Sfb290 TP A2 UP II: ac-susceptibility in UHV
(C. Rüdt, K. Baberschke)

Mutual Inductance (MI) and the Magneto-Optical Kerr-Effect (MOKE) in an ac mode are used to measure the magnetic differential susceptibility of ultrathin single films, bi- and trilayers. The critical temperatures for the onset of a spontaneous magnetization parallel and perpendicular to the film plane are measured. Moreover, the critical exponent gamma as well as the higher harmonics of the ac susceptibility can be determined via MI measurements close to T_C.
 

• The para-/ferromagnetic phase transition in Ni(001) films on Cu(001)

 
For in plane magnetized films the susceptibility peak shows up at the Curie temperature T_C as given by the Curie-Weiss law (Fig. 1). Note the monolayer sensitivity and the absolute calibration of our UHV compatible setup.


Fig. 1




• The influence of interlayer exchange coupling on the para-/ferromagnetic phase transition in magnetic trilayers

 
The ac susceptibility technique was used to investigate the problem of ordering temperatures in magnetic trilayers. Single ultrathin magnetic layers have a T_C where the internal susceptibility chi_int diverges and the experimentally measured susceptibility chi_exp shows large values as Fig. 1 reveals. Now a question arises when one prepares a trilayer, i.e. two single magnetic layers like Co and Ni separated by a non-ferromagnetic spacer such as Cu. Will the interlayer exchange coupled system Co/Cu/Ni show one or two Curie temperatures? In Fig. 2(a) the dotted line depicts chi _exp for a 5 ML /Ni/Cu(001) capped by 25 ML of Cu. The maximum is at about T_C. The solid line represents chi_exp after the evaporation of 2 ML Co on the top of the Cu/Ni bilayer. One sees a very large signal at about 430 K where is the T_C of Co and a small one at about 250 K where is the T_C of the Ni layer [Ref. 206] . Two susceptibility peaks were recorded only for trilayers with very weak coupling. J_inter acting as a field it suppresses chi_exp below the experimental sensitivity and shifts it to higher temperatures as the calculations of Fig. 2(b) carried out by P.J. Jensen/K.H. Bennemann (Sfb290, TPA1) [Ref. 229] and more recent experiments [Ref. 215] reveal. The shift DeltaT of the ordering temperature of Ni in the presence of J_inter was shown by x-ray magnetic circular dichroism (XMCD) experiments to be always positive and to present an oscillatory character following the periodicity of J_inter [Ref. 212] . DeltaT was found to be as large as 90 K when one decreases the Ni layer thickness to about 3 ML. This effect can be only understood in terms of the reduced dimensionality of the ferromagnetic layers and can not be reproduced by the conventional Molecular Field Theory (MFT) which ignores spin fluctuations [see common work with TPA1, Ref. 229] . Finally, the problem of phase transitions in coupled two-dimensional ferromagnetic layers is dealt in [Ref. 252].
 
Fig. 2




• Curie temperature and critical exponent gamma in magnetic superlattices

 
The problem of critical phenomena in Fe₂/V₅ magnetic superlattices is currently studied by ac susceptibility measurements. The high structural and magnetic homogeneity of the samples [Ref. 193] results in very narrow chi_exp peaks (» 3 K), see Fig. 3. The amplitude of the oscillatory field is as small as 17 mG and all static fields were compensated below 10 mG. Before attempting any critical fitting one must determine independently T_C. In Fig. 3 with closed symbols we depict the dispersive chi'_exp and with open symbols the dissipative part, chi''_exp, of chi_exp . It is well-known that in the ferromagnetic phase there are hysteresis losses, while in the paramagnetic not. Thus, the correct T_C has to be placed at the onset of chi''_exp (indicated by a vertical solid line). Note that at the maximum of chi'_exp up to 2-3 K above, there is significant hysteresis as the MOKE loops in the inset of Fig. 3 reveal. Therefore, the maximum of chi'_exp does not correspond to T _C [Ref. 243] . After determining independently the T_C one has to correct chi' _exp for the demagnetizing factor. Then, one may plot in a double logarithmic diagram chi'_int = chi⁺ ₀ t^-gamma as a function of the reduced temperature t, Fig. 4. By linear regression of the data down to t=10^-4 one determines from the slope of the solid line the critical amplitude chi ⁺₀=0.024(3) and a critical exponent gamma=1.72(10) consistent with the 2D-Ising model. A 3D-exponent (gamma=1.25, dashed line) is clearly ruled out. Through the susceptibility analysis we conclude that the reduced dimensionality of the Fe layers determine the critical behavior at T_C and J_inter should fade away [Ref. 256] .

 

Fig.3

Fig. 4




• Higher Harmonics of the ac susceptibility / Separation of para- and ferromagnetic contributions

For the first time, higher harmonic susceptibilities chin(T) are measured for ultrathin film ferromagnets. They give rise to a independent determination of the Curie temperature T_C. Moreover, it is possible to separate para- and ferromagnetic parts of the ac susceptibility close to T_C resulting in a more accurate critical analysis. In general, the magnetic response on an oscillatory magnetic field H(t)=H₀cos(w₀t) in the vicinity of T_C can be divided into para- and a ferromagnetic contributions. This is shown schematically in Fig.5. Above the Curie temperature M(H) follows the well-known Brillouin function as shown in Fig.5(a). In comparison to H(t) the time-dependent response M(t) is also a continuous sinusoidal function in phase with the external field (Fig.5(b)). Below T_C, hysteresis effects are obserbed (Fig.5(d)) and M(t) follows a discontinous square function out of phase with H(t). Such a square function can be expressed as a sum over odd higher harmonics of the ground frequency w₀. Therefore, measurements of the temperature-dependent ac susceptibility at multiples of w can be used to determine the hysteresis temperature-dependent in the vicinity of T_C which is not easily possible using conventional magnetometry. This was done up to w=19w₀ for a (Fe2/V5)50 superlattice in a field of amplitude H₀=0.8 Oe. The results are shown in Fig.6. Solid lines represent the real-, dahed lines the imaginary parts of the higher harmonics chi_n(T). As mentioned in the upper paragraph, T_C is the temperature of the onset of absorption in chi₁(T). The chi_n(T) exhibit (n+1)/2 extrema and (n+3)/2 zeros. The amplitudes of chi_n(T) scale with 1/n as indicated by the magnification factors. In addition, theoretical calculations in the framework of a mean-field theory were performed (not shown here, see. [Ref. 294]).

Fig.5

Fig.6

Figs.7(a) and (b) show the results, M(H) and M(t), of calculating the Fourier sum of all measured chi_n(T) as a function of temperature t=T/T_C. For clarification only an assortment of curves are shown. Due to the high temperature resolution of our MI setup, we are able to determine nearly 200 hysteresis loops in a temperature range of  4% around T_C. For T<T_C, nearly square-like hysteresis loops are observed close to the Curie temperature tilting into the plane at T_C. The saturation magnetization M_S(T) as well as the coercive field H_C(T) vanish for T->T_C as expected. The temperature dependence of both quantities M_S(T) and H_C(T) can be extracted from Fig.7(b). A second independent determination of the Curie temperature is therfore given by the temperature where H_C(T) vanishes.

Fig.7

The separation of para-(short-dashed) and ferromagnetic contributions (long-dashed) of chi_n(T) is shown in Fig.8(a) for theoretical calculations within a mean-field theory (P.J. Jensen) and in (b) for the experimental data of chi'₁(T). The ferromagnetic part is extracted fitting the curves in Fig.7(b) by an ideal square-like hysteresis loop M(H). The paramagnetic part is then given by the difference of both quantities. Obviously, such an analysis of ac susceptibility data is able to yield a more accurate value for the critical exponent gamma of the paramagnetic susceptibility due to the following reasons: (i) T_C is determined twice independently through the onset of the imaginary part chi''₁(T) and the temperature where H_C(T) vanishes; this results in (ii) a more trustworthy value for gamma which in addition can be determined on both sides of the phase transition through the separation of ferro- and paramagnetic parts of chi(T).

Fig.8

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(last update: 21.08.2003)