JOURNAL OF OPTOELECTRONICS AND ADVANCED MATERIALS Vol. 9, No. 4, April 2007, p. 1140 - 1142 Simulation of toggle mode switching in MRAM’S C. S. OLARIU * , L. STOLERIU, A. STANCU Department of Solid State & Theoretical Physics, “Alexandru Ioan Cuza” University, Faculty of Physics, Blvd. Carol I, 11, 700506, Iasi, Romania The magnetization switching in Stoner-like magnetic particles is one of the fundamental issues in magnetic data storage. In develop of magnetoresistance random access memory (MRAM), the theoretical studies are now concentrated in various parameters improving. Some important parameters are the range of the operating field and the switching time. The writing mode proposed by Savtchenko and co-workers is known as the toggle MRAM or toggle write mode, is essentially based on a sequence of fields applied at 45° with respect to the easy axis of an antiferromagnetically coupled system of two single domain particles. We have recently analyzed systematically systems of two magnetic moments coupled with magnetostatic interactions. In this paper we are presenting the effect of the anisotropy of each material on the switching of a SAF in a toggle mode. For the uniaxial anisotropy type analytical approach is possible and simple results and critical curves are presented. For the more general case only the micromagnetic simulation can offer results. The studies are made for different coupling constants between the two ferromagnetic layers and the results are discussed. (Received January 25, 2007; accepted February 28, 2007) Keywords: Magnetic memories, Toggle mode switching, LLG simulation 1. Introduction For increasing the operation margin of MRAM elements, actual applications use magnetic memories cells made from two ferromagnetic layers with antiferromagnetic coupling and separated from a very thin a non magnetic layer, named Synthetic Antiferromagnet (SAF). Recently, Savtchenko and co-workers proposed a new writing method of a MRAM element, named toggle mode. [2] The “word” and “digit” field are applied sequentially with an angle of 45 degrees with respect to the easy axis of the magnetic anisotropy of memory element (Fig. 1). An SAF element are made from two ferromagnetic layers 1 and 2 that have the thickness t 1 and t 2 , magnetizations M 1 and M 2 and uniaxial anisotropy constants K u1 and K u2 . The easy axes of the two layers are parallel and antiferromagnetic coupling. Energy density for unit area W can be expressed: ) cos( ] cos cos [ ] sin cos [ sin sin 2 1 2 2 2 2 1 1 1 1 2 2 2 2 1 2 1 1 θ θ θ θ θ θ θ θ − + + + − − + − − + = J H H t M H H t M t K t K W y x y x u u (1) where 1 θ and 2 θ are the angle between magnetization M 1 and M 2 and easy axis for each layer, H x and H y are components of applied magnetic field from Ox and Oy axis and J are the antiferromagnetic coupling strength between the two layers. We chose a coordinating system in witch Ox axis coincide with easy axis and Oy axis coincide with hard axis, parallel with the layers plane. Normalizing W by 1 1 2 t K u and use identical layers for simplify the discussion ( 2 1 t t = , 2 1 M M = , 2 1 u u K K = ), the free energy can be expressed as: ( ) 2 1 2 2 1 1 2 2 1 2 cos ) sin cos ( ) sin cos ( sin 2 1 sin 2 1 θ θ θ θ θ θ θ θ − + + + − + + − + = J y x y x h h h h h w (2) where all the field are normalized at the anisotropy field of layers and ( ) y x h h , are projections of applied field: k x x H H h = , k y y H H h = , 1 1 2 M K H u k = , 1 1 2 t K J h u J = . Fujiwara and co-workers propose to study the trajectories of the field, giving a constant angle 1 θ and leaving 2 θ to be a variable and vice versa, for easily understand the response of the magnetizations to the applied vector – field in the ( ) y x h h , plane. [1] They call this trajectories “constant angle contours” and can be founded by solving the equilibrium and stability conditions: 0 1 = w , 0 2 = w , 0 11 > w , 0 22 > w , 0 2 12 22 11 ≥ − = w w w D (3) where 1 w , 2 w , 11 w , 22 w and 12 w are the first and the second derivates of energy w with respect to 1 θ and 2 θ , respectively. Expressions of x h and y h are: ⎪ ⎪ ⎩ ⎪ ⎪ ⎨ ⎧ − − + + + − = − − + + + − = ) sin( / )] sin( ) sin (sin ) cos (cos sin [sin ) sin( / )] sin( ) cos (cos ) sin (sin cos [cos 2 1 2 1 2 1 1 2 2 1 2 1 2 1 2 1 1 2 2 1 θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ J y J x h h h h (4)