VOLUME 80, NUMBER 1 PHYSICAL REVIEW LETTERS 5JANUARY 1998 Blocking and Freezing of Magnetic Moments for Iron Nitride Fine Particle Systems H. Mamiya, I. Nakatani, and T. Furubayashi National Research Institute for Metals, Tsukuba 305, Japan (Received 28 July 1997) Equilibrium susceptibility x eq of frozen iron nitride magnetic fluids is estimated as the convergent value of the relaxation curves for various initial states. In the lower temperature range in which the field cooled susceptibility x FC shows a plateau, x eq of the dense sample is nearly the same as x FC , while x eq of the diluted sample increases with decreasing temperature. These indicate that blocked moments are observed for the isolated particles owing to a finite measurement time and that the magnetic moments of the interacting particles freeze cooperatively as seen in a spin glass. [S0031-9007(97)04918-1] PACS numbers: 75.50.Lk, 75.50.Mm Glassy behavior due to random anisotropy and dipo- lar interactions has been intensively investigated in ferro- magnetic fine particle systems [1–3]. However, there is little agreement as to the existence of the spin glasslike phase. One reason is that most properties for the coop- erative freezing of spin glass are similar to those for the blocking of isolated particles in appearance. For example, a plateau for the temperature dependence of the field cooled susceptibility has been observed for both systems. Recently, typical spin glass dynamics has been observed in a concentrated system of g-Fe 2 O 3 fine particles by Jon- sson et al., where the relaxation depends on the time spent at constant temperatures before applying the magnetic field [4]. However, the existence of this dynamics does not by itself imply that there is a thermodynamic spin glass phase. To distinguish a thermodynamic phase from a nonequilib- rium state, the equilibrium properties, in addition to critical phenomena, should be examined. In the spin glass phase, it is known that the equilibrium susceptibility x eq is almost independent of the temperature, and that the nonlinear sus- ceptibility x 2 diverges at the transition. On the other hand, x eq of the blocked magnetic moments is predicted not to be constant and to be superparamagnetic. In this Letter, x eq and x 2 are estimated and the results for isolated particles and interacting particles are compared with the superpara- magnetic model and spin glass. The samples are iron nitride e-Fe 3 N magnetic fluids with kerosene as the carrier liquid [5]. Band structure calculation [6] has shown that e-Fe 3 N is a ferromagnetic substance with magnetic moment per Fe of about 1.9m B and that the easy axis is along the c axis of the hexagonal structure. Electron microscopy shows that the particles have isotropic shapes and uniform size, as shown in Fig. 1. There is a single domain within each particle for this size. Therefore, we can take the magnetization of each particle as a rigid dipole moment m [the mean value is mT ]. The small angle x-ray scattering profiles show no particle agglomeration. Measurements were made on samples cooled in a zero field to 150 K below the freezing point for kerosene. These samples, therefore, are randomly oriented single-domain particles embedded in solidified kerosene. Sample d1 is an as-prepared magnetic fluid and the other samples d2, d3, d4, d5, d6, d7, and d8 are its dilution. We note that the dilution changes only the strength of the dipolar interaction. Saturation magnetization M s , which is equal to N mT , increases with the decreasing temperature (about 20% between 5 and 300 K), where N is the particle number density. The magnitude of M s at 300 K is 29.1, 16.3, 7.80, 5.31, 2.10, 0.87, 0.57, and 0.32 emucm 3 for d1, d2, d3, d4, d5, d6, d7, and d8, respectively. Magnetization M was measured by using an extraction method in a field range between 10 and 60 Oe. In low fields (,6 Oe), which were generated by a normal conducting coil and were checked by a fluxgate sensor, M was measured by using a SQUID magnetometer in a permalloy magnetic shield. The temperature dependence of zero field cooled (ZFC) and field cooled (FC) magne- tization was measured in the temperature range between 5 and 150 K in various applied fields. Measurements were made for samples d1, d2, and d3 contained in the cylindrical cells, whose demagnetizing factors N d are FIG. 1. Particle diameter distribution on an electron micro- graph of the iron nitride fine particles. The scale on the upper axis shows the blocking temperature T B calculated for each par- ticle size from Eq. (1). 0031-9007 98 80(1) 177(4)$15.00 © 1997 The American Physical Society 177