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).