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5
УДК 539.2
Influence of Interface Roughness on Spatial Distribution of Magnetization at Substitutional Adsorption of the Ultrathin Iron Film
Pavel Yu. Ezhkov* Marina V. Mamonova^
Dostoevsky Omsk State University Mira, 55a, Omsk, 644077
Russia
Received 20.08.2016, received in revised form 10.10.2016, accepted 05.11.2016 In this work, we use the variational spin-density functional method for theoretical description conditions of the formation of stable films and calculation of interface energy and spatial distribution of relative magnetization at activated adsorption of Fe film on the W and Au substrates with taking into consideration the interface roughness. We include into consideration the thermal effects of transition metal atoms intermixing inside film and their substitution with atoms of substrate surficial layer.
Keywords: adsorption, ultrathin magnetic films, spin-density functional theory. DOI: 10.17516/1997-1397-2016-9-4-449-453.
Introduction
Studies of thin magnetic films led to the discovery of a number of remarkable phenomena, including GMR and TMR effects, which enabled such systems to be utilized in microelectronics and computer components industry [1,2]. So investigations focused on determination of the conditions for realizing practically useful properties of magnetic films, which determine their application, are of great importance.
In this work, we investigated for Fe/W(110) and Fe/Au(111) systems the behaviour of full interface energy by spin density functional theory (SDFT) with taking into account temperature effects and inhomogeneous spatial distribution of relative magnetization in surficial region. Influence of interface roughness and effects of intermixing between adatoms and substrate atoms is also taken into consideration.
1. Model and approach description
Configuration of our system is presented in Fig. 1(a). In accordance with SDFT total interfacial energy of the system a(D) is functional of n±(z) = n(z)(l ± m(z))/2. Spatial distribution
* ezhkov.pavel@gmail.com t mamonova_mv@mail.ru © Siberian Federal University. All rights reserved
substrate , mlxm9 area
A S, .
P 1-P
I. ■
\l=pd'+( 1 —p')d
(a)
1 adsorbat film
<13 n
c 3
CT>
0
o £ A S,
® p i-p
/i=pi("+(1-p)ds
(b)
Fig. 1. (a) System configuration. Parameters p, p' are a relative fraction of the adsorbate atoms in film and in mixing area of the substrate respectively, da and ds are distances between the most closely packed planes in crystals of the adsorbate and the substrate. (b) Coverage parameters 9min and 9max as a function of temperature. Solid line - Fe/W(110), dashed - Fe/Au(111)
of relative magnetization have the following form
'0.5m2e^+D) [efl-1] + 0.5m,3e/(z-D) [l - e-?h] , m2 [l - 0.5ef(z+D) - 0.5e-«z+D+l)] + 0.5m3ef(z-D) [1 - , 0.5m2e-^(z+D) [1 - e-?l] + 0.5m3e«z-D) [1 - e-^h] ,
i(z) =
-ph]
z < -D - l; -D - l<z< -D; -D< z< D; (1)
.5m2e-p(z+D) [1 - e-pl] + m3 [l - 0.5e-p(z-D) - 0.5ep(z-D-h)] , D<z<D + h; 0.5m2e-p(z+D) [1 - e-pl] + 0.5mse-p(z-D) [eph - l] , z> D + h;
where m2 = m(T)p'(©) and m-3 = m(T)p(©) are characteristic magnetizations in mixing area of substrate and in film respectively. The values of the variational parameters /3,p, p' are obtained from the requirement of the minimum a. For description of temperature dependence for the relative magnetization m(T) we used the relation characteristic for the two-dimensional Ising model (for the Fe/W system):
-4
i(T ) =
1
sinh i —) \ 2.269T )
1/8
(2)
and the relation characteristic for the 2D XY-model (for the Fe/Au system):
AT) ~
Tc- T
Tc
(3)
where Tc = T(s) (0) = 0T,
(b) '
rf
zbulk
is film's Curie temperature, zSUrf is the number of nearest
neighbours in the film. For Fe Tc(s)(© = 1) = 521.5 K.
0.231
More detailed theoretical description is presented in [3].
2. Conditions of the formation of stable films
Analysis of the dependencies of the interface energy a on D shows that there are two "bounding" coverage parameters: 0min(T) and 6>max(T). When 0 < 0min interface energy does not have a minimum at D > 0, while at 0 > 0max minimum of interface energy has a negative value. This may apparently mean that when 0 < 0min interface roughness is negligible and, therefore, system has an ability to show a strong intermixing between substrate and adsorbate, while at 0 > 0max an opportunity for an island adsorption emerges, and, therefore, the stable films are realized at
0min (T ) <0< 0max(T ) only.
Calculated values of 0min and 0max are presented in Fig. 1(b). It can be seen that for both systems decreasing of the temperature shifts mentioned intervals toward lower coverage values. For T < 400 K, the Fe/Au(111) system has a wider interval of stable films compared to the Fe/W(110) system, and conversely for T > 400 K.
3. Equilibrium interface roughness parameter
Further, we present our results of calculating equilibrium interface roughness parameter Do, at which interface energy a reaches its minimum. In cases where the minimum was not detected, Do = 0 was assumed. Dependence of Do on coverage 0 is presented in Fig. 2.
Fig. 2. The dependence of the equilibrium interface roughness parameter D0 on the coverage d for a) Fe/W(110) and b) Fe/Au(111) systems. Temperatures: 1. T = 100 K, 2. T = 350 K, 3. T = 450 K, 4. T = 550 K
It is seen, that for Fe/W(110) system values of Do are in the interval [0,0.61] a.u., and that this quantity decreases with the increase of temperature and grows with the coverage. The Fe/Au(111) system is generally characterized by lower values of interface roughness compared to the first system: values of Do are laid in the interval [0,0.44] a.u.
4. The spatial distribution of magnetization
In Fig. 3 we present our results of calculation the spatial distribution of magnetization for
t = 100, 300 k, e = 0.6, 1.0.
For Fe/W(110) system it can be seen that in some cases taking interface roughness into consideration increases the maximum value of magnetization in film, thus improving its magnetic properties. In other cases changes in the maximum value of the magnetization in connection with
Fig. 3. The spatial distribution of magnetization for (a), (b) Fe/W(110) and (c), (d) Fe/Au(111) systems. Temperatures: (a), (c) T =100 K and (b), (d) T = 300 K. Coverages: 1,2. 0 = 0.6 and 3,4. 0 = 1.0. Accounting of the interface roughness: Solid line - No (D = 0), dashed - Yes (D = Do). Vertical lines denote the boundaries of the areas.
the account of the interface roughness do not occur. Unlike the first system, taking interface roughness into consideration for Fe/Au(111) system led to a minor decrease of maximum value of magnetization, and only in the case T = 300 K, e = 0.6, when maximum value of magnetization was shifted to surficial area of substrate, it has been increased.
Investigations were supported by Russian Scientific Fund, project 14-12-00562.
References
[1] C.A.F.Vaz, J.A.C.Bland, G.Lauhoff, Magnetism in ultrathin film structures, Rep. Prog. Phys., 71(2008), 056501.
[2] J.J.M.Ruigrok, R.Coehoorn, S.R.Cumpson, H.W.Kesteren, Disk recording beyond 100Gb/in2: Hybrid recording? J. Appl. Phys., 87(2000), 5398-5405.
[3] S.P.Klimov, M.V.Mamonova, V.V.Prudnikov, Description of substitutional adsorption of magnetic Ions on metallic surfaces with formation of monolayer ferromagnetic films using the spin-density functional method, Solid State Phenomena, 190(2012), 27-30.
Влияние межфазной шероховатости на пространственное распределение намагниченности при заместительной адсорбции в ультратонких пленках железа
Павел Ю. Ежков Марина В. Мамонова
Физический факультет Омский государственный университет Мира, ббя, Омск, 644077 Россия
В данной 'работе в рамках вариационного метода функционала спиновой плотности представлено теоретическое описание условий форирования стабильных пленок и результаты расчетов межфазной энергии и распределения относительной намагниченности пленок Ев на подложках IV и Аи с учетом межфазной шероховатости. Рассмотрено влияние температурных эффектов перемешивания атомов субстрата и адсорбата в приповерхностной области.
Ключевые слова: адсорбция, ультратонкие магнитные пленки, метод функционала спиновой плотности.
