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Fe/Au(100) : MAGNETISM IN TWO DIMENSIONS
AND COMPARISON TO Fe SURFACE-MAGNETISM
M. Taborelli, O. Paul, O. Züger, M. Landolt
To cite this version:
JOURNAL DE PHYSIQUE
Colloque C8, Suppl6ment au no 12, Tome 49, dhcembre 1988
FelAu(100):
MAGNETISM IN TWO DIMENSIONS AND COMPARISON TO Fe
SURFACE-MAGNETISM1
M. Taborelli, 0. Paul, 0. Ziiger and M. Landolt
ETH-Zurich, CH-8093 Zurich, Switzerland
Abstract. - The temperature dependence of the magnetization for ferromagnetic Fe/Au(100) epitaxial films, for the Fe(ll0) surface, and for the Fe single crystal are measured with spin polarized secondary electrons and Kerr ellipticity. From the low temperature region spin-wave parameters, and from the critical region critical exponents are reported and compared.
The influence of the dimensionality of the system on the magnetic behaviour is experimentally investigated in the present study. We measure the spin polariza- tion of secondary and Auger electrons and the Kerr- ellipticity and we use as model systems an Fe(ll0) bulk single crystal, its surface, and thin films of bcc Fe epi- taxially grown on Au(100).
The secondary electrons are excited by an unpolar- ized electron beam of primary energy Ep and are then analyzed in energy and spin [I]. The spin polarisa- tion is defined as P = (n
t
-n 1)/
(nT+
n 1),
where nT
(1) is the number of electrons with magnetic mo- ment parallel (antiparallel) to the magnetization. At constant energy the secondary electron spin polariza- tion is proportional to the magnetization of the sam- ple. For the single crystal surface study we use a pri- mary energy of 100 eV and an energy of the secondary electrons of 50 eV to achieve a probing depth of only 2 A corresponding to the topmost atomic layer. The effective polarization Peff of the Auger electrons, on the other hand, obtained from the secondary electron spectra after background subtraction in intensity and polarization, reflects the magnetic moment at an ele- mental site, independent of concentration [2].The Fe(ll0) single crystal is prepared by heating and sputtering cycles: sharp LEED patterns confirm a good quality of the surface. The Fe thin films are evap- orated on Au(100). The growth is epitaxial with bcc structure and the [Oll] direction of Fe is parallel to the I0011 axis of Au. For the Fe/Au(fOO) films we confirm
[3] a magnetic single-domain state at remanence with the easy axis of magnetization lying in-plane along a [OOl] direction. All the data presented below are ob- tained in this single-domain remanent state.
The temperature dependences of the remnant mag- netization of Fe thin films, the Fe single-crystal surface, and bulk Fe, obtained from secondary electron spin po- larization and Kerr effect, respectively, are presented in figures 1 and 2. First we consider the values of the ordering temperatures. The critical temperatures of the thin Fe/Au(100) films are lowered with respect to the Curie temperature of bulk Fe, and do strongly in- crease with increasing film thickness. This reflects the variation of the total exchange energy with the coordi- nation number. The critical temweratures for bulk sin- gle crystal and surface, on the other hand, are found to be the same within the accuracy of the measurements: Tc (surf) /Tc (bulk) = I f 0.01. The evident difference
elEF]
o e .-,.. .. a- , , 04 . * I I/..
"'I
' ".,
::::'.
. . .. a Iw 200 300 roo ,wi,r,Fig. 1. - Temperature dependence of the normalized sec- ondary electron polarization for various film thicknessess. The lines are linear extrapolations.
Fig. 2. - Temperature dependence of the normalized spin polarizaiion and Kerr ellipticity. The dotted lines represent a Bloch law M (T) /M (0) = 1 - A.T~/'.
between surface and 2-dimensional system is given by the coupling of the surface layer with the underlying magnetically ordered bulk.
In the following, two distinct temperature regions are considered separately: i) the low temperature re- gion where the magnetization decrease is interpreted in the frame of noninteracting spin waves and ii) the high temperature or critical region, where critical exponents reflect the peculiarities of the system Hamiltonian.
Starting with the low temperature regime, we first consider the thin films. At low temperatures the mag- netization decreases steeper for thinner films as shown in figure 1. From a linear fit in the range between 0 and Tc (D) /2 we obtain a slope which is nearly pro- portional to 1/D. This behaviour is qualitatively ex- plained by a spin-wave model. The modification of the spin-wave spectrum for the thin films introduces a term in the temperature dependence of the magnetiza- tion with nearly linear behaviour, which becomes more and more important with decreasing film thickness. The slope of M (T) is predicted to vary inversely pro- portional to the film thickness [4], well in line with the present observation. Now we turn t o the Fe single erys- tal and compare the surface and bulk behaviour below Tc/2. As expected, the T-dependence of the bulk re- flects a Bloch law M (T) / M (0 = 1
-
AI,,~~.T~'~. A similar decrease of M with T~ is found to occur at the surface. From fit procedures we obtain A,,,f =l ~ e d i c a t e d to Georg Bush on the occasion of his 8oth birthday
C8
-
1660 JOURNAL DE PHYSIQUE2.83 X and Abulk=9.35 X re-
spectively, with a ratio of Asu&/Abu~k=3.0
*
0.3. A recent calculation [5] of the spin-wave excitations pre- dicts a Bloch law also for the surface magnetization, with a prefactor As,& depending on the strength of the exchange interaction between surface and bulk. A value of Asurf/Abu~k = 3 can easily be obtained [5] by a reduced exchange coupling and also wasobserved on amorphous Fe40Ni40B20 [6].
In the following, we deal with the high tempera- ture region and adopt the picture of an exponential law for the order parameter near Tc, P (T)
/P
(0) =M (T) / M (0) = (1
-
T/TC)@ with a critical exponentp.
For the bulk, the surface, and the thin films we find ,8bu1k=0.33 f 0.05,Psu&
= 0.83f
0.08, @film =0.22 (+0.1
-
0.05), respectively. For the thin ferro- magnetic Fe/Au(100) films we expect a 2-dimensional behaviour, since the correlation length perpendicular t o the film plane reaches the film thickness at a tem- perature T* far below Tc. Clearly T* comes closer t o Tc with increasing film thickness. /3 was determined from high-precision P-measurements for films of vari- ous thicknesses between 0.9 ML and 2.5 ML. The prin- cipal error ofp
arises from the uncertainty in the value of Tc since finite-size effects in the film plane provoke a considerable "rounding" in the vicinity of Tc. The value of Tc is determined so that the largest part of the P f T ) curve displays a linear behaviour on a log- arithmic plot of log (P) versus log (1-
T/Tc),
and the given error bars ofp
reflect the ambiguity of Tc. We find a constant critical exponent in the thickness range of 1.2 to 2.5 ML indicating that T* is sufficiently far below Tc for 2.5 ML.0
thus is the exponent of the 2-dimensional phase transition of bcc Fe. We note that the finite-size effects in the film plane become dramatic below 1 ML, as visible in figure 1, because it is not pos- sible to avoid islanding below 1 ML. This breakdown of the behaviour in the critical region just below 1 ML indicates that our thickness calibration on an absolute scale is correct.Various theoretical results are available for
P
in a 2- dimensional magnetic system with fully localized mo- ments. In general the values forp
arep
= 118 (e.g. Ising) and thus much lower than the experimental value reported here, or, as in the case of the Heisen- berg model with 4-fold symmetric anisotropy field, ex- hibit a continuous distribution [7]. Only molecular field approximations (MFA) yield high values for /3 [8]. This is caused by the infinite range of the in- teraction assumed in the MFA approach, in contrast t o the nearest-neighbour-only interactions considered otherwise. The experimental value obtained for the Fe films could be higher than 118 because of an exchange interaction beyond the nearest neighbours and the crit- ical exponents could reflect the range of the exchange interaction.The critical behaviour of the Fe(100) surface, on the
other hand. can be com~ared with various ex~erimen-
tal results: Ni(100) with
p
= 0.825 [9] and EuS withp
= 0.72 1101. The first value agrees very well with our finding for the Fe(ll0) surface and is quite differ- ent from the EuS value. The main difference between these materials is the localization of the magnetic mo- ments in EuS and the itinerant character of Fe and Ni. In contrast, the available theories predict the sameP
for itinerant and localized models. The itinerant model of Hasegawa [ l l ] gives z 0.8 for the Fe(100) sur- face, and for the localized models values of ,8 from 213 to 1 for Ising and ,B = 0.84 for Heisenberg, respectively, are calculated [12]. At present it is obviously not pos- sib!e t o determine the universality class. Moreover, a further itinerant spin-fluctuation theory by Dorantes- Davila et al. I131 predicts an almost identical generalbehaviour for bulk and surface, in pronounced contrast to figure 2.
We conclude that the temperature dependence of the magnetization for thin Fe films and Fe surfaces be- low Tc/2 can be well understood within the spin-wave model. The critical behaviour of 2-dimensional Fe films on Au(100) points towards a more-than-nearest- neighbour interaction. The comparison of the critical behaviour of the surface of Fe(ll0) with previous mea- surements indicates that the itinerant character of the ferromagnet leads t o a fundamental difference in the critical exponent
p,,,f.
Acknowledgments
It is a pleasure to acknowledge stimulating discus- sions with H.-C. Siegmann, expert technical assistance by K. Brunner, and financial support by the Schweiz- erischer Nationalfonds.
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[3] Bader, S. D. and Moog, E. R., J. Appl. Phys. 61 (1987) 3729.
[4] Levy, J. C. and Motchane, J. L., J. Vac. Sci. Technol. 9 (1971) 721 (and refs. cited).
[5] Mathon, J. and Ahmad, S. B., Phys. Rev. B 37 (1988) 660.
[6] Pierce, D. T., Celotta, R. J., Unguris, 3. and Sieg- mann, H. C., Phys. Rev. B 26 (1982) 2566. [7] JosB, J. V., Kadanoff, L. P., Kirkpatrick, S. and
Nelson, D. R., Phys. Rev. B 16 (1977) 1217. [8] Hasegawa, H., Surf. Sci. 182 (1987) 591. [9] Alvarado, S. F., Campagna, M. and Hopster, H.,
Phys. Rev. Lett. 48 (1982) 51.
[lo]
Dauth, B., Diirr, W., Alvarado, S. F., Surf. Sci. 189/190 (1987) 729.[ l l ] Hasegawa, H., J. Phys. F 17 (1987) 165.
[12] Binder, K. and Hohenberg, P. C., Phys. Rev. B 9 (1974) 2194.
