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Surface and 2D magnetism with spin polarized cascade electrons
ELSEVIER
Surface Science 307-309 (1994) 1076-1086
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Invited paper
Surface and 2D magnetism with spin polarized cascade electrons H.C. Siegmann Swiss FederalInstitute of Technology, CH-8093 Ziirich, Switzerland
(Received 20 August 1993)
Abstract
The probing depth A of low energy cascade electrons in transition metals (TM) is dominated by scattering into the unoccupied d-orbitals. Thus A for electrons within 5-10 eV from the Fermi level varies from 1 monolayer in the early TM such as Gd to 6 monolayers in the late TM(Ni). The spin polarization Pc of the cascade electrons is due to the spin polarization P0 of the 3d-electrons plus an additional polarization generated in the process of cascade formation by scattering into the spin polarized holes of the 3d-states. The enhancement f = Pc/Po is small with the early TM but large with the late TM. Nevertheless, Pc is proportional to the magnetization and therefore represents an ideal tool to observe magnetism at surfaces and in nanoscale magnetic structures. Very small exchange couplings of ferromagnets across nonmagnetic spacer layers can be measured if one of the ferromagnets is ultrathin and acts as a giant spin molecule without decaying into domains. Recent applications include the investigation of the exchange coupling across semiconducting spacer layers.
1. Introduction
It is difficult to apply electron spectroscopy to the more interesting topics in solid state physics such as melting, heavy fermions, superconductivity, or magnetism because the energies involved in these p h e n o m e n a are usually much smaller than the energy resolution attainable in the various spectroscopic techniques. However, the development of spin polarized electron spectroscopy makes it possible to distinguish spin up from spin down states even when they are degenerate in energy. Therefore, electron spectroscopy became a major topic in magnetism and generated the new field of surface and two-dimensional magnetism. To appreciate the impact of spin polarized spectroscopy on magnetism, the reader is referred to recent surveys [1,2].
The present p a p e r will be concerned with only one small section of this field, namely magnetometry employing low energy secondary or cascade electrons. The cascade electrons are emitted in great quantities, when a primary electron b e a m of typically a few keV energy strikes the surface of a solid. In the first section it will be shown that the spin polarization Pc of the cascade electrons is proportional to the magnetization M s of the first few atomic layers at the surface. This turns out to be of great value for magnetometry at surfaces, particularly in the case of transition metals. Magnetometry with cascade electrons became widely known by the fabulous high resolution images of magnetic domains or domain walls at the surface of ferromagnets [3] and in ultrathin ferromagnetic films [4], and by the discovery of the small period oscillatory exchange coupling mediated by crys-
0039-6028/94/$07.00 © 1994 Elsevier Science B.V. All rights reserved SSDI 0039-6028(93)E0804-4
H.C. Siegmann/ SurfaceScience307-309 (1994) 1076-1086 talline chromium [5]. In the present paper, attention will be focused on one particular aspect of this technique, namely the measurement of small exchange couplings mediated between ferromagnets by non-ferromagnetic metallic or insulating spacer layers. It will be shown that interface energies as small as 10 -6 J / m 2 corresponding to 10 -7 eV per interface atom can readily be measured. This is far beyond the accuracy of present day computing of energy levels, even far beyond the reliability of the concepts on which the calculations are based. Therefore, with magnetometry based on the spin polarization Pc of the cascade electrons, the experimentalist is now in a position to explore uncharted fields yielding information on the very essence of magnetism, the quantum mechanical exchange interaction. The main issues that have to be dealt with in order to obtain valid results are the depth of information with low energy cascade electrons and the relation between the spin polarization Pc(H, T) of the cascade electrons and the magnetization Ms(H, T) of the surface, where H is the magnetic field and T the temperature.
2. Probing depth of threshold electrons in transition metals The probing depth A is the distance from the surface over which specific electronic properties of a solid can be sampled by spectroscopic analysis of energy, angular distribution, or spin polarization of the emerging electrons. A can be translated via the group velocity into the lifetime ~- of an electron in the excited states within the solid. A large amount of data for A has been accumulated from the overlayer method in which the attenuation of a prominent substrate feature is measured as a function of the overlayer thickness x and fitted with an exponential decay e x p ( - x / A ) . The data for many materials are often displayed as a "universal curve" which shows A as a function of energy [6]. With low energy electrons escaping from the solid close to the vacuum level, the different transition metals are hardly distinguishable. All that can be recognized in the energy distribution curves is the drop of
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the intensity at the Fermi level. Therefore, the overlayer method cannot be applied due to the lack of a distinguishing feature for low energy electrons. However, a well defined magnetization depth profile can be constructed at a surface by depositing either magnetic layers consisting, for example, of Fe on a nonmagnetic substrate or vice versa by depositing nonmagnetic layers on a magnetic surface. The art of fabricating such ultrathin magnetic structures has been greatly developed in the past [7]. If now the increase or decrease of the spin polarization P of the emerging electrons is measured as a function of the overlayer thickness x, one can obtain astonishingly accurate values of A even for threshold electrons.
2.1. Example of an experiment for determining the probing depth In this example, Ta overlayers are sputter deposited onto a well engineered magnetic substrate [8]. The low energy cascade electrons are excited by a primary unpolarized electron beam having an energy of 2-3 keV. An electron optical system collects most of the cascade electrons emerging from the surface in an energy window of 5-10 eV from the Fermi level and focuses them onto the entrance diaphragm of a spin polarization analyzer. The ferromagnetic polycrystalline Fe-substrate is deposited onto a special NiFe alloy (permalloy) that can be magnetically saturated in a low external field comparable to the earth magnetic field, hence the electron optics are not disturbed by it. The sputter deposited Fe film taken by itself would require high magnetic fields for magnetic saturation and furthermore would not show square magnetic hysteresis loops. But, because the Fe film is directly deposited onto the permalloy, it is exchange coupled to it and hence the substrate surface has the desirable magnetic properties of permalloy but the electronic structure of pure Fe. The polarization P of the low energy cascade electrons emitted from the Fe upon irradiation with primary electrons of a few keV can be measured with a high accuracy of ___< 0.5%. If this surface is now covered with increasing amounts of Ta, P de-
H.C. Siegmann/ Surface Science 307-309 (1994) 1076-1086
1078 I
I
~
i
i
i
L
i
i
i
i
~
I
i
i
1.01 0.8 0.6
~ o.4 0.2 0.0
0
1.0
.5
1.5
X [nm]
Fig. 1. The dependence of the relative low energy cascade polarization on the thickness x of the overlayer. Squares Ta on polycrystalline Fe from Ref. [8], circles Ta on Fe(100) from Paul [9]. The solid line is a fit to Eq. (1).
creases because some polarized electrons from the magnetic substrate are removed during passage through the nonmagnetic overlayer, while some unpolarized electrons are added. If the number of electrons from the substrate and overlayer are labelled with subscripts s and o respectively, the polarization as a function of x is given by P = [(J+
-J~-) exp(-x/A)]/J,
(1)
where the total intensity J is given by
J= (J+ +J~-) exp(-x/A) + (Jo+ + J o ) [ 1 - exp(
-x/A)],
and where + and - stand for majority and minority spin electrons, respectively. Fig. 1 shows the relative spin polarization P(x)/P(O) of the low energy threshold electrons versus the thickness x of the Ta overlayer near room temperature. The initial strong reduction of P(x)/P(O) has to be attributed to a reduction of the magnetization in the surface of the Fe substrate due to the proximity of Ta. After completion of the first layer at x = 0.2 nm, an excellent fit to Eq. (1) is possible with 1
distinguishing electrons originating in the substrate from those of the overlayer. Although such short values of the attenuation length A are phenomenologically well defined by the procedure of fitting the intensities in the 2 spin states to an exponential, the theoretical meaning of A is not clear. Previous theoretical treatments assumed that the electron distribution function in the cascade is spatially constant and used the semiclassical Boltzmann equation approach in which the phase space cell must be large in comparison to the lattice cell [10,11]. If A is only about 2 atomic layers, the concept of a mean free path is not clear any more. Hence we will use A and the derived total scattering cross section or= 1/A merely as a phenomenological parameter describing the overlayer experiments.
Results with transition metals: a simple rule emerges 2.2.
With the spin polarized overlayer technique, accurate and reproducible values for the total scattering cross section ~r = 1/A are obtained in the energy range 5 < E < 1 5 eV above E F. It turns out that the results can not be described by the "universal curve" [6] but clearly depend on the transition metal. However, there is still a quite simple behavior independent of whether the metal is magnetic or not. Compilation of the data available from many laboratories reveals that the total scattering cross section o- consists of a constant part cr0 and a part ~rd(5- n) that is proportional to the number of unoccupied states (5 - n ) in the d-band, n is the number of occupied and 5 the total number of d-orbitals available to one spin state. Fig. 2 shows that o-0 and ~rd can be obtained from a fit of the data to the equation = ~0 + ~d( 5 - n).
(2)
With magnetic metals, the spin averaged number of holes n = ½(n++n -) must be inserted into Eq. (2) to obtain the spin averaged total cross section o- = ½(o'++ o'-). To interpret the empirical rule, Eq. (2), one has to consider that the dominant processes by which electrons at within 10 eV from the Fermi
H.C Siegmann / Surface Science 307-309 (1994) 1076-1086 (3 I
I
I
I
I
Cr
3
d-shell increases by An, while the occupancy of the spin down subshell decreases by An. It follows from Eq. (2) that the total inelastic cross section becomes spin dependent according to o-(±) = or0 + trd[5 -- ( n ( + ) A n ) ] ,
Ag: Au~ 0
0
Cu L
I
I
t
I
2
3
4 d-holes
I
Fig. 2. Total scattering cross section tr in nm-t versus number of unoccupied d-orbitals for the transition metals indicated. Data from various sources according to Ref. [2] are valid for electron energies within 5-10 eV from the Fermi level. The circled points indicate average values from different laboratories. The Co value is from Ref. [12]; the upper value for Cr is on NiFe substrate, the lower on Fe(100). The Cu value is by courtesy of Karin Totland and Peter Fuchs [to be published]. level lose energy in a transition metal are elect r o n - e l e c t r o n scattering events. H e n c e tr0 accounts for inelastic scattering other than into the holes of the d-band including, for instance, scattering into the s - p - d e r i v e d bands, whereas trd describes the scattering into one unoccupied dorbital. According to this interpretation, the noble metals Cu, Ag, and Au should have identical tr = o"0. This is indeed the case. The elastic scattering of electrons is of minor importance for threshold electrons, because as many electrons are scattered into the escape cone than out of it. However, one should not expect that Eq. (2) can account for more than the gross features of o-. It neglects, for instance, scattering into surface or interface states. The experimental results in Fig. 1 show very clearly that the interface changes when the overlayer is deposited. Furthermore, the assumption of a constant trd neglects the variable stability of the 3d" configurations. It will be interesting to see whether Mn with a very stable 3d 5 configuration behaves like a noble metal or not.
3. Relating the cascade polarization Pc to the surface magnetization When a transition metal becomes ferromagnetic, the occupancy of the spin up part of the
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(3)
where tr (-+) is the cross section for majority (minority) spins. For the bulk of the material, An can be calculated from the Bohr magneton number n B obtained in conventional magnetometry according to n B = n ÷ - n - = 2 An, because the contribution of s-p-electrons to the magnetization is small. Eq. (3) allows one to independently test the simple behavior of tr in transition metals stated in Eq. (2), because it predicts that electrons travelling through ferromagnetic materials will acquire a transport polarization a. If x is the thickness of the ferromagnetic material over which the transport occurs, one has a = { [ e x p ( t ~ - - t r + ) x ] - 1} / { [ e x p ( t r - - o ' + ) x ] + 1},
(4)
a reaches unity when x ~ ~, but the intensity of transmitted electrons exponentially tends to 0 when x increases, a has been measured directly by letting unpolarized electrons from a nonmagnetic substrate travel through a ferromagnetic overlayer [12]. The results are in good agreement with Eq. (4). Another important consequence of Eq. (4) concerns the spin polarization Pc of the low energy cascade electrons. This polarization shows an enhancement over the average spin polarization P0 of the N electrons in the valence bands made up of d-, p-, and s-orbitals. If one assumes that all valence electrons are excited to an escape level with equal probability, it follows that P0 = An/N where N now includes the s - p electrons, but An is m a d e up almost entirely by the 3d-electrons alone, hence can be determined with conventional magnetometry on bulk material. It has been proposed right after the first observations of the enhanced cascade polarization Pc that scattering into the unoccupied holes of the d-band could be responsible for it. A summary of these first arguments is given in Ref. [10]. However, it must be mentioned that other
H.C. Siegmann / Surface Science 307-309 (1994) 1076-1086
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models explaining the conspicuously high polarization Pc of the low energy cascade electrons have also been put forward. In one model [13] it is assumed that a quasi-elastic scattering occurs which transforms a minority spin into a majority spin electron leaving behind a reversed spin (Stoner excitation). Although Stoner excitations have been experimentally observed [14,15], their role in the formation of the cascade is not important. This is clearly proven by the fact that the total cross section Eq. (2) does not depend on magnetic order. The situation can be summarized by the statement that the mean free path for conservation of spin is larger than the mean free path for conservation of energy. In yet another explanation of the high value of Pc it is proposed that the spin dependence of the elastic scattering of the electrons on the magnetic atoms is responsible for it [16]. While the experiments confirm without doubt that the spin dependence of elastic electron scattering can be quite large at certain electron energies and in some crystal directions, it is impossible to explain the uniformly positive sign of the polarization enhancement over a wide range of energies with all materials alike irrespective of whether they are crystalline or amorphous. The enhancement of Pc over Po can readily be calculated from the transport polarization a(x) given in Eq. (4). One can write for the average transport polarization A of an infinitely thick sample: A =
(So
a ( x ) I ( x ) dx
)(J0
I ( x ) dx
t
=
(5)
where the intensity J(x) from depth x was taken to be: I ( x ) = Jo[eXp(-cr+x) + e x p ( - ~ r - x ) ] . With Eq. (3), Eq. (5)yields: (6)
A = An/[cro/crd + (5 - n ) ] .
Taking cr0/~rd = 0.7 from Fig. 2, one obtains very high values for Pc ---A + P0 that do not agree with the observations. But if one assumes a much larger relative spin independent scattering ~r0/crd = 2.5, one calculates Pc values that are quite close to the observations for all ferromagnetic transition metals Gd, Fe, Co, and Ni. With Gd, the scattering into the 4f 7 levels was neglected because 4f 8 lies 13 eV above 4f 7. Since the magnetic moment of Gd is 7.55/zs, 0.55gB must be attributed to the 5d polarization yielding An = 0.27. The simple model predicts a large increase of the enhancement factor f as the occupancy of the d-shell increases. The fact that this agrees with the observations on all transition metals adjusting o-0/o-d only once is remarkable and would be difficult to explain in any other way. From f =Pc/Po = 1 + A l P c and from Eq. (6) one obtains the further result that f is independent of An, that is f does not depend on the magnetization. This is valid as long as A and P0 are small compared to 1, that is as long as Pc = A + P0. But even in the most unfavorable case of Fe, the corrections are a few percent only and can be taken into account if necessary. Data for Gd, Fe, Co and Ni are given in Table 1. It cannot be expected that the observed cas-
Table 1 Total spin polarization P0 of s-, p-, and d-electrons in the bulk, estimated n u m b e r n of occupied d-orbitals in the paramagnetic state and their increase (decrease) An due to the spontaneous magnetization at T = 0 in Gd, Fe, Co, and Ni; the spin averaged m e a n free path A and the cascade polarization Pc (T ~ 0) are taken from various authors, for complete documentation see Refs. [2,9]
Gd Fe Co Ni
Po
n
An
h (nm)
A
Pc
f = Pc/Po
0.18 0.28 0.19 0.05
0.5 3.50 4.10 4.75
0.27 1.10 0.85 0.25
0.24 0.6 0.8 1.1
0.04 0.28 0.25 0.09
0.22 0.53 0.42 0.14
1.22 1.89 2.21 2.80
H.C. Siegmann/ Surface Science 307-309 (1994) 1076-1086
cade polarization agrees perfectly well with the Pc calculated from bulk magnetization data. Since the cascade is formed in the very few last layers at the surface, this would mean that the surface magnetization is not different from the bulk magnetization. This is generally not the case at finite temperatures as the probability density of spin waves, depending on the strength of the exchange interaction in the surface, can be quite different in the surface [2]. Hence it is important to compare to Pc measured at very low temperatures. Even then the surface magnetization can be somewhat different from the bulk magnetization. The fact that the spin independent scattering is much higher than expected could be due at least in part to scattering into the unoccupied surface states. Inverse photoemission experiments provide direct evidence that this scattering can be significant [1]. The proposed simple model connects the very short probing depth with the enhancement of the cascade polarization Pc over the groundstate polarization P0. It can explain a large number of independent experimental observations. The most important consequence of the model for magnetometry with cascade electron is
Pc =f Po,
(7)
where f is independent of temperature and magnetic field, but depends on the electronic structure according to Table 1. The model assumes conservation of spin in the formation of the cascade, i.e. spin up electrons do not become spin down electrons and vice versa. This is analogous to the two current model with noninteracting parallel spin up and spin down currents with which the giant magnetoresistance in magnetic multilayers can readily be explained [17].
4. Coupling of two ferromagnets over a nonmagnetic spacer layer
The interaction between ferromagnets over a nonmagnetic spacer layer was studied as early as 1902. C. Maurain found that an electrodeposited Fe-film separated by Cu from an Fe cathode had a tendency to have its magnetization parallel to the one of the cathode for sufficiently thin Cu
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spacer layers [18]. Today one describes this coupling by the transfer of an effective field H from the substrate to the overlayer film. However, the simplest interactions that may exist when 2 films are separated by a nonmagnetic spacer layer are the magnetostatic couplings. Before the era of surface science, this type of coupling has been investigated in detail [19]. Magnetostatic coupling may exhibit either sign. It is difficult to separate it from the coupling through pinholes and the exchange coupling. Convincing proof that exchange coupling through a nonmagnetic spacer layer such as Cr exists was given by showing that the coupling changes sign periodically with the thickness of the spacer layer [20]. In most research on the exchange coupling across nonmagnetic spacer layers, multilayers are prepared and the magnetic hysteresis loop of the multilayer assembly as a whole is measured via the magneto-optic Kerr-effect together with the electrical resistivity exhibiting the celebrated giant magnetoresistance [17]. From such measurements, the sign and strength of the exchange coupling can be deduced, yet it is often difficult to ascertain the contribution of each layer separately. Magnetometry with cascade electrons makes it possible to measure the response of one very thin layer at the surface separately while the hysteresis of the underlying substrate can independently be determined with the magneto-optic Kerr-effect because the probing depth of the latter is one order of magnitude larger. It was in fact through magnetometry with cascade electrons in the scanning electron microscope that the two different oscillation periods in the exchange coupling of Fe through Cr spacer layers have been discovered [5]. The effective field Heff transferred through the spacer layer can be as large as 3 × 107 A / m [21] or very small. The measurement of very small Heff of the order of 1 k A / m shall be examined more closely as it opens the possibility to manipulate the sign and magnitude of the exchange coupling by thermally or optically exciting electrons in the spacer layer. Furthermore, insight into critical magnetic properties of the overlayer is also obtained when the hysteresis loops are measured close to H~ff= 0, that is at the thick-
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H.C. Siegrnann/ Surface Science 307-309 (1994) 1076-1086
ness a n d / o r temperature where Herf switches sign.
4.1. Coupling of Ni78Fe22 uia chromium spacers Following Donath et al. [22], the coupling of a 1 nm thick Ni78Fe22 (permalloy) sputter deposited film over a Cr spacer layer to a thick permalloy substrate is used as illustration for the phenomena observed when the exchange coupling is close to 0. Similar to the case of F e / C r / F e with lesser crystalline perfection of the Cr, periodic coupling with the long wavelength of ~ 1 nm is observed in the N i F e / C r / NiFe case as well. The magnetic field acting in the NiFe overlayer is composed of 3 contributions: the transferred exchange field Hell, the external field H and the anisotropy field H A present in the overlayer. The magnetization M of the overlayer adjusts itself to a direction in which the sum of the resulting energies is minimal. The simplest possible assumption is that Heff is homogeneous over the whole interface. This case has been treated in detail [23,24]. It can readily be seen that the hysteresis loop of the overlayer is a replica of the substrate hysteresis loop if both H and H A are much smaller than Heff but changes from regular to inverted when Heff changes sign. The discussion will be simplified by assuming that H A is negligibly small which is reasonable in the case of ultrathin sputtered permalloy films which exhibit very small anisotropy only [25]. The condition Heff ~ 0 must occur when Heff switches sign. This is experimentally realized by varying the thickness x of the Cr spacer, but interestingly enough also by varying the temperature T. None of the theoretical models for exchange coupling across transition metal spacer layers such as Cr, including the most recent one by Bruno and Gyorffy [26], predicts a change of sign with temperature. Note that the change of sign in N i F e / C r / N i F e occurs close to the N6el temperature of bulk chromium. According to Donath et al. [22], the change of sign is fully reversible, hence irreversible processes like interface diffusion are excluded, but it depends on how the films are made.
It is obviously not possible to have Heef = 0 homogeneously over the whole interface. There will always be some fluctuations of thickness and structure of the spacer layer creating patches of radius R, where Herf has a different sign compared to the rest of the film. In this situation, a magnetic domain will form in the patch if the energy of a domain wall around the patch is smaller than the exchange energy gained by coupling to the substrate. If 3' is the energy of a domain wall per unit area, the surface energy of the patch is 2~-R • d • y, where d is the thickness of the NiFe overlayer. The exchange energy gained by coupling to the substrate is R2~j, where J is the exchange energy per unit interface area. The condition for domain formation in the patch is
R > 2d~/J.
(8)
Below a critical patch size R 0 = 2 d y / J the domains will evaporate. This is a two-dimensional analogue to homogeneous nucleation of droplets in a gas. Eq. (8) was also derived by Bloemen et al. [27] for the case of C o N i / C u / C o N i multilayers. Typical values for the present N i F e / C r / N i F e case are J = 10 -2 m J / m 2, y = 5 × 10 -2 m J / m 2, d = 10 -9 m yielding R 0 = 10 nm. If the inhomogeneities are smaller than R0, no domains can be formed. It follows that the ultrathin overlayer acts as one giant spin molecule in which all spins remain parallel. One then can measure the Heff averaged over the whole surface of the film. If, however, the films are not homogeneous on the scale of R0, domains are formed and one cannot determine the average He,. The experiments of Donath et al. [22] and of Bloemen et al. [27] demonstrate that the case of the giant spin molecule can be realized. Fig. 3 depicts schematically the case of N i F e / C r / N i F e at x = 1.2 nm and at T = 200, 270, and 330 K. At T = 330, the hysteresis loop of the surface as measured via the Pc of cascade electrons is normal and a replica of the hysteresis loop of the substrate. This shows that the Heff transferred across the Cr is positive and that the anisotropy of the overlayer film can be neglected. At T = 200 K, the hysteresis loop of the surface is inverted yet still a replica of the substrate loop.
H.C. Siegmann / Surface Science 307-309 (1994) 1076-1086
Therefore one knows that the sign of Herf transferred across Cr is now negative while the anisotropy of the overlayer can still be neglected. At T = 270 K one observes 3 switches of the magnetization as the external field H sweeps from + 2 to - 2 k A / m . The 3 changes of sign of M S can be understood as follows: If H is large, the overlayer magnetization M s must be parallel to H. As H is reduced below Hell, M S switches to the negative direction. When H becomes negative and reaches the coercive field of the substrate, M s switches to the positive direction. At very large negative values of H finally, M s must switch to the negative direction again. In Fig. 3, H = H e f t occurs at H ' = 1 k A / m (& 12 Oe). The transition has a width of A H ' = 0.1 k A / m only. It therefore is obvious that magnetometry with cascade electrons can detect extremely small exchange couplings; in the example of N i F e / C r / N i F e sputtered films with M s -- 1 T, coupling energy densities as small as 10 -3 m J / m 2 can certainly be determined. The thinner the ferromagnetic overlayer can be made, the lower the limit of detection of H , ff. In the present case,
M . Is,
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Pc [%] I0-
-I0-
0-
-I0-2
-I
0 H
I [k&/m]
2
Fig. 4. Example of an actual measurement of the cascade electron spin polarization Pc vs external magnetic field H with the surface of N i F e / C r / N i F e close to the change of sign of the transferred exchange field H~ff. The 2 curves are for 2 different locations of the 0.1 mm wide focus of the primary electron beam on the sample surface. In this way, the magnetization is probed at 2 different locations that actually are 2 mm apart The data show some variation of the saturation polarization, but the 3 switches occur with full amplitude in both locations. This demonstrates that the ultrathin film at the surface remains in a fully magnetized state over macroscopic distances rather than decaying into magnetic domains. Courtesy of M. Donath [22].
i
X =1.2nm
T=330K~ , I hI'~-~I 2=H T=270K//'l- - ] / ~ _
J t,/.U I"
T=2OOK
E=Ms'H"d.
"
['~'- i
f,i'
d = 1.5 nm [22]. The interface energy density is given by
"
Fig. 3. Hysteresis loops M(H) of an ultrathin film of soft magnetic N7sFe22 (permalloy) coupled over a Cr spacer of x = 1.2 nm thickness to bulk permalloy. On changing the temperature T from 200 to 330 K, the exchange coupling transferred from the bulk to the surface changes from antiferromagnetic to ferromagnetic; at T = 270 K, the coupling is close to zero [22]. The fact that the film at the surface switches its magnetization always with full amplitude shows that it acts as a giant spin molecule, that is it does not split up into magnetic domains.
(9)
Fig. 4 shows data from an actual measurement on N i F e / C r / N i F e at T = 284 K demonstrating the occurrence of the giant spin molecule overlayer film. The fact that one observes 3 switches of M S each with nearly the full amplitude of the saturation magnetization demonstrates that magnetic domains are not formed. The fact that this occurs on 2 different locations in the film separated by as much as 2 mm shows that the ultrathin film really is in one magnetic state over macroscopic distances, truly an amazing phenomenon. Eq. (8) suggests that the breaking of the giant spin ultrathin overlayer into domains is more likely when the thickness d is reduced.
H.C. Siegmann/ Surface Science 307-309 (1994) 1076-1086
1084 M
X=0.3 T=90 nK m ~ _ a l q l
H
overlayer film switches always with full amplitude.
4.2. Coupling over semiconducting spacer layers
X=l.2
nm--~ ~1-~,,
Fig. 5. Hysteresis loops M(H) of an ultrathin film of NiFe coupled over Cr spacers of various thicknesses x to bulk NiFe at T = 9 0 K, according to Ref. [22]. At x = 0 . 7 nm, the average exchange field transferred from the bulk to the surface is close to zero, but the switches of the magnetization at the surface occur with reduced amplitude. This indicates that the magnetization of the ultrathin film at the surface is now broken up into domains.
Unique information on exchange interaction at defects might be gained from studying the dependence of domain formation on overlayer thickness d. The above example clearly demonstrates the conditions for measuring extremely small exchange couplings. In the same system, one can however also have the other case in which the patches are larger than the critical radius R 0 and hence magnetic domains are formed. This occurs when Herf = 0 is approached by varying the thickness x of the Cr spacer layer at T = 90 K. Fig. 5 depicts schematically the hysteresis loops of the 1 nm thick NiFe overlayer obtained by Donath et al. [22]. While the normal loop at x = 0.3 nm indicates Heff > 0, the inverted loop at x = 1.2 reveals Heef < 0. At x = 0.7 nm the amplitude of the loop is much reduced, yet the loop is already inverted. The reduced amplitude indicates that the film is broken up into domains in which H~ff is positive and negative depending on the local thickness and structure of the Cr spacer. Yet clearly the average Heff is close to zero at x = 0.7 nm and T = 90 K. The amplitude of the hysteresis yields the average Herf in this case. This transition is different from the one in Fig. 3, where the
Toscano et al. [28] reported that exchange coupling between ferromagnets can also occur through nonmetallic spacer layers such as amorphous Si although it appears that the coupling tends to be weaker with semiconducting materials. The substrate was amorphous NiFeB0. 5. This is a soft magnetic material similar to NiFe that can be sputter cleaned by Ne ÷ bombardment. The first Fe-film of a thickness of 1.5 nm is deposited directly onto the substrate. This arrangement results in square magnetization loops for the Fe film at the surface that are again exact replicas of the substrate magnetization loops which saturate in external fields H < 1 k A / m . Si is deposited onto the Fe film at T = 40 K, and on top of the Si a second Fe-film of 1.5 nm thickness completes this trilayer structure. The magnetization of the Fe film on top is measured by the low energy cascade electron spin polarization Pc. It turns out that at T = 40 K, the coupling through the amorphous Si oscillates from ferro- to antiferromagnetic and back to ferromagnetic as the thickness of the Si spacer is varied from 1 to 2 to 3 nm. Later it turned out that this coupling is temperature dependent and can be influenced by irradiation with light. Mattson et al. [29] reported that the ferromagnetic coupling existing in Fe silicides below 100 K can turn into antiferromagnetic coupling either by heating to room temperature or by irradiation with visible light at a power larger than 1 W / c m 2. There was a time delay of 10-60 s between the switching of the coupling and the start of the exposure to light, yet light heating is not significant and can be excluded as an explanation of the switching according to the authors. Fig. 6 shows schematically the density of states of an amorphous semiconductor sandwiched between 2 metals according to Toscano [30]. The crystalline disorder induces states in the band gap of the semiconductor that are localized and may be singly or doubly occupied. The Fermi level E F
H.C. Siegmann/ Surface Science307-309 (1994) 1076-1086 Fe
Fe
1085
be due to redistribution of the electrons in the localized states in the bandgap.
5. Acknowledgement
Eg
The author would like to express his gratitude to Martin Landolt for helpful discussions and communication of results prior to publication.
Fe valence band
~
spacer valence band
localized electron-states ~
Boltzmann electrons
Fig. 6. Band structure for the case of a F e / S C / F e trilayer from Toscano [30]. SC is an amorphous semiconductor with an energy gap Eg, but localized electron states have been introduced in the energy gap on introducing crystalline disorder, E F is the Fermi level.
is roughly in the middle of the band gap. Band bending at the metal interfaces is absent due to the small thickness of the spacer layer and the large number of electron states at E F. The time delay of the light induced switching of the coupling as well as the dependence of the coupling on temperature suggests that the occupancy of the localized states induced by the crystalline disorder might be responsible for the magnetic coupling. F e / S i / F e is not an easy system because of silicide formation. Additional knowledge or assumptions on the magnetic and electric properties of the interfaces must be available for a convincing explanation of the results. Therefore, Toscano et al. [31] have also used amorphous SiO as a spacer layer which turned out to form sharp interfaces with Fe up to room temperature. Exchange coupling exists also in this case and strongly depends on temperature and spacer thickness. Briner and Landolt reported very recently [32] that the exchange coupling can be switched on or off by irradiation with light. The energy of the photons is below the band gap energy of 2 eV in SiO, hence it is clear that the effects on the magnetic exchange interaction must
6. References [1] M. Donath, Surf. Sci. 287/288 (1993) 722. [2] H.C. Siegmann, J. Phys.: Condensed Matter 4 (1992) 8375. [3] M.R. Scheinfein, J. Unguris, J.L. Blue, K.J. Coakley, D.T. Pierce and R.J. Celotta, Phys. Rev. B 43 (1991) 3395, and references therein. [4] R. AUenspach and A. Bischof, Phys. Rev. Lett. 69 (1992) 3385. [5] J, Unguris, R.J. Celotta and D.T. Pierce, Phys. Rev. Lett. 67 (1991) 140. [6] M.P. Seah and W.A. Dench, Surf. Interface Anal. 1 (1979) 2. [7] A. Bland and B. Heinrich, Eds., Ultrathin Magnetic Structures (Springer, Berlin, 1993). [8] M. Donath, D. Scholl, H.C. Siegmann and E. Kay, Appl. Phys. A 52 (1991) 206. [9] O.M. Paul, Dissertation ETH No. 9210, 1990. [10] D.R. Penn, S.P. Apell and S.M. Girvin, Phys. Rev. B 32 (1985) 7753. [11] D.R. Penn, Phys. Rev. B 35 (1987) 482. [12] G. Sch6nhense and H.C. Siegmann, Ann. Phys. 2 (1993) 498, and references therein. [13] J. Glazer and E. Tosatti, Solid State Commun. 52 (1984) 11507. [14] D.L. Abraham and H. Hopster, Phys. Rev. Lett. 62 (1989) 1157. [15] D. Venus and J. Kirschner, Phys. Rev. B 37 (1988) 2199. [16] M.P. Gokhale and D.L. Mills, Phys. Rev. Lett. 66 (1991) 2251. [17] R. Coehoorn, Europhys. News 24, 2 (1993) 43. [18] C. Maurain, J. Phys. (Paris) 1 (1902) 90. [19] M.H. Francombe and R.W. Hoffman, Eds., Physics of Thin Films, Vol. 6 (Academic Press, New York, 1971). [20] S.S.P. Parkin, Phys. Rev. Lett. 64 (1990) 2304. [21] M. Donath, D. Scholl, H.C. Siegmann and E. Kay, Phys. Rev. B 43 (1991) 3164. [22] M. Donath, D. Scholl, D. Mauri and E. Kay, Phys. Rev. B 43 (1991) 13164. [23] H.C. Siegmann and P.S. Bagus, Phys. Rev. B 38 (1988) 10434. [24] H.C. Siegmann, P.S. Bagus and E. Kay, Z. Phys. B 69 (1988) 485.
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[25] D. Mauri, D. Scholl, H.C. Siegmann and E. Kay, Appl. Phys. A 49 (1989) 439; Phys. Rev. Lett. 61 (1988) 758. [26] E. Bruno and B.L. Gyorffy, Phys. Rev. Lett. 71 (1993) 181. [27] P.J.H. Bloemen, M.T. Johnson, J. aan de Stegge and W.J.M. de Jonge, J. Magn. Magn. Mater. 116 (1992) L 315. [28] S. Toscano, B. Briner, H. Hopster and M. Landolt, J. Magn. Magn. Mater. 114 (1992) L6.
[29] J.E. Mattson, S. Kumar, E.E. Fullerton, S.R. Lee, C.H. Sowers, M. Grimsditch, S.D. Bader and F.T. Parker, Phys. Rev. Lett. 71 (1993) 185. [30] S. Toscano, Dissertation ETH No. 9915, Ziirich 1992. [31] S. Toscano, B. Briner and M. Landolt, in: Magnetism and Structure of Systems in Reduced Dimensions, R.F.C. Farrow et al., Eds., Nato ASI Series B 309 (Plenum, New York, 1993). [32] B. Briner and M. Landolt, Z. Phys. B 92 (1993) 137.
Surface Science 307-309 (1994) 1076-1086
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Invited paper
Surface and 2D magnetism with spin polarized cascade electrons H.C. Siegmann Swiss FederalInstitute of Technology, CH-8093 Ziirich, Switzerland
(Received 20 August 1993)
Abstract
The probing depth A of low energy cascade electrons in transition metals (TM) is dominated by scattering into the unoccupied d-orbitals. Thus A for electrons within 5-10 eV from the Fermi level varies from 1 monolayer in the early TM such as Gd to 6 monolayers in the late TM(Ni). The spin polarization Pc of the cascade electrons is due to the spin polarization P0 of the 3d-electrons plus an additional polarization generated in the process of cascade formation by scattering into the spin polarized holes of the 3d-states. The enhancement f = Pc/Po is small with the early TM but large with the late TM. Nevertheless, Pc is proportional to the magnetization and therefore represents an ideal tool to observe magnetism at surfaces and in nanoscale magnetic structures. Very small exchange couplings of ferromagnets across nonmagnetic spacer layers can be measured if one of the ferromagnets is ultrathin and acts as a giant spin molecule without decaying into domains. Recent applications include the investigation of the exchange coupling across semiconducting spacer layers.
1. Introduction
It is difficult to apply electron spectroscopy to the more interesting topics in solid state physics such as melting, heavy fermions, superconductivity, or magnetism because the energies involved in these p h e n o m e n a are usually much smaller than the energy resolution attainable in the various spectroscopic techniques. However, the development of spin polarized electron spectroscopy makes it possible to distinguish spin up from spin down states even when they are degenerate in energy. Therefore, electron spectroscopy became a major topic in magnetism and generated the new field of surface and two-dimensional magnetism. To appreciate the impact of spin polarized spectroscopy on magnetism, the reader is referred to recent surveys [1,2].
The present p a p e r will be concerned with only one small section of this field, namely magnetometry employing low energy secondary or cascade electrons. The cascade electrons are emitted in great quantities, when a primary electron b e a m of typically a few keV energy strikes the surface of a solid. In the first section it will be shown that the spin polarization Pc of the cascade electrons is proportional to the magnetization M s of the first few atomic layers at the surface. This turns out to be of great value for magnetometry at surfaces, particularly in the case of transition metals. Magnetometry with cascade electrons became widely known by the fabulous high resolution images of magnetic domains or domain walls at the surface of ferromagnets [3] and in ultrathin ferromagnetic films [4], and by the discovery of the small period oscillatory exchange coupling mediated by crys-
0039-6028/94/$07.00 © 1994 Elsevier Science B.V. All rights reserved SSDI 0039-6028(93)E0804-4
H.C. Siegmann/ SurfaceScience307-309 (1994) 1076-1086 talline chromium [5]. In the present paper, attention will be focused on one particular aspect of this technique, namely the measurement of small exchange couplings mediated between ferromagnets by non-ferromagnetic metallic or insulating spacer layers. It will be shown that interface energies as small as 10 -6 J / m 2 corresponding to 10 -7 eV per interface atom can readily be measured. This is far beyond the accuracy of present day computing of energy levels, even far beyond the reliability of the concepts on which the calculations are based. Therefore, with magnetometry based on the spin polarization Pc of the cascade electrons, the experimentalist is now in a position to explore uncharted fields yielding information on the very essence of magnetism, the quantum mechanical exchange interaction. The main issues that have to be dealt with in order to obtain valid results are the depth of information with low energy cascade electrons and the relation between the spin polarization Pc(H, T) of the cascade electrons and the magnetization Ms(H, T) of the surface, where H is the magnetic field and T the temperature.
2. Probing depth of threshold electrons in transition metals The probing depth A is the distance from the surface over which specific electronic properties of a solid can be sampled by spectroscopic analysis of energy, angular distribution, or spin polarization of the emerging electrons. A can be translated via the group velocity into the lifetime ~- of an electron in the excited states within the solid. A large amount of data for A has been accumulated from the overlayer method in which the attenuation of a prominent substrate feature is measured as a function of the overlayer thickness x and fitted with an exponential decay e x p ( - x / A ) . The data for many materials are often displayed as a "universal curve" which shows A as a function of energy [6]. With low energy electrons escaping from the solid close to the vacuum level, the different transition metals are hardly distinguishable. All that can be recognized in the energy distribution curves is the drop of
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the intensity at the Fermi level. Therefore, the overlayer method cannot be applied due to the lack of a distinguishing feature for low energy electrons. However, a well defined magnetization depth profile can be constructed at a surface by depositing either magnetic layers consisting, for example, of Fe on a nonmagnetic substrate or vice versa by depositing nonmagnetic layers on a magnetic surface. The art of fabricating such ultrathin magnetic structures has been greatly developed in the past [7]. If now the increase or decrease of the spin polarization P of the emerging electrons is measured as a function of the overlayer thickness x, one can obtain astonishingly accurate values of A even for threshold electrons.
2.1. Example of an experiment for determining the probing depth In this example, Ta overlayers are sputter deposited onto a well engineered magnetic substrate [8]. The low energy cascade electrons are excited by a primary unpolarized electron beam having an energy of 2-3 keV. An electron optical system collects most of the cascade electrons emerging from the surface in an energy window of 5-10 eV from the Fermi level and focuses them onto the entrance diaphragm of a spin polarization analyzer. The ferromagnetic polycrystalline Fe-substrate is deposited onto a special NiFe alloy (permalloy) that can be magnetically saturated in a low external field comparable to the earth magnetic field, hence the electron optics are not disturbed by it. The sputter deposited Fe film taken by itself would require high magnetic fields for magnetic saturation and furthermore would not show square magnetic hysteresis loops. But, because the Fe film is directly deposited onto the permalloy, it is exchange coupled to it and hence the substrate surface has the desirable magnetic properties of permalloy but the electronic structure of pure Fe. The polarization P of the low energy cascade electrons emitted from the Fe upon irradiation with primary electrons of a few keV can be measured with a high accuracy of ___< 0.5%. If this surface is now covered with increasing amounts of Ta, P de-
H.C. Siegmann/ Surface Science 307-309 (1994) 1076-1086
1078 I
I
~
i
i
i
L
i
i
i
i
~
I
i
i
1.01 0.8 0.6
~ o.4 0.2 0.0
0
1.0
.5
1.5
X [nm]
Fig. 1. The dependence of the relative low energy cascade polarization on the thickness x of the overlayer. Squares Ta on polycrystalline Fe from Ref. [8], circles Ta on Fe(100) from Paul [9]. The solid line is a fit to Eq. (1).
creases because some polarized electrons from the magnetic substrate are removed during passage through the nonmagnetic overlayer, while some unpolarized electrons are added. If the number of electrons from the substrate and overlayer are labelled with subscripts s and o respectively, the polarization as a function of x is given by P = [(J+
-J~-) exp(-x/A)]/J,
(1)
where the total intensity J is given by
J= (J+ +J~-) exp(-x/A) + (Jo+ + J o ) [ 1 - exp(
-x/A)],
and where + and - stand for majority and minority spin electrons, respectively. Fig. 1 shows the relative spin polarization P(x)/P(O) of the low energy threshold electrons versus the thickness x of the Ta overlayer near room temperature. The initial strong reduction of P(x)/P(O) has to be attributed to a reduction of the magnetization in the surface of the Fe substrate due to the proximity of Ta. After completion of the first layer at x = 0.2 nm, an excellent fit to Eq. (1) is possible with 1
distinguishing electrons originating in the substrate from those of the overlayer. Although such short values of the attenuation length A are phenomenologically well defined by the procedure of fitting the intensities in the 2 spin states to an exponential, the theoretical meaning of A is not clear. Previous theoretical treatments assumed that the electron distribution function in the cascade is spatially constant and used the semiclassical Boltzmann equation approach in which the phase space cell must be large in comparison to the lattice cell [10,11]. If A is only about 2 atomic layers, the concept of a mean free path is not clear any more. Hence we will use A and the derived total scattering cross section or= 1/A merely as a phenomenological parameter describing the overlayer experiments.
Results with transition metals: a simple rule emerges 2.2.
With the spin polarized overlayer technique, accurate and reproducible values for the total scattering cross section ~r = 1/A are obtained in the energy range 5 < E < 1 5 eV above E F. It turns out that the results can not be described by the "universal curve" [6] but clearly depend on the transition metal. However, there is still a quite simple behavior independent of whether the metal is magnetic or not. Compilation of the data available from many laboratories reveals that the total scattering cross section o- consists of a constant part cr0 and a part ~rd(5- n) that is proportional to the number of unoccupied states (5 - n ) in the d-band, n is the number of occupied and 5 the total number of d-orbitals available to one spin state. Fig. 2 shows that o-0 and ~rd can be obtained from a fit of the data to the equation = ~0 + ~d( 5 - n).
(2)
With magnetic metals, the spin averaged number of holes n = ½(n++n -) must be inserted into Eq. (2) to obtain the spin averaged total cross section o- = ½(o'++ o'-). To interpret the empirical rule, Eq. (2), one has to consider that the dominant processes by which electrons at within 10 eV from the Fermi
H.C Siegmann / Surface Science 307-309 (1994) 1076-1086 (3 I
I
I
I
I
Cr
3
d-shell increases by An, while the occupancy of the spin down subshell decreases by An. It follows from Eq. (2) that the total inelastic cross section becomes spin dependent according to o-(±) = or0 + trd[5 -- ( n ( + ) A n ) ] ,
Ag: Au~ 0
0
Cu L
I
I
t
I
2
3
4 d-holes
I
Fig. 2. Total scattering cross section tr in nm-t versus number of unoccupied d-orbitals for the transition metals indicated. Data from various sources according to Ref. [2] are valid for electron energies within 5-10 eV from the Fermi level. The circled points indicate average values from different laboratories. The Co value is from Ref. [12]; the upper value for Cr is on NiFe substrate, the lower on Fe(100). The Cu value is by courtesy of Karin Totland and Peter Fuchs [to be published]. level lose energy in a transition metal are elect r o n - e l e c t r o n scattering events. H e n c e tr0 accounts for inelastic scattering other than into the holes of the d-band including, for instance, scattering into the s - p - d e r i v e d bands, whereas trd describes the scattering into one unoccupied dorbital. According to this interpretation, the noble metals Cu, Ag, and Au should have identical tr = o"0. This is indeed the case. The elastic scattering of electrons is of minor importance for threshold electrons, because as many electrons are scattered into the escape cone than out of it. However, one should not expect that Eq. (2) can account for more than the gross features of o-. It neglects, for instance, scattering into surface or interface states. The experimental results in Fig. 1 show very clearly that the interface changes when the overlayer is deposited. Furthermore, the assumption of a constant trd neglects the variable stability of the 3d" configurations. It will be interesting to see whether Mn with a very stable 3d 5 configuration behaves like a noble metal or not.
3. Relating the cascade polarization Pc to the surface magnetization When a transition metal becomes ferromagnetic, the occupancy of the spin up part of the
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(3)
where tr (-+) is the cross section for majority (minority) spins. For the bulk of the material, An can be calculated from the Bohr magneton number n B obtained in conventional magnetometry according to n B = n ÷ - n - = 2 An, because the contribution of s-p-electrons to the magnetization is small. Eq. (3) allows one to independently test the simple behavior of tr in transition metals stated in Eq. (2), because it predicts that electrons travelling through ferromagnetic materials will acquire a transport polarization a. If x is the thickness of the ferromagnetic material over which the transport occurs, one has a = { [ e x p ( t ~ - - t r + ) x ] - 1} / { [ e x p ( t r - - o ' + ) x ] + 1},
(4)
a reaches unity when x ~ ~, but the intensity of transmitted electrons exponentially tends to 0 when x increases, a has been measured directly by letting unpolarized electrons from a nonmagnetic substrate travel through a ferromagnetic overlayer [12]. The results are in good agreement with Eq. (4). Another important consequence of Eq. (4) concerns the spin polarization Pc of the low energy cascade electrons. This polarization shows an enhancement over the average spin polarization P0 of the N electrons in the valence bands made up of d-, p-, and s-orbitals. If one assumes that all valence electrons are excited to an escape level with equal probability, it follows that P0 = An/N where N now includes the s - p electrons, but An is m a d e up almost entirely by the 3d-electrons alone, hence can be determined with conventional magnetometry on bulk material. It has been proposed right after the first observations of the enhanced cascade polarization Pc that scattering into the unoccupied holes of the d-band could be responsible for it. A summary of these first arguments is given in Ref. [10]. However, it must be mentioned that other
H.C. Siegmann / Surface Science 307-309 (1994) 1076-1086
1080
models explaining the conspicuously high polarization Pc of the low energy cascade electrons have also been put forward. In one model [13] it is assumed that a quasi-elastic scattering occurs which transforms a minority spin into a majority spin electron leaving behind a reversed spin (Stoner excitation). Although Stoner excitations have been experimentally observed [14,15], their role in the formation of the cascade is not important. This is clearly proven by the fact that the total cross section Eq. (2) does not depend on magnetic order. The situation can be summarized by the statement that the mean free path for conservation of spin is larger than the mean free path for conservation of energy. In yet another explanation of the high value of Pc it is proposed that the spin dependence of the elastic scattering of the electrons on the magnetic atoms is responsible for it [16]. While the experiments confirm without doubt that the spin dependence of elastic electron scattering can be quite large at certain electron energies and in some crystal directions, it is impossible to explain the uniformly positive sign of the polarization enhancement over a wide range of energies with all materials alike irrespective of whether they are crystalline or amorphous. The enhancement of Pc over Po can readily be calculated from the transport polarization a(x) given in Eq. (4). One can write for the average transport polarization A of an infinitely thick sample: A =
(So
a ( x ) I ( x ) dx
)(J0
I ( x ) dx
t
=
(5)
where the intensity J(x) from depth x was taken to be: I ( x ) = Jo[eXp(-cr+x) + e x p ( - ~ r - x ) ] . With Eq. (3), Eq. (5)yields: (6)
A = An/[cro/crd + (5 - n ) ] .
Taking cr0/~rd = 0.7 from Fig. 2, one obtains very high values for Pc ---A + P0 that do not agree with the observations. But if one assumes a much larger relative spin independent scattering ~r0/crd = 2.5, one calculates Pc values that are quite close to the observations for all ferromagnetic transition metals Gd, Fe, Co, and Ni. With Gd, the scattering into the 4f 7 levels was neglected because 4f 8 lies 13 eV above 4f 7. Since the magnetic moment of Gd is 7.55/zs, 0.55gB must be attributed to the 5d polarization yielding An = 0.27. The simple model predicts a large increase of the enhancement factor f as the occupancy of the d-shell increases. The fact that this agrees with the observations on all transition metals adjusting o-0/o-d only once is remarkable and would be difficult to explain in any other way. From f =Pc/Po = 1 + A l P c and from Eq. (6) one obtains the further result that f is independent of An, that is f does not depend on the magnetization. This is valid as long as A and P0 are small compared to 1, that is as long as Pc = A + P0. But even in the most unfavorable case of Fe, the corrections are a few percent only and can be taken into account if necessary. Data for Gd, Fe, Co and Ni are given in Table 1. It cannot be expected that the observed cas-
Table 1 Total spin polarization P0 of s-, p-, and d-electrons in the bulk, estimated n u m b e r n of occupied d-orbitals in the paramagnetic state and their increase (decrease) An due to the spontaneous magnetization at T = 0 in Gd, Fe, Co, and Ni; the spin averaged m e a n free path A and the cascade polarization Pc (T ~ 0) are taken from various authors, for complete documentation see Refs. [2,9]
Gd Fe Co Ni
Po
n
An
h (nm)
A
Pc
f = Pc/Po
0.18 0.28 0.19 0.05
0.5 3.50 4.10 4.75
0.27 1.10 0.85 0.25
0.24 0.6 0.8 1.1
0.04 0.28 0.25 0.09
0.22 0.53 0.42 0.14
1.22 1.89 2.21 2.80
H.C. Siegmann/ Surface Science 307-309 (1994) 1076-1086
cade polarization agrees perfectly well with the Pc calculated from bulk magnetization data. Since the cascade is formed in the very few last layers at the surface, this would mean that the surface magnetization is not different from the bulk magnetization. This is generally not the case at finite temperatures as the probability density of spin waves, depending on the strength of the exchange interaction in the surface, can be quite different in the surface [2]. Hence it is important to compare to Pc measured at very low temperatures. Even then the surface magnetization can be somewhat different from the bulk magnetization. The fact that the spin independent scattering is much higher than expected could be due at least in part to scattering into the unoccupied surface states. Inverse photoemission experiments provide direct evidence that this scattering can be significant [1]. The proposed simple model connects the very short probing depth with the enhancement of the cascade polarization Pc over the groundstate polarization P0. It can explain a large number of independent experimental observations. The most important consequence of the model for magnetometry with cascade electron is
Pc =f Po,
(7)
where f is independent of temperature and magnetic field, but depends on the electronic structure according to Table 1. The model assumes conservation of spin in the formation of the cascade, i.e. spin up electrons do not become spin down electrons and vice versa. This is analogous to the two current model with noninteracting parallel spin up and spin down currents with which the giant magnetoresistance in magnetic multilayers can readily be explained [17].
4. Coupling of two ferromagnets over a nonmagnetic spacer layer
The interaction between ferromagnets over a nonmagnetic spacer layer was studied as early as 1902. C. Maurain found that an electrodeposited Fe-film separated by Cu from an Fe cathode had a tendency to have its magnetization parallel to the one of the cathode for sufficiently thin Cu
1081
spacer layers [18]. Today one describes this coupling by the transfer of an effective field H from the substrate to the overlayer film. However, the simplest interactions that may exist when 2 films are separated by a nonmagnetic spacer layer are the magnetostatic couplings. Before the era of surface science, this type of coupling has been investigated in detail [19]. Magnetostatic coupling may exhibit either sign. It is difficult to separate it from the coupling through pinholes and the exchange coupling. Convincing proof that exchange coupling through a nonmagnetic spacer layer such as Cr exists was given by showing that the coupling changes sign periodically with the thickness of the spacer layer [20]. In most research on the exchange coupling across nonmagnetic spacer layers, multilayers are prepared and the magnetic hysteresis loop of the multilayer assembly as a whole is measured via the magneto-optic Kerr-effect together with the electrical resistivity exhibiting the celebrated giant magnetoresistance [17]. From such measurements, the sign and strength of the exchange coupling can be deduced, yet it is often difficult to ascertain the contribution of each layer separately. Magnetometry with cascade electrons makes it possible to measure the response of one very thin layer at the surface separately while the hysteresis of the underlying substrate can independently be determined with the magneto-optic Kerr-effect because the probing depth of the latter is one order of magnitude larger. It was in fact through magnetometry with cascade electrons in the scanning electron microscope that the two different oscillation periods in the exchange coupling of Fe through Cr spacer layers have been discovered [5]. The effective field Heff transferred through the spacer layer can be as large as 3 × 107 A / m [21] or very small. The measurement of very small Heff of the order of 1 k A / m shall be examined more closely as it opens the possibility to manipulate the sign and magnitude of the exchange coupling by thermally or optically exciting electrons in the spacer layer. Furthermore, insight into critical magnetic properties of the overlayer is also obtained when the hysteresis loops are measured close to H~ff= 0, that is at the thick-
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H.C. Siegrnann/ Surface Science 307-309 (1994) 1076-1086
ness a n d / o r temperature where Herf switches sign.
4.1. Coupling of Ni78Fe22 uia chromium spacers Following Donath et al. [22], the coupling of a 1 nm thick Ni78Fe22 (permalloy) sputter deposited film over a Cr spacer layer to a thick permalloy substrate is used as illustration for the phenomena observed when the exchange coupling is close to 0. Similar to the case of F e / C r / F e with lesser crystalline perfection of the Cr, periodic coupling with the long wavelength of ~ 1 nm is observed in the N i F e / C r / NiFe case as well. The magnetic field acting in the NiFe overlayer is composed of 3 contributions: the transferred exchange field Hell, the external field H and the anisotropy field H A present in the overlayer. The magnetization M of the overlayer adjusts itself to a direction in which the sum of the resulting energies is minimal. The simplest possible assumption is that Heff is homogeneous over the whole interface. This case has been treated in detail [23,24]. It can readily be seen that the hysteresis loop of the overlayer is a replica of the substrate hysteresis loop if both H and H A are much smaller than Heff but changes from regular to inverted when Heff changes sign. The discussion will be simplified by assuming that H A is negligibly small which is reasonable in the case of ultrathin sputtered permalloy films which exhibit very small anisotropy only [25]. The condition Heff ~ 0 must occur when Heff switches sign. This is experimentally realized by varying the thickness x of the Cr spacer, but interestingly enough also by varying the temperature T. None of the theoretical models for exchange coupling across transition metal spacer layers such as Cr, including the most recent one by Bruno and Gyorffy [26], predicts a change of sign with temperature. Note that the change of sign in N i F e / C r / N i F e occurs close to the N6el temperature of bulk chromium. According to Donath et al. [22], the change of sign is fully reversible, hence irreversible processes like interface diffusion are excluded, but it depends on how the films are made.
It is obviously not possible to have Heef = 0 homogeneously over the whole interface. There will always be some fluctuations of thickness and structure of the spacer layer creating patches of radius R, where Herf has a different sign compared to the rest of the film. In this situation, a magnetic domain will form in the patch if the energy of a domain wall around the patch is smaller than the exchange energy gained by coupling to the substrate. If 3' is the energy of a domain wall per unit area, the surface energy of the patch is 2~-R • d • y, where d is the thickness of the NiFe overlayer. The exchange energy gained by coupling to the substrate is R2~j, where J is the exchange energy per unit interface area. The condition for domain formation in the patch is
R > 2d~/J.
(8)
Below a critical patch size R 0 = 2 d y / J the domains will evaporate. This is a two-dimensional analogue to homogeneous nucleation of droplets in a gas. Eq. (8) was also derived by Bloemen et al. [27] for the case of C o N i / C u / C o N i multilayers. Typical values for the present N i F e / C r / N i F e case are J = 10 -2 m J / m 2, y = 5 × 10 -2 m J / m 2, d = 10 -9 m yielding R 0 = 10 nm. If the inhomogeneities are smaller than R0, no domains can be formed. It follows that the ultrathin overlayer acts as one giant spin molecule in which all spins remain parallel. One then can measure the Heff averaged over the whole surface of the film. If, however, the films are not homogeneous on the scale of R0, domains are formed and one cannot determine the average He,. The experiments of Donath et al. [22] and of Bloemen et al. [27] demonstrate that the case of the giant spin molecule can be realized. Fig. 3 depicts schematically the case of N i F e / C r / N i F e at x = 1.2 nm and at T = 200, 270, and 330 K. At T = 330, the hysteresis loop of the surface as measured via the Pc of cascade electrons is normal and a replica of the hysteresis loop of the substrate. This shows that the Heff transferred across the Cr is positive and that the anisotropy of the overlayer film can be neglected. At T = 200 K, the hysteresis loop of the surface is inverted yet still a replica of the substrate loop.
H.C. Siegmann / Surface Science 307-309 (1994) 1076-1086
Therefore one knows that the sign of Herf transferred across Cr is now negative while the anisotropy of the overlayer can still be neglected. At T = 270 K one observes 3 switches of the magnetization as the external field H sweeps from + 2 to - 2 k A / m . The 3 changes of sign of M S can be understood as follows: If H is large, the overlayer magnetization M s must be parallel to H. As H is reduced below Hell, M S switches to the negative direction. When H becomes negative and reaches the coercive field of the substrate, M s switches to the positive direction. At very large negative values of H finally, M s must switch to the negative direction again. In Fig. 3, H = H e f t occurs at H ' = 1 k A / m (& 12 Oe). The transition has a width of A H ' = 0.1 k A / m only. It therefore is obvious that magnetometry with cascade electrons can detect extremely small exchange couplings; in the example of N i F e / C r / N i F e sputtered films with M s -- 1 T, coupling energy densities as small as 10 -3 m J / m 2 can certainly be determined. The thinner the ferromagnetic overlayer can be made, the lower the limit of detection of H , ff. In the present case,
M . Is,
1083
Pc [%] I0-
-I0-
0-
-I0-2
-I
0 H
I [k&/m]
2
Fig. 4. Example of an actual measurement of the cascade electron spin polarization Pc vs external magnetic field H with the surface of N i F e / C r / N i F e close to the change of sign of the transferred exchange field H~ff. The 2 curves are for 2 different locations of the 0.1 mm wide focus of the primary electron beam on the sample surface. In this way, the magnetization is probed at 2 different locations that actually are 2 mm apart The data show some variation of the saturation polarization, but the 3 switches occur with full amplitude in both locations. This demonstrates that the ultrathin film at the surface remains in a fully magnetized state over macroscopic distances rather than decaying into magnetic domains. Courtesy of M. Donath [22].
i
X =1.2nm
T=330K~ , I hI'~-~I 2=H T=270K//'l- - ] / ~ _
J t,/.U I"
T=2OOK
E=Ms'H"d.
"
['~'- i
f,i'
d = 1.5 nm [22]. The interface energy density is given by
"
Fig. 3. Hysteresis loops M(H) of an ultrathin film of soft magnetic N7sFe22 (permalloy) coupled over a Cr spacer of x = 1.2 nm thickness to bulk permalloy. On changing the temperature T from 200 to 330 K, the exchange coupling transferred from the bulk to the surface changes from antiferromagnetic to ferromagnetic; at T = 270 K, the coupling is close to zero [22]. The fact that the film at the surface switches its magnetization always with full amplitude shows that it acts as a giant spin molecule, that is it does not split up into magnetic domains.
(9)
Fig. 4 shows data from an actual measurement on N i F e / C r / N i F e at T = 284 K demonstrating the occurrence of the giant spin molecule overlayer film. The fact that one observes 3 switches of M S each with nearly the full amplitude of the saturation magnetization demonstrates that magnetic domains are not formed. The fact that this occurs on 2 different locations in the film separated by as much as 2 mm shows that the ultrathin film really is in one magnetic state over macroscopic distances, truly an amazing phenomenon. Eq. (8) suggests that the breaking of the giant spin ultrathin overlayer into domains is more likely when the thickness d is reduced.
H.C. Siegmann/ Surface Science 307-309 (1994) 1076-1086
1084 M
X=0.3 T=90 nK m ~ _ a l q l
H
overlayer film switches always with full amplitude.
4.2. Coupling over semiconducting spacer layers
X=l.2
nm--~ ~1-~,,
Fig. 5. Hysteresis loops M(H) of an ultrathin film of NiFe coupled over Cr spacers of various thicknesses x to bulk NiFe at T = 9 0 K, according to Ref. [22]. At x = 0 . 7 nm, the average exchange field transferred from the bulk to the surface is close to zero, but the switches of the magnetization at the surface occur with reduced amplitude. This indicates that the magnetization of the ultrathin film at the surface is now broken up into domains.
Unique information on exchange interaction at defects might be gained from studying the dependence of domain formation on overlayer thickness d. The above example clearly demonstrates the conditions for measuring extremely small exchange couplings. In the same system, one can however also have the other case in which the patches are larger than the critical radius R 0 and hence magnetic domains are formed. This occurs when Herf = 0 is approached by varying the thickness x of the Cr spacer layer at T = 90 K. Fig. 5 depicts schematically the hysteresis loops of the 1 nm thick NiFe overlayer obtained by Donath et al. [22]. While the normal loop at x = 0.3 nm indicates Heff > 0, the inverted loop at x = 1.2 reveals Heef < 0. At x = 0.7 nm the amplitude of the loop is much reduced, yet the loop is already inverted. The reduced amplitude indicates that the film is broken up into domains in which H~ff is positive and negative depending on the local thickness and structure of the Cr spacer. Yet clearly the average Heff is close to zero at x = 0.7 nm and T = 90 K. The amplitude of the hysteresis yields the average Herf in this case. This transition is different from the one in Fig. 3, where the
Toscano et al. [28] reported that exchange coupling between ferromagnets can also occur through nonmetallic spacer layers such as amorphous Si although it appears that the coupling tends to be weaker with semiconducting materials. The substrate was amorphous NiFeB0. 5. This is a soft magnetic material similar to NiFe that can be sputter cleaned by Ne ÷ bombardment. The first Fe-film of a thickness of 1.5 nm is deposited directly onto the substrate. This arrangement results in square magnetization loops for the Fe film at the surface that are again exact replicas of the substrate magnetization loops which saturate in external fields H < 1 k A / m . Si is deposited onto the Fe film at T = 40 K, and on top of the Si a second Fe-film of 1.5 nm thickness completes this trilayer structure. The magnetization of the Fe film on top is measured by the low energy cascade electron spin polarization Pc. It turns out that at T = 40 K, the coupling through the amorphous Si oscillates from ferro- to antiferromagnetic and back to ferromagnetic as the thickness of the Si spacer is varied from 1 to 2 to 3 nm. Later it turned out that this coupling is temperature dependent and can be influenced by irradiation with light. Mattson et al. [29] reported that the ferromagnetic coupling existing in Fe silicides below 100 K can turn into antiferromagnetic coupling either by heating to room temperature or by irradiation with visible light at a power larger than 1 W / c m 2. There was a time delay of 10-60 s between the switching of the coupling and the start of the exposure to light, yet light heating is not significant and can be excluded as an explanation of the switching according to the authors. Fig. 6 shows schematically the density of states of an amorphous semiconductor sandwiched between 2 metals according to Toscano [30]. The crystalline disorder induces states in the band gap of the semiconductor that are localized and may be singly or doubly occupied. The Fermi level E F
H.C. Siegmann/ Surface Science307-309 (1994) 1076-1086 Fe
Fe
1085
be due to redistribution of the electrons in the localized states in the bandgap.
5. Acknowledgement
Eg
The author would like to express his gratitude to Martin Landolt for helpful discussions and communication of results prior to publication.
Fe valence band
~
spacer valence band
localized electron-states ~
Boltzmann electrons
Fig. 6. Band structure for the case of a F e / S C / F e trilayer from Toscano [30]. SC is an amorphous semiconductor with an energy gap Eg, but localized electron states have been introduced in the energy gap on introducing crystalline disorder, E F is the Fermi level.
is roughly in the middle of the band gap. Band bending at the metal interfaces is absent due to the small thickness of the spacer layer and the large number of electron states at E F. The time delay of the light induced switching of the coupling as well as the dependence of the coupling on temperature suggests that the occupancy of the localized states induced by the crystalline disorder might be responsible for the magnetic coupling. F e / S i / F e is not an easy system because of silicide formation. Additional knowledge or assumptions on the magnetic and electric properties of the interfaces must be available for a convincing explanation of the results. Therefore, Toscano et al. [31] have also used amorphous SiO as a spacer layer which turned out to form sharp interfaces with Fe up to room temperature. Exchange coupling exists also in this case and strongly depends on temperature and spacer thickness. Briner and Landolt reported very recently [32] that the exchange coupling can be switched on or off by irradiation with light. The energy of the photons is below the band gap energy of 2 eV in SiO, hence it is clear that the effects on the magnetic exchange interaction must
6. References [1] M. Donath, Surf. Sci. 287/288 (1993) 722. [2] H.C. Siegmann, J. Phys.: Condensed Matter 4 (1992) 8375. [3] M.R. Scheinfein, J. Unguris, J.L. Blue, K.J. Coakley, D.T. Pierce and R.J. Celotta, Phys. Rev. B 43 (1991) 3395, and references therein. [4] R. AUenspach and A. Bischof, Phys. Rev. Lett. 69 (1992) 3385. [5] J, Unguris, R.J. Celotta and D.T. Pierce, Phys. Rev. Lett. 67 (1991) 140. [6] M.P. Seah and W.A. Dench, Surf. Interface Anal. 1 (1979) 2. [7] A. Bland and B. Heinrich, Eds., Ultrathin Magnetic Structures (Springer, Berlin, 1993). [8] M. Donath, D. Scholl, H.C. Siegmann and E. Kay, Appl. Phys. A 52 (1991) 206. [9] O.M. Paul, Dissertation ETH No. 9210, 1990. [10] D.R. Penn, S.P. Apell and S.M. Girvin, Phys. Rev. B 32 (1985) 7753. [11] D.R. Penn, Phys. Rev. B 35 (1987) 482. [12] G. Sch6nhense and H.C. Siegmann, Ann. Phys. 2 (1993) 498, and references therein. [13] J. Glazer and E. Tosatti, Solid State Commun. 52 (1984) 11507. [14] D.L. Abraham and H. Hopster, Phys. Rev. Lett. 62 (1989) 1157. [15] D. Venus and J. Kirschner, Phys. Rev. B 37 (1988) 2199. [16] M.P. Gokhale and D.L. Mills, Phys. Rev. Lett. 66 (1991) 2251. [17] R. Coehoorn, Europhys. News 24, 2 (1993) 43. [18] C. Maurain, J. Phys. (Paris) 1 (1902) 90. [19] M.H. Francombe and R.W. Hoffman, Eds., Physics of Thin Films, Vol. 6 (Academic Press, New York, 1971). [20] S.S.P. Parkin, Phys. Rev. Lett. 64 (1990) 2304. [21] M. Donath, D. Scholl, H.C. Siegmann and E. Kay, Phys. Rev. B 43 (1991) 3164. [22] M. Donath, D. Scholl, D. Mauri and E. Kay, Phys. Rev. B 43 (1991) 13164. [23] H.C. Siegmann and P.S. Bagus, Phys. Rev. B 38 (1988) 10434. [24] H.C. Siegmann, P.S. Bagus and E. Kay, Z. Phys. B 69 (1988) 485.
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[25] D. Mauri, D. Scholl, H.C. Siegmann and E. Kay, Appl. Phys. A 49 (1989) 439; Phys. Rev. Lett. 61 (1988) 758. [26] E. Bruno and B.L. Gyorffy, Phys. Rev. Lett. 71 (1993) 181. [27] P.J.H. Bloemen, M.T. Johnson, J. aan de Stegge and W.J.M. de Jonge, J. Magn. Magn. Mater. 116 (1992) L 315. [28] S. Toscano, B. Briner, H. Hopster and M. Landolt, J. Magn. Magn. Mater. 114 (1992) L6.
[29] J.E. Mattson, S. Kumar, E.E. Fullerton, S.R. Lee, C.H. Sowers, M. Grimsditch, S.D. Bader and F.T. Parker, Phys. Rev. Lett. 71 (1993) 185. [30] S. Toscano, Dissertation ETH No. 9915, Ziirich 1992. [31] S. Toscano, B. Briner and M. Landolt, in: Magnetism and Structure of Systems in Reduced Dimensions, R.F.C. Farrow et al., Eds., Nato ASI Series B 309 (Plenum, New York, 1993). [32] B. Briner and M. Landolt, Z. Phys. B 92 (1993) 137.