A definition of the magnetic transition temperature using valence bond theory

Macroscopic magnetic properties are analyzed using Valence Bond theory. Commonly the critical temperature TC for magnetic systems is associated with a maximum in the energy-based heat capacity Cp(T). Here a more broadly applicable definition of the magnetic transition temperature TC is described using spin moment expectation value (i.e. applying the spin exchange density operator) instead of energy. Namely, the magnetic capacity Cs(T) reflects variation in the spin multiplicity as a function of temperature, which is shown to be related to ∂[χT(T)]/∂T. Magnetic capacity Cs(T) depends on long-range spin interactions that are not relevant in the energy-based heat capacity Cp(T). Differences between Cs(T) and Cp(T) are shown to be due to spin order/disorder within the crystal, that can be monitored via a Valence Bond analysis of the corresponding magnetic wavefunction. Indeed the concept of the Boltzmann spin-alignment order is used to provide information about the spin correlation between magnetic units. As a final illustration, the critical temperature is derived from the magnetic capacity for several molecular magnets presenting different magnetic topolo- gies that have been experimentally studied. A systematic shift between the transition temperatures associated with Cs(T) and Cp(T) is observed. It is demonstrated that this shift can be attributed to the loss of long-range spin correlation. This suggests that the magnetic capacity Cs(T) can be used as a predictive tool for the magnetic topology, and thus for the synthetic chemists

Pitfalls on evaluating pair exchange interactions for modelling molecule-based magnetism

Molecule-based magnetism is a solid-state property that results from the microscopic interaction between magnetic centres or radicals. The observed magnetic response is due to unpaired electrons whose coupling leads to a particular magnetic topology. Therefore, to understand the magnetic response of a given molecule-based magnet and reproduce the available experimental magnetic properties by means of statistical mechanics, one has to be able to determine the value of the JAB magnetic exchange coupling between radicals. The calculation of JAB is thus a key point for modelling molecule-based magnetism. In this Perspectives article, we will build upon our experience in modelling molecular magnetism to point out some pitfalls on evaluating JAB couplings. Special attention must be paid to the cluster models used to evaluate JAB, which should account for cooperative effects among JAB interactions and also consider the environment (counterions, hydrogen bonding) of the two radicals whose interaction has to be evaluated. It will be also necessary to assess whether a DFT-based or a wavefunction-based method is best to study a given radical. Finally, in addition to model and method, the JAB couplings have to be able to adapt to changes in the magnetic topology due to thermal fluctuations. Therefore, it is most important to appraise in which systems molecular dynamics simulations would be required. Given the large number of issues one must tackle when choosing the correct model and method to evaluate JAB interactions for modelling magnetic properties in molecule-based materials, the “human factor” is a must to cross-examine and challenge computations before trusting any result

Satellite ligand effects on magnetic exchange in dimers. A structural, magnetic and theoretical investigation of Cu2L2X4 (L = methylisothiazolinone and X = Cl−, Br−)

Halide-bridged polymers have gained significant interest due to their diverse properties and potential applications. Stacked Cu2L2X4 dimers, where L is an organic ligand and X can be Cl− or Br−, are of interest because a chloride analogue where L = 2-pyridone, had previously been reported to exhibit bulk ferromagnetism, which augured great potentiality for this class of compounds. The synthesis, structural characterization, magnetic susceptibility measurements, and computational studies of two isostructural CuClMI (MI = methylisothiazolinone) and CuBrMI polymers of Cu(ii), along with a related CuClPYR (PYR = 2-pyridone) is reported. CuClMI and CuBrMI were found to exhibit AFM bulk properties, due to FM/AFM alternating chains along the halide-bridged polymer axis, while FM bulk properties were confirmed for CuClPYR exhibiting a FM spin ladder. In combination with a benzamide analogue, CuClBA, three O-donor amides, CuClMI, CuClBA and CuClPYR were analyzed and revealed that the kinetic exchange is affected by the identity, but more importantly, the orientation of the satellite ligands. The torsional angle of the ligand with the dimer plane is shown to significantly affect the magnetic exchange in the dimer, and between dimers, explaining the reported FM bulk properties of CuClPYR. This finding is exceedingly important, as it suggests that a spin device can be constructed to flip between singlet/triplet states by manipulating the orientation of the satellite/terminal ligand. © 2023 The Royal Society of Chemistry. This article includes supplementary data, also available for download

Revising the common understanding of metamagnetism in the molecule-based bisdithiazolyl BDTMe compound

The BDTMe molecule-based material is the first example of a thiazyl radical to exhibit metamagnetic behavior. Contrary to the common idea that metamagnetism occurs in low-dimensional systems, it is found that BDTMe magnetic topology consists of a complex 3D network of almost isotropic ferromagnetic spin-ladders that are coupled ferromagnetically and further connected by some weaker antiferromagnetic interactions. Calculated magnetic susceptibility χT(T) data is in agreement with experiment. Calculated M(H) data clearly show the typical sigmoidal shape of a metamagnet at temperatures below 2 K. The calculated critical field becomes more apparent in the dM/dH(H) plot, being in very good agreement with experiment. Our computational study concludes that the magnetic topology of BDTMe is preserved throughout the entire experimental range of temperatures (0–100 K). Accordingly, the ground state is the same irrespective of the temperature at which we study the BDTMe crystal. Revising the commonly accepted understanding of a metamagnet explained as ground state changing from antiferromagnetic to ferromagnetic, the Boltzmann population of the different states is here suggested to be the key concept: at 2 K the ground singlet state has more weight (24%) than at 10 K (1.5%), where excited states have an important role. Changes in the antiferromagnetic interactions that couple the ferromagnetic skeleton of BDTMe will directly affect the population of the distinct states that belong to a given magnetic topology and thus its magnetic response. Accordingly, this strategy could be valid for a wide range of bisdithiazolyl BDT-compounds whose magnetism can be tuned by means of weak antiferromagnetic interactions

Satellite ligand effects on magnetic exchange in dimers. A structural, magnetic and theoretical investigation of Cu2L2X4 (L = methylisothiazolinone and X = Cl-, Br-)

Halide-bridged polymers have gained significant interest due to their diverse properties and potential applications. Stacked Cu2L2X4 dimers, where L is an organic ligand and X can be Cl or Br , are of interest because a chloride analogue where L = 2-pyridone, had previously been reported to exhibit bulk ferromagnetism, which augured great potentiality for this class of compounds. The synthesis, structural characterization, magnetic susceptibility measurements, and computational studies of two isostructural CuClMI (MI = methylisothiazolinone) and CuBrMI polymers of Cu(II), along with a related CuClPYR (PYR = 2-pyridone) is reported. CuClMI and CuBrMI were found to exhibit AFM bulk properties, due to FM/AFM alternating chains along the halide-bridged polymer axis, while FM bulk properties were confirmed for CuClPYR exhibiting a FM spin ladder. In combination with a benzamide analogue, CuClBA, three O-donor amides, CuClMI, CuClBA and CuClPYR were analyzed and revealed that the kinetic exchange is affected by the identity, but more importantly, the orientation of the satellite ligands. The torsional angle of the ligand with the dimer plane is shown to significantly affect the magnetic exchange in the dimer, and between dimers, explaining the reported FM bulk properties of CuClPYR. This finding is exceedingly important, as it suggests that a spin device can be constructed to flip between singlet/triplet states by manipulating the orientation of the satellite/terminal ligand.The University of Pretoria, Sasol, the National Research Foundation, PCI Synthesis Inc., the Kresge Foundation, the Spanish Ministerio de Economía y Competitividad, Spanish Structures of Excellence María de Maeztu program and Generalitat de Catalunya.http://pubs.rsc.org/en/Journals/JournalIssues/CPam2024ChemistryNon

Constrained clipping for peak power reduction of multicarrier systems by tone reservation

In this paper we introduce a new method to limit the peak factor of a multicarrier signal based on tone reservation. A peak-reducing signal is computed by clipping the original OFDM symbol. The peak-reducing signal is forced to have the constraints of tone reservation, so that when added to the original signal, the peak factor is reduced without increasing the BER and the out-of-band radiation. The proposed method has low computational complexity requirements and is fast-converging. Moreover, simulation results show that it has higher PAPR-reduction capabilities than other PAPR-reducing methods based on TR in the literature. © 2007 IEEE

A definition of the magnetic transition temperature using valence bond theory

Macroscopic magnetic properties are analyzed using Valence Bond theory. Commonly the critical temperature TC for magnetic systems is associated with a maximum in the energy-based heat capacity Cp(T). Here a more broadly applicable definition of the magnetic transition temperature TC is described using spin moment expectation value (i.e. applying the spin exchange density operator) instead of energy. Namely, the magnetic capacity Cs(T) reflects variation in the spin multiplicity as a function of temperature, which is shown to be related to ∂[χT(T)]/∂T. Magnetic capacity Cs(T) depends on long-range spin interactions that are not relevant in the energy-based heat capacity Cp(T). Differences between Cs(T) and Cp(T) are shown to be due to spin order/disorder within the crystal, that can be monitored via a Valence Bond analysis of the corresponding magnetic wavefunction. Indeed the concept of the Boltzmann spin-alignment order is used to provide information about the spin correlation between magnetic units. As a final illustration, the critical temperature is derived from the magnetic capacity for several molecular magnets presenting different magnetic topolo- gies that have been experimentally studied. A systematic shift between the transition temperatures associated with Cs(T) and Cp(T) is observed. It is demonstrated that this shift can be attributed to the loss of long-range spin correlation. This suggests that the magnetic capacity Cs(T) can be used as a predictive tool for the magnetic topology, and thus for the synthetic chemists