Chao-Zhong Li(李超眾), Chang-Jun Jiang(蔣長(zhǎng)軍), and Guo-Zhi Chai(柴國(guó)志)

Key Laboratory for Magnetism and Magnetic Materials of the Ministry of Education,Lanzhou University,Lanzhou 730000,China

Keywords: angular control,multi-mode resonance,rotatable stripe domain,non-uniform precession

1. Introduction

Nevertheless,in some special structures of magnetic materials, there are not only the FMR mode but also other resonance modes resulting from the non-uniform precession. The spin wave resonance is one of the non-uniform modes dominated by exchange interaction, which has been fully studied in theory and experiment.[26,27]However, the resonance frequency of the spin wave mode can seldom be controlled because of its stability in a certain magnetic film.[28]The optical mode resonance,as another non-uniform resonance mode,has also been extensively studied in bilayer or trilayer film with two ferromagnetic layers coupled by the ferromagnetic or antiferromagnetic interlayer exchange interaction.[13,15,29]The optical mode resonance frequency can be tuned by using the variable strength of the interlayer exchange coupling through changing the thickness values of the different layers.[30]Due to the interlayer exchange coupling, the precessions of magnetic moments in different layers can be fully out-of-phase.Many researches including our recent research revealed that the similar out-of-phase resonance mode also exists in the film with stripe domain structure.[31-34]In the films with stripe domains, the magnetic moments in neighboring domains or domain walls are not completely parallel or antiparallel.[35,36]Therefore, the high-frequency resonance mode related to the out-of-phase precession in the film with stripe domain structure is called the non-uniform precession mode instead of the optical resonance mode.[31,36,37]By employing the Landau Lifshitz’s equation,[38]the Kittel’s formula of the non-uniform precession mode under zero field can be replaced by[30,34,39,40]

where fnon?uniis the resonance frequency of non-uniform precession mode,and Hexis the effective field caused by the interdomain exchange coupling. This behavior has been verified in our paper,[34]in which the fnon?unican be adjusted by tuning the strength of inter-domain exchange coupling dependent on the domain width.

In this paper,CoZr thin films,each with a large saturation magnetization and a small magneto-crystalline anisotropy,are chosen to form stripe domain structures and construct rotatable anisotropic systems.[34]Combining the non-uniform precession mode with the rotatable anisotropy, the multi-mode resonance is achieved in the obliquely deposited CoZr thin film with rotatable stripe domains. Furthermore, the angular control range of multi-mode resonance frequency can be adjusted more flexibly by changing the oblique deposition angle.

2. Experimental details

The 250-nm-thick CoZr thin films were obliquely deposited on 1 cm×2 cm Si(100)substrates from a pure Co target decorated with six doping Zr cylinders by radio frequency magnetron sputtering. The diameter of Co target was 3 inches(1 inch=2.54 cm). The diameter and the height for each of small Zr cylinders were 1.8 mm and 3 mm, respectively. Six Zr cylinders were uniformly arranged on the sputtering area of the Co target. The background pressure of the vacuum chamber was 8.5×10?5Pa. The sputtering power was chosen to be 100 W and the Ar pressure was 0.25 Pa during the deposition. A series of samples was obtained at different oblique deposition angles of 0?,10?,30?,40?,45?,and 50?.

The Co component in each CoZr film can be detected to be 81.25%from the result of energy dispersive x-ray spectroscope(EDX,JEOL JSM-5600LV,Japan). The static hysteresis loops were measured in plane by using a vibration sample magnetometer (VSM, Lakeshore 7304, USA) and the magnetic domain images were taken by a magnetic force microscope(MFM,Asylum Research MFP3D,UK).The frequencydependent permeability spectra of the samples were obtained by a vector network analyzer (VNA, Agilent E8363B, USA)equipped with a short-circuited microstrip line[41,42]in a frequency range of 100 MHz-9 GHz at room temperature. With this facility,the angle-dependent permeability spectra were investigated by using a home-made angular scaler.

3. Results and discussion

Figures 1(a) and 1(b) show the hysteresis loops of CoZr thin films, which present the static magnetic properties of CoZr thin films grown by vertical deposition and oblique deposition. The loops measured along the easy axis marked as EA have the largest remanence magnetization(Mr). When the direction is perpendicular to the easy axis but still in plane,it is defined as the hard axis marked as HA.The hysteresis loops of the vertical sputtered CoZr thin film are shown in Fig.1(a).The magnetization first decreases linearly with the change of field value from saturation to negative due to the rotation of the magnetization in the domain, and then suddenly reverses to opposite direction because of the motion of domain walls.This is a typical characterization of hysteresis loops of thin films with stripe domains when the magnetic field decreases from the saturated field.[37]The hysteresis loops of its EA and HA are nearly coincided, indicating that the vertically sputtered film is isotropic. Figure 1(b)shows the hysteresis loops of the film grown by an oblique deposition angle at 40?. The Mrin the EA loop is significantly larger than that in the HA loop due to the weak perpendicular anisotropy possessed by the stripe domain structure.[35,43-45]That is, part of magnetic moments in the film are warped out of the film plane along the z-axis direction. While the hysteresis loop is measured along the EA, the magnetic moments are more likely to lie in the plane. Thus, the z-component of magnetization in the EA is less than that in the HA.This can be verified by the differences between the light and dark area of the MFM images. The hysteresis loop along the HA in Fig.1(b)is induced by the competition between the uniaxial anisotropy and the rotatable stripe domain structure of CoZr film. Figures 1(c)-1(e) display the magnetic domain images of CoZr films in the remanence state.The different colors in the magnetic domain images represent the value of Δ f measured by MFM, which are related to the out-of-plane component of magnetization. Figure 1(c) is the magnetic domain image of the vertically sputtered CoZr thin film. The MFM images in Figs.1(d)and 1(e)illustrate the rotatable stripe domains existing in the obliquely deposited CoZr thin film at 40?, of which the magnetic domain direction can be rotated after applying an external saturation field.

Fig.1. Hysteresis loops of(a)vertically deposited and(b)obliquely deposited CoZr thin films at oblique deposition angle 40?. Dark lines are measured along easy axis direction of uniaxial anisotropy,which have maximum remnant magnetization,marked as EA,and red lines are taken along perpendicular direction of easy axis direction,marked as HA.MFM images of(c)vertically and((d)and(e))obliquely deposited CoZr thin films,with arrows indicating directions of easy axis and applied external fields. The unit 1 Oe=79.5775 A·m?1.

Fig.2. Permeability spectra of CoZr thin films measured at zero external field. Real parts of permeability spectra measured along(a)easy axis and(b)hard axis,and imaginary parts of permeability spectra measured along(c)easy axis and(d)hard axis.

Figure 3(a)shows the relation between the resonance frequency and the oblique deposition angle. The funiincreases from 2.47 GHz to 4.80 GHz along the EA,but decreases from 2.32 GHz to 1.86 GHz along the HA,which is consistent with our previous result.[25]The fnon?uniincreases from 4.89 GHz to 5.79 GHz along the EA.In other words,the resonance frequency can be tuned in a wide frequency range from 1.86 GHz to 5.79 GHz by combining with the rotatable anisotropy and the inter-domain exchange coupling. The damping α of the film is another key property of the high frequency magnetic material. As shown in Fig.3(b),the α for each of the films is less than 0.2 when oblique deposition angle is less than 30?,then the value of α increases to 0.5 when oblique deposition angle increases to 50?.

Fig.3. Obliquely deposited angle dependence of (a) resonance frequency and(b)damping α.

To further understand the angular dependence of highfrequency permeability of CoZr films and compare the experimental results with the results from the theoretical model,the relationship between funiand inplane angle θ of the CoZr film is shown in Figs.4(a)and 4(b). Figure 4(a)shows the results of the vertically deposited film, and figure 4(b) displays the funiversus θ curve of the obliquely deposited CoZr film. The results can be explained by

Fig.4. Angular dependence of resonance frequency of uniform precession mode in obliquely deposited CoZr thin films at oblique deposition angle of(a)0?and(b)40?.

Fig.5. Experimental results and fitting curves of angular dependence of square of resonance frequency of uniform precession mode in obliquely deposited films at oblique deposition angle of(a)0?,(b)30?,(c)40?,and(d)50?,respectively.

Fig.6. Oblique deposition angle dependence of rotatable anisotropy (dark squares and black line)and uniaxial anisotropy(red circles and red line)in obliquely deposited CoZr thin films.

4. Conclusions

We report the controllable resonance frequency in obliquely deposited CoZr thin films with rotatable stripe domains. The angular control of resonance frequency originates from the angular tunable effective anisotropy in plane,arising from the competition between the uniaxial anisotropy induced by oblique deposition technique and the rotatable anisotropy produced by rotatable stripe domains. Furthermore, the nonuniform precession resonance mode which is induced by the exchange coupling of magnetic moments in adjacent domains can broaden the adjustable resonance frequency range. Finally, a wide range of resonance frequency from 1.86 GHz to 5.79 GHz is realized in a single film,which might be useful for high-frequency microwave devices.