PHYSICAL REVIEW B 100, 104419 (2019) Competing cubic and uniaxial anisotropies on the energy barrier distribution of interacting magnetic nanoparticles Marcelo Salvador * and Lucas Nicolao † Departamento de Física, Universidade Federal de Santa Catarina, Campus Universitário, Trindade, 88040-900 Florianópolis, Santa Catarina, Brasil W. Figueiredo ‡ Departamento de Física, Universidade Federal de Santa Catarina, Campus Universitário, Trindade, 88040-900 Florianópolis, Santa Catarina, Brasil and Instituto de Física, Universidade de São Paulo, Rua do Matão, 1371, 05508-090 São Paulo, São Paulo, Brasil (Received 6 July 2019; revised manuscript received 22 August 2019; published 16 September 2019) We study the magnetic behavior of a two-dimensional set of interacting magnetic nanoparticles. The single- domain nanoparticles exhibit competing cubic and uniaxial anisotropies, and they interact themselves through long-range dipolar interactions. We employ the stochastic Landau-Lifshitz-Gilbert equation to describe the time evolution of the magnetic moments of the system. We determine the magnetic relaxation of the system as a function of the ratio between cubic and uniaxial anisotropies, and from the strength of dipolar coupling. From the relaxation curves we calculate the effective energy barrier distribution by considering both situations where the uniaxial axes are completely aligned or randomly oriented relative to an external magnetic field. When the axes are randomly oriented, two peaks are observed in the distribution of energy barriers depending on the ratio of cubic and uniaxial anisotropies, as well as on the intensity of dipolar coupling. Through the zero-field-cooled curves we also determine the blocking temperature of the system and we show that it increases both with the ratio between the cubic and uniaxial anisotropies, as well as with the magnitude of dipolar interactions. DOI: 10.1103/PhysRevB.100.104419 I. INTRODUCTION The study of single-domain magnetic nanoparticles started around the middle of the last century with the pioneering studies of Stoner and Wohlfarth [1], Nèel [2], and Brown [3] concerning the magnetization reversal of the individual magnetic nanoparticles across energy barriers due to thermal fluctuations. After the synthesis of the first single-domain magnetic nanoparticles [4–6] the theoretical predictions were finally confirmed. Since then, magnetic nanoparticles have been synthesized with specific properties that can be applied in many different areas of science, ranging from engineering to medicine [7–11]. Single-domain magnetic nanoparticles [12] are formed by hundreds or thousands of individual magnetic moments coupled by exchange interactions. The magnetic energy of an isolated nanoparticle can generally be described by uniaxial and cubic anisotropy contributions [13,14]. However, when they are put together, the long-range dipolar coupling appears among them, the strength of which increases with the concentration of the system. The role played by these dipolar interactions in the magnetic properties of magnetic nanoparticles is still not completely understood. For instance, we find in the literature some conflicting trends concerning the effects of dipolar interactions on the blocking * celofsco@gmail.com † lucas.nicolao@gmail.com ‡ wagner.figueiredo@ufsc.br temperature of a system of magnetic nanoparticles [15]. In some studies the blocking temperature increases with the strength of the dipolar interactions [16–18], while in other studies it decreases [19,20]. In this work we investigate the role played by dipolar interactions in the magnetic properties of a set of interacting magnetic nanoparticles in a square lattice. The single-domain magnetic nanoparticles exhibit uniaxial and cubic anisotropies and the particle sizes are selected from a log-normal distri- bution. By employing the stochastic Landau-Lifshitz-Gilbert equation we determine the time evolution of the magneti- zation of the system, from which we are able to build the zero-field-cooled (ZFC) magnetization curve as a function of temperature for different values of the ratio between uniaxial and cubic anisotropies, as well as the magnitude of the dipo- lar couplings. We show that the blocking temperature is an increasing function of the strength of the dipolar coupling and also of the ratio between the cubic and uniaxial anisotropies. We also determine the thermal magnetic relaxation curve of the system as a function of the time and temperature. From these curves we find the corresponding effective energy barrier distribution, which is determined in the cases both where the uniaxial axes of the anisotropy are parallel, as well as randomly oriented relative to an external magnetic field. As in the previous studies of noninteracting systems [21] we find two peaks in the energy barrier distribution only when the uni- axial axes are randomly distributed in space. For the uniaxial axes parallel to the magnetic field we find only a single broad peak. For the case of interacting magnetic nanoparticles our 2469-9950/2019/100(10)/104419(7) 104419-1 ©2019 American Physical Society