Curie-Weiss Type Law Research Articles

Towards an understanding of dynamic phase transitions

We review the equivalencies and dissimilarities between ferromagnetic systems in thermodynamic equilibrium and those subjected to an external oscillating field. While the former undergo a thermodynamic phase transition at the Curie temperature, the latter show a dynamic phase transition at a critical period of the oscillating field. Over two decades of research have led to the conclusion that dynamic and thermodynamic phase transitions correspond to the same universality class and have analogous phase diagrams, among other similarities. Recently, the amplitude of the oscillating field driving the dynamic phase transition has emerged as a key variable, not only because it determines the value of the critical period directly and thus the speed of the critical dynamics, but also because it affects very substantially the degree of similarity in between thermodynamic and dynamic phase transitions. In particular, we discuss how low amplitudes of the oscillating field and corresponding slow critical dynamics lead to a suppression of the dynamic phase transition at surfaces and deviations from a Curie-Weiss type law at large periods. We also discuss the presence of metamagnetic anomalies in the paramagnetic dynamic phase and a severe shrinking of the critical region, which we have observed in magneto-optical Kerr effect experiments on in-plane uniaxial Co films and which we have analyzed in detail by means of mean-field calculations. At higher amplitudes of the oscillating field, and thus for faster critical dynamics, these phenomena are far less prominent and the equivalency picture between dynamic and thermodynamic phase transitions can be recovered.

MAGNETIC PROPERTIES OF THE (DyxU1-x)2AlCo3 SYSTEM

The magnetic properties of the Dy x U 1-x AlCo 3 system, investigated in the 4–800 K temperature range and fields up to 80 kOe indicated ferrimagnetic order for x≥0.2. The cobalt magnetic moments opposite to dysprosium and the Curie temperatures decrease with decreasing Dy content. The internal magnetic field dependence of the Co moment shows that cobalt moment becomes saturated above 1000 kOe. The high temperature paramagnetic behavior follows a Curie–Weiss type law evidencing effective magnetic moments on Co positions. The paramagnetic properties are analyzed in the spin fluctuations model.

EPR AND MAGNETIC SUSCEPTIBILITY STUDIES OF V4+ IONS IN 2B2O3·SrO GLASS MATRIX

Electron paramagnetic resonance (EPR) and magnetic susceptibility studies on x V 2 O 5 ·(100 - x)[2 B 2 O 3 · SrO ] glasses with 0 ≤ x ≤ 30 mol% were performed. The covalence degree of vanadium bonds was estimated according to the LCAO-MO model. The EPR data show the presence of V4+ ions in a square-pyramidal coordination (C4v). The experimental EPR spectra are simulated assuming a superposition of two signals, one with hyperfine structure (HFS) typical for isolated ions and the other one consists of a broad line without HFS characteristic for clustered ions. These results are consistent with the magnetic data which indicate that for x ≥ 5 mol% V2O5 the temperature dependence of the reciprocal magnetic susceptibility is described by a Curie–Weiss type law with negative paramagnetic Curie temperature. The magnetic data also allow the estimation of NV4+ / Ntotal ratio.

EPR AND MAGNETIC SUSCEPTIBILITY STUDIES OF V4+ IONS IN THE 2B2O3 · SrO GLASS MATRIX

Electron paramagnetic resonance (EPR) and magnetic susceptibility studies on x V 2 O 5 · (100 - x) [2 B 2 O 3 · SrO ] glasses with 0 ≤ x ≤ 30 mol% were performed. The covalence degree of vanadium bonds was estimated according to the LCAO-MO model. The EPR data show the presence of V 4+ ions in a square-pyramidal coordination ( C 4v). The experimental EPR spectra are simulated assuming a superposition of two signals, one with hyperfine structure (HFS) typical for isolated ions and the other one consisting of a broad line without the HFS characteristic for clustered ions. These results are consistent with the magnetic data which indicate that for x ≤ 5 mol% V 2 O 5 the temperature dependence of the reciprocal magnetic susceptibility is described by a Curie–Weiss type law with negative paramagnetic Curie temperature. The magnetic data also allow the estimation of N V 4+ / N V total ratio.

EPR and magnetic susceptibility studies on V 2 O 5 -P 2 O 5 -PbO glasses

EPR and magnetic susceptibility investigations on the \(x{\text{V}}_{\text{2}} {\text{O}}_{\text{5}} \cdot {\text{(100}} - {\text{x)[2P}}_{\text{2}} {\text{O}}_{\text{5}} \cdot {\text{PbO]}}\) glass system with 0 20 mol %) suggests the increase of the associated ion number coupled by superexchange interactions. This result is consistent with magnetic susceptibility data for >3 mol % where the temperature dependence of magnetic susceptibility is described by the Curie–Weiss type law with a negative paramagnetic Curie temperature. The magnetic susceptibility results allowed the estimation of the V4+/V4+ + V5+ ratio in the sample studied.

High temperature mechanical spectroscopy of CaO–ZrO 2 cubic single crystals

The high temperature anelastic properties of cubic CaO–ZrO 2 single crystals have been studied by mechanical spectroscopy. A relaxation peak superimposed on an exponential background has been observed at 1580 K for a frequency of 1 Hz. The mechanism giving rise to the peak is thermally activated, the activation energy is 4.3 eV and the limit relaxation time is about 4×10 −15 s. The peak depends on the crystal orientation and the intensity of the relaxation follows a Curie–Weiss type law. These characteristics lead to the interpretation that this peak is the stress induced ordering of substitutional Ca–Ca pairs (orthorhombic 〈011〉 elastic dipoles). The deviations of the relaxation time from the Arrhenius behavior and of the relaxation intensity from the Curie–Weiss law observed below 1440 K might result from the order–disorder transition occurring in this temperature range. The exponential background may be attributed to dislocation motion. The apparent activation energy associated with this background was found to be 6.4 eV.

The effect of 3d-transition metal solutes on the ferrimagnetism of Fe 7Se 8

The effect of 3d-transition metal solutes on the magnetization of Fe 7Se 8 has been investigated by studying two series of alloys with constant solute concentrations of 3 and 10 at%, respectively. Small additions of Ti and V were sufficient to reduce the magnetization by one order of magnitude, whereas Ni slightly increased the magnetization. The changes due to the presence of Cr, Mn and Co were less noticeable. In certain cases the thermal treatment turned out to be a decisive factor in determining the type of magnetism. Alloys with Cr quenched from 1070 K were clearly antiferromagnetic. Quenched samples containing ten percent Ti were paramagnetic following a Curie-Weiss type law, but slow cooling from 1070 K reestablished the ferrimagnetic state. Order-disorder phenomena were assumed to be responsible for the changes due to the thermal treatment.

Ultrasonic Velocities of K2PbCu(NO2)6near the Cooperative Jahn-Teller Phase Transitions

The sound velocities in K 2 PbCu(NO 2 ) 6 were measured in the vicinity of its structural phase transition point of 281 K. The velocity of the transverse sound wave traveling along the [110] direction with the polarization vector in the [1\bar10] direction was found to follow the Curie-Weiss type law; V T [110] = V 0 T [110] - V 1 T [110] ( T 0 /( T - T 0 )), where V 0 T [110] =1.13×10 3 m/sec, V 1 T [110] =2.52×10 2 m/sec and T 0 =172.8 K. The anomalous behavior in the sound velocity was atrributed to the linear coupling between the strain and one of the order parameters associated with local distortion.