crystal electric field (CEF) spin-orbit coupling

We present the results of non-free parameter calculations of properties of HoAl 2 and ErAl 2 single crystals, performed with our new computation system called ATOMIC MATTERS MFA [1, 2]. A localized electron approach was applied to describe the electronic structure evolution of Ho and Er ions over a wide temperature range and estimate Magnetocaloric Effect (MCE). Thermomagnetic properties of HoAl 2 and ErAl 2 were calculated based on the fine electronic structure of the 4f 10 and 4f 11 electronic configuration of the Ho and Er ions, respectively. Our calculations yielded: magnetic moment value and direction; single-crystalline magnetization curves in zero field and in external magnetic field applied in various directions m(T,B ext); the 4f-electronic components of specific heat c 4f (T,B ext); and temperature dependence of the magnetic entropy and isothermal entropy change with external magnetic field-S(T,B ext). The cubic universal CEF parameters values used for all CEF calculations was taken from [3] and recalculated for universal cubic parameters set for the RAl 2 series: A 4 =+7.164Ka 0 and A 6 =-1.038Ka 0. Magnetic properties were found to be anisotropic due to cubic Laves phase C15 crystal structure symmetry. These studies reveal the importance of multipolar charge interactions when describing thermomagnetic properties of real 4f electronic systems and the effectiveness of an applied self-consistent molecular field in calculations for magnetic phase transition simulation.

We present the results of non-free parameter calculations of properties of TbAl 2 and GdAl 2 single crystals, performed with our new computation system called ATOMIC MATTERS MFA [1,2]. A localized electron approach was applied to describe the electronic structure evolution of Tb and Gd ions over a wide temperature range and estimate Magnetocaloric Effect (MCE). Thermomagnetic properties of TbAl 2 and GdAl 2 were calculated based on the fine electronic structure of the 4f 8 and 4f 7 electronic configuration of the Tb and Gd ions, respectively. Our calculations yielded: magnetic moment value and direction; single-crystalline magnetization curves in zero field and in external magnetic field applied in various directions m(T,B ext); the 4f-electronic components of specific heat c 4f (T,B ext); and temperature dependence of the magnetic entropy and isothermal entropy change with external magnetic field-S(T,B ext). The cubic universal CEF parameters values used for all CEF calculations was taken from [3] and recalculated for universal cubic parameters set for the RAl 2 series: A 4 =+7.164Ka 0 and A 6 =-1.038Ka 0. Magnetic properties were found to be anisotropic due to cubic Laves phase C15 crystal structure symmetry. These studies reveal the importance of multipolar charge interactions when describing thermomagnetic properties of real 4f electronic systems and the effectiveness of an applied self-consistent molecular field in calculations for magnetic phase transition simulation.

We present the concept and scientific methods of a new computation system called ATOMIC MATTERS MFA. This computation system is useful for magnetocaloric effect (MCE) estimations for defined materials. ATOMIC MATTERS MFA provides magnetic, calorimetric and spectroscopic properties of atomic-like localized electron systems under the influence of Crystal Electric Field (CEF), spin-orbit coupling, and magnetic interactions, taken as both Mean Field Approximation (MFA) and the influence of external magnetic fields. ATOMIC MATTERS MFA provides macroscopic properties of materials in different temperature regions, especially around phase transition temperature, such as: magnetic moment (spin and orbit components), localized electron specific heat, localized electron entropy (with a useful tool set for MCE estimations), evolution of energy level positions, and total free energy temperature dependences in a definable temperature region. ATOMIC MATTERS MFA computation system is an extension of the ATOMIC MATTERS application, a system for describing fine electronic structure and predicting basic magnetic and spectral properties of materials.

We present the results of calculations of properties of DyAl2 single crystals performed with our new computation system called ATOMIC MATTERS MFA [1,2]. A localized electron approach methodology was applied to describe the electronic structure evolution of Dy ions over a wide temperature range and estimate Magnetocaloric Effect (MCE). Thermomagnetic properties of DyAl 2 were calculated based on the fine electronic structure of the 4f n9 configuration of the Dy atom. Our calculations yielded: magnetic moment value and direction; single-crystalline magnetization curves in zero field and in external magnetic field applied in various directions m(T,B ext); the 4f-electronic components of specific heat c 4f (T,B ext); and temperature dependence of the magnetic entropy and isothermal entropy change with external magnetic field-S(T,B ext). The cubic universal CEF parameters values used for all CEF calculations was taken from [3] and recalculated for universal cubic parameters set for the RAl 2 series A 4 =+7.164Ka 0 and A 6 =-1.038Ka 0. Magnetic properties were found to be anisotropic due to cubic Laves phase C15 crystal symmetry. These studies reveal the importance of multipolar charge interactions when describing thermomagnetic properties of real 4f electronic systems and the effectiveness of an applied self-consistent molecular field in calculations for magnetic phase transition simulation.

The single ionic properties of paramagnetic ions are the core magnetic properties of magnetic materials. We present examples of calculation results for compounds RE2Fe14B, RERu2Si2 and RENi5 (RE: rare earth element), generated with our computation systems ATOMIC MATTERS and ATOMIC MFA. The synergy of the ATOMIC MATTERS and ATOMIC MFA systems makes it possible to describe magnetic, calorimetric, and spectroscopic properties of atomic-like localized electron systems that are subject to electrostatic interactions taken as Crystal Electric Field (CEF), spin-orbit coupling, and magnetic interactions, taken as both Mean Field Approximation (MFA) and external magnetic fields. Our solution applies to situations in which any unclosed electron subshell of an ion interacts with the electrostatic potential of definable symmetry and the magnetic field comes from induced moments of identical paramagnetic neighbors. In this paper, we present some 4f (rare earth) cases of hard magnetic materials. Based on CEF and MFA theoretical methods, we are able to analyze the magnetization process and magnetic phase transition of materials as a function of temperature and an external magnetic field. These calculation systems make it possible to predict macroscopic properties such as magnetic moment (spin, orbit and total, and its directional components), localized electron specific heat cmol (both Schottky-like type and -type), magnetic entropy, magneto-crystalline anisotropy constants Ki(T), energy levels and total free energy as temperature dependences in a definable region of temperature, including the phase-transition region. We emphasize the importance of symmetry of charge surroundings of an atom/ion, spin-orbit interactions (spin-orbit coupling) and the use of complex number matrices in the definition of the Hamiltonian. Our computation systems make it possible to understand existing materials and are useful for developing new materials for permanent magnet technology.

We present the concept and scientific methods of a new computation system called ATOMIC MATTERS MFA. This computation system is useful for magnetocaloric effect (MCE) estimations for defined materials. ATOMIC MATTERS MFA provides magnetic, calorimetric and spectroscopic properties of atomic-like localized electron systems under the influence of Crystal Electric Field (CEF), spin-orbit coupling, and magnetic interactions, taken as both Mean Field Approximation (MFA) and the influence of external magnetic fields. ATOMIC MATTERS MFA provides macroscopic properties of materials in different temperature regions, especially around phase transition temperature, such as: magnetic moment (spin and orbit components), localized electron specific heat, localized electron entropy (with a useful tool set for MCE estimations), evolution of energy level positions, and total free energy temperature dependences in a definable temperature region. ATOMIC MATTERS MFA computation system is an extension of the ATOMIC MATTERS application, a system for describing fine electronic structure and predicting basic magnetic and spectral properties of materials.