Optimization of magnetic parameters for toggle magnetoresistance random access memory

ARTICLE IN PRESS

Journal of Magnetism and Magnetic Materials 286 (2005) 27–30 www.elsevier.com/locate/jmmm

Optimization of magnetic parameters for toggle magnetoresistance random access memory Shengyuan Wang, Hideo Fujiwara MINT Center and Department of Physics and Astronomy, University of Alabama, P.O. Box 870209, Tuscaloosa, AL 35487, USA Available online 12 October 2004

Abstract The magnetic parameters of the synthetic antiferromagnetic (SAF) elements for toggle-mode magnetoresistance random access memories (Toggle-MRAMs) have been optimized using the critical field curves obtained by analytical method with the aid of numerical calculations, to maximize the operating field margin taking into account the required memory density, storage lifetime, half-select disturb robustness, and the available strength of operating field. The control of especially low-exchange coupling strength in the SAF in addition to the increase of the operating field has been found to be essential for the development of toggle-MRAM in near future. r 2004 Elsevier B.V. All rights reserved. PACS: 75.50.Ss; 85.70.Ay Keywords: Toggle-MRAM; Operating field margin; Synthetic antiferromagnet; Thermal stability; Exchange coupling strength

1. Introduction There has been a strong interest in magnetoresistance random access memory (MRAM) because of its nonvolatility, high rewritability, low-power consumption and fast switch [1–3]. To realize a memory density compatible with the semiconductor memory technology, the MRAM element should have an extremely small volume, which tends to decrease the thermal stability of memory Corresponding

author. Tel.: +1 205 348 7543; fax: +1 205 348 2346. E-mail address: [email protected] (H. Fujiwara).

elements [3–5]. Recently, a new scheme of an MRAM device has been proposed by Savtchenko et al. [3], in which a synthetic antiferromagnet (SAF) with a uniaxial anisotropy is used and the operating word field (H w ) and digit field (H d ) are sequentially applied at 451 and
451 with respect to the easy axis of the magnetic anisotropy, which potentially increases the operating field margin and element scalability. However no magnetic parameters of the element showing a reasonable operating field margin have been disclosed. We have recently proposed an optimization method using the tools obtained through analytical/ numerical calculations [6], in which the memory

0304-8853/$ - see front matter r 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2004.09.030

ARTICLE IN PRESS S. Wang, H. Fujiwara / Journal of Magnetism and Magnetic Materials 286 (2005) 27–30 12


M s t½H x cos y1 þ H y sin y1 
M s t½H x cos y2 þ H y sin y2  þ J cosðy1
y2 Þ;

ð1Þ

where H k M s =2 is equal to K u ; y1 and y2 the magnetization angles of the first and second FM layers with respect to the positive easy axis, J the exchange coupling strength, and H x and H y the external fields in the easy and hard direction respectively. The energy density in Eq. (1) basically includes the anisotropy, Zeeman and exchange coupling energy densities, which can be normalized by H k M s t: w ¼ 0:5½sin2 y1 þ sin2 y2 
½hx cos y1 þ hy sin y1 
½hx cos y2 þ hy sin y2  þ hJ cosðy1
y2 Þ;

ð2Þ

where w ¼ W =ðH k M s tÞ; hx ¼ H x =H k ; hy ¼ H y =H k ; and hJ ¼ J=ðH k M s tÞ: Two examples of the critical field curves are shown in Fig. 1(a) and (b); (a) for hJ ¼ 2 and (b)

hy

0

hs h cr 0 hx

h cr h s

-6

5

-12 -12

(b)

hd

W ¼ 0:5H k M s t½sin2 y1 þ sin2 y2 

h

w

h 0

-5

(a)

The two ferromagnetic (FM) layers of the SAF are assumed to have the same thickness t, magnetization M s ; and uniaxial anisotropy constant K u : The easy axes of the FM layers are assumed to be parallel to each other and the antiferromagnetic exchange coupling is strong enough to make the antiparallel magnetization configuration when no external field is applied. Critical field curves for switching and saturation are obtained from the equilibrium conditions of the following energy density (per unit area) expression:

6

hd

hw

-5

2. Critical field curves of SAF

w

5

hd

volume, memory lifetime, half-select disturb effect and available field strength for the memory operation are taken into account. This paper presents the optimization results we obtained for the element volumes which may cover the requirements for the memory density of the first and second device generations.

hy

28

-6

0 hx

6

12

Fig. 1. Critical curves for (a) hJ ¼ 2 and (b) hJ ¼ 5; the critical points hcr and hs are marked on the positive hx axis. The trajectory for toggle switching is shown by the vectors, hw ; hd ;
hw and
hd :

for hJ ¼ 5; respectively. In Fig. 1(a), the critical curve is composed of an oval-like outermost curve and two small astroid-like curves, which we simply call ‘astroids’, hereafter. With the increase of hJ ; the outermost curve expands, but the astroid reduces its size and eventually shrinks into a spot (Fig. 1(b)). The outermost curve is the critical curve for saturation and the astroid is the critical curve for switching which corresponds to the ‘astroid’ well known for the single uniaxial anisotropy layers. The two critical points hcr and hs in hx -axis marked in Fig. pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi 1 can be solved analytically as hcr ¼ 2hJ þ 1 and hs ¼ 2hJ
1: In the memory operation, the operating field must be restricted within the saturation curve. A smooth toggle mode switching occurs only when the operating field trajectory goes around the astroid within the saturation curve [6], as is shown in Fig. 1(a).

3. Optimization of the SAF parameters We assume that the absolute values of the word field H w and the digit field H d are set equal to each other, which may be a reasonable choice considering the symmetry of the magnetic characteristics of the SAF element as is seen from the critical curves shown in Fig. 1. Then, the field tip falls pffiffioperating ffi onto the hx -axis at hx ¼ 2hw ; when both hw and hd are applied coincidently. The maximum operating field margin is obtained when this point coincides with the mid point of hcr and hs : This

ARTICLE IN PRESS S. Wang, H. Fujiwara / Journal of Magnetism and Magnetic Materials 286 (2005) 27–30

Solving Eq. (3), we obtain pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffi ffi pffiffiffi 3
9 þ 8 2hw hJ ¼ 2hw þ : 4

(4)

Therefore, once the anisotropy field of the element, H k ; is given, hw is obtained from H w to be used, which in turn determines the hJ value. The H k of the element has to be determined from the required storage lifetime by using the Ne´el–Arrhenius formula. Assuming that both of the SAF magnetizations relax simultaneously, it is deduced that the energy barrier 2K u V must satisfy the following condition: 2K u V XkB T lnðt0 f 0 N 0 Þ;

(5)

where V is the single FM layer volume, kB is the Boltzmann constant, T is the storage temperature, t0 is the relaxation time of each memory element, N 0 is total number of applicable memory elements, and f 0 is the frequency factor. Since K u ¼ M s H k =2; HkX

kB T lnðt0 f 0 N 0 Þ : MsV

(6)

In the following we assume M s ¼ 850 emu=cm3 ; T ¼ 360 K; f 0 ¼ 109 Hz; N 0 ¼ 1012 ; and 10-year storage lifetime (t0 ¼ 3:15 108 s), which may be typical conditions for the MRAM under development. Then, from Eqs. (5) and (6) we obtain 2K u V =kB T\68; and H k X3:4 10
12 erg=ðM s V Þ Oe, where V is in cm3 : For a conceivable volume of MRAM elements like V ¼ 1–10 10
16 cm3 ; we obtain H k ¼ 40–4 Oe: In the MRAM operation, the loss of memory due to the half-select disturbance must be prevented. The required energy barrier DE can be obtained similarly to that for the memory life as discussed above DE ¼ kB T lnðtp f 0 N p Þ;

(7)

where tp is the pulse duration of either the word field or the digit field, and N p is the number of pulse disturbances to which each element must endure. Assuming tp ¼ 10 ns; N p ¼ 1012 ; we ob-

tain DE=kB T 30; and DE c  1:5 10
12 erg at T ¼ 360 K and the single FM layer thickness t ¼ 4 nm: On the other hand, the energy barrier between the two stable magnetization configurations changes as a function of hw (or hd ), which can be calculated using Eq. (2) taking into account the stability conditions. An example of the barrier height DE normalized by M s H k V calculated for V ¼ 5 10
16 cm3 is shown in Fig. 2(a). For the calculations, H k ¼ 7:9 Oe; H w ¼ 25 Oe (hw ¼ 3:1), and hJ ¼ 3:5 were used, where H k and hJ having been calculated from Eqs. (6) and (4), respectively. The energy barrier height corresponding to the required height 1:5 10
12 erg is about 0.44, which is marked by the horizontal straight line in the figure, from which the maximum value allowable for hw can be read as hw;max 5:3: In Fig. 2(b), the operating field margin thus obtained is shown as the gray area. Here, we define the relative operating field margin (Rmargin ) as Rmargin ¼

hs
hcr ; hs þ hcr

(8)

pffiffiffi where ðhs þ hcr Þ=2 is equal to 2hw : The relative margin is 0:36 for the particular example discussed above (Fig. 2(b)). Figs. 3(a) and (b) show the Rmargin and the optimized J value vs. the element volume relationships with H w value as a parameter, which is obtained in the same manner as above. It is seen how the margin increases with increasing the element volume and available H w value. For lower available H w of 50 and 25 Oe, we lose the margin at 1 and 2 10
16 cm3 ; 5.3

2.5

hw

2.0 ∆ε

gives a sort of hw
hJ optimization relationship: pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffi ð2hJ
1Þ þ 2hJ þ 1 2hw ¼ : (3) 2

29

hx hx,max hs

hw,max

1.5 1.0 0.5

0.44

hw,min

hcr

0.0

3

4

5

hw

6

7

8

hd,min

hd hd,max

Fig. 2. (a) Energy barrier between the two stable configurations vs. the single switching field hw : From the critical energy barrier Dwc ¼ 0:44; maximum applied field can be obtained as hw;max

5:3: (b) Operating field margin (gray area) for hJ ¼ 3:5 with the consideration of half-select disturbs.

ARTICLE IN PRESS S. Wang, H. Fujiwara / Journal of Magnetism and Magnetic Materials 286 (2005) 27–30

30

J (×10-2 erg/cm2 )

R margin

1

A

0.5

B

C

D

0

A

8 6 4

B

2

C D

Acknowledgements

0

0

(a)

possesses some elongated shape in one direction. The details will be presented elsewhere.

10

2

4

6

8

V (×10-16cm3)

10

0

(b)

2

4

6

8

10

V (×10-16cm3)

Fig. 3. (a) Relative margin ðRmargin Þ and (b) Optimized coupling strength (J) vs. the element single FM layer volume (V) at different operating field, H w ; (A) 200 Oe, (B) 100 Oe, (C) 50 Oe, and (D) 25 Oe.

Partial supports of this research are from MRSEC Grant (DMR-0213985).

References respectively. Special attention is to be paid to the fact that the exchange coupling strength to be controlled is in an extremely low value range compared to the ordinary SAF of the order of

1 erg=cm2 : In the above we did not include the effect of the magnetostatic coupling between the two layers of the SAF, which may act similarly to the antiferromagnetic coupling with a difference that it shows an angular dependence if the element

[1] J.M. Daughton, Thin Solid Film 216 (1996) 162–168. [2] S.S.P. Parkin, K.P. Roche, M.G. Samant, P.M. Rice, R.B. Beyers, J. Appl. Phys. 85 (1999) 5828–5833. [3] L. Savtchenko, A.A. Korki, B.N. Engel, N.D. Rizzo, J.A. Janesky, US Patent, 6,545,906 B1 April 2003. [4] S.V. Pietambaram, R.W. Dave, J.J. Sun, J. Janesky, G. Steiner, J.M. Slaughter, GE-03, Ninth Joint MMM/ INTERMAG Conference, 2004. [5] B.N. Engel, J. Akerman, B. Butcher, et al., GE-05, Ninth Joint MMM/INTERMAG Conference, 2004. [6] H. Fujiwara, S.-Y. Wang, M. Sun, Trans. Mag. Soc. Jpn, 2 (4) (2004), in press.