R. Schumann

Angular dependence of the coercive force of textured rare earth permanent magnets

Abstract On the basis of model calculations experimental results on the angular dependence of the coercivity H c and the remanence coercivity H R of hard magnetic materials of the type SmCo 5 , Sm 2 (Co, Fe, Cu, Zr) 15 and Nd 2 Fe 14 B are discussed. In the model coherent rotation as well as incoherent magnetization jumps (e.g. 180°-Bloch walls) are included. The texture is described by an axial symmetric distribution of the easy axes with only oneparameter. For Sm 2 (Co, Fe, Cu, Zr) 15 the model explains irreversible ( H R (θ)-curves) as well as reversible ( H R ( θ )− H c ( θ )) magnetization processesin good agreement with the experiments, whereas stronger deviations exist for SmCo 5 and Nd 2 Fe 14 B, especially in the H c (θ)-curves. These deviations should be caused by other reversible magnetization processes

Thermodynamics of a 4-site Hubbard model by analytical diagonalization

By use of the conservation laws a four-site Hubbard model coupled to a particle bath within an external magnetic field in z-direction was diagonalized. The analytical dependence of both the eigenvalues and the eigenstates on the interaction strength, the chemical potential and magnetic field was calculated. It is demonstrated that the low temperature behaviour is determined by a delicate interplay between many-particle states differing in electron number and spin if the electron density is away from half-filling. The grand partition sum is calculated and the specific heat, the susceptibility as well as various correlation functions and spectral functions are given in dependence of the interaction strength, the electron occupation and the applied magnetic field. For both the grand canonical and the canonical ensemble the high-temperature crossing points of the specific heat are calculated. Whereas in the weak correlation regime the universal value calculated by second order perturbation theory for several Hubbard systems being in the thermodynamic limit is confirmed, these crossing points vanish for intermediate to strong correlation.

Theory of thermal remagnetization of permanent magnets

Abstract A self-consistent mean-field theory explaining the thermal remagnetization (TR) of polycrystalline permanent magnets is given. The influence of the environment of a grain is treated by an inclusion approximation, relating the field inside the grain to the local field outside by means of an internal demagnetization factor n . For the switching fields and the fluctuations of the local fields around the mean field, Gaussian distributions of widths σ s , and σ f , respectively, are assumed. The isothermal hysteresis curve, the recoil curves, and the TR dependent on the model parameters n , σ s , and σ f are calculated. Furthermore, the influence of the initial temperature and the strong dependence of the TR on the demagnetization factor of the sample are studied, and it is shown that for reasonable parameter sets TR effects up to 100% are possible. The theoretical results correspond well with the experimental situation.

Analytical solution of a Hubbard model extended by nearest neighbour Coulomb and exchange interaction on a triangle and tetrahedron

The Hubbard model extended by either nearest-neighbour Coulomb correlation and/or nearest neighbour Heisenberg exchange is solved analytically for a triangle and tetrahedron. All eigenvalues and eigenvectors are given as functions of the model parameters in a closed form. The groundstate crossings and degeneracies are discussed both for the canonical and grand-canonical energy levels. The grand canonical potential and the electron occupation of the related cluster gases were calculated for arbitrary values (attractive and repulsive) of the three interaction constants. In the pure Hubbard model we found various steps in the electron occupation higher than one. It is shown that the various degeneracies of the grand-canonical energy levels are partially lifted by an antiferromagnetic exchange interaction, whereas a moderate ferromagnetic exchange modifies only slightly the results of the pure Hubbard model. A repulsive nn Coulomb correlation lifts these degeneracies completely. The relation of the cluster gas results to extended systems is discussed.

On the irreversible susceptibility of a textured Stoner-Wohlfarth ensemble

For models containing both reversible and irreversible magnetization processes the time-dependent irreversible susceptibility and the differentiated remanence curve differ from each other. To demonstrate this, both quantities were calculated for a non-interacting Stoner-Wohlfarth ensemble in dependence on the degree of alignment, the magnitude and the application time of an opposite field. For the differentiated remanence curve at t = 0 s an analytical expression was derived. For general times the calculation was carried out numerically.

The Hubbard model extended by nearest-neighbor Coulomb and exchange interaction on a cubic cluster – rigorous and exact results

The Hubbard model on a cube was revisited and extended by both nearest-neighbor (nn) Coulomb correlation and {nearest-neighbor} Heisenberg exchange. The complete eigensystem was computed exactly for all electron occupancies and all model parameters ranging from minus infinity to plus infinity. For two electrons on the cluster the eigensystem is given in analytical form. For six electrons and infinite on-site correlation U we determinded the groundstate and the groundstate energy of the pure Hubbard model analytically. For fixed electron numbers we found a multitude of ground state level crossings in dependence on the various model parameters. Furthermore the groundstates of the pure Hubbard model in dependence on a magnetic field h coupled to the spins are shown for the complete U-h plane. For the cubic cluster gas we calculated the density

Rigorous solution of a Hubbard model extended by nearest-neighbour Coulomb and isotropic exchange interaction on a triangle and tetrahedron

n(\mu,T,h)

Investigation of the thermal remagnetization in sintered hard magnets

and the thermodynamical density of states from the grand potential. The ground states and the various spin-spin correlation functions are studied for both attractive and repulsive values of the three interaction constants. The anomalous degeneration lines are calculated. For the cases where these lines end in triple points we give the related parameter values. The influence of the nn-exchange and the nn-Coulomb correlation onto the anomalous degeneration is discussed.

The charge-transfer gap within the Gutzwiller approximation

The Hubbard model extended by both nearest-neighbour (nn) Coulomb correlation and nearest-neighbour Heisenberg exchange is solved rigorously for a triangle and tetrahedron. All eigenvalues and eigenvectors are given as functions of the model parameters in a closed analytical form. For fixed electron numbers we found a multitude of level crossings, both in the ground state and in the excited states in dependence on the various model parameters. By coupling an ensemble of clusters to an electron bath we get the cluster gas model or the cluster gas approximation, if an extended array of weak-interacting clusters is considered. The grand-canonical potential Ω (μ, T, h) and the electron occupation N (μ, T, h) of the related cluster gases were calculated for arbitrary values (attractive and repulsive) of the three interaction constants. For the cluster gases without the additional interactions we found various steps in N (μ, T = 0, h = 0) higher than one. The reason is the degeneration of ground states differing in their electron occupation by more than one electron. For the triangular cluster gas we have one such degeneration point. For the tetrahedral cluster gas two. As a consequence, we do not find areas with one electron in the μ-U ground-state phase diagram of the triangular cluster gas or with one, two and five electrons in the case of the tetrahedral cluster gas. The degeneration point of the triangular cluster gas can not be destroyed by an applied magnetic field. This holds also for the lower degeneration point of the tetrahedral cluster gas. Otherwise, the upper degeneration point breaks down at a critical magnetic field hc. The dependence of hc on U shows a maximum for strong on-site correlation. The influence of nn-exchange and nn-Coulomb correlation on the ground-state phase diagrams is calculated. Whereas antiferromagnetic nn-exchange breaks the degeneration points of the tetrahedral cluster gas partially only, a repulsive nn-Coulomb correlation lifts the underlying degeneracies completely. Otherwise both ferromagnetic nn-exchange and attractive nn-Coulomb interaction stabilise the degeneration points. The consequences of the cluster gas results for extended cluster arrays are discussed.

Transformations of the Hubbard interaction to quadratic forms

The maximum thermal remagnetization (TR) after dc-demagnetization was studied at sintered RE/T hard magnets and at barium ferrite. We found very large TR-effects for SmCo/sub 5/, large effects for hard ferrites, medium for NdFeB and a very low effect for Sm/sub 2/Co/sub 17/ magnets. The experimental results are interpreted on the basis of a theory taking into account the local fluctuations of the internal magnetic field as well as the internal demagnetization effects. The relevant model parameters were estimated for SmCo/sub 5/ and barium ferrite.