# Temperature dependence of the energy barrier in X/1X nm shape-anisotropy magnetic tunnel junctions

Junta Igarashi, Butsurin Jinnai, Valentin Desbuis, Stéphane Mangin,

Shunsuke Fukami, Hideo Ohno

► To cite this version:

Junta Igarashi, Butsurin Jinnai, Valentin Desbuis, Stéphane Mangin, Shunsuke Fukami, et al. Temperature dependence of the energy barrier in X/1X nm shape-anisotropy magnetic tunnel junctions. Applied Physics Letters, 2021, 118 (1), 10.1063/5.0029031. [hal-05006575](https://hal-univ-lorraine.fr/hal-05006575v1)

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# Temperature dependence of the energy barrier in X/1X nm shape-anisotropy magnetic tunnel junctions ✅

Junta Igarashi ⚙️; Butsurin Jinnai 🟧; Valentin Desbuis ⚙️; Stéphane Mangin ⚙️; Shunsuke Fukami ⚙️;
Hideo Ohno ⚙️

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Appl. Phys. Lett. 118, 012409 (2021)

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# Temperature dependence of the energy barrier in X/1X nm shape-anisotropy magnetic tunnel junctions

Cite as: Appl. Phys. Lett. **118**, 012409 (2021); doi: 10.1063/5.0029031

Submitted: 9 September 2020 · Accepted: 13 December 2020 ·

Published Online: 8 January 2021

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Junta Igarashi,<fnref n="1" /> ID Butsurin Jinnai,<fnref n="2" />,ª ID Valentin Desbuis,<fnref n="3" /> ID Stéphane Mangin,<fnref n="3" /> ID Shunsuke Fukami,<fnref n="1" />,<fnref n="2" />,<fnref n="4" />,<fnref n="5" />,<fnref n="6" /> ID and Hideo Ohno<fnref n="1" />,<fnref n="2" />,<fnref n="4" />,<fnref n="5" />,<fnref n="6" /> ID

## AFFILIATIONS

## ABSTRACT

Shape-anisotropy magnetic tunnel junctions (MTJs) are attracting much attention as a high-performance nonvolatile spintronic device in the X/1X nm regime. In this study, we investigate an energy barrier relevant to the retention property in CoFeB/MgO-based shape-anisotropy MTJs with various diameters at high temperatures and compare it with that in conventional interfacial-anisotropy MTJs. We find that the scaling relationship between the energy barrier and the spontaneous magnetization in shape-anisotropy MTJs is well described by a model assuming the dominant contribution of shape anisotropy to the energy barrier. Also, the scaling exponent is much smaller than that for the interfacial-anisotropy MTJs, indicating that the properties of shape-anisotropy MTJs are less sensitive to the temperature. Using the experimentally determined scaling relationship, we discuss the design window of the MTJ dimensions to achieve data retention of 10 years at various temperatures. This study demonstrates that the shape-anisotropy MTJ holds promise of scaling beyond 20 nm for high-temperature applications.

Published under license by AIP Publishing. https://doi.org/10.1063/5.0029031

Scaling magnetic tunnel junctions (MTJs) has been one of the critical challenges to realize high-performance spin-transfer torque magnetoresistive random access memory (STT-MRAM) integrated with the advanced silicon technology.<fnref n="1" /> An interfacial perpendicular anisotropy MTJ employing CoFeB/MgO systems allows reducing the MTJ size down to 20 nm (2X nm), while maintaining a high thermal stability factor $\Delta$ (≡ $E/k_B T$, where $E$ is an energy barrier between two magnetization states, $k_B$ is the Boltzmann constant, and $T$ is the absolute temperature).<fnref n="2" />⁻<fnref n="4" /> However, further scaling beyond 20 nm is challenging due to an insufficient anisotropy energy density.<fnref n="1" />,<fnref n="4" /> Recently, shape-anisotropy MTJs, whose free layer is patterned into a cylindrical nanomagnet,<fnref n="5" /> have been shown to be promising to achieve high $\Delta$ in such a small region of X/1X nm at room temperature (RT).<fnref n="5" />,<fnref n="6" />

To utilize MTJ devices in applications at various temperatures, such as cryogenic computing systems⁷ and automobiles (up to 150 °C),⁸ data-retention performance characterized by $\Delta$, or $E$, is needed to be engineered considering the temperature dependence of relevant factors. Also, as $E$ is proportional to the effective magnetic anisotropy energy density $K_{eff}$ in a coherent reversal model, the temperature dependence of $E$ is expected to reflect the origin of the magnetic anisotropy.⁹ Thus, understanding the temperature dependence of $\Delta$, or $E$,¹⁰⁻¹⁶ is of significant interest from both fundamental and technological viewpoints.

The temperature dependence of magnetic properties has been investigated experimentally and theoretically for various material systems such as CoFeB,¹⁰⁻²² FePt,⁹,²³⁻²⁶ and MnAl.⁹,²⁷ In the conventional interfacial-anisotropy MTJs using the CoFeB/MgO interfacial

<footnote n="1">¹Laboratory for Nanoelectronics and Spintronics, Research Institute of Electrical Communication, Tohoku University, Sendai 980-8577, Japan</footnote>

<footnote n="2">²WPI Advanced Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan</footnote>

<footnote n="3">³Université de Lorraine, Institut Jean Lamour, UMR CNRS 7198, Nancy, France</footnote>

<footnote n="4">⁴Center for Spintronics Research Network, Tohoku University, Sendai 980-8577, Japan</footnote>

<footnote n="5">⁵Center for Science and Innovation in Spintronics, Tohoku University, Sendai 980-8577, Japan</footnote>

<footnote n="6">⁶Center for Innovative Integrated Electronic Systems, Tohoku University, Sendai 980-0845, Japan</footnote>

<footnote>ªAuthor to whom correspondence should be addressed: butsurin@tohoku.ac.jp</footnote>
system with a diameter D down to ~30 nm (3X nm), data-retention and/or switching performance has been experimentally investigated at various temperatures.10–16 In the shape-anisotropy MTJ, on the other hand, only experimental results on the temperature dependence of coercivity,22 an indirect indication of the data-retention performance, were reported to date, and the temperature dependence of Δ and physics behind it have not been studied yet. In this study, we evaluate the temperature dependence of Δ in the shape-anisotropy MTJs at X/1X nm and compare with that of the interfacial-anisotropy MTJ. Also, based on the experimental results, we show a design window for the MTJ dimensions in the X/1X nm regime to meet 10-year data retention at various temperatures.

A stack structure of, from the substrate side, Ta (5)/Ru (10)/Ta (15)/Pt (5)/[Co (0.4)/Pt (0.4)]<sub>6</sub>/Co (0.4)/Ru (0.4)/[Co (0.4)/Pt (0.4)]<sub>2</sub>/ Co (0.4)/Ta (0.2)/CoFeB (1)/MgO/(Co<sub>0.25</sub>Fe<sub>0.75</sub>)<sub>75</sub>B<sub>25</sub> (t<sub>CoFeB</sub> = 15)/ MgO/Ru (5) is deposited by dc/rf magnetron sputtering on a thermally oxidized Si substrate. The numbers in parentheses are nominal thicknesses in nm, and t<sub>CoFeB</sub> represents the free-layer CoFeB layer thickness. The stack is processed into circular MTJs with various diameters by electron beam lithography, reactive ion etching, and multistep Ar ion milling.5 Figure 1(a) shows a scanning electron microscope image from a tilted angle for a junction with D < 20 nm after the ion milling process, together with a corresponding illustration for an MTJ. After processing, MTJs are annealed at 300 °C for 1 h. A diameter is electrically determined from the resistance (R)-area (A) product (RA = 5.4 Ωµm<sup>2</sup>) and the resistance of the parallel state of MTJs. We find that at diameters less than about 15 nm, the easy axis direction changes from in-plane to perpendicular owing to the shape anisotropy. In this study, we focus on the MTJs with diameters ranging from 5 to 12 nm. We evaluate Δ and an effective magnetic anisotropy field H<sub>K</sub><sup>eff</sup> from the switching probability P<sub>SW</sub> measurement using a pulse magnetic field

H<sub>pulse</sub>.28 We apply H<sub>pulse</sub> for 50 times, which is confirmed to provide reliable switching probability measurements to determine Δ and H<sub>K</sub><sup>eff</sup>. The measurements are carried out at temperatures from RT up to around 190 °C. We note that MTJs studied here are designed not to have too high Δ so that the property change can be clearly observed within the temperature range we can access in our setup. We also measure the temperature dependence of spontaneous magnetization M<sub>S</sub> using a vibrating sample magnetometer capable of changing the sample-holder temperature.

Figure 1(b) shows the tunnel magnetoresistance (TMR) ratio as a function of the magnetic field H applied along the cylinder direction for the shape-anisotropy MTJ with D = 5.8 nm at various temperatures. P<sub>SW</sub><sup>P(AP)</sup> is plotted as a function of H<sub>pulse</sub> at various temperatures in Fig. 1(c). Here, superscripts to P<sub>SW</sub> denote an initial magnetization configuration [P(AP): parallel (anti-parallel) state] before the magnetization switching takes place. We then fit the following equation to the experimental results with Δ, H<sub>K</sub><sup>eff</sup>, and a shift field H<sub>shift</sub> as fitting parameters,

$$P_{\text{SW}}^{\text{P(AP)}} = 1 - \exp \left[ - \frac{\tau}{\tau_0} \exp \left\{ -\Delta \left( 1 \mp \frac{H_{\text{pulse}} - H_{\text{shift}}}{H_{\text{K}}^{\text{eff}}} \right)^2 \right\} \right], \quad (1)$$

where Δ is assumed to be the same for the switching between P to AP and AP to P once the shift field is canceled out, τ is the pulse duration (= 1 s) of H<sub>pulse</sub>, and τ<sub>0</sub> is the inverse of the attempt frequency (1 ns in this study). Note that we assume that coherent magnetization switching, where Eq. (1) is applicable, takes place in the studied MTJs.5,6 The obtained Δ and H<sub>K</sub><sup>eff</sup> for the MTJs with diameters of 5.8, 8.4, and 11.9 nm are summarized in Figs. 1(d) and 1(e), respectively. While Δ monotonically decreases with temperature, H<sub>K</sub><sup>eff</sup> is less sensitive to temperature. We here note that the trend of H<sub>K</sub><sup>eff</sup> is different

<figure><img src="image_10.png" /><figcaption>FIG. 1. (a) Scanning electron microscope image with a tilted angle and corresponding illustration of the MTJ structure after the ion milling process. An arrow shows the direction of the applied magnetic field H. (b) TMR ratio as a function of H and (c) P<sub>SW</sub> measured under the application of H<sub>pulse</sub> with a pulse width of 1 s for D = 5.8 nm at various temperatures. Temperature T dependence of (d) Δ and (e) μ<sub>0</sub>H<sub>K</sub><sup>eff</sup> for D = 5.8, 8.4, and 11.9 nm.</figcaption></figure>
from previous reports for interfacial-anisotropy MTJs, where $H_K^{eff}$, as well as $\Delta$, monotonically decreases with temperature,¹⁰ suggesting different mechanisms governing the temperature dependence between the shape- and interfacial-anisotropy MTJs.

Accordingly, we examine the relationship between the temperature dependence of $E$ and $M_S$ for the shape-anisotropy and interfacial-anisotropy MTJs. In the coherent reversal model, $E$ is expressed as

$$E = K_{\text{eff}} V, \qquad (2)$$

$$K_{\text{eff}} = K_b + \frac{K_i}{t} - \delta N \frac{M_S^2}{2\mu_0}, \qquad (3)$$

where $V$ is the volume of the free layer, $K_b$ is the bulk (magnetocrystal-line) anisotropy energy density, $K_i$ is the interfacial anisotropy energy density, $\delta N$ is the difference in the dimensionless demagnetization coefficient, or the shape anisotropy coefficient, between the perpendicular and in-plane orientations, and $\mu_0$ is the permeability in free space. The relationship between the temperature dependence of magnetic anisotropy energy density $K$ and $M_S$ is known to be described by a power law scaling relationship expressed as²⁹

$$\frac{K(T)}{K(T^*)} = \left\{ \frac{M_S(T)}{M_S(T^*)} \right\}^n, \qquad (4)$$

where $T^*$ is a normalizing temperature and $n$ is the scaling exponent that varies depending on a physical mechanism providing the magnetic anisotropy. As one can see from Eq. (2), $E$ in the coherent reversal model is expected to follow the similar power law scaling relationship to Eq. (4). We calculate $E (= \Delta k_B T)$ from the obtained $\Delta$ and plot it with respect to $T$ for the shape-anisotropy MTJs with $t_{\text{CoFeB}} = 15$ nm and $D = 5.8, 8.4$, and 11.9 nm in Fig. 2(a). For comparison, the results analyzed from our previous report on an interfacial-anisotropy MTJ with a free layer of MgO/(Co$_{0.25}$Fe$_{0.75}$)$_{75}$B$_{25}$ ($t_{\text{CoFeB}} = 2$ nm)/MgO and $D = 30$ nm¹³ are also plotted, which were prepared through essentially the same process as the present work. Figure 2(b) shows the temperature dependence of $M_S$ of MgO/CoFeB (2 and 15)/MgO films. Solid curves are fit using the Bloch law, $M_S(T) = M_{S0}(1 - aT^{3/2})$, where $M_{S0}$ is $M_S$ at 0 K and $a$ is a material-dependent parameter, providing an $M_{S0}$ value of 1.59 (1.73) T and an $a$ value of 2.47 (3.88) × 10⁻⁵ K⁻³/² at $t_{\text{CoFeB}} = 15$ (2) nm. From Figs. 2(a) and 2(b), the double-logarithm plots of $E(T)/E(RT)$ vs $M_S(T)/M_S(RT)$ are obtained, as shown in Fig. 2(c). The slope of linear fits (solid lines) that gives $n$ shows a clear difference between the two types of MTJs. The obtained $n$ for all the studied MTJs is summarized in Fig. 2(d). The $n$ values of the shape-anisotropy MTJs for all the studied diameters are close to 2, whereas $n$ of 4.7 is obtained for the interfacial-anisotropy MTJ. This result is in line with the observed weak temperature dependence of $H_K^{eff}$ shown in Fig. 1(e), as small $n$ results in reduced temperature sensitivity.

Next, we discuss the mechanism accounting for the difference in $n$ between the shape- and interfacial-anisotropy MTJs. While $n$ is expected to be 3 for materials with uniaxial magnetic anisotropy,²⁹,³⁰ experimental studies on the scaling relationship between $K_i$ and $M_S$ for blanket samples with CoFeB/MgO material systems have shown $n$ ranging from 2 to 3,¹⁶,¹⁹,²¹ and such reduced $n$ was attributed to a two-site anisotropic exchange interaction.²¹ For nanoscale devices with a MgO/CoFeB/Ta free layer, a few experimental studies have

<figure><img src="image_11.png" /><figcaption>FIG. 2. (a) $E (= \Delta k_B T)$ plotted with respect to temperature $T$ for the shape-anisotropy MTJs with $t_{\text{CoFeB}} = 15$ nm and $D = 5.8, 8.4$, and 11.9 nm along with the results analyzed from previously published data for an interfacial-anisotropy MTJ with $t_{\text{CoFeB}} = 2$ nm and $D = 30$ nm (Ref. 13). (b) The temperature dependence of $M_S$ of MgO/CoFeB (2 and 15)/MgO films. Solid curves are fitting using the Bloch law. (c) The double-logarithm plot of $E(T)/E(RT)$ vs $M_S(T)/M_S(RT)$ obtained from (a) and (b). Scaling exponent $n$ is given by linear fits (solid lines). (d) Summary of the obtained $n$ values from all the studied MTJs with $t_{\text{CoFeB}} = 2$ and 15 nm.</figcaption></figure>

been performed,¹⁴,¹⁷,²⁰ where larger $n$ (3–4.5) was reported.¹⁴ A numerical study pointed out that the increased $n$ could be explained by a variation in magnetic properties such as magnetic anisotropy, spontaneous magnetization, and exchange stiffness near the device edge caused by a patterning process.³¹ Our result for the interfacial-anisotropy MTJ is consistent with the reported large value of $n$ for nanoscale MTJs.¹⁴ On the other hand, the obtained value of $n$ (~2) for the shape-anisotropy MTJs can be understood from Eq. (3) in which indeed the third term proportional to $M_S^2$ is the dominating term for the energy barrier. While it is not fully understood why large $n$ is observed in interfacial-anisotropy MTJ, it is worth noting that the difference in the $n$ values implies that the impact of the MTJ fabrication process is different between the interfacial- and shape-anisotropy MTJs. In fact, while the MTJ fabrication process is likely to crucially affect the quality of the CoFeB/MgO interface that governs the anisotropy for the interfacial-anisotropy MTJ, its impact is expected to be less significant for the shape-anisotropy MTJs as the total anisotropy is determined by the shape of the nanomagnet. We also note that the reduced $n$ is favorable for the retention property because it makes it less sensitive to the temperature, a feature needed for wide-temperature applications.

The experimentally obtained $n$ allows us to discuss the design window of the MTJ dimensions (a diameter $D$ and a free-layer thickness $t$) considering the shape and interfacial anisotropies to satisfy high thermal stability at various temperatures, as shown in Fig. 3. To illustrate the design window, we use $\Delta$ to realize the error rate (ER) of 10⁻⁹ for a 10⁹-bit system in 10 years. According to the following equation,
<figure><img src="image_12.png" /><figcaption>FIG. 3. Design window of the MTJ dimensions ($t$ and $D$ of a free layer) to satisfy $\Delta$ of 82 or higher at various temperatures calculated using the experimentally obtained $n$ (= 2). A MgO/CoFeB/MgO material system is assumed as a free layer.</figcaption></figure>

$$ER = 1 - \left[ \exp\left\{ -\frac{\tau_{\text{ret}}}{\tau_0} \exp(-\Delta) \right\} \right]^m, \quad (5)$$

where the number of bits $m = 10^9$ bits (1 Gbit) and the retention time of stored information $\tau_{\text{ret}} = 10$ years, such $\Delta$ is 82. From Eqs. (2)–(4) with the obtained $n$ (= 2), we map out the design spaces (shaded regions) meeting $\Delta$ of 82 or higher at various temperatures of particular interest for applications: RT (27 °C), 85 °C, and 150 °C for automobile applications⁸ and 225 °C for the 260 °C solder-reflow process.³² A free-layer structure of MgO/CoFeB/MgO layers is assumed for the calculation. The difference in dimensionless demagnetization coefficient $\delta N$ in Eq. (3) is numerically calculated.³³ The following parameters at RT are used: $M_S = 1.38$ T, $K_i = 1.55$ mJ/m², and $K_b = 0$ J/m³. $M_S$ and $K_i$ at high temperatures are calculated using the Bloch law and Eq. (4) with $n = 2$, which gives the lower bound of the scaling limit for the interfacial-anisotropy MTJ. In the interfacial-anisotropy MTJ region (a shaded region with $t < 2.5$ nm), the MTJ scaling is limited down to ~20 nm to maintain $\Delta > 82$ at higher temperatures. On the other hand, one can see the potential scaling of the shape-anisotropy MTJ region beyond 20 nm at 225 °C and beyond 10 nm at 85 °C. We note that there may be an upper limit of thickness, and hence $\Delta$, due to a formation of a domain wall that may trigger incoherent reversal.⁶

In summary, we investigate the temperature dependence of $\Delta$, or $E$, in the shape-anisotropy MTJ with diameters of X/1X nm and compare it with that of an interfacial-anisotropy MTJ. We show that the relationship between the temperature dependence of $E$ and $M_S$ is described by a power law scaling relationship with the scaling exponent $n$ of 2 and 4.7 for the shape- and interfacial-anisotropy MTJs, respectively. Whereas $n$ for the shape-anisotropy MTJ is close to the expected value, that for the interfacial-anisotropy MTJ is greater than that expected, implying different influences from the fabrication process between the two types of MTJs. The experimentally obtained $n$ enables us to discuss the design window of the MTJ dimensions to satisfy high thermal stability at various temperatures, showing that the shape-anisotropy MTJ holds promise to scaling down to 20 nm and beyond for high-temperature applications. We also note that in the shape-anisotropy MTJs, current-induced switching is observed within switching voltage below 1 V even with high $\Delta$ (see the supplementary material and Ref. 34). This study provides insightful information on

the temperature dependence of the energy barrier in the MTJs based on shape and interfacial anisotropies and guides the design of the MTJ structure for various applications.

See the supplementary material for a result of current-induced switching in the shape-anisotropy MTJ.

The authors thank H. Sato, K. Watanabe, Y. Takeuchi, T. Funatsu, R. Okuda, K. Hayakawa, I. Morita, R. Ono, and M. Musya for discussion and technical support. This work was supported in part by JST-OPERA Grant No. JPMJOP1611, JSPS KAKENHI Nos. JP19J12926 and JP19K04486, the JSPS Bilateral Joint Research Program, the Core-to-Core Program of JSPS, Tohoku University-Université de Lorraine Matching Funds, Cooperative Research Projects of RIEC, and DIARE of Tohoku university. J.I. acknowledges financial support from GP-Spin of Tohoku University and JST-OPERA. V.D. and S.M. acknowledge financial support from the PHC Sakura program and the French PIA project “Lorraine Université d’Excellence” Ref. No. ANR-15-IDEX-04-LUE and GP-Spin of Tohoku University.

## DATA AVAILABILITY

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

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