Magnetic phase transitions second-order

A second-order phase transition is one in which the enthalpy and first derivatives are continuous, but the second derivatives are discontinuous. The Cp versus T curve is often shaped like the Greek letter X. Hence, these transitions are also called -transitions (Figure 2-15b Thompson and Perkins, 1981). The structure change is minor in second-order phase transitions, such as the rotation of bonds and order-disorder of some ions. Examples include melt to glass transition, X-transition in fayalite, and magnetic transitions. Second-order phase transitions often do not require nucleation and are rapid. On some characteristics, these transitions may be viewed as a homogeneous reaction or many simultaneous homogeneous reactions. 

II) At S 0 we have h2 i> hi, and the transition occurs continuously in the field interval Ah = h2 — h (Fig.15b). In this interval solution B) is realized. In an increased magnetic field a second-order phase transition takes place at h = hi and the magnetic susceptibility reveals a jump-like... 

The temperature at which the phase transition occurs is called the critical temperature or Tg. Most, but not all, magnetic phase transitions are continuous , sometimes called second order . From a microscopic point of view, such phase transitions follow a scenario in which, upon cooling from high temperature, finite size, spin-correlated, fractal like, clusters develop from the random, paramagnetic state at temperatures above Tg, the so-called critical regime . As T Tg from above, the clusters grow in size until at least one cluster becomes infinite (i.e. it extends, uninterrapted, throughout the sample) in size at Tg. As the temperature decreases more clusters become associated with the infinite cluster until at T = 0 K all spins are completely correlated. 

Fig. 27. Temperature dependence of the spontaneous muon spin precession frequency in single-crystalline TbNij with a Curie temperature of 23 K. The dashed curve is the appropriate fiee-ion Brillouin function. Inclusion of CEF interaction in the ground-state multiplet gives the solid curve which fits the data well. The behavior around the critical temperature is typical for a second-order magnetic phase transition. After Dalmas de Reotier et al. (1992).

J. Mira, J. Rivas, F. Rivadulla, C. Vazquez, M.A. Lopez-Quintela, Change from first- to second-order magnetic phase transition in La2/3Ca, Sri/3Mn03 perovskites. Phys. Rev. B 60, 2998 (1999)... 

It turns out that a third order process is possible which combines Vi and the k-f interaction characterized by (A,. T) = (1,1). Details can be found in Fulde (1975). The net result is that this time the quadrupole susceptibility diverges as TJ T - Tc) in molecular field approximation as the magnetic phase transition is approached from above. This would imply that an elastic constant becomes soft at a second order magnetic phase transition. In practice this requires the presence of the interaction (A, i ) = (1, 1) with reasonable strength. 

Although in CeBi the magnetic phase transition is of second order, the decrease in its p(T) curve at (25.5 K) is as sharp as for CeSb. As in the case of CeSb, the complex field dependence of the electrical resistivity of CeBi indicates the existence of different magnetic phase transitions (see fig. 125). 

Inoue and Shimizu (1988), in the framework of the model described above, calculated the volume dependence of the transition temperature to the magnetically ordered state at the boundary between the first- and second-order transition, see fig. 7. Thus, pressiure can alter the order of the magnetic phase transition. Such a behavior can be explained by the decrease of the molecular field acting on the 3d-electron subsystem which causes the reduction of the Co moment (Inoue and Shimizu 1988). 

The thermodynamic model stated above gives the following internal friction behavior for second-order magnetic phase transitions ... 

The Ag (100) surface is of special scientific interest, since it reveals an order-disorder phase transition which is predicted to be second order, similar to tire two dimensional Ising model in magnetism [37]. In fact, tire steep intensity increase observed for potentials positive to - 0.76 V against Ag/AgCl for tire (1,0) reflection, which is forbidden by symmetry for tire clean Ag(lOO) surface, can be associated witli tire development of an ordered (V2 x V2)R45°-Br lattice, where tire bromine is located in tire fourfold hollow sites of tire underlying fee (100) surface tills stmcture is depicted in tlie lower right inset in figure C2.10.1 [15]. 

An extensive treatment of the thermodynamic properties of second-order phase transitions in magnetic crystals has been given by K. P. Belov, Magnetic Transitions, Consultants Bureau, Enterprises, Inc., New York, 1961. 

Fig. 5 Magnetic phase diagram of [Mn(Cp )2][Pt(tds)2] M(T) (filled diamonds) M(H) (//] (filled triangles), H (filled inverted triangles), x (T) (open circles) x (H) (open squares) Tt is the tricritical temperature I denotes the first-order MM transition II denotes a second-order transition (AF-PM phase houndary) and III denotes a higher order transitions (from a PM to a FM like state). From [45]...

Figure 2.9 The B-Tphase diagram of MnP [13] with the magnetic field along the b-axis. Three different magnetically ordered phases - ferro, fan and screw - are separated by first-order phase transitions. The transitions to the disordered paramagnetic state are of second order and given by a dashed line.

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