Comment on "Magnetic phase transition in Co/Cu/Ni/Cu(100) and Co/Fe/Ni/Cu(100)"

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by  P. J. Jensen

1
To be published in: but not a singularity. The phase transition line I-IV re-
Phys. Rev. Lett. 93, 039703 (2005) sults if this resonance and the “real” singularity merge
into a single peak. Note furthermore that in addition to
Comment on ”Magnetic phase transition in the crossoverII-IV [8], also the crossoverIII-IV [11] and
Co/Cu/Ni/Cu(100) and Co/Fe/Ni/Cu(100)” the transition I-IV [12] have been reported previously.
5 In a recent Letter [1] the phase diagram of
1.6
0 Co/Cu/Ni/Cu(100)andCo/Fe/Ni/Cu(100)trilayerswas
20 determined experimentally as well as theoretically. nits) 1.4
n Wmahrekretahsatwepudbolisnhoetdobwjoerckt wthaespnroetsecnotmedmreenstueldtso,nw.eEres-- arb. u 2.3 MLCo
Ja pecially, much more information can be extracted out of on ( 0.4 / experiment 43..03 MMLLNCui
5 the measurements by a quantitative comparisonwith an zati calculation Cu (100)
2 appropriate model, allowing for a determination of im- eti 0.2
n J =34.3meV
portantparameterssuchasexchangecouplingconstants. g Co
a J =10.2meV
i] In particular: M J iNn it = 13meV
c 1. For the theoretical investigation in [1] an Ising- 0.0
s 0 50 100 150 200 250 300
- type model has been assumed. To obtain a satisfac- Temperature (K)
l tory agreementwith the measuredphase diagrama very
r
mt large interlayer coupling Jint/JNi,Co ∼ 0.1...1 as com- FIG. 1: Ni and Co magnetizations of a Co/Cu/Ni/Cu(100)
pared to the ones of Ni and Co has been assumed, in trilayer system as function of the temperature T. The mea-
t. disagreementwithpreviousresults[2,3,4]. However,we surements have been obtained by XMCD [7]. For the calcu-
a lation we have assumed integer thicknesses next to the real
like to point out that this large value is caused by the
m
ones, and exchangeinteractions as indicated.
use of Ising-like magnetic moments. By consideration
-
d of three-component Heisenberg spins, as appropriate for
n 3d-transition-metalferromagnets,muchsmallervaluesof To conclude, we note that, in addition to the varying
o Jint are sufficient to explainthe measurements. The rea- thicknesses of the ferromagnetic layers, many more fea-
c
son for this large difference is the existence of collective tures of the trilayer system occur if also the thicknesses
[
magnetic excitations (spin waves), which are (i) absent of the spacer and the cap layers are varied. Quite in-

1 forIsing-likespins,andwhichare(ii)particularlyimpor- terestingly, the exchange couplings of the ferromagnetic
v
tant for ultrathin films. Therefore, the resulting bound- layers may depend sensitively on these thicknesses [13].
4
8 ary values of Jint/J1,2 calculated in [1] are unphysically A nonmonotonous behavior of the ordering temperature
5 large. Inaddition, the shape of the magnetizationM(T) may result [2].
1 asafunctionofthe temperaturedepends alsosensitively
0 on the type of spins involved. For Ising-like spins M(T) P. J. Jensen, C. Sorg, A. Scherz, M. Bernien,
5
is almost constant over a large temperature range and K. Baberschke, and H. Wende
0
/ dropsrapidlytozeroclosetotheCurietemperature. On Physics Department, Freie Universit¨at Berlin,
at theotherhand,themeasuredmagnetizationcurveM(T) Arnimallee 14, D-14195 Berlin, Germany
m canbe describedmuch better by three-componentspins.
Hence, for the description of the trilayer system a Received 27 February 2004
-
d Heisenberg model should be applied, solved with im- PACS numbers: 75.70.Cn, 79.60.Jv
n
proved approximations like a many-body Green’s func-
o
tiontheory(GFT)[5]orMonteCarlosimulations[6]. As
c
: an example, in Fig.1 we present the Ni and Co magneti-
v
zation curves as measured by XMCD [7] and calculated
Xi fromGFT[3,5]. Incontrast,asimplemeanfieldapprox- [1] C. Won et al., Phys.Rev.Lett. 91, 147202 (2003).
[2] G. Bayreuther et al., J. Appl.Phys. 79, 4509 (1996).
r imation neglects collective excitations and yields similar [3] P. J. Jensen et al.,Phys. Rev.B 60, R14 994 (1999).
a
unphysicalvalues for Jint as obtainedby anIsing model. [4] W. Kuch et al., Phys.Rev.B 65, 064406 (2002).
2. The boundaries between phases I-IV as presented [5] P. Fr¨obrich et al.,Europ. Phys. J. B 13, 477 (2000).
in [1] are not always phase transition lines in the ther- [6] P. A. Serenaet al.,Phys. Rev.B 47, 5027 (1993).
modynamic sense. The ones between II-IV and III-IV [7] C. Sorg et al., Phys.Scripta, in press (2004).
are merely crossovers between thickness regions where [8] U. Bovensiepen et al.,Phys. Rev.Lett. 81, 2368 (1998);
A. Ney et al., Phys.Rev.B 59, R3938 (1999).
magnetic domains in one of the ferromagnetic films can
[9] R. W. Wang and D. L. Mills, Phys. Rev. B 46, 11 681
or cannot be detected. However, they are not accompa-
(1992).
nied by critical phenomena and by the (dis)appearance [10] P. J. Jensen et al.,J. Appl.Phys.87, 6692 (2000).
of an order parameter. As has been measured in [8] and [11] A. Scherzet al., J. Magn. Magn. Mater. 236, 1 (2001).
calculated in [1, 9, 10], the corresponding susceptibility [12] A. Scherzet al., J. Synchrotron Rad.8, 472 (2001).
exhibits a maximum (“resonance”) at those boundaries [13] P. Bruno, Phys. Rev.B 52, 411 (1995).