Using ferromagnetic resonance to measure the magnetic moments of ultrathin films

N.T-I

ELSEVIER

Journal of Magnetismand Magnetic Materials 166 (1997) 6-26

~ JH ~H

Journalof magnetism and magnetic materials

Using ferromagnetic resonance to measure the magnetic moments of ultrathin films Z. Celinski l, K.B. Urquhart, B. Heinrich Surface Physics Laboratory, Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6

Received 2 April 1996; revised 14 June 1996

Abstract A technique that uses ferromagnetic resonance (FMR) to measure the saturation magnetization of ultrathin ferromagnetic films is described. It has been used to measure the layer averaged magnetic moments of ultrathin Fe films located in A g / F e / A g , A u / F e / A g , C u / F e / A g , P d / F e / A g , and N i / F e / A g structures relative to that of an Au/5.7 ML Fe/Ag reference film. The ratios obtained using method have a total measurement error of a little over 1%. The measurements were carried out to investigate theoretical predictions that Fe atoms located at or near surfaces and interfaces should possess enhanced magnetic moments compared those of Fe atoms in the bulk. All of the bcc Fe(001) films used in our work were approximately 5 monatomic layers (ML) thick and were all grown on bulk fcc Ag(001) substrates. The covering layers of Cu, Pd, and Ag were all 7 ML thick while the covering layers of Ni were 2-3 ML thick and the covering layers of Au were 20 ML thick. All FMR measurements were carried out at a temperature of 77 K. An Ag/5.5 ML Fe/Ag specimen and an Ag/10.9 ML Fe/Ag specimen (the thick Fe specimen) were determined to have a moment ratio of 1.06 ± 0.01. This compared well to a layer averaged, ground state, moment ratio of 1.05 calculated for the two films using results obtained from published first principles calculations. Ratios of 1.08_ 0.01 and 1.10 + 0.01 were obtained for A u / 5 . 7 F e / A g and Cu/5.8 Fe/Ag structures, respectively, when compared to the thick Fe specimen. In a similar manner, ratios of 1.11 + 0.01 and 1.12 + 0.01, respectively, were determined for P d / 5 . 6 F e / A g and P d / 5 . 7 F e / A g sandwiches. Finally, the layer averaged moment of a 2 N i / 5 . 7 F e / A g structure was in a ratio of 1.15 + 0.01 with the thick Fe specimen while two 3 N i / 5 . 7 F e / A g sandwiches were in ratios of 1.24 + 0.01 and 1.20 + 0.01, respectively. All measured values were in excellent agreement with published first-principles calculations and with the layer averaged moments obtained from polarized neutron reflection (PNR) studies carried out on many of our specimens. Keywords: Ferromagneticresonance;Magnetic moments;Ultrathinfilms

1. Introduction Ferromagnetic resonance is a powerful technique for determining the fundamental magnetic properties

t PresentAddress: Departmentof Physics and Energy Sciences, University of Colorado at Colorado Springs, Colorado Springs, CO 80933-7150.

of ultrathin ferromagnetic films [1,2]. It has been used to accurately measure the magnetic anisotropies, g-factors, and magnetic damping parameters of ultrathin magnetic structures and to measure the exchange coupling (ferromagnetic or anti-ferromagnetic) between two ferromagnetic layers that are separated by non-magnetic interlayers [2], This paper describes another interesting and use-

0304-8853/97/$17.00 Copyright © 1997 Elsevier Science B.V. All rights reserved. PI1 S0304- 8853(96)00428-3

Z Celinski et al./Journal of Magnetism and Magnetic Materials 166 (1997) 6-26

ful application of FMR: the ability to determine the layer averaged magnetic moment of an ultrathin film by comparing FMR data collected for the film with that of a reference specimen of known magnetization. While our technique requires careful control and calibration of the FMR spectrometer, as well as a precise knowledge of the film thickness, we will show that it is capable of determining the ratio of the saturation magnetizations of two bcc Fe(001) films with a total measurement error of approximately 1%. Our technique was developed in response to advances in ab initio numerical calculations over the past 10 years that allow the electronic and magnetic properties of low-dimensional magnetic systems to be determined to a high degree of accuracy. An excellent overview of these efforts can be found in the review paper by Freeman and Wu [3]. Basically, the calculations have predicted that changes in the symmetry and the coordination number of ferromagnetic atoms located at or near a surface or a metalmetal interface leads to narrowed d bands and localized electronic states. This results in a noticeable enhancement of the magnetic moments of surface and interfacial atoms compared to atoms located in the bulk. For example, calculations by three different groups using three different methods (Bliigel et al. [4], Fu and Freeman [5], and Richter et al. [6]) have all predicted that an Fe atom located in a single layer of bcc Fe(00t) grown on an Ag(001) substrate should have a moment of approximately 3 /z B. This represents a 36% enhancement over the 2.2 /z B moment of a bulk Fe atom. While a great deal of theoretical data has been generated, there has been little experimental data available for comparison. The FMR technique that we describe here has allowed us to obtain accurate experimental measurements of the ratio of the layer averaged magnetic moment of ultrathin Fe films located in A g / F e / A g , C u / F e / A g , P d / F e / A g , and N i / F e / A g sandwiches to the average moment of an ultrathin Fe film located in a reference A u / F e / A g specimen. These structures were chosen because they have all been the subject of published first-principles magnetic moment calculations and because we are very familiar with the growth of clean, well-defined, single crystal metal films of these types using molecular beam epitaxy (MBE). Our technique is straightforward. An FMR spec-

7

trometer is used to collect absorption data from a film of unknown magnetization and a reference film of known magnetization. The resulting pair of FMR datasets are then fitted to a theoretical FMR absorption lineshape using a X 2 function minimization program. Along with many of the fundamental magnetic properties of the films, the fitting process and subsequent integration of datasets allows us to extract the value of K(Msd) for each film where K is a constant, (Msd) is the total magnetic moment per unit area, M s is the saturation magnetization (the average magnetic moment per unit volume), and d is the film thickness. The precise value of K depends upon the FMR spectrometer but we will show in Section 3 that it will be same for all FMR datasets collected by a given spectrometer provided that: (1) the spectrometer is carefully calibrated prior to each data collection run and (2) the datasets are properly normalized using information obtained from the calibration process before they are fitted to the theoretical FMR absorption lineshape. Under these two conditions, the ratio of the extracted K(M~d)values will give us the ratio of (Msd) in the two films. Assuming that we know M S in the reference film, as well as accurate measures of the film thicknesses, we can determine M S in the unknown film. Our paper is organized as follows. Section 2 calculates the FMR absorption lineshape for an ultrathin film and shows how to extract M s from measured FMR data. We will show that the properties of ultrathin ferromagnetic films allow us to derive an analytic expression for the absorption lineshape that is almost perfectly Lorentzian. This is in sharp contrast to the case of a metallic film of arbitrary thickness where is no simple, analytic solution and we must use numerical methods to calculate the absorption. Section 3 describes our experimental methods. It begins with a short description of how we prepared our ultrathin film structures using the techniques of molecular beam epitaxy (MBE) and how we accurately measured the various film thicknesses by monitoring reflection high energy electron diffraction (RHEED) intensity oscillations during film growth. This is followed by a detailed description of our FMR spectrometer and the all-important calibration procedure. Section 4 discusses data collection, the fitting process and the integration of datasets. Since

8

Z. Celinski et al./Journal of Magnetism and Magnetic Materials 166 (1997) 6-26

FMR spectrometers measure either the microwave power absorbed by the specimen as a function of the applied dc magnetic field H or the derivative of the absorption with respect to H, we present two methods for the extraction of K(M~d). An approach that involves integrating absorption derivative data with respect to H, and then extracting K(M~d) by a second integration of the resulting absorption peak, seems to work best. The integration steps substantially reduce the noise level in the original data. This typically results in a more accurate value for K(M~ d). Section 5 presents the results of our measurements of the layer averaged magnetic moments of ultrathin Fe films located in A g / F e / A g , Au/Fe/Ag, Cu/Fe/Ag, Pd/Fe/Ag, and N i / F e / A g structures. The layer averaged moments are compared to values obtained from published theoretical calculations. Section 6 contains a short summary of our work and our conclusions.

2. Calculation of the absorption lineshape FMR absorption experiments measure either the microwave power absorbed by a specimen as a function of an applied dc magnetic field, H, or the derivative of the absorption with respect to H. In either case, the resulting curve is described by a resonance field, HFMR, that corresponds to maximum power absorption, and by an absorption linewidth, A H. In this section we will calculate the microwave absorption of an ultrathin ferromagnetic film as a function of the applied field H and the fundamental magnetic properties of the film. The latter include the surface and bulk anisotropies, the spectroscopic g-factor, the magnetic damping parameter (that is responsible for the finite linewidth A H), and the quantity of interest: the saturation magnetization, M~. The usual approach is to follow the prescription of Ament and Rado [7] and combine Maxwell's equations for the rf electric and magnetic fields in the specimen with the Landau-Lifshitz equation of motion for the magnetization (including exchange) and then set up and solve a boundary value problem appropriate for the experimental geometry. In this

case, surface anisotropies enter into the problem through the boundary conditions on the rf magnetization components [8]. The solution of the boundary value problem for a film of arbitrary thickness is complex: the coefficients of a sixth-order, complex valued, polynomial must first be calculated using chosen values of the magnetic parameters of the film and for H. The six roots of this equation are numerically extracted and then used to set up an 8 X 8 set of simultaneous equations that represents the boundary value problem. The absorption is then calculated from the solutions of the eight equations. Fortunately, the absorption calculation can be considerably simplified for the case of an ultrathin film because the thickness of the film is typically much less than both the rf skin depth, 6, and the 'exchange length', dex (the characteristic distance over which individual atomic moments are locked parallel to one another by the strong exchange interaction [2]). The first condition implies that the rf electric and magnetic fields will be essentially constant across the film while the second condition guarantees that all of the magnetic moments in the film are aligned in the same direction. The ultrathin film therefore behaves like a single magnetic 'molecule' immersed in uniform dc and rf fields. In this limiting case, the Landau-Lifshitz equation of motion can be solved to yield an analytic expression for the absorption lineshape. We can even show that the lineshape is almost perfectly Lorentzian (provided the film has a reasonably narrow linewidth). We can use the definitions for skin-depth and exchange length to quantify exactly what we mean by 'ultrathin' Fe films. The skin-depth is defined to be 6 = C/(2~toOr) 1/2 while the exchange length is dex = (a/2"rrM2) 1/2 (see Heinrich and Cochran [2] for a derivation of dex). Here, tr is the conductivity of the metal, to = 27rf is the circular microwave frequency, A is the exchange stiffness constant, and M~ is the saturation magnetization (the magnetic moment per unit volume). All quantities are expressed in Gaussian units. For bulk bcc Fe at room temperature, where A = 2 X 10 -6 ergcm -1, tr-1017 S -1, and 4-rrM~=21.5 kOe, and for a microwave frequency of f = t o / 2 ~ = 36.6 GHz, the skin depth is 6 ~ 6 × 10 -5 cm and the exchange length is d e x = 3 X 10 7 cm. Given that the atomic planes of a bcc Fe(001) film are separated by a

Z Celinski et aL/Journal of Magnetism and Magnetic Materials 166 (1997) 6 - 2 6 o

distance of 1.425 A, we can say that Fe films thinner than 21 monatomic layers are 'ultrathin'. 2.1. The Landau-Lifshitz equation of motion The Landau-Lifshitz equation of motion for a specimen's magnetization vector M, --

--

0t

=MX

Hef f

(2.1)

describes the response of M to the total effective magnetic field, Herf, that acts on the magnetic moments in the specimen. Here, y = g r e l / 2 m c = ( g / 2 ) 1 . 7 5 8 8 × 107 H z O e -1 is the gyromagnetic ratio and g is the spectroscopic splitting factor. For the ultrathin films the effective field is given by the expression [9]: OF H elf = - - -

(2.2)

OM i '

where F is the magnetic free energy and i = x, y, and z. In ultrathin bcc Fe(001) films, the effective field H e ft is composed of two external fields, H and h, and four 'internal' fields related to the magnetic properties of the film: 1. Externally applied dc magnetic field: H 2. Driving rf microwave magnetic field: h 3. Demagnetizing field: h d 4. Magnetocrystalline anisotropy field: H~ 5. Exchange field: h~x 6. Magnetic damping field: h C Additional effective fields associated with surface anisotropy energies enter through the boundary conditions on the rf fields at the film surfaces [2]. The FMR spectrometer used in our experiments made the specimen the central part of one end-wall of a cylindrical microwave cavity. The cavity operated in the TE0~2 mode which meant that the rf magnetic field, h, at the surface of the film was radially symmetric. The dc field H was applied parallel to the surface of the film (in the so-called 'parallel' configuration). The experimental configuration allowed H to be rotated about the long-axis of the cavity so that it could make an arbitrary angle with any of the film's in-plane crystallographic axes. This situation can be modeled by assuming that the ultrathin film is of thickness d in the z-direction

and of infinite extent in the x and y-directions. The front surface of the film is located at z = 0, the rear is located at z = d, and the film is surrounded by free space. All quantities will therefore have a spatial variation in the z-direction only. A linearly polarized microwave traveling wave in the positive z-direction impinges on the z = 0 surface of the film at normal incidence. The rf electric field component, e, of this wave is oriented along the x-axis while the rf magnetic field component, h, is directed along the y-axis and written as h = (0, h 0, 0). The metal is assumed to be body-centered cubic (bcc) with its [001] direction parallel to the z-axis and its [100] direction making an arbitrary angle 0 with the x-axis. The rf magnetic field h drives the rf components of the magnetization vector. We have assumed that this driving field is weak enough so that we can limit ourselves to linear response. This turns out to he an excellent approximation given the microwave power levels used in our FMR experiments. It is also the reason that we can approximate the radially-symmetric h field with a uniform field directed along the y-axis: only the component of h that is perpendicular to the dc field H drives the film's rf magnetization component when we assume linear response. We will assume that, in equilibrium, M = M~-(M s, 0, 0) and will consider only small deviations from equilibrium so that the magnetization can be written as:

M = ( M x, My, Mz) = M s + m ( z, t),

(2.3)

where re(z, t) is the rf component of M. The magnitude of m is assumed to be much less than M s so that, to first order in m, the magnetization in Eq. (2.3) can be written as M = (~/M2 - my2 - m 2z , my, m z) ~-(M~, my, mz). Since we consider only the linear response to the applied rf driving h = (0, hy, 0), all terms in Herf that are second and higher order in my and m z are neglected. Detailed derivation, assuming a time variation of exp( - i tot), of the linearized Landau-Lifshitz equations of motion for m was presented by B. Heinrich and co-workers [2,10]. Quoted below are the two equations of motion (Eq. 2.4a, b) which describe the response of the average rf magnetization components

10

z. Celinski et al. / Journal of Magnetism and Magnetic Materials 166 (1997) 6-26

per unit area in the film, ~"x and f{y, to an average rf driving field hy represented by h o +

Y-it°(

= o,

G--G-- ~ / y + i - ~ f c ' z = M s d h o, T\TM~

(2,4a)

2.2. The absorption curve and the FMR condition Using Eq. (2.4a) to eliminate l/~ from Eq. (2.4b) yields a simple expression for the rf susceptibility of an ultrathin bcc Fe(001) film:

(2,4b) Xy

o

where K~ff = H + 4wMef f + 7-E- (3 + c o s 4 0 ) ,

(2.9) (2.5)

Z IV1 s

2K~ ff gg'=H+

Ms

cos40,

(2.6)

1

2 K eee 4rrMeff = 4¢rDzM ~ - ~ ,

Ms

Pa(H) = -~ ~o Im[ Xy]lh012.

(2.10)

(2.7) Ferromagnetic resonance therefore occurs when Ira[ Xy] is a maximum (corresponding to maximum power absorption by the film). If we ignore damping in Eq. (2.9) by setting the damping parameter G to zero, we find that this maximum occurs when

and K~ ff = K 1 +

The microwave power, Pa(H), absorbed by a magnetic film in our experimental geometry is given by [141

K~(O) + K~( d) d

Keff__K + u ----u

K~(O) + K ~ ( d )

d

,2,1,

(2.8)

Factors, K[(0) and K~(d), and KAY(0)and K~(d) are respectively the surface in-plane four fold and uniaxial anisotropy constants for two surfaces of the film. Constant K u is a bulk contribution to the uniaxial anisotropy. In the analysis of data from our (001) films we have ignored K u as we have no direct evidence for its existence. Eqs. (2.8) show that the surface anisotropies enter the integrated equations of motion in the same way as bulk anisotropy fields, except that they are divided by the thickness of the film, d. K~ff is the effective in-plane four-fold anisotropy while Kueff is the effective uniaxial anisotropy. The effective uniaxial anisotropy enters the equations of motion like an effective demagnetizing field, therefore, effective magnetization, 4'lTMeff, is given by Eq. (2.7). D z is a demagnetizing factor, which is a function of both the film thickness and crystallographic structure of the film [11,12]. G is the Gilbert damping parameter [13].

The contribution of the magnetic damping term to the resonance condition is small and can usually be neglected. The largest values of G, y, and M s measured in our work were G = 2 × 108 s -~, -/= 1.84;< 10 7 0 e -1 s -1, and Ms= 1715 Oe. Thus, we find G / ( T M ~ ) < 0.006 in Eq. (2.9). In contrast, the values of ~ , • , and (~o/y) were much larger with ~T(, and ( o ) / T ) comparable to one another and the order of 10000 Oe. Substituting Eq. (2.5) to Eq. (2.6) into Eq. (2.11) yields an explicit expression for the FMR condition for fully saturated samples:

=

HvMR+4'rrMeff+-~---~ss(3WCOS40 )

I X

g~ff HFM R -1-- 2M~ cos40

] .

(2.12)

Z Celinski et al./Journal of Magnetism and Magnetic Materials 166 (1997) 6-26

Eq. (2.12) summarizes, in part, the power of the FMR measurement technique. All of the magnetic parameters in Eq. (2.12) can be determined from the measurement of HFMR as a function of 0 at two different microwave frequencies to I and w 2. The angular dependence of HFMR yields K~ ff. Inserting the values of g~ ff obtained for several different film thicknesses, d, into the first of Eqs. (2.8) will sort out the contributions from the surface and the bulk in-plane anisotropies. The frequency dependence of HFMR determines the gyromagnetic ratio, y, and the effective demagnetizing field 4";rMef f. The g-factor is obtained from 3/= g[e[/2mc. Note that the use of a cylindrical microwave cavity in the TErn2 mode, with the specimen forming the central part of one end-wall of the cavity, insures that the component of the driving rf field that is perpendicular to the direction of the applied dc field H has the same magnitude regardless of the angle, 0, that H makes with the film's [100] direction. This is a consequence of the radial symmetry of the rf driving field. One thing that we cannot do is extract a value for the saturation magnetization, M~, directly from the measured values of HFMR. All we can get is a value for 4"rrMeff that, according to Eq. (2.6) contains both M s and K. In order to extract Ms, we must consider the actual lineshape of the absorption curve.

2.3. The lineshape of the absorption curve The FMR absorption lineshape for an ultrathin bcc Fe(001) film is almost perfectly Lorentzian (that is, it has the form A/(1 + x2)). This can be shown by replacing H with H ~ R + 8 H (8H - H - HFMR) in Eq. 2.9, utilizing the FMR condition (Eq. (2.11)) to simplify the resulting denominator, and then keeping terms that are linear in 8 H + (w/y)(G/yM~). The susceptibility becomes ~o

G

M~d

Xy = ['-~fmr "q- ~¢fmr]

8H-iT

(2.13) where ~ and ~,~ are both evaluated at H = HFMR.

11

Rationalizing the denominator yields these real and imaginary parts for Xy:

"-~fmr Im[ Xy]

---

1

Msd [._~fmr + ,ff2~,fmr] "~

×

= 1+

(2.14)

zl

'~fmr

M~d

1

Re[ Xy] = fmr + fmr] + M°d[ fmr +Xf,.,] -a

×

(H-HFM ) 1+

2'

(2.15)

A

where

Eq. (2.14) clearly shows that our absorption lineshape is almost purely Lorentzian. It is defined by the resonance field, HFMR, and a half-width at halfmaximum (HWHM) of A. One can see from Eq. (2.16) that the HWHM is directly proportional to the damping parameter G. The amplitude, ~¢', of the absorption peak is given by:

~=

"~fmr 1 ( m s d ) [~.~fmr ..[_ ¢~fmr] "~.

(2.17)

The quantity ,~fmr/[,~fmr "[-~fmr] is called the 'ellipticity factor'. The precise value of the ellipticity factor depends primarily upon the size of effective saturation magnetization, 47rMeff, in relation to HFMR. In our work, the ellipticity factor was ~ 0.7. The only assumption we made in deriving Eqs. (2.14) and (2.15) is that 8 H << ~(efmr near H = HEMR. We can readily see that the absorption lineshape is almost perfectly Lorentzian unless fi~fmr becomes comparable to A. This situation never occurred in our absorption experiments. Typically we had A _< 0.14 kOe and ~g'~fmr~ 10 kOe.

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Z Celinski et al. / Journal of Magnetism and Magnetic Materials 166 (1997) 6-26

2.4. The lineshape of the absorption deriuative FMR experiments typically measure the derivative of the absorbed power with respect to H (see Section 3). Differentiating Eqs. (2.14) and (2.15) with respect to H gives us:

"~frnr

0

1

- 2x

~--~Im[ X>,]=Msd[,~,fmr +ffffmr] A2

(1

-}-X2)2' (2.18)

0 "~'fmr 1 1- x 0HRe[ XY] =Msd['~fmr q-a~frnr] A2 (1 "-FX2)2' (2.19) where, for simplicity, we have written x = ( H H~q~R) / A. The absorption derivative has a lineshape governed by Eq. (2.18). The absorption derivative is characterized by the resonance field, HvMR, and a linewidth, A H, that is defined to be the field interval between the extrema of Eq. (2.18). Differentiating Eq. (2.18) with respect to H, and then setting the result to zero, gives us the location of the two extrema. They are symmetric about HEMR and located at HFMR ~ A H / 2 . Expressing this in terms of A, the half-width at half-maximum, shows

AH=Ta

-

--

~

1 . 1 5 5 - -

.

(2.2O) Finally, the amplitude, J ' , of the absorption derivative is defined as the difference between the curve's maximum and minimum values and is given by 1

dg'=

4

( M,d)

[ ,.~fmrq- a,~fmr] A 2

- --.~, 4A (2.21)

where ae' is the amplitude of the absorption peak as given by Eq. (2.17).

quencies, o9, and various film thicknesses, d, would allow us to deduce values for all of the fundamental magnetic properties of a ferromagnetic film except for the saturation magnetization and the magnetic damping parameter. Eqs. (2.16) and (2.20) show that we can extract the magnetic damping parameter from knowledge of the absorption linewidth. Eqs. (2.17) and (2.21) show that M~ appears in the expressions for the amplitude of the absorption peak and the amplitude of the absorption derivative. We will see in Section 3 that an FMR spectrometer's output signal is proportional to Im[ Xy]. By integrating the absorption line (Eq. (2.14)) one gets the total absorbed power that is proportional to the product of d and A. We performed integration for the finite region ( + 7A) around HFMR. The area, A, under the absorption line is given then by: A

dH J,HFMR--7A l + (H--HFMR) 2 A

= K,3~f HFMR+7A

= K~'A 2 arctan(7),

where K is a constant, geometrical factor, that will be the same for all datasets collected using a given FMR spectrometer. In a similar manner, we have calculated the total absorbed power by integrating twice the measured absorption derivative line within the finite region around HFMR (q-7A).

2.6. Relating the magnetic moment to the saturation magnetization First principles calculations usually evaluate the atomic moment per atom, JI~atom"Since we are interested in making comparisons with such calculations, we need to define the relationship between the saturation magnetization, M S, and the atomic moment per atom. Assuming that the spatial variations of all quantities of interest are slow compared to the lattice spacing (an excellent approximation in most ultrathin films) we can write

2.5. Extraction of the saturation magnetization MS= At the end of Section 2.2 we showed that knowledge of HFMR for various directions of H in the specimen plane, along with various microwave fie-

(2.22)

}-Zatom , v0

(2.23)

where V0 is the atomic volume and ~[£atom is the average atomic moment in the film.

Z. Celinski et al. / Journal of Magnetism and Magnetic Materials 166 (1997) 6-26 0.4

3. Experimental techniques "-~

The success of our technique for measuring M S in ultrathin ferromagnetic films depends upon: (1) careful calibration of the FMR spectrometer prior to data collection and (2) a precise knowledge of the film thickness. The first conditions insures that repeated FMR absorption measurements carried out on a given film will always yield the same value of K(M~d) and that the value of K will be a constant for all films measured using the same FMR spectrometer. The second condition is necessary simply because M S and d appear together in K(Msd). It is important to realize that the calibration process is not a typical part of an FMR measurement. Usually one is content if the FMR signal simply exhibits a good signal to noise ratio. Absolute reproducibility of all measurements carried out on a given film is typically not important. In our work, it is absolutely essential.

3.1. Specimen preparation and film growth All epitaxial growths were carried out in a PHI Model 400 MBE machine that was equipped with the surface analysis tools of reflection high energy electron diffraction (RHEED) and Auger electron spectroscopy (AES). The base vacuum of the system was in the mid 10-11 Tort range. All ultrathin films were grown on bulk fcc Ag(001) substrates that were spark-cut from 99.99% pure silver single crystal boules. The substrates were in the form of disks approximately 15 mm in diameter and 4 mm thick. Laue back-reflection X-ray photography was used to align the growth surface of each substrate to within _+0.2 ° of the (001) plane prior to cutting. Surface damage caused by spark-cutting was removed by grinding the surfaces of each substrate on adhesive-backed, #600 grit silicon carbide paper mounted on a sheet of glass. Water was used for lubrication. Final grinding was carried out using successively finer grades of aluminum oxide abrasive mixed with water on adhesive-backed nylon polishing pads mounted on sheet glass. Polishing was accomplished using a cyanide-free electropolish [15]. The resulting substrate surfaces were smooth on the atomic scale over large areas and free from mechanical strain and chemical contamination. Corn-

13

Fe(001) on Ag(001) substrate

~0.3

N 0.2

~ O.1

0.0 0

100

200

300

400

500 600 Time (s)

Fig. 1. RHEED intensity oscillations during the growth of bcc Fe(001) on an fcc Ag(001) single crystal substrate. The angle of incidence of the electron beam was 1°, close to first anti-Bragg condition for Fe(001). An angle of incidence that satisfies the anti-Bragg condition results in pronounced oscillations due to destructive interference between electrons scattered from adjacent surface layers of the film.

plete information on the preparation technique can be found in Ref. [16] while a detailed overview can be found in Ref. [17]. Ultrathin film depositions were carried out in the growth chamber of the MBE machine at pressures typically in the low 10 -~° Torr range with an exception for Au overlayers for which depositions took place at pressures the order of 5 × 10-10 Torr. All films were deposited at a rate of approximately 1 monolayer (ML) of atoms per 45 s. All growths were carried out with the Ag substrates held at room temperature. Film thicknesses were determined using a Mathis quartz-crystal thickness monitor in combination with observations of RHEED intensity oscillations during growth [18]. The total Fe film thickness was determined from the RHEED oscillations. We found that for the given angle of incidence of the RHEED electron beam, the intensity oscillations during Fe deposition were very reproducible. This allowed us to determine the thickness of a given Fe film to an accuracy of approximately _+0.1 ML (see Fig. 1). By comparing the thickness monitor data with the RHEED oscillations, we were able to determine the absolute thickness of our Fe films to an accuracy of better than + 0.2 ML. Film roughness was minimized by terminating

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Z. Celinski et al. / Journal of Magnetism and Magnetic Materials 166 (1997) 6-26

each growth at a RHEED intensity oscillation maximum. The total thickness of a given film was rarely a whole number of atomic layers due to the vertical mismatch between the bcc Fe and fcc Ag lattices [17]. We found that the films would not grow in a layer-by-layer mode until approximately an equivalent of 4 monolayers (ML) of iron had been deposited. This resulted in a non-integral number of atomic layers of Fe being laid down for films which growth was terminated at RHEED intensity maxima. Subsequent layers would grow in a quasi layer-bylayer mode where one RHEED oscillation would correspond to the growth of one monolayer. A small amount of Ag flows on the Fe surface ( ~ 0.1 ML), however, the floating Ag is not confined to the Fe interface. After the deposition of subsequent cover layers the floating Ag was always lifted to the top surface. See Ref. [17] for a detailed summary of our growth characterization studies of bcc Fe(001) films. All of our bcc Fe(001) films were approximately 5.7 ML thick. While thinner films would have allowed the atomic moments at the interfaces to make a larger contribution to the film's total magnetic moment, the 5 ML film thickness represented a compromise between the need to grow well-defined bcc Fe(001) structures and the need to have a reasonable fraction of the total number of atomic moments in each film located in the surface layers.

3.2. The FMR spectrometer A 36.6 GHz FMR spectrometer was used to carry out all of the FMR absorption measurements described in this paper. A block diagram of the spectrometer, along with its computerized data collection system, is shown in Fig. 2. The spectrometer utilized a cylindrical resonant cavity operating in the TE012 mode. This mode is characterized by radially symmetric rf magnetic fields covering both of the flat end-walls of the cavity and rf electric fields circulating about the cavity's long axis. As a result, eddy currents are confined to the cylindrical walls of the cavity. No currents flow between end-wall and the cylindrical walls of the cavity. The long-axis was vertical, with the ultrathin film specimen forming the lower end-wall. A thin layer of kapton (a microwave permeable non-conductor) was placed between the film and the cavity end-wall to

insure that the cavity operated only in TE012 mode. As such, the film could absorb energy only from the radially symmetric rf field. The cavity could be surrounded by liquid N 2 filled vacuum dewars so that FMR measurements could be carried out at temperatures down to approximately T = 77 K. The cavity was suspended between the pole pieces of a Varian V-3800 electromagnet that was capable of generating 18 kOe fields in a 3.5" gap. The magnet supplied the required uniform, dc magnetic field H. A klystron generated 36.6 GHz microwaves that traveled down a waveguide to the cavity. A small hole in the upper end-wall of the cavity served to coupled microwave energy into the cavity where some of it was absorbed by the specimen and the cavity walls. The reflected microwave beam traveled back along the waveguide to a signal diode whose output voltage, Vr, was linearly proportional to the amplitude of the reflected microwave electric field, e r. The data collection system was dedicated to measuring the variation of this diode voltage as a function of the applied field H. The microwave frequency was locked to the frequency of the resonant cavity by weakly modulating the klystron output at 68 kHz, detecting the 68 kHz component of Vr with a lock-in amplifier. The output of the amplifier was then used in a feedback loop to control the klystron's power supply. We will see in Section 3.3 that the variations in the diode voltage that are due to changes in the energy absorption by the ultrathin film as H is swept through HFMR are small and superimposed on a large constant background. In order to emphasize the variations of Vr with H, the applied dc field was weakly modulated at 176 Hz and another lock-in amplifier was used to detect and amplify the 176 Hz component of the diode voltage. The output of this amplifier was fed into a digital voltmeter that was connected to a data collection computer over an IEEE-488 data bus. The voltmeter therefore measured a signal that was proportional to OVr/OH or, equivalently, Oer/OH (the derivative of the reflected microwave electric field amplitude with respect to H). The strength of the dc field H was measured by a Hall probe that was attached near the center of one of the electromagnet's pole pieces. The Hall probe's

Z. Celinski et al. / Journal of Magnetism and Magnetic Materials 166 (1997) 6-26

Klystron Power Supply

__

Variable Attenuator

U

15

Lock-in output~ -j Amplifier ]_ reference signalinU

Microwave Circulator

Isolator

Signal Diode Frequency Meter

a.c. Power m I ISupply I ]~

__

Microwave Cavity ~ Specimen ...

]

LCmC kp1-iifner r : ~ a T ~ '

°utputD--~

Electromagnet -~ Modulation Pickup Coil

/

Modulation

signal i n J ~ - Lock-in reference in

I Amplifier

output

Probe Gauss

Meter

~

cDomputer

"n

IEEE-488 Data Bus

Digital Voltmeter|

~

Digital Voltmeter]-

Fig. 2. Block diagram of the 36.6 GHz FMR spectrometer. The klystron supplies microwavesto a resonant cavity suspended between the poles of an electromagnet. The ferromagnetic film forms part of the bottom end-wall of the cavity. The klystron output and the applied dc field H are weakly modulated and the microwavesreflected by the cavity are detected using a point-contactdiode. Output from the diode is fed into two lock-in amplifiers. One is used to lock the klystron frequency to the resonant frequency of the cavity. The second outputs a signal proportional to the derivative of the specimen's microwaveabsorption with respect to H.

voltage was read by a second digital voltmeter that was also connected to the data collection computer over the IEEE-488 bus. The Hall probe output was calibrated after each data collection run using a nuclear magnetic resonance (NMR) probe placed at the same position between the poles of the electromagnet that the specimen had occupied. Magnetic field values covering the range used during data collection were simultaneously measured by the NMR probe and by the Hall probe. Fitting this data to a linear or a cubic polynomial (depending on how large the range was) provided an excellent magnetic field calibration since

the NMR probe could determine magnetic fields to an accuracy of + 1 0 e . The 176 Hz modulation of H was accomplished using a pair of Helmholtz coils attached to the pole pieces of the electromagnet. The amplitude of this ac modulation drive remained fixed while H increased during FMR data collection. As such, the signal output by the second lock-in amplifier would steadily decrease as H increased. In order to account for this, the amplitude of the ac modulation field was recorded during data collection using a small pick-up coil that was placed as close to the specimen as possible and always in the same location between the pole pieces.

16

Z. Celinski et al./ Journal of Magnetism and Magnetic Materials 166 (1997) 6-26

The 176 Hz component of the pick-up coil's output signal was fed into a third lock-in amplifier whose output went into a digital voltmeter that was connected to the computer over the IEEE-488 bus. Data collection was carried out by slowly sweeping the dc field H upwards through FMR while the data collection computer repeatedly read the digital output of the three voltmeters. The resulting dataset had four columns: the time (relative to the start of data collection) that each point was collected, the voltage output from the Hall probe, the lock-in amplifier voltage that corresponded to the OVJOH, and the lock-in amplifier voltage that corresponded to the output from the pick-up coil. The NMR calibration data would convert the raw Hall probe voltages into magnetic field values H while dividing each raw OVr/OH value in column 3 by the corresponding pick-up coil voltage value in column 4 would eliminate the steady decrease in OVr/OH values with increasing H. After these two conversion steps, all that was left was to multiply each normalized OVr/OH value by the correction factor obtained from the calibration process described in Section 3.3. In some cases we have measured also a dc signal from diode, Vr(H) (absorption signal); we found measurements of the absorption line much noisier.

3.3. Calibrating the FMR spectrometer So far, we have described a typical FMR spectrometer. The only difference has been to include a way to measure the amplitude of the small ac modulation field that was added to the dc field H. Failure to account for this will introduce a small decrease in the measured values of OVJOH with increasing H. Our process for measuring the magnetization of an ultrathin film required us to go one step further. We had to develop a calibration process that would insure that all FMR datasets collected for a given film using a given FMR spectrometer would be exactly the same. The practical result of such a calibration process would be that any variations between the FMR datasets collected for two different films would be due entirely to the differences in their fundamental magnetic properties and not due to any aspect of the measurement process. Only then would it be possible to use the 'ratio' technique described

/

Klystron ~

Wa egu" e

Diode (voltage output oce r )

7o,,\1 H

Resonant Microwave Cavity

Fig. 3. A stylized depiction of an FMR spectrometer (see text).

in Section 2.5 to determine the saturation magnetization of an ultrathin film. The calibration process is best understood using a simplified diagram of an FMR spectrometer. Fig. 3 shows such a diagram for a cylindrical cavity spectrometer. The ultrathin film and its substrate form the central part of the flat, rear end-wall of a cavity. A klystron generates low-power microwaves that travel to the cavity via waveguide. The electric field amplitude of this beam is e 0. A small hole in the front end-wall of the cavity couples a portion of the incident microwave power into the cavity where some of it is absorbed by the ultrathin film, more is absorbed by the cavity walls, and the rest is radiated back out through the coupling hole. A directional coupler diverts part of the reflected microwave beam to a signal diode. The power-level of this wave is such that the output voltage, V~, of the diode is proportional to the electric field amplitude, er, of the reflected wave. The isolator prevents the reflected microwaves from feeding back into the klystron. The dc magnetic field, H, is applied in the plane of the ultrathin film (the 'parallel' configuration). As mentioned in Section 3.2, a thin layer of a microwave permeable insulator such as kapton can be placed between the film and the cavity end-wall to insure that the cavity will operate only in the TE012 mode. The total power absorbed by the cavity determines the amplitude of the reflected microwave beam. Measuring the diode voltage, Vr, as a function of H therefore yields a measure of the microwave power, Pa(H) that is absorbed by the ultrathin film. The relatively few ferromagnetic atoms present in the ultrathin film, coupled with small surface area of

17

Z Celinski et al./Journal of Magnetism and Magnetic Materials 166 (1997) 6-26

the film in relation to the total surface area of the cavity, causes the power absorbed by the film to be much less than the power absorbed by the cavity walls. Hence the variation of V~ with H is small and superimposed on a large constant background. The changes in Vr due to specimen absorption are usually emphasized by adding a weak ac modulation field of frequency f0 to the applied field H and then detecting and amplifying the corresponding ac component of V~ using a lock-in amplifier. FMR absorption experiments therefore typically measure OVr/~H as a function of H. The precise relationship between Vr and Pa(H) or, equivalently, between OVr/OH and OPa(H)/OH, can be derived from the expression for er/e 0, the ratio of the reflected microwave electric field amplitude (e r) to the incident microwave electric field amplitude (e0). This ratio is typically derived as follows (see Ginzton [19], Feher [20], or Poole [21] for details). We begin by noting that a microwave cavity is the equivalent of a resonant LCR circuit that is characterized by a resonant frequency, fr~, and a quality factor, Q. The resonance frequency is chosen to match the frequency of the incident microwave radiation. The Q-factor relates the energy that is stored into the cavity in one cycle to the energy that is dissipated by the cavity in one cycle: 1

1

Q

gdissipated

2,rr Estored

(3.1)

Energy is dissipated by the cavity in three ways: (1) by resistive losses in the cavity walls, (2) through absorption by the ultrathin film, and (3) by radiation loss through the coupling hole. Each mechanism can be assigned a corresponding Q-factor: 1

1 gwall s

Qwalls

2 ']T Estored '

1 Qfilm

1 Qhole

1

Enlm

2 '1"i" Estored ' 1

Ehole

27r gstored '

(3.2)

(3.3)

(3.4)

along with a Q-factor related to the total energy lost in the cavity: 1

1 Ecavity

Qcavity

1 ( Ewall~ +

2 "IT Estored

2 "iT

Efilm)

Estored

(3.5)

Conservation of energy fixes the relationship between the Q-factors:

1(1

Qtota¿

1) l

Qx~alls "[- Qfilm 1 -

Qcavity

-[- Qhole

1 + - - .

(3.6)

Qhole

Defining the cavity 'coupling parameter', /3, as: ahole Qhole Qhole /3 = acavit-"~ = awall--""~ q'- afilm

(3.7)

allows us to express the ratio of the electric field amplitudes er/e 0 as [19-21]: er

1-/3

e0

1+/3"

(3.8)

Eq. (3.7) shows that /3 consists of two parts. The first part, /30 = Qhole/Qwans, depends only on the energy absorbed by the cavity walls and is therefore independent of H. Only the second part, i l l ( H ) = ahole/Qfilm, depends on the energy absorbed by the film. However, /3l(H) will be much less than /30 since Ewall s >> Efilm so that, by Eqs. (3.2) and (3.3), Qwalls << Qfilm. We may therefore separate our the component of er/e 0 that varies with H by replacing /3 by /30 + /31(H) in Eq. (3.8) and then expanding the numerator and the denominator on the right hand side to first order in ill: er= (1-/30) e 0 ~ 1 +/30

2 (1 +/30) 2 i l l ( H ) '

(3.9)

Next, we express the coupling parameter, /31(H) = Qnole/Qnlrn in terms of the microwave absorption, Pa(H), that was defined by Eq. (2.20) by explicitly evaluating both Qhole and afitm. The details are uninteresting and basically involve a lot of tedious algebra combined with straightforward spatial inte-

18

Z. Celinski et al. / Journal of Magnetism and Magnetic Materials 166 (1997) 6-26

grals of the rf magnetic field distributions over the volume of the cavity and across the surface of the film [19]. The results are that Qhole is a constant for a given microwave cavity and:

1 Qlilm

r/Im[ X~],

(3.10)

where ~7 is the 'cavity filling factor' and X>, is the rf susceptibility defined by Eq. (2.9). Much like Qhole, the filling factor depends only on the geometry of the cavity. It is roughly equal to the surface area of the film divided by the volume of the cavity [19]. Combining Qho)e and ~7 into the single constant K allows us to write /31(H) as: /31(H) = K Im[

X>.].

(3.11)

All we have left is to relate Eq. (3.9) to the voltage diode V~. This can be accomplished by noting that if we completely 'de-tune' the resonant microwave cavity by inserting a metallic rod into it, then the cavity will act like a 'dead short' (all power is reflected). In this case, e r = e 0 and the diode voltage will be proportional to e o. If we call this diode voltage Vo, then we can write Vr/Vo = e r / e 0 and combine Eq. (3.9) and Eq. (3.11) to obtain the desired results:

Vr=V0

-/3° 1+/30

2V°Kim[xy](3.12

)

(1+/3o) 2

and OH

2V0 Olm[ (I +/30) 2 K 0 ~

Xy] (3.13)

The V~ has two components, V~0 and AV~. V0 is measured by inserting a metal rod into the cavity to de-tune it and then measuring the diode voltage. We can measure /3o simply by measuring the diode voltage with the cavity tuned and the dc field H set far from HFMR. In that case, the second term in Eq. (3.12) will be nearly zero and the measured diode voltage, V)o, a field independent component, will by related to /3o by V~0 V0

1 -/30 1 +/30 "

(3.14)

We carried out our measurements with a constant V~0 voltage on the detector diode using an approach

similar to that of Feher [20]. Eq. (3.13) can be rewritten as 0V~

OH

2Vr0

i -/30 K

0Im[

Xy]

OH

(3.15)

and clearly shows that we can remove all dependence of our measured values of OVJOH on anything other than the fundamental magnetic properties of the film by multiplying each OVr/OH value by

(1 - / ~ 2 ) / 2 Vr0.

4. Data collection and analysis Data collection and analysis was carried out the same way for each of our ultrathin film structures. First, the specimen was mounted in the spectrometer and cooled to liquid nitrogen temperature ( T = 77 K). Next, the klystron was adjusted until the frequency of its output matched the 36.6 GHz resonance frequency of the microwave cavity. The electromagnet was then turned on and the value of HFMR was measured as a function of the angle 0 between the applied dc field, H, and the in-plane [I00] direction of the bcc Fe(001) film. This data was later fit to Eq. (2.12) in order to determine the effective anisotropy field, 2 K~ff/M,, that enters into our expression for the absorption lineshape. For consistency, we determined the M~ from FMR measurements with the dc field, H, set along the in-plane [I00] direction of each Fe film. This direction could be easily determined from the HFMR versus 0 measurements described above. Once the magnet was positioned along [I00], the field was set several kOe away from HFMR and the spectrometer was calibrated using the technique outlined at the end of Section 3.3. We began by tuning our cavity and then adjusting the reflected microwave power using an attenuator until the diode voltage, V~0, was exactly 75 mV. This value of V~o was chosen based on the operating characteristics of the diode - we wanted the output to be in the range where the voltage was linearly proportional to the electric field amplitude of the reflected microwave beam. We then inserted a metal rod into the cavity to de-tune it and measured Vo. The exact value of V~0 depends on the type of cavity, the size of the coupling hole, the type

Z. Celinski et al. / Journal of Magnetism and Magnetic Materials 166 (1997) 6-26

of specimen, and (to a lesser extent) on how well the specimen was mounted on the cavity end-wall. Following calibration, the FMR dataset was collected as described in Section 3.2. At the end of each data collection run, the values of V~ and V0 were re-measured to insure that they had not drifted. Data analysis began by massaging the raw datasets into something suitable for fitting. This involved carrying out the data conversion process described at the end of Section 3.2 and then multiplying the normalized OVr/OH values by the ( 1 - flE)/2V~0 correction factor. Each converted dataset was then fed into a multi-parameter X 2 function minimization program that was modeled after the MINUIT package distributed by CERN. Four of the fitting parameters supplied to the program had to be known in advance and remained fixed throughout the fitting process. They were the microwave frequency, f, the g-factor, the direction of H in the crystal (always the [100] easy axis), and the value of the in-plane, 4-fold, effective anisotropy field, 2K~ff/Ms , t h a t

0.20

0.15 0.10 0.05 0.00 g -0.05 -0.10

I

I

I

I

I

I

____j(--

0

I

I

7.00

7.50

8.00

)(y]

0 + K sin(e) ~--~Re[ Xy] - (bmn + bint) • (4.1)

-0.20 [

was obtained from the HUM R v e r s u s 0 measurements. The magnetic parameters that the program extracted from a given dataset were the resonance field, HFMR, which determines the effective saturation m a g n e t i z a t i o n , 4 ~ M e f f , the half-width at half-maximum, A, the ellipticity factor, ~q~fmr/[~-~fm~+ ,Uem~], and the sought-after value of r,(Msd). Three other parameters were also extracted from the data. The first was a small mixing angle, e. The mixing angle accounted for the fact that we did not actually measure just K3Im[ X y ] / 3 H w h e n we collected data. The lock-in amplifier would usually pick up a small component of KORe[ X y ] / / ~ ) n n o matter how carefully it was set up. The net effect was that we measured the quantity K;3Im[xyei']/OH. The other two parameters were the slope, bm, and y-intercept, bint, of a small linear background signal that we introduced to account for any systematic increase in the diode voltage with increasing H. Such an increase could be caused, for example, by a small change in the liquid nitrogen level in the metal dewar surrounding the cavity. Inclusion of these three parameters led to the fitting function:

f ( H) = K COS(e) ~--~Im[

-0.15

6.50

19

i

J

I

8.50

9.00

9.50

Applied d.c. magnetic field H (kOe) Fig. 4. The results of a fit to an FMR dataset recorded for a 5.7 ML bcc Fe(001) film grown on an fcc Ag(001) substrate and covered with a 7 ML Pd film. The coverlayer was 20 ML of Au. The absorption derivative was fit using the simple Lorentzian functions calculated in Section 2.4. The input parameters were: f = 36.6 GHz and 2 K~ff/Ms = 0.225 kOe. The fitted parameters were: HFMR = 8.00 kOe, A = 147 Oe, 4'rrMeff = 10.59 kOe, • = 2.4X10 -3 rad, b m = 6 . 6 8 × 1 0 -4 kOe - t , and b i n t = - 4 . 6 × 10 -3. The ellipticity factor was 0.701.

As shown in Section 2, we could calculate Im[ Xy] and Re[ Xy] using the complete expressions for the rf susceptibility (Eq. (2.9)). We determine the e, b m, bint, and A by fitting our data to function f ( H ) (Eq. (4.1)) with region from HFMR-7A to HFMR + 7A. Fits obtained using our theoretical expressions were excellent. Fig. 4 shows a fit of the Lorentzian lineshape to a dataset collected for an A g / F e / P d / A u ultrathin film structure (an fcc Ag(001) substrate covered with a 5.7 ML film of bcc Fe(001), followed by a 7 ML film of Pd, and then protected by a 20 ML film of Au). This was typical for our collected datasets. We found that the presence of random noise in the data could affect the quality of the fits and hence

Z Celinski et al. / Journal of Magnetism and Magnetic Materials 166 (1997) 6-26

20

the values of the fitted parameters. The effect of noise could be greatly reduced by integrating the dataset once with respect to H, and then fitting the resulting absorption peak to the function: g ( H ) = K COS(e) Im[

Xy]

"[- K

sin(e) Re[

)(y].

(4.2) Integration was accomplished using the trapezoidal rule. More complicated approaches were unnecessary given the close spacing of our data points (typically we recorded more than 500 points over 3 kOe range). For a dataset consisting of the N points (Hi, Yi), the trapezoidal rule we used for creating the set of integrated points (H i, Yi) was: i-l

1

Yi = -~yl(H2-HI) + E y j ( H j - H j _ , ) j=2

integrating the dataset shown in Fig. 4. The peak was fitted using the Lorentzian functions derived in Section 2.3. The second integration provided us with value of K(Msd), which for this structure was equal 8.520 X 1 0 - 3 . The integrations averaged out random noise and thus yield the more accurate value of K(M~d). We established an error bound on our technique by collecting several sets of FMR data for selected specimens and then analyzing the variations in the values of K(M~d) and fitting parameters. Provided the spectrometer is properly calibrated prior to each run, and the raw data is handled as described above, the total measurement error of K(M~ d) was approximately 1%. This agreed with the statistical errors that were obtained during fitting by studying the variations in X 2.

1

+ -~Yi( Hi - Hi-, ).

(4.3)

Fig. 5 shows the absorption peak obtained by

0,05

I

I

r

I

[

I

I

0.04

,s:~ 0.03

0.02 O ..~

0.01

0.00

..) k.. 6.50

7.00

7.50

I

I

I

L

8.00

8.50

9.00

9.50

Applied d.c. magnetic field H (kOe) Fig. 5. A fit to the FMR dataset recorded for a 5.7 M L bcc Fe(001) film grown on an fcc Ag(001) substrate and covered with a 7 M L Pd film. The covedayer was 20 ML of Au. The absorption peak was obtained by integrating the dataset once with respect to H. The fit was to the Lorentzian functions calculated in section 2.3. The input parameters were: f = 36.6 GHz and 2K~ff/Ms = 0.225 kOe. The fitted parameters were: HFMR = 8.00 kOe, A = 143 Oe, 4 ~ M e f f = 10.59 kOe, • = 2.1 × 10 -2 rad, and K(Msd) = 8.520X 10 -3. The ellipticity factor was 0.701.

5. Results and discussion

Our results are summarized in Table 1. The specimens consisted of bcc Fe(001) films grown on fcc Ag(001) substrates and covered with Ag, Au, Cu, Pd, and Ni overlayers. All structures were covered with 20 ML of Au to protect them during FMR measurements in ambient conditions. The first column of Table 1 shows the structure of each specimen and the thicknesses of the individual films. The second column shows the ratios of the K(M s) values relative to the 20 ML Au/5.7 ML Fe/Ag(001) reference specimen (specimen #3) as determined by FMR at 77 K. The error estimates were obtained by collecting several sets of FMR data for selected specimens and then analyzing the variations in the values of K ( M j ) obtained by fitting integrated absorption peaks. The third column gives the corresponding ratios estimated from polarized neutron reflection (PNR) measurements carried out by Bland et al. [22] near absolute zero. The use of ratios eliminates the temperature dependence of the layer averaged moments [22]. The values in columns two and three may therefore be directly compared. The values in the fourth column are estimates of the layer averaged, ground state, magnetic moment of each specimen obtained by scaling the values in column two by 2.33/0.93. This is the ratio of the layer

Z. Celinski et al. / Journal of Magnetism and Magnetic Materials 166 (1997) 6-26

averaged moment of the Ag/10.9 ML Fe/Ag(001) specimen (specimen # 1) as measured by Bland et al. [22] using PNR to the MFMg/M(5.7) ratio measured for specimen # 1 using FMR. The fifth column lists layer averaged, ground state, magnetic moments for selected specimens as determined from first principles theoretical calculations. The sixth column lists the value of 4~Mef f as determined for each specimen from FMR data. All FMR measurements were carried out at T = 77 K with the applied dc magnetic field oriented along the in-plane {100} magnetically easy direction of the bcc Fe(001) films.

21

instead of Ag(001) and found a similar enhancement of the Fe moment (2.98 /z~). There seems to be no calculation for the case of a metastable bcc Cu(001) overlayer grown on bcc Fe(001). The closest calculation was for metastable fcc Fe(001) grown on fcc Cu(001) [24]. It predicted an enhanced Fe moment of 2.69/z B at the F e / C u interface. The first two specimens in Table 1 consisted of bcc Fe(001) films grown on fcc Ag(001) substrates and covered by fcc Ag(001). Ohnishi et al. [25] considered such structures when they calculated the ground state magnetic moments in each layer of a 5 ML film of bcc Fe(001) in contact with fcc Ag(001). They predicted that the Ag layer in contact with the Fe film would be weakly polarized with a moment of 0.08 /x B. The Fe atoms in the first Fe layer were predicted to have moments of 2.52 /z B, atoms in the second layers had moments of 2.37/z 8, while atoms in the innermost layer had moments of 2.27/~B. We first consider specimen # 2 with its 5.5 ML Fe film. In order to compare the theoretical predictions with our experimental results, we consider our 5.5 ML film to consist of 6 layers. The top Fe layer is 50% complete and possess a moment of 2.52 /z B. The next layer is 50% covered by Ag and 50% covered by Fe. We will assume that the portion covered by Ag will have a moment of 2.52 tz 8 while the rest will have a moment of 2.37 /~B- In a like manner, 50% of the third layer of Fe will have a moment of 2.37/z B and the other 50% will have a moment of 2.27/x B. The fourth layer will be assumed to have a moment of just 2.27 P~B" As we approach the Ag

5.1. Magnetic moments of Fe films in contact with Ag, Au, and Cu First principles theoretical calculations predict that changes in symmetry and coordination number at the surfaces of ultrathin Fe films leads to narrowed 3d bands and localized electronic states. These effects combine to significantly enhance the magnetic moments of Fe atoms located in first few layers of an Fe film [3]. The effect should be only weakly reduced by s p - d hybridization when an Fe film is covered by metals from the 1B column of the periodic table such as Ag, Au, and Cu. For example, independent calculations by Bit±gel et al. [4], Fu and Freeman [5], and Richter et al. [6] for one monolayer (ML) of bcc Fe(001) supported by Ag(001) predicted Fe moment enhancements of 3.01 /x B, 2.96 /z B and 3.0/z B, respectively (the magnetic moment of a bulk Fe atom is 2.2 /ZB). Chun Li et al. [23] used Au(001)

Table 1 The magnetic parameters of the Fe/Ag, Fe/Au, Fe/Cu, Fe/Pd, and Fe/Ni structures defined in the first column. All structures were grown on Ag(001) single crystals and covered with Au (see Section 5.0). Specimen (thicknesses in ML)

MFMR M(5.7)

MpNR M(5.7)

1.20 Au/7 Ag/10.9 Fe/Ag(001) 2. 20 Au/7 Ag/5.5 Fe/Ag(001) 3.20 Au/5.7 Fe/Ag(001) 4. 20 Au/7 Cu/5.8 Fe/Ag(001) 5.20 Au/7 Pd/5.6 Fe/Ag(001) 6. 42 Au/8 Pd/5.7 Fe/Ag(001) 7. 20 Au/2 Ni/5.7 Fe/Ag(001) 8.20 Au/3 Ni/5.7 Fe/Ag(001) 9. 20 Au/3 Ni/5.7 Fe/Ag(001)

0.93 4- 0.01 0.99 ___0.01 1 1.02 ± 0.01 1.03 ± 0.01 1.04 ± 0.01 1.07 _+0.01 1.15 ± 0.01 1.12 ± 0.01

0.93 ± 1.03 ± 1 0.99 ± 1.06 ± 1.04 ±

a

For a discussion of error estimates on this value see Section 5.4.

0.05 0.05 0.05 0.04 0.09

Pest a (/~B)

~calc (/~B)

4~Meff (kOe)

2.32 2.48 2.51 2.56 2.58 2.61 2.68 2.88 2.81

2.32 2.45

7.06 1.21 7.44 0.94 10.91 9.87 8.07 8.26 8.31

2.57 2.57 2.68 2.80 2.80

22

Z. Celinski et al. / Journal of Magnetism and Magnetic Materials 166 (1997) 6-26

substrate, the fifth layer will have a moment of 2.37 /~B while the sixth layer, the one in contact with the Ag substrate, will have a moment of 2.52 /z B. The Ag layers on both sides of the Fe film will be assumed to have moments of 0.08 ~B- The layer averaged, ground state, moment of specimen # 2 is therefore:

1(

~Ag / Fe(5.5)/Ag

-

5.5

0.08 + 2.52 + 2.37

+ ( 1-~)2.27 + 2.27 + 2.37 + 2-52 + 0.08} = 2.43/x,.

(5.1)

Specimen #1 had a 10.9 ML Fe film surrounded on both sides by Ag. We assume that the film is 11 layers thick with the topmost layer of Fe 90% complete. We further assume that the first three layers on each side of the film behave as predicted by Ohnishi et al. [25], the five innermost layers have moments equal to the bulk Fe value of 2.2 /z B, and the Ag layers in contact with the Fe film are weakly polarized with moments of 0.08 /x B. Proceeding as above shows that the layer averaged, ground state, moment of specimen # 1 is ~Ag / Fe(10.9)/Ag 1

-

10.9

{0.08 + 2.52 + 2.37 + (0.9)2.27

+ (5)2.2 + 2.27 + 2.37 + 2.52 + 0.08} = 2.32/z,.

(5.2)

The ratio of Eq. (5.1) to Eq. (5.2) can be directly compared to the ratio of the MFMR/M(5.7) values of specimens #1 and # 2 that are given in the second column of Table 1. The result shows excellent agreement between theory and experiment: /ZAg/ Fe(5.5)/Ag

= 1.05,

I'LAg/ Fe(10.9)/Ag

Ms( ag/Fe( 5.5) / Ag) M~(Ag/Fe(10.9)/Ag)

= 1.06 _ 0.01.

(5.3)

Specimens # 3 and # 4 have Fe films in contact with Au and Cu. To the best of our knowledge, there

are no calculations equivalent to Ohnishi et al. [25] for Au or Cu grown on bcc Fe(001) films. We therefore cannot make comparisons to theory for specimens # 3 and # 4 as we have done with specimens # 1 and #2. What we can do is note that Table 1 shows that the layer averaged moments of specimens #2, #3, and # 4 are all equal to within experimental error. While the magnetic moment distributions inside A g / F e / A g , Au/Fe/Ag, and C u / F e / A g specimens may differ, the layer averaged moments of all three types of films are essentially equal.

5.2. Magnetic moments of Fe films in contact with Pd Palladium films grown on Fe have been the subject of intense theoretical and experimental investigation. See papers by Celinski et al. [26,27], Bland et al. [22] and Fullerton et al. [28] for details. Basically, metallic Pd is believed to be on the threshold of becoming ferromagnetic. When Pd is grown on bcc Fe(001), the resulting lattice distortion in the Pd film causes the first two layers of Pd to become ferromagnetic. Calculations carried out by Stoeffier and Ounadjela in Ref. [28] determine the distribution of magnetic moments in a P d / F e / A g structure similar to that of specimens # 5 and #6. Their structure consisted of a 5 ML bcc Fe(001) film grown on a 5 ML Ag(001) film and covered with 6 ML of Pal. We can use their numbers to calculate the layer averaged, ground state, magnetic moment of specimen # 5 (a 5.6 ML Fe film grown on Ag(001) and covered with a 7 ML layer of Pd). The contribution to the total moment from our 7 ML Pd film will be assumed to be equal to the total moment contribution calculated for the 5 ML Pd film: 0.34 /x B. The total moment of specimen # 5 is calculated as follows. First, the 5.6 ML Fe film will be assumed to be 6 layers thick with the first Fe layer 60% complete and possessing a moment of 2.77/~B- The next Fe layer will be assumed to be 40% covered by Pd and 60% covered by Fe. The portion covered by Pd will have a moment of 2.77 /x B while the rest will have a moment of 2.39 /~B. In a like manner, 40% of the third layer of Fe will have a moment of 2.39/~B and the other 60% will have a moment of 2.41 /z B. The fourth layer will be assumed to have a moment of

Z Celinski et al./Journal of Magnetism and Magnetic Materials 166 (1997) 6-26

23

2.41 /%. The fifth layer will have a moment of 2.33 /z B and the sixth layer, the one in contact with the Ag substrate, will have a moment of 2.67 ~a. The net moment induced in the Ag substrate will be assumed to be the same as that calculated for the 5 ML Ag film: 0.04 /%. The resulting layer averaged moment is:

All theoretical Fe magnetic moments used to calculate Eq. (5.4) were taken from Ref. [20]. Note that these moment values were significantly different from the values calculated by Ohnishi et al. [25] for a simple F e / A g interface. However, the agreement between theory and experiment is still excellent.

~Pd(7)/Fe(5.6)/Ag

5.3. Magnetic moments of Fe films in contact with Ni

=

1((6)

5.6

0.34 + 2.77 + 2.39 +

2.41 + 2.41

+2.33 + 2.67 + 0.04) = 2.57/x B •

(5.4)

We can compare the layer averaged, ground state, moment (5.4) to the value of MFMR/M(5.7) for specimen # 5 if we proceed as we did in Section 5.1 when we wrote expression (5.3). We begin by scaling (5.4) by the layer averaged, ground state, moment of 2.32 /z B calculated for specimen #1 using the results of Ohnishi et al. [25]. Then we scale the value of MFMR/M(5.7) for specimen # 5 by the corresponding value of MFMR/M(5.7) for specimen #1. The result is: ~[ZPd(7)/Fe(5.6)/ Ag

= 1.11,

/'LAg/ Fe(l 0.9)/Ag Ms(Pd(V)/Fe(5.6)/Ag) Ms(Ag/Fe (10.9)/ag)

=1.11+0.01.

(5.5)

Much like the case of A g / F e / A g specimens, there is excellent agreement between a first-principles calculation and our experimental results. Repeating the steps leading up to Eq. (5.4) for specimen # 6 yields the same layer averaged, ground state, moment of 2.57 /xB. Taking the ratio of the M~R/M(5.7) values of specimens # 6 and #1 gives a result equal to Eq. (5.5) within the experimental error: ~Pd(8)/Fe(5.7)/ Ag

= 1.11,

/'LAg/ Fe(lO.9)/Ag M~(Pd(8)/Fe(5.7)/Ag) Ms ( A g / F e ( 1 0 . 9 ) / A g )

=1.12_0.01.

(5.6)

Metallic Ni is ferromagnetic on its own and there is strong coupling between the Ni and Fe atoms located at N i / F e interfaces. Furthermore, Ni grown on bcc Fe(001) is metastable. It begins by growing as bcc Ni(001) for the first two layers. Thicker Ni films undergo complex structural reconstruction that result in significant variations in the measured magnetic properties of two Ni films of the same thickness. A complete discussion of metastable 'bcc' Ni can be found in Ref. [11]. Lee et al. [29] carried out ground state magnetic moment calculations for metastable bcc Ni(001) grown on bcc Fe(001). The results for 2 ML of metastable bcc Ni(001) grown on bcc Fe(001) can be applied to calculate the layer averaged moment of specimen # 7 in Table 1. According to Lee et al. [29], each of the two Ni layers should have average moments of 0.69 /x B while the first layer of Fe should have a moment of 2.59/z B. The second layer of Fe should have a moment of 2.40 /x B and the third (center) layer an average moment of 2.38 /x~. For the three Fe atomic layers which are adjacent to the F e / A g interface the atomic moments were assigned according to Ohnishi et al. [25] calculations (2.52, 2.37, and 2.27/z B respectively) We assume that the incomplete first layer of Fe would have an average moment of 2.59 /%. The second layer would be 30% covered with Ni so that 30% of it would have a moment of 2.59 ~B and 70% of it would have a moment of 2.40 /x B. Continuing on, 30% of the third layer would have a moment of 2.40 /x B while 70% of it would have a moment of 2.38 /z B. We now switch to the calculated F e / A g results that were discussed in section 5.1 and assume that the fourth layer would have a moment of 2.27 /z B, the fifth a moment of 2.37 /z B, and the sixth a moment of 2.52 /%. The Ag layer in contact with the rear of the film will be assumed to be weakly

24

Z. Celinski et al. / Journal of Magnetism and Magnetic Materials 166 (1997) 6-26

polarized with a moment of 0.08 /z B. The layer averaged moment is therefore: i /ZNi(2)/Fe(5.7)/ Ag

= 5.7 0 . 6 9 + 0 . 6 9 + 2 . 5 9 + 2 . 4 0 +

-iO 2.38

+2.27 + 2.37 + 2.52 + 0.08} -- 2.68 /~B (5.7) Scaling this result by the layer averaged moment assigned to specimen #1 yields the value of 1.16 which compares well to the ratio of the measured M~R/M(5.7) values of specimens # 7 and #1" ~Ni(2)/Fe(5.7)/ Ag

=

1.16,

/-/'Ag/ Fe(l 0.9)/Ag

M~(Ni(2)/Fe(5.7)/gg) Ms(gg/Fe(10.9)/Ag)

= 1.15 + 0.1.

(5.8)

If we were to assume that a 3 ML Ni film would have an average moment of 0.69 /,zB in its third layer, then repeating the above calculation for the specimens # 8 and # 9 leads to the expected ratio: ~Ni(3)/Fe(5.7)/Ag = 1.21.

Ms/Ms(5.7) using FMR and PNR are equal within experimental error. The PNR technique has the virtue that it can determine absolute moments while the FMR technique determines only relative moments. PNR measurements determine the layer averaged magnetic moment of a given specimen to an accuracy of 0.1 to 0.2 /z B [22]. We can use our results for specimens #1 and # 2 (Ag/10.9 ML F e / A g and Ag/5.5 ML Fe/Ag) to establish an error bound on the average Fe moment measured at an A g / F e interface using FMR. We begin by writing the magnetic moment of the first Fe layer as ~[Zl(Ag/re) =

2.2 + Am,

where A m represents the enhancement over the bulk Fe moment of 2.2 /z a. Next, we assume that the relative moment increase in the second and third layers follows Ohnishi et al. [25] who predicted that the first, second, and third Fe layers would have moments of 2.52 /~B, 2.37/z B, and 2.27/x B, respectively. The average magnetic moments of the second and third Fe layers are therefore written as ~tL2(Ag/Fe) =

2.2 +

(5.9)

~Ag / Fe(10.9)/Ag

The experimental ratios for the sample # 8 and # 9 are 1.24 and 1.20 +0.01, respectively. Again we must point out that the agreement between theory and experiment is excellent and yet the contribution of Ni to the total layer averaged magnetic moment is significantly greater than for the specimens discussed in Sections 5.1 and 5.2 where the moment increase was primarily due to Fe moment enhancement at the interfaces.

5.4. Comparison with polarized neutron reflection studies Table 1 shows that most of our ultrathin film structures were also studied by Bland et al. [22] using polarized neutron reflection (PNR). This technique determines the absolute value of the total magnetic moment of ultrathin film structures. Table 1 clearly shows that the values obtained for the ratio

(5.11)

2.52

2.2 Am

1

= 2.2 +

/Z3~Ag/re)=2.2 +

1.88 Am,

(5.12)

(2.27-2.2) 2.52 2.2 Am 1

= 2.2 + 4.57 Am.

(5.13)

Further layers are assumed to have magnetic moments equal to bulk Fe. Repeating the calculation leading up to result Eq. (5.1) using the moment values given by Eq. (5.11) to Eq. (5.13) for the first three layers of the Fe film, yields the following expression for the layer averaged moment of the Ag/5.5 ML Fe/Ag(001) specime n:

1/

~Ag/Fe(5.5)/Ag -- 5.5 0.08 + (5.5)2.2

+ 2 + 1.88 + 4.57

Am + 0.08} (5.14)

Z. Celinski et al. / Journal of Magnetism and Magnetic Materials 166 (1997) 6-26

and this expression for the moment of the Ag/lO.9 ML Fe/Ag(O01) specimen: FAg / Fe(10.9)/Ag

1 -

10.9

{ 0.08 + (10.9)2.2

+ 2 + 1.8----8+ 4.57

Am + 0.08 .

(5.15)

Taking the ratio of Eq. (5.15) and Eq. (5.14) gives a result that can be compared to the experimentally measured moment ratios determined for the two films: ~Ag / Fe(10.9)/Ag

0.93 + 0.01

FAg / Fe(5.5)/Ag

0.99 + 0.01

~

lute moment measurements carried out on our specimens using polarized neutron reflection (PNR) [22]. Our results were also compared to the layer averaged, ground state, moments calculated for our specimens using results obtained from published, first principles, theoretical calculations [25,28,29]. In nearly all cases there was agreement to within experimental error and in many cases there was almost exact agreement. Such harmony between experiment and theory is gratifying to us and, at the same time, stunning.

Acknowledgements

(5.5)(24.14+3.48Am) =

25

(12.26+3.39Am) (5.16)

The experimentally determined moment ratio of (0.93 ___0.01)/(0.99 ± 0.01) is equal to 0.94 + 0.02 where the total error is determined from the rms average of the errors of the numerator and denominator. Solving Eq. (5.16) for Am using the extreme values of 0.92 and 0.96 shows that the moment enhancement at an A g / F e interface is 0.46 + 0.20 /x B. This is comparable with the maximum error of 0.2 /x B associated with the PNR measurements carried out on our specimens.

6. Summary We have developed a new application of FMR that allows the ratio of the layer averaged magnetic moments of two ultrathin ferromagnetic films to be accurately determined. The total measurement error for the moment ratios of pairs of ultrathin bcc Fe(001) films was found to be approximately 1%. We have used this new method to measure the average magnetic moments of A g / F e / A g , Au/Fe/Ag, C u / F e / A g , P d / F e / A g , and N i / F e / A g ultrathin film structures. The measured moment ratios relative to a 20 Au/5.7 ML F e / Ag(001) reference specimen were found to be in good agreement within experimental error with results obtained from abso-

This work was supported by grants from the National Research Council of Canada. The authors would like to thank J.F. Cochran for very useful discussions and K. Myrtle and J. Rudd for their help during the course of this work.

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