Related Experiment Video
Updated: Jun 30, 2025
![Measuring the Spin-Lattice Relaxation Magnetic Field Dependence of Hyperpolarized [1-13C]pyruvate](/_next/image?url=https%3A%2F%2Fcloudfront.jove.com%2FCDNSource%2Fteasers%2F59399.jpg&w=3840&q=50)
Measuring the Spin-Lattice Relaxation Magnetic Field Dependence of Hyperpolarized [1-13C]pyruvate
Published on: September 13, 2019
Effectiveness of the recursive-lattice technique in the investigation of magnetic systems with the pyrochlore
1Institute of Experimental Physics, Slovak Academy of Sciences, Watsonova 47, 040 01 Košice, Slovakia.
Abstract:
A well-defined higher recursive approximation of the pyrochlore lattice is introduced and its relevance and effectiveness for the systematic investigation of magnetic systems with the pyrochlore structure is studied within the classical antiferromagnetic as well as ferromagnetic spin-1/2 Ising model in the presence of the external magnetic field. The exact solution of the model is found with the explicit analytic expression for the free energy per site of the lattice. The magnetization and entropy properties of all ground states of the antiferromagnetic model are determined and compared to those obtained within the lower recursive approximation of the model on the recursive tetrahedral lattice. The exact analysis of the residual entropies of the model on the introduced recursive lattice explicitly shows that the well-known Pauling entropy of the water ice cannot represent the true residual entropy of the antiferromagnetic model on the regular pyrochlore lattice in the zero external magnetic field. The improvement of the value of the critical temperature of the ferromagnetic model obtained within the introduced higher recursive approximation is also discussed. The analysis performed demonstrates the great efficiency of recursive approximations in the investigation of various magnetic systems with the pyrochlore structure, especially for frustrated antiferromagnetic systems.
More Related Videos
08:55Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses
Published on: June 7, 2018
06:53Author Spotlight: Magnetometric Characterization of Intermediates in the Solid-State Electrochemistry of Redox-Active Metal-Organic Frameworks
Published on: June 9, 2023
Related Concept Videos
02:42Valence Bond Theory
03:02Colors and Magnetism
When atoms or molecules absorb light at the proper frequency, their electrons are excited to higher-energy orbitals. For many main group atoms and molecules, the absorbed photons are in the ultraviolet range of the electromagnetic spectrum, which cannot be detected by the human eye. For coordination compounds, the energy difference between the d orbitals often allows photons in the visible range to be absorbed and emitted, which is seen as colors by the human...
01:05Atomic Nuclei: Magnetic Resonance
02:54Trends in Lattice Energy: Ion Size and Charge
01:31Ferromagnetism
02:58Crystal Field Theory - Octahedral Complexes
To explain the observed behavior of transition metal complexes (such as colors), a model involving electrostatic interactions between the electrons from the ligands and the electrons in the unhybridized d orbitals of the central metal atom has been developed. This electrostatic model is crystal field theory (CFT). It helps to understand, interpret, and predict the colors, magnetic behavior, and some structures of coordination compounds of transition metals.
CFT focuses on...