FIRST-ORDER MAGNETIC PHASE TRANSITIONS*
Abstract:
The general properties of the first-order magnetic phase transitions between ordered structures have been investigated. The number of possible models has been limited by supposing the sensitivity of the exchange energy to the interatomic distance to be responsible for the phase transition. It is shown that the magnetic phase transition occurs as a result of a sign change in the proper combination of the exchange parameters. The transition may be influenced by the variation of the pressure and the magnetie field. The actual phase transition is, however, hindered in both directions by the elastie energy wall, separating the free energy minima of the different phases.
The T--P phase diagram has been calculated and the conditions for the existenee of a triple point in the T---P plane have been investigated in the case of antiferromagnetic ~ ferromagnetie transitions. The temperature hysteresis, i.e. the differenee between the upper (TsuD) and lower (Ttnf) transition temperatures has been determined at different pressures and for both temperatures a linear dependence has been obtained.
The character of the disappearance of the magnetic order has been also studied and it has been found that under certain conditions the order of the ferromagnetic--paramagnetic transition may be different from that of the antiferromagnetic--paramagnetic one. The T--H coexistencc curve between the ferromagnetic and the spin-flop antiferromagnetic phases has been determined.
The upper and the lower phase transition temperature versus magnetic field curves ate calculated and it is found that with increasing magnetic field and decreasing temperature the difference between these two curves (i. e. the hysteresis width) becomes increasingly small until at a critical field (Ht) and temperature (Tt) they end in a common point with the eoexistence curve. Below T t the variation of the magnetic field does not lead to a first-order antiferromagnetic ~- ferromagnetic transformation. The ferromagnetic phase is nothing, but the antiferromagnetic phase in a magnetie field strong enough to turn the moments parallel to the field direetion.
Above H t but below H~ the variation of the temperature brings about also a second-order ferromagnetic ~ antiferromagnetic transition. The diseontinuous change of the lattice parameter and that of the sublattice magnetization have been calculated at the coexistence temperature and at both the upper and lower transition temperatures. It has been shown that the entropy change of the transition has two contributions: ona of them is assoeiated with the volume ehange while the other with the magnetization change. Under certain conditions the order of magnitude of both eontributions may be the same.
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The subject of this paper is related to first-order magnetic phase ~ransitions. The expression, first-order phase transition is used in its usual thermodynamic sense, i.e. the first derivatives of the system's Gibbs free-energy with intensive parameters (temperature, pressure, magnetic field, e.g.) exhibit a discontinuity at the critical values of these parameters. In other words, the molar entropy, molar volume, molar magnetization, and other molar parameters suffer discontinuous change. In the higher-order phase transitions the molar parameters ate continuous but their derivatives are discontinuous. It is worthwhile to note here that the most characteristic feature of the higher-order phase transformations is the diseontinuous change in symmetry of the system with the continuous change of the state of system. This approach was very successfully developed many years ago by LANDAU and LIFSHITZ [1].
In order to systematize in a very simple way the magnetic phase transformations a "family tree" has been constructed fromdifferent types of transitions. This "family tree" is shown in Fig. 1. Some magnetic systems that exhibir transitions of first-order ate listed in Table I. It is clear that the simplest case is when the crystal structure does not change during the magnetic structure transition and when this latter takes place between ordered magnetic phases. As substantial theoretical diffieulties are assoclated with those phase transformations where the magnetic order disappears, such transformations will be excluded from our considerations.
It has been known since the last century that the onset of the magnetic order (e.g. ferromagnetism) results in a smaller or larger distortion of the crystal lattice (in many cases without any crystal symmetry change). This phenomenon is related to the dependence of the exehange energy on the interatomic spacing.
Asa result of this dependence the free-energy of the crystal may be lowered by a distortion of the lattice in the direction of decreasing exchangeenergy. The distortion will introduce to the free-energy aterm in strain energy which will increase the free-energy, and thus, a compromise between distortion and exchange is reached, which minimizes the free-energy. In the case of order-disorder phase transformations (i.e. ferromagnetic ~ paramagnetie, antiferromagnetic ~ paramagnetic) the magneto-elastic coupling between the magnetic and elastic part of the system's free-energy may drastieally alter the character of phase transitions. If the exchange parameter dependence on the interatomic spacing is rather strong a first-order phase transition will be observed instead of the usual second-order one.
The reason for this is quite obvious. The elastic distortion tends to stabilize the magnetic order and, thus, slows down its decrease with temperature. Ata certain temperature, however, the magnetie order can find no way for deereasing smoothly to zero since the stabilizing influence of the lattice distortion ceases to act below a certainmagnetic order, i.e. at a critical temperature the magnetic order and lattice distortion go to zero discontinuously. Using BEA~'s formulation [2] the situation is like that of aman who has run beyond the brink of a cliff; there is no gentle way down.
1. Introducuon
The subject of this paper is related to first-order magnetic phase ~ransitions. The expression, first-order phase transition is used in its usual thermodynamic sense, i.e. the first derivatives of the system's Gibbs free-energy with intensive parameters (temperature, pressure, magnetic field, e.g.) exhibit a discontinuity at the critical values of these parameters. In other words, the molar entropy, molar volume, molar magnetization, and other molar parameters suffer discontinuous change. In the higher-order phase transitions the molar parameters ate continuous but their derivatives are discontinuous. It is worthwhile to note here that the most characteristic feature of the higher-order phase transformations is the diseontinuous change in symmetry of the system with the continuous change of the state of system. This approach was very successfully developed many years ago by LANDAU and LIFSHITZ [1].
In order to systematize in a very simple way the magnetic phase transformations a "family tree" has been constructed fromdifferent types of transitions. This "family tree" is shown in Fig. 1. Some magnetic systems that exhibir transitions of first-order ate listed in Table I. It is clear that the simplest case is when the crystal structure does not change during the magnetic structure transition and when this latter takes place between ordered magnetic phases. As substantial theoretical diffieulties are assoclated with those phase transformations where the magnetic order disappears, such transformations will be excluded from our considerations.
It has been known since the last century that the onset of the magnetic order (e.g. ferromagnetism) results in a smaller or larger distortion of the crystal lattice (in many cases without any crystal symmetry change). This phenomenon is related to the dependence of the exehange energy on the interatomic spacing.
Asa result of this dependence the free-energy of the crystal may be lowered by a distortion of the lattice in the direction of decreasing exchangeenergy. The distortion will introduce to the free-energy aterm in strain energy which will increase the free-energy, and thus, a compromise between distortion and exchange is reached, which minimizes the free-energy. In the case of order-disorder phase transformations (i.e. ferromagnetic ~ paramagnetie, antiferromagnetic ~ paramagnetic) the magneto-elastic coupling between the magnetic and elastic part of the system's free-energy may drastieally alter the character of phase transitions. If the exchange parameter dependence on the interatomic spacing is rather strong a first-order phase transition will be observed instead of the usual second-order one.
The reason for this is quite obvious. The elastic distortion tends to stabilize the magnetic order and, thus, slows down its decrease with temperature. Ata certain temperature, however, the magnetie order can find no way for deereasing smoothly to zero since the stabilizing influence of the lattice distortion ceases to act below a certainmagnetic order, i.e. at a critical temperature the magnetic order and lattice distortion go to zero discontinuously. Using BEA~'s formulation [2] the situation is like that of aman who has run beyond the brink of a cliff; there is no gentle way down.
Hello, my name is Dr Abderrahmane Reggad. I'm a 51 year old and I am a researcher in materials' sciences. 
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