Shape effect in FMR of NiCo-Mn-In layers obtained by pulsed laser deposition

We have studied thin layers of Ni50-xCoxMn50-yIny alloys on (001) Si substrate obtained by pulsed laser deposition method (PLD) using YAG Nd laser operating at second harmonic. The target was bulk Ni50-xCoxMn50-yIny (x = 5, y = 14.5) alloy prepared by induction melting of pure elements under argon atmosphere. Magnetic properties were investigated on Bruker X band EPR spectrometer (9.36 GHz) at room temperature. The magnetic resonance spectrum consists of nonsymmetric lines with resonance field within wide field range (2500-4800 Gs) depending on the orientation of the static field in the plane perpendicular to the layer. Calculated spectroscopic splitting factor g = 2.09.


Introduction
The alloys system Ni 50-x Co x Mn 25+y Z 25-y (Z = Sn, In, Ga, etc.), is Co-doped off-stoichiometric version of betterknown Ni 2 MnZ full Heusler alloys [1].Addition of Co caused important changes in magnetism and structure [2].
The advantageous properties of Heusler films have initiated study of this group of material [8,9].In addition the thin film technology is promising for application in nanodevices (see at [1] chapter 5).In this research, we registered ferromagnetic resonance (FMR) spectra of a NiCoMnIn layers which were prepared on Si substrate by using pulsed laser deposition method.

Sample preparation and experimental techniques
The NiCoMnIn films were deposited on silicon substrates by pulsed laser deposition (PLD).The off-stoichiometric bulk Ni 45 Co 5 Mn 35.5 In 14.5 was made by arc melting [10] and was used as a target.Films were grown in PREVAC PLD system using the YAG: Nd 3+ laser with the 532 nm (II harmonics) wavelength, 6 ns pulse time, 10 Hz repetition rate and fluence F in the range of 16 J/cm 2 .The laser beam was focused on the target using a quartz lens with focal distance of 600 mm.The growth temperature T s was 300 K.The deposition of the layers was carried out at 10 -7 mbar vacuum.
The FMR measurements were performed on Bruker ELEXSYS E580 spectrometer using the X-band (9.36 GHz).Angular dependence was registered with the use of uniaxial goniometer at room temperature.The samples for these measurements were fixed in the microwave cavity in such a way that applied static field was perpendicular to rotating sample (Fig. 1).The xyz coordinate system in Fig. 1 is the system connected with a sample.The z is a rotation axis.The spectra were recorded as a function of angle with a 4 degrees step.

Results and discussion
The addition of Co and change of composition influence on the martensitic transformation and Curie temperature.[10][11][12].In the Ni 50-x Co x Mn 25+y In 25-y alloys with the 5 at.% of Co (x = 5) a T C A (Curie temperature in austenite phase) temperature was shifted to 343 K [10].Therefore at the room temperature we could registered ferromagnetic resonance.FMR spectra of the investigated sample at room temperature are shown in Fig. 2 for different angle φ B between normal to the plane (x axis) and external field B 0 (see Fig. 1).The spectra contain a broad and asymmetrical line of the Dyson shape [13,14].The asymmetry FMR line suggested that investigated sample is conductive and line shape is connected with skin effect.The FMR spectra of Ni 50-x Co x Mn 50-y In y film were fitted by using derivative of Dyson function: where B res is the resonance field, ΔB is the linewidth and α is the parameter of asymmetry which describes the absorption and dispersion ratio [14].The examples of fitting are presented in Fig 3.It could be seen that the line shape depends on the angle between applied static field and the film (Fig. 1).The careful study of obtained spectra reveals overlapping signals.The analysis of FMR parameters was done in this paper for the strongest asymmetric line, whereas the complexity of spectrum will be investigated elsewhere.The parameters of fitted lines are collected in table 1.The ferromagnetic resonance field is described by Landau-Lifshitz equation (LL equation) where ‫ۻ‬ is magnetization vector, ۰ is the effective magnetic field, ߛ is the gyromagnetic ratio and ߙ is Gilbert damping parameter associated with a relaxation mechanisms of vector ‫.ۻ‬In the case of a ferromagnetic resonance of a flat plane with external magnetic field ‫ܤ‬ perpendicular or parallel to the plane the solution of LL equation reduced to two Kittel equation [16]: where ‫ܤ‬ = ‫ܤ‬ ∥ is a resonance field in plane case and ‫ܤ‬ = ‫ܤ‬ ୄ corresponds to of plane case.Taking into account that ߛ = ఓ ಳ ℏ , these two equations could be written as: Comparing right sites of equations ( 3) and ( 4) we obtain the equation where ‫ݔ‬ ≡ ߤ ‫.ܯ‬ Inserting to (7) experimental values ‫ܤ‬ ∥ = 2534 Gs and ‫ܤ‬ ୄ = 4803 Gs given by fitting curves (see Tab. 1), the equation is reduced to From the set of eq. ( 5) and ( 6) the g-factor and effective saturation magnetization ߤ ‫ܯ‬ could be calculated.The solution are: ݃ = 2.09 and ߤ ‫ܯ‬ = 1576 Gs.The value of g-factor is similar to g-factor ݃ = 2.01 listed by Kittel (see Table I [17]) for Heusler alloys.

Conclusion
The layers of Ni 50-x Co x Mn 50-y In y have been grown on (100) Si substrate by PLD method.Angular dependence of FMR spectra was registered at room temperature.The obtained FMR spectra were fitted by Dyson function.
The experimental FMR lines exhibited a strong angular dependence and shape anisotropy with resonance field changed from 2600 Gs (for parallel geometry) until 4800 Gs (for perpendicular geometry).Calculation of g-factor (g = 2.09) provides a typical value for Heusler alloys [17].

Fig. 1 .
Fig. 1.Schematic orientation of film with respect to static field B 0 .

Fig. 2 .
Fig.2.The angular dependence of the FMR spectra of a film at room temperature.The spectra have been shifted vertically for better visibility.

Table 1 .
The fitting parameter of the EPR signals for φ B = 0 and 90 deg.