) for different Fe and Co thicknesses and compare with the case of pure Fe, as shown in Fig. 2(a). Unlike in Fe, where the effective PMA decreases with Fe thickness and becomes negative for thicknesses above 11 MLs, in the proposed structure, we see a steady increase of PMA vs. Co thickness. The tunneling magnetoresistance (TMR) estimated from the extended Julliere model is around 300%, comparable with that of the pure Fe|MgO case. After studying the electronic structure of strained bcc Co, we can explain why the large PMA emerges. Calculations based on the second-order perturbation theory [7] reveal that strain leads in bcc Co to a significant shift in the energies of dyz and dz2 minority-spin bands further away from the Fermi level. This is shown to cause an overall increase in PMA. Replacing the middle Fe layers with Co also decreases the negative demagnetizing energy [the magnetocrystalline and demagnetizing energies separately are shown in Fig. 2(b)]. The PMA enhancement can result in a possible downscaling of the cell area by 200% to 300% if an atomically sharp Fe/Co interface can be fabricated. In the case of interfacial mixing, the PMA is reduced by a few 10%. The impact is excessive only in the thinnest Fe2Co3Fe2/MgO structure, where the drop is about 70%. The thicker structures are far more robust against interdiffusion: in Fe3Co4Fe3/MgO, the drop is only 22%. In conclusion, we propose bcc Fe(3ML)Co(4ML)Fe(3ML) as a storage layer for MgO-based double-barrier MTJ with greatly enhanced perpendicular magnetic anisotropy.

**References:**

[1] B. Dieny and M. Chshiev, Rev. Mod. Phys., Vol. 89, p.025008 (2017) [2] S. Ikeda, K. Miura and H. Yamamoto, Nat. Mater., Vol. 9, p.721 (2010) [3] P. F. Carcia, A. D. Meinhaldt, and A. Suna, Appl. Phys. Lett., Vol. 47, p.178 (1985) [4] S. Mizukami, E. P. Sajitha and D. Watanabe, Appl. Phys. Lett., Vol. 96, p.152502 (2010) [5] K. Hotta, K. Nakamura and T. Akiyama, Phys. Rev. Lett., Vol. 110, p.267206 (2013) [6] K. Nakamura, Y. Ikeura and T. Akiyama, J. Appl. Phys., Vol. 117, p.17C731 (2015) [7] Y. Miura, S. Ozaki and Y. Kuwahara, J. Phys. Condens. Matter, Vol. 25, p.106005 (2013)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/1267c7a4e6c05f78f2aa57129c3eaa08.jpg)
The proposed MTJ with enhanced PMA. FeCoFe trilayer is used as the storage layer. Replacing the middle Fe layers with Co provides a high positive contribution to perpendicular magnetocrystalline anisotropy, as shown in the plot.

![](https://assets.underline.io/uploads/markdown_image/1/image/9e6cc171bc4887cbfad3109a5b85de05.jpg)
(a) Effective PMA (EMCA + Edd) of the proposed Fe(n)Co(m)Fe(n)/MgO MTJ with different Fe and Co thicknesses. In Fe(n)Co(m)Fe(n)/MgO, the perpendicular anisotropy is preserved, while in pure Fe/MgO, it would turn in-plane above certain thickness (the Fe thickness is m+4 MLs). (b) The magnetocrystalline (EMCA) and demagnetizing energy (Edd) shown separately for structures with n=2. (c) Example of the proposed MTJ storage layer with enhanced PMA.

 Giant Perpendicular Magnetic Anisotropy Enhancement in MgO-Based Magnetic Tunnel Junction by Using Co/Fe Composite Layer

Spin transfer-torque Magnetic Random Access Memory (STT-MRAM) is expected to play a major role in the future development of information and communication technologies. One of the drivers of the technology is the non-volatile character of this type of memory that allows to reduce the energy consumption compared to SRAM or DRAM. [1] Globally, we are seeking to develop technologies that help reduce carbon emissions. However, the nature of the materials involved in such technologies is also a concern both in terms of environmental impact and supply risk. [2,3] MRAM contains several materials classified as critical raw materials, in particular by the European Union (EU), being of high importance to the EU economy and whose supply is classified of high risk. [4] In order to improve the stability of the reference layer whose magnetic configuration has to remain fixed during the lifetime of the memory, a synthetic antiferromagnet (SAF) is typically used. This SAF structure is normally based on Co/Pt or Co/Pd multilayers antiferromagnetically coupled through a thin Ru layer. Platinum Group Metals (PGMs) have been classified as critical materials with high supply risk. In addition, obtaining these metals in their refined form requires extensive amounts of energy and CO2 emissions due to the low initial ore concentration. In this work, an assessment of the impact of the substitution of the Pt required in STT-MRAM for the SAF layer has been made. Alternative solutions can be envisaged such as the use of multilayers based on Co/Ni exhibiting perpendicular anisotropy [5]. A second more challenging approach based on the use of perpendicular shape anisotropy (PSA) does not rely on the use of PGMs. However, this PSA based approach is more challenging from technological point of view due to the requirement of a strict control of the cell diameter at sub-20nm dimensions during the etching process. The possibility of using Co/Ni multilayers for the SAF of MRAM has been already demonstrated [6,7]. We have observed how similar properties to Co/Pt SAF can be obtained by using Co/Ni multilayers (Figure 1). Our study has the added advantage of using a seed layer free of Hf, used in some previous studies to promote the required (111) texture for the Co/Ni multilayers growth [6,7]. Hf is also a material classified as critical and whose production is strongly concentrated in two countries, France and USA. In our study a Cu seed layer is used allowing for more diverse production sources. An evaluation of the environmental (energy and global warming potential) and economic impact of the substitution has been performed. Strong improvements in both economic and environmental aspects can be achieved by the substitution. However due to the tiny amounts of PGM materials used in STT-MRAM, in comparison to the mass of the silicon wafer itself, the environmental impact and price of the silicon wafer on which these memory devices are grown is much higher as shown in Figure 2. Our conclusion is that more attention should be focused on the process of fabrication of silicon wafers or find a substitution to this type of wafers whenever possible. Nevertheless, the high supply concentration of Pt as four mining companies represent the 80% of the global production [8] makes the presence of these alternatives a key aspect to ensure the survival of the technology in case of supply disruptions.

**References:**

1. B. Dieny and I. L. Prejbeanu, ‘Magnetic Random-Access Memory’, in Introduction to Magnetic Random-Access Memory, John Wiley & Sons, Ltd, pp. 101–164. (2017) doi:10.1002/9781119079415 2. European Commission. Critical materials for strategic technologies and sectors in the EU - a foresight study. (2020) doi: 10.2873/58081 3. Ku, A. Y. Sustainable Materials and Technologies, 15, 27-32. (2018) doi:10.1016/j.susmat.2017.10.001 4. European Commission. Study on the Review of the List of Critical Raw Materials - Critical Raw Materials Factsheets European Commission. (2017) doi: 10.2873/398823 5. Nuss P, Eckelman MJ. PLoS ONE 9(7): e101298. (2014) doi: 10.1371/journal.pone.0101298 6. Kar, G. S., Kim, W., Tahmasebi, T. et al., IEEE International Electron Devices Meeting. (2014) doi:10.1109/iedm.2014.7047080 7. Tomczak, Y., Lin, T., Swerts, J., et al. IEEE Transactions on Magnetics, 52(7), 1-4. (2016) doi:10.1109/tmag.2016.2515109 8. Sinsalo, Pia, and Mari Lundström. Metals, vol. 8, no. 4, p. 203. (2018) doi:10.3390/met8040203.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/c8b57764016ecc1627245e1d0345fc1e.jpg)
Fig 1. VSM measurements on a MTJ with conventional SAF based on Co/Pt multilayers (red) versus a MTJ with SAF comprising Co/Ni multilayers (green) after annealing at 300°C for 10 minutes. Sample based on Co/Pt SAF has the following composition (thickness in nm) : Ta3/Pt25/[Co0.5/Pt0.25]6/Co0.5/Ru0.9/[Co0.5/Pt0.25]3/ Co0.5/Ta0.2/FeCoB1.2/MgO0.7/Ox/MgO0.5/FeCoB1.5/Ta3/Pt5. Sample based on (Co/Ni) multilayers is Pt-free and has the following composition Ta22/FeCoB0.8/Ta3/Cu3/[Co0.2/Ni0.4]6/Co0.5/Ru0.9/Co0.5/[Co0.2/Ni0.4]3/Ta0.2/FeCoB1.2/MgO0.7/Ox/MgO0.5/FeCoB1.5/Ta3/Al2.

![](https://assets.underline.io/uploads/markdown_image/1/image/471f429389b4483ff4e1a167fcaeea84.jpg)
Fig 2. Energy per 300mm wafer, global warming potential (GWP) and price in log scale required to obtain the amount of Pt comprised in a conventional SAF, of Co in the PSA based substitution, of Ni in the case of (Co/Ni) based SAF alternative and for the production of a 300mm bare Si wafer.

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