Thermal resistance investigation of the giant magnetoresistance thin layers by the PTD technique

Investigation of thermal properties giant magneto-resistance constituted with an assembly of alternated Mn/Fe layers according to the Mn thickness using the Photother mal Deflexion Technique. We show in this work that the thermal resistance passes by a maximum value for a Mn critical thickness corresponding to the antiparallel ferromagnetic coupling.


Introduction
Since the 1980's many researches have been carried out on the magnetic multi-layers containing ferromagnetic and nonmagnetic materials. In October 2007, the Nobel Prize in Physics was discerned to Albert Fert and Peter Grünberg for the Giant magneto-resistance (GMR) effect observed in magnetic multi-layers [1][2][3].
The GMR samples are an assembly of multi-layers alternated by ferromagnetic-metal and nonmagnetic-metal (FM/NM) with a thickness of about 1 nm. One of the first manifestations of the new properties of these structures was the observation, in 1986, of an antiferromagnetic coupling between layers of iron in three layers Fe/Cr/Fe epitaxially deposited by molecular jets on AsGa substrate [2].
Several theorists such as Camley, Trigui, Barthélémy [4][5][6][7] tried to develop mathematical models allowing the interpretation of these multi-layers. Duvail et al. [8] were interested in the dependence versus temperature and thickness of the resistivity and the magneto-resistance of Co/Cu multi-layer. Over the past 30 years a large interest of the GMR samples has been motivated by the understanding of their very magnetic properties, which are briefly described as follow: the ferromagnetic-metal is microscopically formed by small zones called Weiss-zones. Each zone is characterized by magnetic moments aimed at in the same direction. In the case of a small lateral dimension, a magnetic interaction between the ferromagnetic layers giving a global magnetization oriented in the same direction, one says for this balance situation that there is a parallel coupling between the magneticlayers. By increasing the thickness of the nonmagnetic-metal layer, one crosses a value which, a e-mail : taher.ghrib@yahoo.fr beyond the coupling, becomes antiparallel. The resistance is higher for antiparallel configuration and smaller for parallel magnetization configuration. In this work, we studied the effect of Mn layer thickness on the thermal properties of the GMR samples constituted by an assembly of alternated Manganese thin layers (nonmagnetic metal) with a thickness varying from 0.3 to 1.7 µm and 1.5 µm iron layer (ferromagnetic metal). The thermal properties were determined by the Photo-Thermal Deflection (PTD) technique [8][9][10].

Sample preparation
The evaporation enclosure is equipped with a turbo-molecular pump, allowing a vacuum of about 10 -9 mbar. The materials to evaporate (Mn and Fe) are placed in alumina crucibles and are heated by radiation up to 1250°C. Each overflowing cell is equipped with an electro-pneumatic mask, which makes it possible to deposit alternatively the various materials without stopping their evaporations. These layers are deposited with evaporation rates of m.s 2.10 -1 -12 for iron and -1 -12 m.s 6.10 for manganese. The thickness of each layer is measured via a quartz oscillator calibrated at the deposition temperature. We obtain an assembling composed of 21 identical layers deposited on silicon substrate: Si/ Mn/ Fe/ Mn/……Fe/ Mn. The protective layer is Mn with 22 nm thickness.

Magnetic properties
From magnetization measurements recorded versus magnetic applied field, we have plotted the hysteresis loops (Fig. 1). We can noticed that, the larger value of Mn thickness is, the more the cycles are flat, i.e., more need for applying a large field H to reach the saturation is required. This behavior has been observed for an antiparallel coupling. Whereas for thin Mn layers we observe square cycles, signature of parallel manganese ions coupling.

Thermal properties
The thermal properties such as the thermal conductivity and the thermal properties are determined by the PTD technique. . The thermal wave generated by the optical absorption of the sample will propagate in the sample and in the surrounding fluid (air in our case). The thermal wave in the fluid will induce a temperature gradient then a refractive index gradient in the fluid which will cause the deflection ψ of a probe Laser beam skimming the sample surface. This deflection may be related to the thermal properties of the sample.
The sample is a stack of 21 layers (Fig. 2), We write the heat equations in these areas and in the two surrounding fluid by designating K i , D i and l i respectively the thermal conductivity, the thermal Diffusivity and the thickness of the layer i.

Probe beam deflection
In the case of a uniform heating we can use a 1-dimensional approximation, and the amplitude ψ and phase ϕ of the probe beam deflection ψ are given by: T that is calculated as follows.

Surface temperature
The resolution of the heat equation gives the following temperature equation: We can then write the flow equation in each medium The temperature and heat flow continuity at the interface x=-ln permit to obtain: By writing of the heat flow and temperature continuity at the interfaces x=0 and x= -l 3 -l 2 -l 1 , we obtain respectively: That is n E T X

Experimental set-up
The sample is heated by a halogen lamp light of 100W power modulated thanks to a mechanical chopper at a variable frequency. A (He-Ne) Laser probe beam skimming the sample surface at a distance z is deflected. This deflection can be detected by a four quadrant photo-detector and converted into an electrical signal which is measured by a lock-in amplifier. Through the intermediary of interfaces, the mechanical chopper and the Look-in amplifier a microcomputer will set the desired modulation frequency and read the values of the amplitude and phase of the photothermal signal and then draw their variations according to the square root modulation frequency (Fig.  3). 00041-p.5   The thermal resistance of the sample is given by Where i e , S and i K are respectively the thickness, the surface and the thermal conductivity of the sample and for a surface equal to 2 1 cm S = we can trace the evolution of the thermal resistance of the GMR materials versus the Mn thickness as shown in Figure 5. We notice from these curves that the thermal resistance and the Mn absorption coefficient present maximum values for a Mn thickness equal to1.5nm . According to the theoretical study proposed in section IV, this thickness correspond to the transition ferromagnetic parallel-antiparallel and more precisely corresponds to an antiparallel coupling of the dipoles. Several experimental studies [1-3, 7, 9] showed that the magneto-resistance also reaches a maximum value for a critical thickness of nonmagnetic material. Thus one can deduce a mathematical relation which relates the magnetic and thermal resistances similar to that proposed by Wiedemann-Franz [10] T L K e σ = giving a relationship between the electronic conductivity of and T is the sample temperature, which shows that the two parameters have the same evolution.

Conclusion
In this work we have studied the evolution of the thermal properties of the giant magneto-resistance samples made of an assembly of alternated Mn/Fe layers using photothermal deflection technique. A developed mathematical model has been given. We have also been interested in the thermal resistance evolution as a function of Mn thickness, and we have noticed that it reaches a maximum value for a Mn critical thickness corresponding to an antiparallel ferromagnetic coupling.