Effect of Temperature on the Ferromagnetic-Resonance ... - IEEE Xplore

IEEE TRANSACTIONS ON MAGNETICS, VOL. 45, NO. 10, OCTOBER 2009

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Effect of Temperature on the Ferromagnetic-Resonance Field and Line Width of Epitaxial Fe Thin Films Bijoy K. Kuanr1 , V. Veerakumar1 , Alka V. Kuanr2 , R. E. Camley1 , and Z. Celinski1 Center for Magnetism and Magnetic Nanostructures, Department of Physics, University of Colorado at Colorado Springs, Colorado Springs, CO 80918 USA Rajguru College of Applied Science for Women, Jhilmil Colony, Vivek Vihar, Delhi-110 092, India The temperature dependence of the ferromagnetic-resonance field (Hres ) and line width (1H) of epitaxial Fe thin films were studied. It is observed that Hres increases whereas 1H decreases with the increase in temperature. The change in Hres is governed by the temperature dependence of the saturation magnetization and the magneto-crystalline anisotropy energy of the film. The present lowtemperature investigations of Hres obeys the well-known T3 2 Bloch law. The resonance line width as a function of temperature shows a transition temperature (T1 ) separating two different regimes. This behavior may be associated with the temperature dependence of the anistropy. The Hres results are confirmed theoretically by simulating the power absorbed at ferromagnetic resonance by using the Landau–Lifsthiz–Gilbert equation. Index Terms—Fe thin film, ferromagnetic resonance, magnetic thin films.

I. INTRODUCTION ITH the rapid progress of nanotechnology and high-density recording, there is great interest in studying magnetization dynamics in magnetic nanostructures. Ferromagnetic thin films and metallic multilayers have been the subject of intensive work during the last decades [1]–[10]. Epitaxial growth of magnetic layers on semiconductor substrates has been widely attempted for the integration of magnetic/semiconductor hybrid devices [1]–[3]. One of the major issues in the magnetic data-storage industry is the data-transfer rate. Frequencies for writing and reading are now in the microwave region, which raises the question, “How fast can magnetic materials switch?” The answer is determined in part by the relaxation mechanisms in the magnetic film [3]–[7]. In addition, the anisotropy field of the epitaxial Fe system can act as an internal field that can boost the resonance frequency of microwave bandpass/bandstop filters at the zero applied magnetic field [4], [5]. The interfaces play an important role in these structures. It has been reported that for Fe films deposited directly on gallium-arsenide (GaAs) substrates at high temperature, interdiffusion of As species into the upper iron layer could occur. The compound forms a magnetically dead layer at resulting the interface, which can severely degrade the magnetization of the sample and leads to a disruptive effect at the semiconductor/ metal interface. The fundamental magnetic, electronic, and optical properties of ultra-thin film structures can be quite different from their bulk counterparts. In addition, the magnetic parameters of thin films are highly affected by growth conditions, sample treatment, purity of the alloys, temperature, etc. One of the most interesting questions on this subject is the dependence of the magnetic anisotropies with temperature [2]. In

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Manuscript received March 07, 2009; revised April 30, 2009. Current version published September 18, 2009. Corresponding author: B. K. Kuanr (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMAG.2009.2023231

this context, Fe has been one of the most extensively used materials for studying magnetic properties of ferromagnetic thin films [6]–[11]. In this paper, we present ferromagnetic-resonance (FMR) measurements on single crystal Fe films grown on the GaAs(001)/Fe(1 nm)/Ag(150 nm) template as a function of temperature between 20 and 300 K. Experimental and theoand resonance line retical studies of the resonance field were performed at different temperatures. Also, width dependence of was performed at the inplane angle different temperatures. The model assumes that the observed temperature variations of resonance field and line width are due to the temperature dependence of the anisotropy and magnetization. II. EXPERIMENT The experiments were carried out on samples with the following principal structure: GaAs(001) substrate, 1-nm Fe seed layer, 150–nm Ag layer, principal Fe films 16 and 6 nm, and the 500-nm ZnS layer [1]. A GaAs(001)/Fe(1 nm)/Ag(150 nm) template was chosen for epitaxial growth of the principal Fe film. The films were grown by molecular-beam-epitaxy at a background pressure of Torr and at a deposition rate of 0.01 nm/s. The recipe of epitaxial growth is given elsewhere [1]. In-situ characterization is performed by Auger electron spectroscopy, low-energy electron diffraction (LEED), and reflection high-energy electron diffraction (RHEED). Both RHEED and LEED indicated the epitaxial growth of Fe. Room temperature magneto-optic Kerr effect (MOKE) measurements were performed. The coercivity of the Fe films was determined by MOKE hysteresis loops (Fig. 1) and is found to be 8 Oe. The analysis of the easy and hard-axis MOKE graphs gives the cubic anisotropy for the 16-nm Fe sample as 610 Oe. Conventional FMR investigations at 24 GHz were performed with an FMR spectrometer using the field-modulation technique. The temperatures were measured using the resistance thermometer. Low-temperature measurements were performed by using a closed-cycle helium Dewar system at a vacuum of

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Fig. 1. Room temperature magneto-optic hysteresis loops showing the magnetic easy and hard-axis measurements for the Fe 16-nm sample. Fig. 3. FMR spectra for the Fe (16-nm) sample at different temperatures.

from the differential FMR signal and the reported value is the easy-axis values. III. RESULTS AND DISCUSSION

Fig. 2. FMR fields for 6-nm Fe (top) and 16-nm Fe (bottom) film measured at 24 GHz versus inplane angles. The solid line is the fit to the FMR relation. The inset shows the derived magnetic parameters.

10 Torr pressure to cool the sample from 300 K down to 20 K. At room temperature, the angular dependence of the FMR spectra was recorded as a function of the inplane orientation of to [001] crystallographic axis the external magnetic field , the (Fig. 2). From these measurements, the magnetization crystalline anisotropy constants were deduced self-consistently. These angular-dependent measurements were used to determine the exact orientations of the samples for easy-axis determination for the temperature-dependent measurements treated in this paper. The peak-to-peak line width was measured

Fig. 2 shows the inplane resonance field for 6 nm (top) and 16 nm (bottom) Fe films as a function of the inplane angle . The FMR data were analyzed by means of the phenomenological model [3], [7]. The equilibrium position of the magnetization vector was obtained from the total free energy which consists of Zeeman, demagnetizing and cubic anisotropy. The solid lines in Fig. 2 show the results of this calculation. At observed for the 6-nm film is 20.24 room temperature, the kOe whereas for 16-nm film, it is 21.34 kOe (the bulk value). The g-factors obtained for both films were 2.1. The values of crystalline anisotropy obtained from the fit were 630 and 512 Oe, respectively, for 16- and 6-nm films. Fig. 3 shows typical FMR spectra at four different temperatures. As the temperature decreases, the resonance line widths increase but resonance fields decrease. In addition, there is a decrease in FMR signal intensity as the temperature decreases [10]. Fig. 4 shows the observed resonance field (4A) as well as line width (4B) data for Fe 16- and 6-nm films along the easy-axis as a function of temperature. It is observed that the resonance field decreases with the decrease of temperature, whereas the resonance line width increases with the decrease of temperature. The decrease of temperature enhances the cubic anisotropy as . According to Mauri’s model [8], well as magnetization the temperature dependence of the saturation magnetization for Bloch law. The Bloch ferromagnetic metal satisfies the law has been tested [11], [12] very precisely in large single crystals of nickel and iron and found to be very accurate for low temperatures. In the 1960s [13], it was understood that as the dimension of the crystalline ferromagnetic solid is reduced to that of a plane, the critical exponent is reduced from 3/2 to 1. In the present investigation, we fit the temperature dependence of the resonance field instead of the magnetization because the field is the measured quantity. If the magnetization , then follows the usual Bloch law it is easy to show that in the limit when the applied field is much

KUANR et al.: EFFECT OF TEMPERATURE ON THE FERROMAGNETIC-RESONANCE FIELD

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Fig. 5. Temperature dependence of the saturation magnetization for the 16-nm fit. Fe film. The solid line in the figure is the T

Fig. 4. Resonance field H (a) and resonance line width (1H) versus temperature. The solid lines show the theoretical behavior.

smaller than , one obtains the formula for the resonance field as a function of temperature (1) (T) since both 16- and The best theoretical power-law fits law. The 6-nm Fe films show values close to that for a solid lines to the data show the theoretical fits. Reasonable fits can be obtained by using values which range from about 1.5 to (0) as 2.058 about 2.2. The fits provide an offset value of and 2.44 kOe for 16- and 6-nm films, respectively. The higher offset value for 6-nm film is due to the reduced magnetization from the bulk value as described [1]–[5], [14]. at the lowest temperature (20 K) is about The value of four times the room temperature value. The resonance line width [Fig. 4(b)], in general, shows two characteristic features: , below which 1) a low-temperature region changes quasilinearly and 2) a higher temperature regime , where is almost temperature independent. As the temperature is lowered from room temperature, the FMR signal broadens for all of the films (Fig. 3). From the angular FMR data, we found that there is a significant increase in the anisotropy field as the temperature is decreased. This correlates 200 K. well with the change in line width below Fig. 5 shows the experimentally observed results of (solid dots) for the 16-nm Fe film and a theoretical fit by using . The fit value the expression [7] is obtained of the magnetization at zero temperature as 22.8 kOe. The coefficient B was obtained as , which is indicative of long wavelength spin-wave excitations [10]. In order to study the qualitative behavior of the temperature dependence of the FMR field and line hapes, we have carried

out a theoretical investigation using the LLG equation for the 6and 16-nm-thick film. The set of LLG equations for each layer in the Fe sample is given by (2) is the magnetization in the th layer coupled to the Here, other layers through the effective field , is the Gilbert damping parameter, and is the gyromagnetic ratio. The efis given by a sum of the dipole, anisotropy, fective field exchange, and applied fields [14], [15] (3) where

and To take the effect of temperature into account, we employ a local mean-field approximation. Obviously, this will not give behavior correctly, but it will provide a general guide to the the temperature dependence, including the effect of the surfaces. The thermal averaged magnetization in each layer is calculated using the Brillouin function [15], [16] (4) where

is the Brillouin function and (5)

Here, is the Boltzmnann constant and is the temperature. The time-averaged power absorbed by the ferromagnetic material is given by the relation [15]

(6)

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IV. CONCLUSION In conclusion, we have observed that approximately law, similar to the Bloch law for for follows a the low-temperature regime. The linewidth data show distinct temperature regions with a sharp increase below 200 K. This increase in line width is associated with a significant increase in cubic anisotropy at lower temperatures. ACKNOWLEDGMENT This work at UCCS was supported by DOA Grant No. W-911NF-04-1-0247.

Fig. 6. Theoretical resonance for the 6-noon Fe sample at different temperatures.

Here, is the RF field applied in a direction perpendicular to the external dc field. In the FMR experiment, the frequency is fixed while the strength of the applied dc field is varied. To compare our theoretical results with the experiment, we follow this convention. The coupled equation (2) is solved numerically forward in time using the Runge–Kutta method. The parameters used in the , anisotropy field , calculations Fe are 0.005. The average power absorbed is not calculated until values reach equilibrium. Once the equilibrium is reached, we calculate the power absorbed by the Fe layers and, hence, the FMR field using the relation (6). Fig. 6 shows the power absorbed with the change in the applied dc field at different temperatures for the 6-nm Fe sample. With increasing temperature, two features are observed: 1) a shift of the maximum of the power absorbed to higher fields and 2) a decrease of the width of the absorbed spectrum. Both of these effects are associated with the decrease in the magnetization value and the anisotropy field. Using the maxima of the differentiated Lorenztian curve we found the linewidth values as observed in the experiments. At temperatures below the char[see Fig. 4(b)], we find that the line acteristic temperature width increases as the temperature decreases. For 6-nm- thick film, the decrease in the line width is comparable to the experiment while for thicker film (16 nm), the decrease is not as large as observed in the experiment.

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