The granular layered magnetic system Co80Fe20(t)/Al2 O3 (3 nm), where the Co80Fe20 layers of nominal thickness t form separate, almost spherical magnetic granules of typical diameter 2-3 nm between the Al2O3 spacers, was studied. We discuss measurements of the dc and ac magnetic susceptibility χ for 1 n

Binek, Christian

Cardoso de Freitas, Susana

Freitas, P.P.

Kakazei, G.N.

Kleemann, Wolfgang

Lesnik, N.A.

Pereira de Azevedo, M.M.

Petracic, O.

Pogorelov, Y.G.

Rokhlin, Stanislav

Santos, J.A.M.

Sousa, J.B.

Wigen, P.E.

English

DigitalCommons@University of Nebraska

University of Nebraska - Lincoln DigitalCommons@University of Nebraska - Lincoln Christian Binek Publications Research Papers in Physics and Astronomy 7-4-2001 Magnetic states of granular layered CoFe-Al2O3 J.B. Sousa IFIMUP, Faculdadede Ciencias, Universidade do Porto, Rua do Campo Alegre Porto, Portugal G.N. Kakazei Institute of Magnetism NAS of Kiev, Ukraine Y.G. Pogorelov Universidade do Porto, Rua do Campo Alegre, Portugal. J.A.M. Santos IFIMUP, Faculdadede Ciencias, Universidade do Porto, Rua do Campo Alegre Porto, Portugal O. Petracic Laboratorium für Angewandte Physik, Gerhard-Mercator-Universität, Duisburg, Germany See next page for additional authors Follow this and additional works at: https://digitalcommons.unl.edu/physicsbinek  Part of the Physics Commons Sousa, J.B.; Kakazei, G.N.; Pogorelov, Y.G.; Santos, J.A.M.; Petracic, O.; Kleemann, Wolfgang; Binek, Christian; Cardoso de Freitas, Susana; Freitas, P.P.; Pereira de Azevedo, M.M.; Lesnik, N.A.; Rokhlin, Stanislav; and Wigen, P.E., "Magnetic states of granular layered CoFe-Al2O3" (2001). Christian Binek Publications. 26. https://digitalcommons.unl.edu/physicsbinek/26 This Article is brought to you for free and open access by the Research Papers in Physics and Astronomy at DigitalCommons@University of Nebraska - Lincoln. It has been accepted for inclusion in Christian Binek Publications by an authorized administrator of DigitalCommons@University of Nebraska - Lincoln. Authors J.B. Sousa, G.N. Kakazei, Y.G. Pogorelov, J.A.M. Santos, O. Petracic, Wolfgang Kleemann, Christian Binek, Susana Cardoso de Freitas, P.P. Freitas, M.M. Pereira de Azevedo, N.A. Lesnik, Stanislav Rokhlin, and P.E. Wigen This article is available at DigitalCommons@University of Nebraska - Lincoln: https://digitalcommons.unl.edu/physicsbinek/26 2200 IEEE TRANSACTIONS ON MAGNETICS, VOL. 37, NO. 4, JULY 2001Magnetic States of Granular Layered CoFe–Al2O3SystemJ. B. Sousa, G. N. Kakazei, Yu G. Pogorelov, J. A. M. Santos, O. Petracic, W. W. Kleemann, Ch. Binek, S. Cardoso,P. P. Freitas, M. M. Pereira de Azevedo, N. A. Lesnik, M. Rokhlin, and P. E. WigenAbstract—The granular layered magnetic systemCo80Fe20( )/Al2O3(3 nm), where the Co80Fe20 layers of nominalthickness form separate, almost spherical magnetic granules oftypical diameter 2–3 nm between the Al2O3 spacers, was studied.We discuss measurements of the dc and ac magnetic susceptibilityfor 1 nm 1.3 nm at temperatures 10 K 300 Kand ac frequencies 0.01 Hz 103 Hz, revealing a richvariety of magnetic states, including superparamagnetic (SPM),ferromagnetic (FM)-like, and glass (G)-like. In order to describethe ac response in this disordered planar system, a generalizationof the Néel–Brown approach is proposed, including randomanisotropy and random molecular fields acting on the granules.The observed magnetic states are summarized in a phase diagramin the variables , which is explained through the competitionof thermal energy with two kinds of interaction between granules:usual dipolar (point-like) and FM “exchange” (due to straydipolar fields from nonspherical granules). In particular, thecoincidence of maximum low field sensitivity with theSPM–FM transition line on this diagram is confirmed.Index Terms—Discontinuous metal–insulator films, ferromag-netic transition, magnetic phase diagram, spin–glass transition.I. INTRODUCTIOND ISCONTINUOUS metal–insulator multilayers (DMIM)were proposed in expectation of high sensitivity of mag-netoresistance ( ) to a magnetic field ,like their metal–metal predecessors [1], but much less exposedto degradation. Pioneering work on Co/SiOand CoFe/HfODMIMs demonstrated their higher sensitivity compared tocermet films of the same composition and concentration [2].Manuscript received October 13, 2000.This work was partially supported by the program PRAXIS XXI (Portugal)through the Projects 3/3.1/MMA/1787/95, 2/2.1/FIS/302/94, P/CTM/11242/98and the Grants BPD/3866/96 (G.N.K.) and BD/11533/97 (S.C.). This work wasalso supported by DFG (Graduate School “Structure and dynamics of heteroge-neous systems”), DAAD (Germany) and CRUP (Portugal).J. B. Sousa, G. N. Kakazei, and J. A. M. Santos are with IFIMUP, Facul-dade de Ciencias, Universidade do Porto, Rua do Campo Alegre 687, 4169-007Porto, Portugal. G. N. Kakazei is on leave from Institute of Magnetism NAS ofUkraine, Kiev, Ukraine (e-mail: kgleb@fc.up.pt).Y. G. Pogorelov is with CFP and Departamento de Física, Universidade doPorto, Rua do Campo Alegre 687, 4169-007 Porto, Portugal.O. Petracic, W. W. Kleemann, and C. Binek are with Laboratorium für Ange-wandte Physik, Gerhard-Mercator-Universität, 47048 Duisburg, Germany.S. Cardoso and P. P. Freitas are with INESC, Rua Alves Redol 9-1, 1000Lisbon, Portugal.M. M. Pereira de Azevedo is with Departamento de Física, Universidade doAveiro, 3810 Aveiro, Portugal.N. A. Lesnik is with Institute of Magnetism NAS of Ukraine, 36Vernad-skogo blvd., 03142 Kiev, Ukraine.M. Rokhlin and P. E. Wigen are with Department of Physics, The Ohio StateUniversity, Columbus, OH 43210 USA.Publisher Item Identifier S 0018-9464(01)06520-7.Recently, we studied and at room temperature (RT)as functions of nominal thicknessof ferromagnetic layer inCo Fe ( )/Al O (3 nm) DMIMs with 1 2.5 nm. Inparticular, a sharp peak of was observed near 1.3 nm[3]. The magnetization curves for different valuesdisplayed a crossover from SPM to FM-like behavior just above, when the remanence onsets in a pronounced criticalway: [4]. These anomalies in andwere attributed to the so-called magnetic percolationover disconnected granules (high resolution TEM at1.4 nmshowed separate, nearly spherical granules with a narrow sizedistribution and average diameter3 nm).Also, measuring vs we observed the onset of hys-teresis and coercivity below 100 K in the samples with1.6 nm, increasing as temperature decreases. The increase inhysteresis is accompanied by a strong enhancement of the satu-ration value [3].This evidence of various nontrivial magnetic states inCo Fe ( )/Al O (3 nm) films, important for its practicalproperties (like , , ) motivated us to make a detailedstudy of the dc and ac magnetic susceptibility, complementedby measurements of low field with current-in-plane, overa wide temperature range. In parallel, theoretical models wereworked out to give a consistent account of the experimentalr sults, leading to a full phase diagram of the mentionedmagnetic states, in the variables .II. EXPERIMENTAL[Co Fe ( )/Al O (3 nm)] DMIMs were prepared byion-beam deposition using methods described elsewhere [3],[4]. Susceptibility data for samples with different weretaken using a Superconducting Quantum Interference Device(SQUID) magnetometer Quantum Design MPMS-5S at tem-peratures 10 300 K and ac frequencies 0.01 Hz10 Hz at an ac amplitude mT in virtually zeroexternal field. Fig. 1 shows the data obtained for four differentDMIMs at several frequencies 0.1 100 Hz. For thenm sample [Fig. 1(a)] and are sim-ilar to the data observed previously on frozen FeC ferrofluids[5]. A sizable dispersion in the range 40 80 K canbe associated to the onset of superspin glass (SSG) phase,while nondispersive Curie–Weiss (CW)-type decay ofwith an extrapolated FM Curie temperature 58 K isencountered at 80 K [see 1 curves for Hz andthe best-fitted CW plot within 200 300 K in Fig. 1(a)].At higher nominal thickness, 1.1 nm, a dispersionlessbackground appears at higher temperatures, in addition to the0018–9464/01$10.00 © 2001 IEEESOUSAet al.: MAGNETIC STATES OF GRANULAR LAYERED CoFe–AlO SYSTEM 2201Fig. 1.  (f; T ) and (f; T ) vs.T of CoFe/Al O DMIMs with (a) t =1.0, (b) 1.1, (c) 1.2, and (d) 1.3 nm measured at frequencies 0.1 f  100 Hz.Note the magnification factor (5) applicable to all data. Inverse curves (f = 0:1 Hz, T ) with best-fitted Curie–Weiss (CW) lines define themean-field transition temperatures, as marked by arrowheads together withT ; T andT [(c) and (d) only], so thatT < T < T < .Fig. 2. Low-field magnetization curvesM vs. H obtained on the DMIMwith (a)t = 1:2 and (b) 1.3 nm after ZFC from 300 K to (a) 300, 260, 220, 180,140, 120, 100, and 80 K and (b) 300, 260, 220, 180, 140, and 120 K, respectively.polydispersive response curves of the glassy subsystem at low[Fig. 1(b)–(d)]. Its high- tails are described by a CW law withFM mean-field Curie temperatures 114, 165 and 270 Kfor 1.1, 1.2 and 1.3 nm, respectively [see 1curves forHz and CW plots best-fitted above 240 K in Fig. 1(b)–(c)].We attribute the background curves to the prevalence of FM “ex-change” (due to stray dipolar fields from nonspherical granules,see below) over pure dipolar coupling [6], between “magneti-cally percolated” granules. Their aggregate (the infinite cluster)behaves like a FM with finite in-plane anisotropy, which causesthe susceptibility to decrease upon cooling below the FM or-dering temperature, . Notably, the dispersionless partof is not linked (through a usual scaling relation [7])with the energy losses seen from .To clarify the nature of this FM state, which can be also calledsuperferromagnetic (SFM) as resulting from FM ordering ofSPM moments, we have measured the dc magnetizationin the range 4.5 4.5 mT. The field step was 0.1 mTfor nm and 220–260 K, but also an enhancedresolution (0.005 mT) was used atdescending from 300 Kto 80 K ( nm), and to 120 K ( nm), respec-tively. Each of the curves (partially shown in Fig. 2) was ob-tained after zero-field cooling (ZFC) from 300 K. Langevin-typeSPM magnetization curves are observed at high, but uponcooling to below a certain Curie temperature they developfinite jumps at . Particular values were defined( nm) and 240 K ( nm). Upon furthercooling is growing, accordingly to the stabilization ofSFM order and similarly to growing .Obviously the SFM system behaves like a soft ferromagnet.Just below the respective it is demagnetized in zero fieldand may be switched into its spontaneous valuesby applying external fields in the order0.1 mT. The quantity( ) vs taken from the curves measuresSPM susceptibility at . At it is proportional(within less than 0.1 mT) to , which is a measure of.For each, at a certain temperature the curveturns to be hysteretic as evidenced by finite values ofandcoercive field (Fig. 2). For instance, we defined 120and 190 K for 1.2 and 1.3 nm, respectively. Obviously, thefree energy barrier due to the weak intraplanar anisotropy is nolonger overcome by thermal activation, and both andincrease upon further cooling to below. Since the valuesroughly coincide with the onset of low-dispersion in the acsusceptibility data [Fig. 1(c)–(d)], the observed hysteresis maybe related to the metastability of the reentrant superspin glass(RSSG) phase. Indeed, there is an observable decrease of thehysteresis with waiting time between the data points, e.g.,in the nm sample at K goes from 0.085to 0.065 mT when increases from 90 to 900 s. This suggestssome link between the hysteresis and lossy dynamics of the SSGcomponent, also seen in its frequency dispersion (Fig. 1).Finally, under yet deeper cooling to some thehysteresis reaches saturation while the energy lossesreach a maximum. We associate this with the SSG transition inthe subsystem of magnetically nonpercolated SPM moments.Thus, the emerging SSG phase is spatially separated from theSFM phase, allowing for coexistence of the two phases in such“re-entrant” state (unlike transformation of FM into SG inusual re-entrant transitions [8]).It is known that an independent characterization of magneticphase states, in particular reflecting theshort-rangecorrelationsbetween granule magnetic moments, can be obtained from lowfield measurements. We thus performed a detailed studyof the temperature dependence at a fixed low fieldmT [it thus scales with the field sensitivity( )]for a selected sample with nm, the results being shownin Fig. 3. The observed maximum of near 250 K is,within experimental errors, fairly close to the above determinedSPM–SFM transition temperature for this sample. For com-parison, the inset of Fig. 3 shows the thickness dependencemeasured at RT, with a sharp and symmetrical peak at[3]. It isclearly seen that the maximum of is much broader andhas a sizable asymmetry on the two sides from. The latterindicates the difference in short-range magnetic correlations forSPM and SFM states.III. M ODEL AND DISCUSSIONTo treat the temperature dependence of ac susceptibility,we modify the known Néel–Brown approach, supposing eachgranule moment be subjected to certain random uniaxial2202 IEEE TRANSACTIONS ON MAGNETICS, VOL. 37, NO. 4, JULY 2001Fig. 3. Magnetoresistance of the 1.3 nm sample in a fixed applied field H =4:5 mT as a function of temperature (the points are experimental, the line isonly a guide for the eye). Estimated peak position (shown by the arrow) is about250 K, close to the Curie temperatureT  240 K for this sample determinedin Figs. 1 and 2.anisotropy and random local field , all lying in the DMIMplane, with the energy:(1)where and are respectively the angles thatand makewith the anisotropy axis. Depending on the ratio betweenand , the function can have one (for) or two (for ) minima , andin the latter case the ac field , canproduce nonequilibrium occupation of the minima and give riseto energy losses. The kinetic equation for the occupation numberof the metastable minimum is:(2)where , , and the “at-tempt” frequency s . But small contributionsinto instantaneous values of energy barriers for escape frommetastable and stable minima: , bringsome time dependence into . The general solution to (2) is:(3)with , and, after a waiting time , itattains a steady state regime , which is the mostimportant in practice. It is the difference between and theequilibrium value (where) that defines a contribution to complex ac susceptibility:(4)Fig. 4. Magnetic phase diagram of CoFe (t)/Al O (3 nm) DMIMs in thevariablest andT : () SPM–SFM transition by ;  andMR data; ( )onset of SSG state, by . Theoretical curves: (1)T / t (t   t ); (2)T / t ; (3) T / (t   t) , T  950 K (as for bulk Co Fe ,note the axis break).with the average over time and orientations of random fields andanisotropies. At high enough, such that , the steadystate is simply whereadiabatically follows the variation of the energylevels. Then we obtain:(5)and the self-consistency relation , with the aboveused FM “exchange” leads to CW law with .Equations (3) and (4) still apply for a more complicate nona-diabatic case ( ) taking place at . Here we onlynote that the estimate for energy barriers givesK for our system. This is too high to be accountedfor by the typical interaction energy of two granulesK, and gives a hint that effective SPM moments (super-spins) should involve up to 10 granules.Finally, the phase diagram of magnetic states in variables(Fig. 4) can be summarized as follows. The SPM–SFMtransition (line 1 in Fig. 4) occurs when the dipolar interac-tion energy, which is continuously frustrated for point dipoles[6] or spherical granules, obtains a growing contribution fromstray fields produced by nonspherical particles. The latter ap-pear due to coalescence at growing size ofspherical granules, nucleated at random centers with mean dis-tance . The relative number of coalesced granules rapidly in-creases with nominal thicknessas ,hence their structural percolation occurs at 0.5 and3, while the magnetic percolation begins at only slightlylower 0.45 but at notably thinner 5. The ef-fective Curie temperature rapidly grows as ,eventually reaching K when the infi-nite SFM cluster turns into usual FM.A rough estimate of temperature at is given bythe mean fluctuation of dipolar field , resulting in its-dependence (SPM–SSG, line 2). Thisincrease of is limited at and drops to zeroat (SFM–RSSG, line 3), due to vanishingSOUSAet al.: MAGNETIC STATES OF GRANULAR LAYERED CoFe–AlO SYSTEM 2203probability to find SPM clusters in almost FM medium, and thiscan be described, e.g., by the percolation index [9].REFERENCES[1] B. Dieny, S. Sankar, M. R. McCartney, D. J. Smith, P. Bayle-Guille-maud, and A. E. Berkowitz, “Spin-dependent tunneling in discontin-uous metal/insulator multilayers,”J. Magn. Magn. Mater., vol. 185, pp.283–292, June 1998.[2] S. Sankar, B. Dieny, and A. E. Berkowitz, “Spin-polarized tunnelingin discontinuous CoFe/HfOmultilayers,”J. Appl. Phys., vol. 81, pp.5512–5514, Apr. 1997.[3] G. N. Kakazei, P. P. Freitas, S. Cardoso, A. M. L. Lopes, M. M. Pereirade Azevedo, Y. G. Pogorelov, and J. B. Sousa, “Transport properties ofdiscontinuous Co Fe /Al O multilayers,” IEEE Trans. Magn., vol.35, pp. 2895–2897, Sept. 1999.[4] G. N. Kakazei, Y. G. Pogorelov, A. M. L. Lopes, J. B. Sousa, S. Car-doso, P. P. Freitas, M. M. Pereira de Azevedo, and E. Snoeck, “Tunnelmagnetoresistence and magnetic ordering in ion-beam sputteredCo Fe /Al O discontinuous multilayers,”. unpublished.[5] T. Jonsson, P. Svedlindh, and M. F. Hansen, “Static scaling on an in-teracting magnetic nanoparticle system,”Phys. Rev. Lett., vol. 81, pp.3976–3979, Nov. 1998.[6] J. M. Luttinger and L. Tisza, “Theory of dipole interaction in crystals,”Phys. Rev., vol. 70, pp. 954–964, Dec. 1946.[7] A. T. Ogielski, “Dynamics of three-dimensional Ising spin glasses inthermal equilibrium,”Phys. Rev. B, vol. 32, pp. 7384–7398, Dec. 1985.[8] B. K. Srivastava, A. Krishnamurthy, V. Ghose, J. Mattson, and P. Nord-blad, “Re-entrant spin glass like behavior of (FeCr Ni ) P,”J. Magn. Magn. Mater., vol. 132, pp. 124–130, Apr. 1994.[9] D. Stauffer, “Scaling theory of percolation clusters,”Phys. Reports, vol.54, pp. 1–74, 1979.

Magnetic states of granular layered CoFe-Al\u3csub\u3e2\u3c/sub\u3eO\u3csub\u3e3\u3c/sub\u3e

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Christian Binek Publications Research Papers in Physics and Astronomy 
7-4-2001 
Magnetic states of granular layered CoFe-Al2O3 
J.B. Sousa 
IFIMUP, Faculdadede Ciencias, Universidade do Porto, Rua do Campo Alegre Porto, Portugal 
G.N. Kakazei 
Institute of Magnetism NAS of Kiev, Ukraine 
Y.G. Pogorelov 
Universidade do Porto, Rua do Campo Alegre, Portugal. 
J.A.M. Santos 
IFIMUP, Faculdadede Ciencias, Universidade do Porto, Rua do Campo Alegre Porto, Portugal 
O. Petracic 
Laboratorium für Angewandte Physik, Gerhard-Mercator-Universität, Duisburg, Germany 
See next page for additional authors 
Follow this and additional works at: https://digitalcommons.unl.edu/physicsbinek 
 Part of the Physics Commons 
Sousa, J.B.; Kakazei, G.N.; Pogorelov, Y.G.; Santos, J.A.M.; Petracic, O.; Kleemann, Wolfgang; Binek, 
Christian; Cardoso de Freitas, Susana; Freitas, P.P.; Pereira de Azevedo, M.M.; Lesnik, N.A.; Rokhlin, 
Stanislav; and Wigen, P.E., "Magnetic states of granular layered CoFe-Al2O3" (2001). Christian Binek 
Publications. 26. 
https://digitalcommons.unl.edu/physicsbinek/26 
This Article is brought to you for free and open access by the Research Papers in Physics and Astronomy at 
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Authors 
J.B. Sousa, G.N. Kakazei, Y.G. Pogorelov, J.A.M. Santos, O. Petracic, Wolfgang Kleemann, Christian Binek, 
Susana Cardoso de Freitas, P.P. Freitas, M.M. Pereira de Azevedo, N.A. Lesnik, Stanislav Rokhlin, and P.E. 
Wigen 
This article is available at DigitalCommons@University of Nebraska - Lincoln: https://digitalcommons.unl.edu/
physicsbinek/26 
2200 IEEE TRANSACTIONS ON MAGNETICS, VOL. 37, NO. 4, JULY 2001
Magnetic States of Granular Layered CoFe–Al2O3
System
J. B. Sousa, G. N. Kakazei, Yu G. Pogorelov, J. A. M. Santos, O. Petracic, W. W. Kleemann, Ch. Binek, S. Cardoso,
P. P. Freitas, M. M. Pereira de Azevedo, N. A. Lesnik, M. Rokhlin, and P. E. Wigen
Abstract—The granular layered magnetic system
Co80Fe20( )/Al2O3(3 nm), where the Co80Fe20 layers of nominal
thickness form separate, almost spherical magnetic granules of
typical diameter 2–3 nm between the Al2O3 spacers, was studied.
We discuss measurements of the dc and ac magnetic susceptibility
for 1 nm 1.3 nm at temperatures 10 K 300 K
and ac frequencies 0.01 Hz 103 Hz, revealing a rich
variety of magnetic states, including superparamagnetic (SPM),
ferromagnetic (FM)-like, and glass (G)-like. In order to describe
the ac response in this disordered planar system, a generalization
of the Néel–Brown approach is proposed, including random
anisotropy and random molecular fields acting on the granules.
The observed magnetic states are summarized in a phase diagram
in the variables , which is explained through the competition
of thermal energy with two kinds of interaction between granules:
usual dipolar (point-like) and FM “exchange” (due to stray
dipolar fields from nonspherical granules). In particular, the
coincidence of maximum low field sensitivity with the
SPM–FM transition line on this diagram is confirmed.
Index Terms—Discontinuous metal–insulator films, ferromag-
netic transition, magnetic phase diagram, spin–glass transition.
I. INTRODUCTION
D ISCONTINUOUS metal–insulator multilayers (DMIM)were proposed in expectation of high sensitivity of mag-
netoresistance ( ) to a magnetic field ,
like their metal–metal predecessors [1], but much less exposed
to degradation. Pioneering work on Co/SiOand CoFe/HfO
DMIMs demonstrated their higher sensitivity compared to
cermet films of the same composition and concentration [2].
Manuscript received October 13, 2000.
This work was partially supported by the program PRAXIS XXI (Portugal)
through the Projects 3/3.1/MMA/1787/95, 2/2.1/FIS/302/94, P/CTM/11242/98
and the Grants BPD/3866/96 (G.N.K.) and BD/11533/97 (S.C.). This work was
also supported by DFG (Graduate School “Structure and dynamics of heteroge-
neous systems”), DAAD (Germany) and CRUP (Portugal).
J. B. Sousa, G. N. Kakazei, and J. A. M. Santos are with IFIMUP, Facul-
dade de Ciencias, Universidade do Porto, Rua do Campo Alegre 687, 4169-007
Porto, Portugal. G. N. Kakazei is on leave from Institute of Magnetism NAS of
Ukraine, Kiev, Ukraine (e-mail: kgleb@fc.up.pt).
Y. G. Pogorelov is with CFP and Departamento de Física, Universidade do
Porto, Rua do Campo Alegre 687, 4169-007 Porto, Portugal.
O. Petracic, W. W. Kleemann, and C. Binek are with Laboratorium für Ange-
wandte Physik, Gerhard-Mercator-Universität, 47048 Duisburg, Germany.
S. Cardoso and P. P. Freitas are with INESC, Rua Alves Redol 9-1, 1000
Lisbon, Portugal.
M. M. Pereira de Azevedo is with Departamento de Física, Universidade do
Aveiro, 3810 Aveiro, Portugal.
N. A. Lesnik is with Institute of Magnetism NAS of Ukraine, 36Vernad-
skogo blvd., 03142 Kiev, Ukraine.
M. Rokhlin and P. E. Wigen are with Department of Physics, The Ohio State
University, Columbus, OH 43210 USA.
Publisher Item Identifier S 0018-9464(01)06520-7.
Recently, we studied and at room temperature (RT)
as functions of nominal thicknessof ferromagnetic layer in
Co Fe ( )/Al O (3 nm) DMIMs with 1 2.5 nm. In
particular, a sharp peak of was observed near 1.3 nm
[3]. The magnetization curves for different values
displayed a crossover from SPM to FM-like behavior just above
, when the remanence onsets in a pronounced critical
way: [4]. These anomalies in and
were attributed to the so-called magnetic percolation
over disconnected granules (high resolution TEM at1.4 nm
showed separate, nearly spherical granules with a narrow size
distribution and average diameter3 nm).
Also, measuring vs we observed the onset of hys-
teresis and coercivity below 100 K in the samples with
1.6 nm, increasing as temperature decreases. The increase in
hysteresis is accompanied by a strong enhancement of the satu-
ration value [3].
This evidence of various nontrivial magnetic states in
Co Fe ( )/Al O (3 nm) films, important for its practical
properties (like , , ) motivated us to make a detailed
study of the dc and ac magnetic susceptibility, complemented
by measurements of low field with current-in-plane, over
a wide temperature range. In parallel, theoretical models were
worked out to give a consistent account of the experimental
r sults, leading to a full phase diagram of the mentioned
magnetic states, in the variables .
II. EXPERIMENTAL
[Co Fe ( )/Al O (3 nm)] DMIMs were prepared by
ion-beam deposition using methods described elsewhere [3],
[4]. Susceptibility data for samples with different were
taken using a Superconducting Quantum Interference Device
(SQUID) magnetometer Quantum Design MPMS-5S at tem-
peratures 10 300 K and ac frequencies 0.01 Hz
10 Hz at an ac amplitude mT in virtually zero
external field. Fig. 1 shows the data obtained for four different
DMIMs at several frequencies 0.1 100 Hz. For the
nm sample [Fig. 1(a)] and are sim-
ilar to the data observed previously on frozen FeC ferrofluids
[5]. A sizable dispersion in the range 40 80 K can
be associated to the onset of superspin glass (SSG) phase,
while nondispersive Curie–Weiss (CW)-type decay of
with an extrapolated FM Curie temperature 58 K is
encountered at 80 K [see 1 curves for Hz and
the best-fitted CW plot within 200 300 K in Fig. 1(a)].
At higher nominal thickness, 1.1 nm, a dispersionless
background appears at higher temperatures, in addition to the
0018–9464/01$10.00 © 2001 IEEE
SOUSAet al.: MAGNETIC STATES OF GRANULAR LAYERED CoFe–AlO SYSTEM 2201
Fig. 1.  (f; T ) and (f; T ) vs.T of CoFe/Al O DMIMs with (a) t =
1.0, (b) 1.1, (c) 1.2, and (d) 1.3 nm measured at frequencies 0.1 f  100 Hz.
Note the magnification factor (5) applicable to all data. Inverse curves
 (f = 0:1 Hz, T ) with best-fitted Curie–Weiss (CW) lines define the
mean-field transition temperatures, as marked by arrowheads together with
T ; T andT [(c) and (d) only], so thatT < T < T < .
Fig. 2. Low-field magnetization curvesM vs. H obtained on the DMIM
with (a)t = 1:2 and (b) 1.3 nm after ZFC from 300 K to (a) 300, 260, 220, 180,
140, 120, 100, and 80 K and (b) 300, 260, 220, 180, 140, and 120 K, respectively.
polydispersive response curves of the glassy subsystem at low
[Fig. 1(b)–(d)]. Its high- tails are described by a CW law with
FM mean-field Curie temperatures 114, 165 and 270 K
for 1.1, 1.2 and 1.3 nm, respectively [see 1curves for
Hz and CW plots best-fitted above 240 K in Fig. 1(b)–(c)].
We attribute the background curves to the prevalence of FM “ex-
change” (due to stray dipolar fields from nonspherical granules,
see below) over pure dipolar coupling [6], between “magneti-
cally percolated” granules. Their aggregate (the infinite cluster)
behaves like a FM with finite in-plane anisotropy, which causes
the susceptibility to decrease upon cooling below the FM or-
dering temperature, . Notably, the dispersionless part
of is not linked (through a usual scaling relation [7])
with the energy losses seen from .
To clarify the nature of this FM state, which can be also called
superferromagnetic (SFM) as resulting from FM ordering of
SPM moments, we have measured the dc magnetization
in the range 4.5 4.5 mT. The field step was 0.1 mT
for nm and 220–260 K, but also an enhanced
resolution (0.005 mT) was used atdescending from 300 K
to 80 K ( nm), and to 120 K ( nm), respec-
tively. Each of the curves (partially shown in Fig. 2) was ob-
tained after zero-field cooling (ZFC) from 300 K. Langevin-type
SPM magnetization curves are observed at high, but upon
cooling to below a certain Curie temperature they develop
finite jumps at . Particular values were defined
( nm) and 240 K ( nm). Upon further
cooling is growing, accordingly to the stabilization of
SFM order and similarly to growing .
Obviously the SFM system behaves like a soft ferromagnet.
Just below the respective it is demagnetized in zero field
and may be switched into its spontaneous values
by applying external fields in the order0.1 mT. The quantity
( ) vs taken from the curves measures
SPM susceptibility at . At it is proportional
(within less than 0.1 mT) to , which is a measure of
.
For each, at a certain temperature the curve
turns to be hysteretic as evidenced by finite values ofand
coercive field (Fig. 2). For instance, we defined 120
and 190 K for 1.2 and 1.3 nm, respectively. Obviously, the
free energy barrier due to the weak intraplanar anisotropy is no
longer overcome by thermal activation, and both and
increase upon further cooling to below. Since the values
roughly coincide with the onset of low-dispersion in the ac
susceptibility data [Fig. 1(c)–(d)], the observed hysteresis may
be related to the metastability of the reentrant superspin glass
(RSSG) phase. Indeed, there is an observable decrease of the
hysteresis with waiting time between the data points, e.g.,
in the nm sample at K goes from 0.085
to 0.065 mT when increases from 90 to 900 s. This suggests
some link between the hysteresis and lossy dynamics of the SSG
component, also seen in its frequency dispersion (Fig. 1).
Finally, under yet deeper cooling to some the
hysteresis reaches saturation while the energy losses
reach a maximum. We associate this with the SSG transition in
the subsystem of magnetically nonpercolated SPM moments.
Thus, the emerging SSG phase is spatially separated from the
SFM phase, allowing for coexistence of the two phases in such
“re-entrant” state (unlike transformation of FM into SG in
usual re-entrant transitions [8]).
It is known that an independent characterization of magnetic
phase states, in particular reflecting theshort-rangecorrelations
between granule magnetic moments, can be obtained from low
field measurements. We thus performed a detailed study
of the temperature dependence at a fixed low field
mT [it thus scales with the field sensitivity( )]
for a selected sample with nm, the results being shown
in Fig. 3. The observed maximum of near 250 K is,
within experimental errors, fairly close to the above determined
SPM–SFM transition temperature for this sample. For com-
parison, the inset of Fig. 3 shows the thickness dependence
measured at RT, with a sharp and symmetrical peak at[3]. It is
clearly seen that the maximum of is much broader and
has a sizable asymmetry on the two sides from. The latter
indicates the difference in short-range magnetic correlations for
SPM and SFM states.
III. M ODEL AND DISCUSSION
To treat the temperature dependence of ac susceptibility,
we modify the known Néel–Brown approach, supposing each
granule moment be subjected to certain random uniaxial
2202 IEEE TRANSACTIONS ON MAGNETICS, VOL. 37, NO. 4, JULY 2001
Fig. 3. Magnetoresistance of the 1.3 nm sample in a fixed applied field H =
4:5 mT as a function of temperature (the points are experimental, the line is
only a guide for the eye). Estimated peak position (shown by the arrow) is about
250 K, close to the Curie temperatureT  240 K for this sample determined
in Figs. 1 and 2.
anisotropy and random local field , all lying in the DMIM
plane, with the energy:
(1)
where and are respectively the angles thatand make
with the anisotropy axis. Depending on the ratio between
and , the function can have one (for
) or two (for ) minima , and
in the latter case the ac field , can
produce nonequilibrium occupation of the minima and give rise
to energy losses. The kinetic equation for the occupation number
of the metastable minimum is:
(2)
where , , and the “at-
tempt” frequency s . But small contributions
into instantaneous values of energy barriers for escape from
metastable and stable minima: , bring
some time dependence into . The general solution to (2) is:
(3)
with , and, after a waiting time , it
attains a steady state regime , which is the most
important in practice. It is the difference between and the
equilibrium value (where
) that defines a contribution to complex ac susceptibility
:
(4)
Fig. 4. Magnetic phase diagram of CoFe (t)/Al O (3 nm) DMIMs in the
variablest andT : () SPM–SFM transition by ;  andMR data; ( )
onset of SSG state, by . Theoretical curves: (1)T / t (t   t ); (2)
T / t ; (3) T / (t   t) , T  950 K (as for bulk Co Fe ,
note the axis break).
with the average over time and orientations of random fields and
anisotropies. At high enough, such that , the steady
state is simply where
adiabatically follows the variation of the energy
levels. Then we obtain:
(5)
and the self-consistency relation , with the above
used FM “exchange” leads to CW law with .
Equations (3) and (4) still apply for a more complicate nona-
diabatic case ( ) taking place at . Here we only
note that the estimate for energy barriers gives
K for our system. This is too high to be accounted
for by the typical interaction energy of two granules
K, and gives a hint that effective SPM moments (super-
spins) should involve up to 10 granules.
Finally, the phase diagram of magnetic states in variables
(Fig. 4) can be summarized as follows. The SPM–SFM
transition (line 1 in Fig. 4) occurs when the dipolar interac-
tion energy, which is continuously frustrated for point dipoles
[6] or spherical granules, obtains a growing contribution from
stray fields produced by nonspherical particles. The latter ap-
pear due to coalescence at growing size of
spherical granules, nucleated at random centers with mean dis-
tance . The relative number of coalesced granules rapidly in-
creases with nominal thicknessas ,
hence their structural percolation occurs at 0.5 and
3, while the magnetic percolation begins at only slightly
lower 0.45 but at notably thinner 5. The ef-
fective Curie temperature rapidly grows as ,
eventually reaching K when the infi-
nite SFM cluster turns into usual FM.
A rough estimate of temperature at is given by
the mean fluctuation of dipolar field , resulting in its
-dependence (SPM–SSG, line 2). This
increase of is limited at and drops to zero
at (SFM–RSSG, line 3), due to vanishing
SOUSAet al.: MAGNETIC STATES OF GRANULAR LAYERED CoFe–AlO SYSTEM 2203
probability to find SPM clusters in almost FM medium, and this
can be described, e.g., by the percolation index [9].
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Magnetic states of granular layered CoFe-Al\u3csub\u3e2\u3c/sub\u3eO\u3csub\u3e3\u3c/sub\u3e

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