VOLUME 71, NUMBER 24 PHYSICAL REVIEW LETTERS 13 DECEMBER 1993 Magnetic Moments of Iron Clusters with 25 to 700 Atoms and Their Dependence on Temperature Isabelle M. L. Billas, J. A. Becker, * A. Chatelain, and Walt A. de Heer (Received l 5 July l 993) Magnetic moments p(N) of iron clusters in a molecular beam, with temperatures ranging from 100 to 1000 K, are investigated from their Stern-Gerlach deflections. We find that at a temperature of 120 K, p (25 ~ N ~ l 30) is 3pa per atom, decreasing to about the bulk value (2.2pa per atom) near N =500. For all sizes, p decreases with increasing temperature, and is approximately constant above a tempera- ture Tc(N). For example, Tc(130) is about 700 K, and Tc(550) is about 550 K (Tc bulk =l043 K). Limitations of the superparamagnetic model due to rotational eAects are discussed. PACS numbers: 75.50. Bb, 36. 40.+d, 61. 46.+w Ferromagnetism is caused by the spontaneous mutual alignment of magnetic moments. This effect, caused by the exchange interaction mediated by the itinerant elec- trons, is well understood in the bulk. However, much less is known about ferromagnetism in small systems such as thin films and very small particles or clusters. A fascinat- ing, still open question is how ferromagnetic properties evolve from the atom via clusters to the bulk. The molec- ular beam is ideally suited to study this problem [ll, but since most experiments in this interesting size regime have concentrated on very small ferromagnetic particles embedded in a host matrix [2], we first briefiy review some of their relevant properties. In a magnetic field 8, the magnetic moment p of a monodomain particle tends to align with B. However, thermal motion counteracts the alignment, so that in equilibrium the magnetization M is related to the temper- ature and field by M =pL(pB/kT), where L is the Langevin function [3]. By definition M is the average projection of p along the magnetic field direction: M =~lp B~//B. For small values of the argument this sim- plifies to M=p B/3kT. In this model the particles are treated as if they were paramagnetic with large magnetic moments (and hence are called superparamagnetic [4]). The large moment in turn is caused by the ferromagnetic alignment of the atomic moments po, so that (at low temperatures T) p = Npn [4], where N is the number of atoms in the par- ticle. However, p also depends on T and vanishes at a sufficiently high temperature. In earlier work we found that very small iron clusters are ferromagnetic. Furthermore, we observed that spin relaxation occurs even when the clusters are isolated in the molecular beam [1]. This was in fact unexpected since it contradicted an earlier similar experiment [5]. Spin relaxation in turn suggests a thermodynamic treat- ment, leading to the superparamagnetic model (however, see Ref. [6] for an alternative). In contrast, our experi- ments show a reversed temperature dependence when the clusters are cooled in the supersonic expansion of the source [1, 7]. We attributed these eA'ects to the cluster rotations. Curiously, when they are not thus cooled, the superparamagnetic model does apply [7]. In this Letter, we first investigate the applicability of the superparamag- netic model. This requires some background in superson- ic beam properties. Next we discuss the temperature dependence of the magnetic moments of iron clusters with 25 to 700 atoms. In our experiments clusters are formed in a laser vapor- ization cluster source with He carrier gas (see Refs. [1, 8] for detailed descriptions). In this source the nozzle tem- perature T„„can be adjusted between 100 and 1000 K. The beam is collimated and the clusters are deflected in the field of a Stern-Gerlach magnet. Deflections of mass selected clusters are measured using a time-of-flight mass spectrometer by sweeping the collimated ionizing light from an excimer laser across the cluster beam and syn- chronously recording the selected cluster ion intensity. The magnetization of the cluster is related to its deflec- tion by d =K(dB/dz)M/Nmov where d is the defiec- tion, v is the velocity, 1Vmo is the mass, K is a constant, and dB/dz is the field gradient in the Stern-Gerlach magnet. Cluster velocities and dwell times (see below) are determined using a beam chopper mounted in front of the source. In the laser vaporization cluster source a pulse of He gas fills a 1 cm cavity at time t=0, coincident with the laser pulse [8]. The clusters are formed and thermalize in the cavity within 1 ps [9, 10], after which the gas/ cluster mixture is ejected out of the nozzle. Hence the helium pressure in the cavity PH, is time dependent. In particular, from the He flow rates [9] we find that PH, (t) = Poe — (t — to)/r, where Po =100-200 Torr, to= 100 ps, and z = 150-200 ps. Clusters are selected depending on the time they exit the nozzle (i.e. , their dwell time r). This is important because the clusters are cooled due to the adiabatic expansion of the helium into the vacuum [9]. In particular, when the PH, is high, the beam is supersonic and the cooling is effective. The cool- ing is less effective when the pressures are reduced and ultimately, for very low PH, the clusters are not cooled [9]. (For brevity we call this source condition quasief- 0031-9007/93/71 (24)/4067 (4) $06.00 1993 The American Physical Society