Ultrathin Films and Surface Effects II Hua-Ching Tong, Chairman ...

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May 15, 2002 - This might be interpreted as a verification of the Mermin–Wagner theorem in the ... that the Mermin–Wagner theorem usually will not be in.
JOURNAL OF APPLIED PHYSICS

VOLUME 91, NUMBER 10

Ultrathin Films and Surface Effects II

15 MAY 2002

Hua-Ching Tong, Chairman

Onset of magnetic anisotropy in epitaxial Fe films on GaAs„001… F. Bensch, R. Moosbu¨hler, and G. Bayreuthera) Institut fu¨r Experimentelle und Angewandte Physik, Universita¨t Regensburg, Universita¨tsstrasse 31, D-93040 Regensburg, Germany

It was shown previously that ultrathin Fe films epitaxially grown on GaAs共001兲 exhibit a strong in-plane uniaxial magnetic anisotropy which turns out to be a pure interface contribution with an anisotropy constant K U S , expressed as an energy per unit area, which is constant in a wide thickness range. However, for films thinner than ⬃10 monolayers 共ML兲, K U S decreases with decreasing thickness when measured at 300 K. In order to eliminate effects of thermal excitations, Fe共001兲 films grown on GaAs共001兲 by molecular beam epitaxy were investigated by superconducting quantum interference device magnetometry at low temperature. The extrapolated room temperature values and the ground state data both indicate that K U S vanishes at t⫽2.5 ML. This is the thickness at which the onset of ferromagnetism takes place, i.e., where the Curie temperature T C becomes nonzero. This might be interpreted as a verification of the Mermin–Wagner theorem in the sense that long-range ferromagnetic order is stabilized by the magnetic anisotropy. It is discussed whether the onset of ferromagnetism is indeed triggered by the appearance of magnetic anisotropy or if there is a common origin of both phenomena. Finally, it is found that the uniaxial anisotropy does not vanish at T C , but persists up to temperatures of ⬃1.5 T C . This means that K U S does not scale with a certain power of the spontaneous magnetization. The disparity between the persistence of the anisotropy above T C and its disappearance below the critical thickness of 2.5 ML is discussed. © 2002 American Institute of Physics. 关DOI: 10.1063/1.1456391兴 The Mermin–Wagner theorem1 states that in twodimensional systems ferromagnetic order is not possible at any temperature different from zero in the absence of magnetic anisotropy and in the absence of long-range magnetic interactions 共i.e., magnetic interactions that decay with the third power of distance or less兲. This conclusion extends to the case of the so-called two dimensional 共2D兲 XY model, i.e., strong uniaxial magnetic anisotropy with a hard axis perpendicular to the plane. Therefore, ferromagnetism in thin films may be triggered by magnetic anisotropy with in-plane easy axis if the films behave like 2D systems and if longrange interactions 共e.g., dipolar interactions兲 are negligible. The latter may be assumed if the magnetization lies in the film plane and if the interfaces are flat. First attempts to experimentally verify this theorem focused on the investigation of magnetic order in the vicinity of a spin reorientation transition. For example, fcc Fe on Cu共001兲 was investigated for film thickness and temperature where the uniaxial interface magnetic anisotropy contribution with easy axis perpendicular to the film plane balances the shape anisotropy.2 It was found that the magnetic remanence, averaged over a macroscopic area of the film, vanishes in a certain temperature interval. This seemed to prove the expectation of vanishing long-range magnetic order. However, later scanning electron microscopy with polarization analysis experiments showed that very small magnetic stripe domains are formed in this temperature interval, while

magnetic order is conserved.3 Therefore it was concluded that the Mermin–Wagner theorem usually will not be in practice since its assumptions are not usually fulfilled. For thin Co layers on Cu共001兲 it was reported that the anisotropy constant of the in-plane uniaxial magnetic anisotropy becomes nonzero at essentially the same nominal Co coverage where ferromagnetism sets in.4 However, in later publications on the same thin film system, a percolation phenomenon was claimed to be responsible for the onset of ferromagnetism.5 Recently, for Co films on Cu共110兲 it was found that ferromagnetic order breaks down when the magnetic anisotropy is tuned to zero by controlled adsorption of CO to the Co surface.6 This is taken as a confirmation of the expectation deduced from the Mermin–Wagner theorem. However, these experiments were done only at room temperature and, therefore, they do not prove the absence of ferromagnetic order at low temperature. In a recent publication, the onset of ferromagnetism in thin Fe layers, epitaxially grown on GaAs共001兲 at room temperature, was discussed in detail.7 The Curie temperature T C was determined as a function of nominal Fe coverage t Fe and was found to be different from zero above a critical Fe coverage of t Fe,C⫽2.5 monolayers 共ML兲. The onset of ferromagnetism at this critical Fe coverage was attributed to the percolation of direct exchange coupling between very small Fe islands during their coalescence. However, it is of particular interest to determine whether an alternative interpretation based on the Mermin–Wagner theorem is possible in this case, i.e., if the onset of ferromagnetism is connected with an

a兲

Author to whom correspondence should be addressed; electronic mail: [email protected]

0021-8979/2002/91(10)/8754/3/$19.00

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© 2002 American Institute of Physics

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J. Appl. Phys., Vol. 91, No. 10, 15 May 2002

onset of magnetic anisotropy at t Fe,C⫽2.5 ML. This is the topic of the present article. Magnetic anisotropy of thin epitaxial Fe films on GaAs共001兲 was studied extensively in the past by Brockmann et al.8 It was found that there is a uniaxial contribution with easy axis in-plane parallel to the 关110兴 axis in addition to a fourfold in-plane magnetic anisotropy. Since the uniaxial contribution dominates in the range of film thickness t Fe ⬍10 ML, which is of primary interest here, the fourfold contribution will be ignored in the following. Regarding the volume density of the anisotropy energy ␧, the uniaxial magnetic anisotropy can be expressed quantitatively by an effective anisotropy constant K U eff due to the expression eff •cos2 ␪ , ␧⫽K U

where ␪ denotes the angle between the direction of magnetization and the axis. K U eff may be split into a volume contribution K U V and an interface contribution K U S according to eff V ⫽K U ⫹ KU

A S •K , V U

with A representing the area of the interface and V the volume of the ferromagnetic film. K U S comprises the contribution of the interface between the magnetic film and the substrate as well as the interface to vacuum or a capping layer, respectively, S S,sub S,cap KU ⫽K U ⫹K U .

Although these two interfaces are generally inequivalent, their contributions cannot be separated easily. If the area of each interface can be identified with the area of the substrate surface the expression above simplifies to 1 S eff V ⫽K U ⫹ •K U KU t with film thickness t. For Fe films on GaAs共001兲, Brockmann et al.8 plotted t Fe•K U eff versus t Fe and compared it to

Bensch, Moosbu¨hler, and Bayreuther

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FIG. 1. Plot of the quantity t FeK U eff that should be equal to the magnetic interface anisotropy constant K U S vs nominal Fe film thickness t Fe . Data obtained at T⫽300 K by Brockmann et al. 共Ref. 8兲 are shown together with recent data for T→0.

For a sample of 3.1 ML Fe, grown at room temperature on (4⫻2) reconstructed GaAs共001兲 and capped by 20 ML of Au as described elsewhere,7,9 Fig. 2 shows branches of magnetization curves measured by superconducting quantum interference device magnetometry for both, 关110兴 共easy兲 and 关⫺110兴 共hard兲 directions, from H⫽7 kOe down to H⫽0, at different temperature between 10 and 300 K. The quantity K U S is determined in absolute units by the area enclosed between the two curves and the m axis. This area can be evaluated by numerical integration. In principle, this should be done for magnetic fields between H⫽0 and H→⬁. However, in practice the integration must be restricted to a finite field interval. So, a lower limit for this area is obtained from integration between H⫽0 and 7 kOe in the present case. The results are plotted versus temperature in Fig. 3. As generally expected, K U S decreases for increasing temperature. From a linear fit the ground state value of the S anisotropy constant K U,T→0 ⬇0.04 erg/cm2 , is obtained. This is significantly smaller than the value of 0.12 erg/cm2 found for t Fe⬎10 ML. 8 This means that the strength of the uniaxial

eff V S ⫽K U •t Fe⫹K U . t Fe•K U

In the thickness range t Fe⬎10 ML the quantity t Fe •K U eff apV ⫽0. Therefore, it is peared to be independent of t Fe , i.e., K U proved that the uniaxial in-plane magnetic anisotropy is a pure interface effect. It originates from the Fe/GaAs共001兲 interface rather than from the interface to the Au capping layer.8 In Fig. 1 corresponding data are plotted for the thickness range of t Fe⫽4–10 ML, showing a decrease of K U S ⫽t Fe •K U eff with decreasing t Fe . Since the experiments of Brockmann et al. were done at room temperature and regarding the fact that the Curie temperature approaches room temperature when reducing the film thickness, it was not clear whether this decrease of K U S is due to magnetic excitations, or if the uniaxial in-plane magnetic interface anisotropy is also thickness dependent in the ground state. To clarify this, the anisotropy constant must be determined for T⫽0.

FIG. 2. 共a兲–共d兲 Magnetic moment per area of 3.1 ML Fe on GaAs(001)-(4⫻2), plotted vs in-plane magnetic field along the easy 共关110兴兲 and hard 共关⫺110兴兲 axes at four selected temperatures. Each curve was measured with magnetic field decreasing from H⫽7 kOe to H⫽0. For each temperature the anisotropy constant of the in-plane uniaxial magnetic interface anisotropy K U S is determined from the hatched area enclosed between the two curves and the m axis.

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Bensch, Moosbu¨hler, and Bayreuther

J. Appl. Phys., Vol. 91, No. 10, 15 May 2002

FIG. 3. Plot of the uniaxial magnetic interface anisotropy constant K U S vs temperature T for 3.1 ML Fe on GaAs(001)-(4⫻2).

in-plane interface anisotropy for t Fe⫽3.1 ML is indeed reduced compared to the case of thicker films also in the ground state. In addition to the data point for t Fe⫽3.1 ML, Fig. 1 also shows results of similar measurements on samples with t Fe ⫽2.0 ML, t Fe⫽2.5 ML, and t Fe⫽3.6 ML at T⫽10 K, that should represent more or less the interface anisotropy constant K U S for T→0. As a guide to the eye, these data, as well as the data of Brockmann et al., are connected by continuous curves. Both the data obtained at T⫽300 K and the ground state data approach zero for t Fe→2.5 ML. Interestingly, this is exactly the same Fe coverage at which the Curie temperature was found to vanish.7 This suggests that the onset of ferromagnetism is connected with the onset of magnetic anisotropy. However, it is not immediately clear if magnetic anisotropy is the reason for or a result of ferromagnetism, or if there is a common origin of both phenomena. Regarding the fact that our reflective high energy electron diffraction experiments do not show spots of Fe until at least 2.0 ML of Fe are deposited onto GaAs共001兲, one may argue that a structural transition from an amorphous to a crystalline state takes place at 2.5 ML. This structural transition may be responsible for the observed behavior of magnetic anisotropy. The structural transition may take place during the coalescence process of Fe islands, so that the appearance of an extended network of directly exchange coupled Fe and the onset of magnetic anisotropy coincide at the same nominal Fe coverage of t Fe,C⫽2.5 ML. Calculations have shown that the anisotropy constant contributes logarithmically to T C while the exchange coupling constant enters linearly.10 This means that ferromagnetic order is just ‘‘triggered’’ by magnetic anisotropy while the value of the Curie temperature is determined primarily by the average strength of exchange coupling. Therefore, one can expect that the dependence of T C on nominal Fe coverage is described quite well by the percolation model mentioned in Ref. 7, even if the dependence of T C on the strength of magnetic anisotropy is neglected. Usually it is expected that anisotropy constants scale like a certain power of the spontaneous magnetization. This means that the magnetic anisotropy should vanish for temperatures T⭓T C . For the film of 3.1 ML Fe the Curie temperature was unequivocally found to be T C ⬇180 K from: 共i兲

the disappearance of the easy axis remanence and hysteresis and 共ii兲 a sharp peak of the easy axis differential susceptibility in zero field 共as explained in Ref. 7兲. However, Fig. 3 shows that for 3.1 ML Fe on GaAs共001兲 the magnetic anisotropy constant K U S at T⫽T C still amounts to about 30% of the ground state value and there is no change of the trend in K U S as a function of T at T⫽T C . Indeed, from a theoretical point of view it is not strictly required that magnetic anisotropy vanishes in the absence of spontaneous ferromagnetic order. First, the spin–orbit coupling is independent of magnetic order. Furthermore, it is possible to induce a net spin magnetization even in a nonferromagnetic state by applying an external magnetic field. This magnetization will be subject to the spin–orbit coupling, leading to magnetic anisotropy in compliance with the local crystal symmetry. The observed linear decrease of K U S with increasing temperature in Fig. 3, however, is not understood at present and deserves theoretical consideration. In conclusion, a strong correlation between the onset of ferromagnetism and of magnetic anisotropy has been found for Fe on GaAs共001兲: ferromagnetic long-range order and uniaxial magnetic anisotropy both appear for T⬎0 above a critical thickness of 2.5 ML. The interpretation of ferromagnetic order being the origin of the anisotropy can be ruled out because the anisotropy constant K U S does not vanish at the Curie temperature, but persists up to 1.5 T C in a 3.1 ML Fe film. On the other hand, the interpretation that the ferromagnetic long-range order is triggered by the onset of magnetic anisotropy in the spirit of the Mermin–Wagner theorem would be compatible with the experimental finding that both phenomena set in at the same thickness. However, in this case the question that still remains is what is responsible for the onset of the anisotropy at 2.5 ML. There is a clear disparity between the persistence of the anisotropy above T C for ferromagnetic films and the disappearance of the anisotropy below the critical thickness for the onset of ferromagnetic order of 2.5 ML. One possible reason could be the structural transformation from a disordered state in the early growth regime to an ordered bcc lattice. Such a transition might be connected with the segregation of As and Ga atoms to the surface and the formation of a stable Fe/GaAs interface. A direct check of this assumption might be provided by detailed extended x-ray absorption fine structure studies at different stages of the growth process. N. D. Mermin and H. Wagner, Phys. Rev. Lett. 17, 1133 共1966兲. D. P. Pappas, C. R. Brundle, and H. Hopster, Phys. Rev. B 45, R8169 共1992兲. 3 R. Allenspach, J. Magn. Magn. Mater. 129, 160 共1994兲. 4 P. Krams, L. Lauks, R. L. Stamps, B. Hillebrands, and G. Gu¨ntherodt, Phys. Rev. Lett. 69, 3674 共1992兲. 5 F. O. Schumann, M. E. Buckley, and J. A. C. Bland, Phys. Rev. B 50, 16424 共1994兲. 6 S. Hope, B.-Ch. Choi, P. J. Bode, and J. A. C. Bland, Phys. Rev. B 61, 5876 共2000兲. 7 F. Bensch, G. Garreau, R. Moosbu¨hler, G. Bayreuther, and E. Beaurepaire, J. Appl. Phys. 89, 7133 共2001兲. 8 M. Brockmann, S. Miethaner, M. Zo¨lfl, and G. Bayreuther, J. Magn. Magn. Mater. 198–199, 384 共1999兲. 9 R. Moosbu¨hler, F. Bensch, M. Dumm, and G. Bayreuther, J. Appl. Phys. 91, 8757 共2002兲. 10 P. Bruno, Mater. Res. Soc. Symp. Proc. 231, 299 共1992兲. 1 2

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