The standard experimental set-up enabling observation of rotational motion of a bar around its centre of mass, which is set into motion due to the external torque generated by the small weight, was extended with an optical gate and position sensor and connected to a computer with software, which made it possible to display measured values of bar half-rotations during accelerated and decelerated motion as well as to process the data immediately. The detailed analysis of experimental data obtained for decelerated rotational motion due to frictional torque only (without small weight) showed that, besides the constant term due to dry friction at an axle, the expression for friction forces in the system has to include terms depending on the first and/or second power of angular speed, which is evidence that viscous forces influence the motion of a bar. The frictional torque due to viscous forces can be evaluated as the difference between the effective frictional torque acting on the system and the frictional torque due to dry friction at an axle. The data obtained in the experiment in which the bar performed damped oscillatory motion provided the values of effective frictional torque and the moment of inertia of rotating bodies. The frictional torque due to dry friction can be obtained as a minimum torque (calculated using minimum mass of weight) needed to start rotational motion. The last two proposed experiments can be included in undergraduate laboratory practicals.
The ferromagnetic phase transition in ultra thin films is studied by the many body Green's function method based upon the Heisenberg model with the different surface exchange couplings with respect to bulk one plus a surface second order uniaxial anisotropy. The critical temperature of the system is studied as a function of the ratio S S J J ∆ = / of the surface exchange couplings to the bulk ones and as a function of the surface single ion anisotropic strength K (cross over points). If, the critical temperature of the thin film is larger than the bulk one. We analyse various possible configurations for the surface exchange couplings S J and the surface single ion anisotropic strength
The reorientation temperature in an antiferromagnetic square lattice is studied within the framework of many-body Green function theory. The model Hamiltonian includes a Heisenberg term, second-order single-ion anisotropy, and a transverse external magnetic field in the x-direction. We investigate the orientation temperature as a function of the single-ion anisotropy parameter and for different transverse magnetic fields.
Green's function theory is applied to an alternating two-element multilayer ferromagnetic film. The Hamiltonian is based on the Heisenberg model with a second-order uniaxial single-ion anisotropy and with the interaction between the layer in the interfaces. Magnetization and the phase transition in such system are derived for several sets of material parameters.
Within the framework of many-body Green's function theory there are studied the properties of the quantum Blume-Capel model for ferromagnetic films with an alternating single-ion anisotropy on the odd atomic layers and on the even ones. We analyse various possible phase diagrams for the surface exchange couplings and the single-ion anisotropy parameters. Model and methodThe ferromagnetic Blume-Capel-Ising (BCI) model has been studied within the mean field approximation [1], the effective field theory [2], the two-spin cluster approximation in the cluster expansion method [3,4], Monte Carlo simulations [5], a thermodynamically self-consistent theory based on an Ornstein-Zernike approximation [6], the exact solution based on the Bethe lattice by means of the exact recursion relations [7]. Most of the studies mentioned above displays also the existence of a tricritical point at which the phase transition changes from second order to first order when the value of K 2 becomes negative. Our work represents the first atempt to consider a quantum version of BCI model. Within quantum Blume-Capel (QBC) model we will study the influence of the enhancement of the surface exchange coupling and the alternative single-ion anisotropy K 2 (1) on the odd atomic layers and K 2 (2) on the even ones on the critical behaviour of thin ferromagnetic films.The Hamiltonian of the considered system consists a Heisenberg exchange interaction with strength J ij > 0 between nearest neighbour lattice sites, an exchange anisotropy with strength D > 0, and a second-order single-ion anisotropy with strength K 2 > 0: (197)
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.