IEEE TRANSACTIONS ON MAGNETICS, VOL. 50, NO. 11, NOVEMBER 2014 2303304 Dynamics in Superspin Glass Systems Davide Peddis 1 , Marianna Vasilakaki 2 , K. N. Trohidou 2 , and D. Fiorani 1 1 Consiglio Nazionale delle Ricerche, Instituto di Struttura della Materia, Rome 00133, Italy 2 Institute of Advanced Materials Physicochemical Processes Nanotechnology and Microsystems, Institute of Nanoscience and Nanotechnology, National Center for Scientific Research Demokritos, Athens 15310, Greece The out-of-equilibrium dynamical properties of two very different superspin glass systems are discussed: 1) MnFe 2 O 4 nanoparticles, in powder form, with very strong dipolar interactions and 2) a system consisting of a film of Co particles dispersed (5%–10% volume filling fraction) in an Mn matrix, where interparticle interactions are mainly mediated by the matrix. In the latter system, the influence of interface exchange coupling between the ferromagnetic particles and the antiferromagnetic matrix on the out-of-equilibrium dynamics is discussed. Index Terms—Exchange bias (EB), out-of-equilibrium dynamics, superspin glass (SSG). I. I NTRODUCTION I N A magnetic nanoparticle system, the thermal evo- lution of the dynamics depends on the particle con- centration and the nature of the interparticle interactions. In sufficiently concentrated systems, strong dipolar interac- tions combined with random orientation of anisotropy axes determine a competition between different moment align- ments leading to a collective freezing of particle moments in a disordered magnetic state, known as superspin glass (SSG), below a characteristic freezing temperature (T f ) [1], [2]. A SSG exhibits slow magnetization dynamic that is qualitatively indistinguishable from that observed in atomic spin glasses (SGs). On the other hand, being the collective freezing between particle moments rather than between atomic spins, the dynamics in SSG is much slower, as the microscopic flip time of one superspin (in the order of 10 -9 s at room temperature and up to 10 -6 in the frozen state at low temperature) is much longer than an atomic spin flip time (in the order of 10 -12 s). The growth of dynamical correlation length is slower in SSG, and thus the slower dynamics of these systems is of particular interest because a much shorter time scale becomes experimental accessible [3]–[5]. The dynamical properties below T f are characterized by ageing and memory effects, which are manifestation of an out-of-equilibrium state, associated to the onset of a random collective state of particle moments. As in SG, even in SSG, it was observed a slowing down of the relaxation of the Zero Field Cooled (ZFC) magnetization with increasing the time spent at a constant temperature (waiting time, t w ) below T f , before the application of the magnetic field [6]. This reflects the slow evolution of the system towards an equilibrium configuration, during the aging, starting at the time of the quench below T f . SSG behavior of nanoparticle has been recently observed also in diluted systems, where ferromagnetic (FM) nanoentities are embedded in an antiferromagnetic (AFM) matrix that transmits an effective long-range interparticle interaction [7]–[9]. These systems are particularly interesting because the exchange cou- pling at the FM/AFM interface, dependent on the particle size, Manuscript received March 7, 2014; accepted May 2, 2014. Date of current version November 18, 2014. Corresponding author: D. Fiorani (e-mail: dino.fiorani@ism.cnr.it). Digital Object Identifier 10.1109/TMAG.2014.2327384 induces an additional anisotropy (exchange bias, EB) [10]. The EB provides a tool of tuning the magnetic anisotropy, and thus SSG systems exhibiting EB [10] deserve a partic- ular interest [7], [11]. In this paper, the dynamical proper- ties of two basically different SSG systems are discussed: 1) MnFe 2 O 4 nanoparticles, in powder form, with strong dipolar interactions responsible for the collective freezing as in a typical SSG system and 2) Co particles dispersed (5%–10% volume filling fraction, VFF) in a Mn matrix, where interparticle interactions are mainly mediated by the matrix. In the latter system, Monte Carlo (MC) simulations results are also presented, highlighting the correlation between FM/AFM interface exchange coupling and the magnetization dynamics of nanoparticles assembly. II. EXPERIMENT A. Magnetization Measurements The dc magnetization measurements were performed by a QuantumDesign SQUID magnetometer ( H max = 5 T). B. MC Simulations For the simulation of the Co@Mn system, we consider an assembly of spherical nanoparticles. Each nanoparticle has an FM core and an AFM disordered shell morphology, and it is located randomly on the nodes of a hexagonal lattice inside a box. The nanoparticle assembly is assumed monodispersed in accordance with the low size dispersion characterizing films grown by cluster beam technique [8]. We use a mesoscopic model of six spins to simulate each nanoparticle in the assembly: one spin for the FM core, one spin for the FM interface, two spins for the AFM shell, and two spins for the AFM interface [12]. The energy of the system includes the anisotropy energy of the core (with anisotropy energy constant K C = 0.1), the interface ( K IF = 0.5), and the shell ( K SH = 1.0), the intraparticle nearest neighbors Heisenberg- type exchange interactions of the spins in the core (with exchange energy strength J C = 1.0 taken as the reference value of the pure FM core), at the interface ( J IF = 0.5), and in the shell ( J SH =-0.5), and the interparticle dipolar interactions (dipolar strength g = 0.6). The energy parameters for the anisotropy and exchange interaction strength are based 0018-9464 © 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.