manifest a novel physical phenomenon, called the quantum orientational melting (QOM) [1, 2]. It was found that the phase diagram of the system is similar to the ...
REENTRANT ORIENTATIONAL PHASE TRANSITIONS AND CRITICAL POINTS AT QUANTUM ORIENTATIONAL MELTING
*
Yu. A. Freiman, S. Tretyak, and Andrzej Jezowski
Verkin Institute for Low Temperature Physics & Engineering 47 Lenin Ave., 310164 Kharkov, Ukraine
*
Trzebiatowski Institute for Low temperatures and Structure Research Polish Acad. of Sci., P.O.Box 937, 50-950 Wroclaw 2, Poland
It was recently shown that the system of rotors along with the traditional high temperature orientational melting can manifest a novel physical phenomenon, called the quantum orientational melting (QOM) [1, 2]. It was found that the phase diagram of the system is similar to the P-T diagram of the solid
3
He, that is, there is a minimum at the line of the orienta-
tional phase transitions, which suggests a reentrant behavior of the system. The system of rotors undergoes two first-order phase transitions with rising temperature: the low-temperature one from the orientationally disordered to the ordered state and the high-temperature one from the ordered to the disordered state. The former is of a quantum nature, and the latter is the common orientational melting. In this paper an affect was studied of the crystal field on the system of rotors under the conditions of QOM. In the molecule field approximation the Hamiltonian of the system cam be written in the form: H = BL
2
h + U1) Y20 + U0h2/2
- (U0
(1)
where L is the operator of angular momentum, U0 and U1 are molecular and crystal field constants generated by the coupling and single-molecular terms, respectively, in the intermolecular interaction potential,
B
is
the
rotational
π / 5 is the order parameter, and denotes thermodynamic averaging with the Hamiltonian (1).
constant,
h
=
4
Fig 1.
Fig 2.
Fig 4.
Fig 3.
Fig 5.
Fig 6.
h of a system of rotors for different molecular field constants U0/B a. The dash curve is the line of equilibrium phase transitions; the dot curve is the line of
Fig. 1-6. Temperature dependence of the order parameter and different crystal field constants
points of absolute instability of orientationally ordered phase. Temperature is given in units of B.
The results of calculations of the order parameter of the system of rotors for different values of U0 and different values and signs of the reduced crystal field
a = U0/U1 are given in Figs. 1-6.
As one can see, the nonmonotonic temperature behavior typical for the QOM preserves in the crystal field, but all the curves
h(T) for positive (Figs. 2-5) or negative (Fig. 6) a are shifted, respectively, up or down relative to the case a = 0 which
is given for comparison in Fig. 1. At very small positive
a (Fig. 2), the main difference with the case a = 0 lies in the fact that the phase transitions, in-
stead of separating the orientationally ordered and disordered states, having generally speaking a different symmetry, they separate more and less ordered states of the same symmetry. Thus, these phase transitions are of the order-order type. Let us consider one of the curve
h(T) of the whole family, that is a curve corresponding to a certain value of U0. As the
crystal field increases, the jump in the order parameter at the high-temperature or "classical" side of the curve decreases and at a certain value of
a (0.009 > a > 0.008) turns to zero (Fig. 3) - the first order phase transition changes into the second ora) and Tc (a) (Fig.
der one. This means that a critical point has appeared at the phase diagram of the system at the point U0c(
7). For U0 > U0c there are no classical phase transitions and the order parameter changes continuously with temperature; for U0 < U0c the system undergoes the first order phase transitions. Fig. 7. The U-T phase diagram for the system
of
the
interacting
crystal field constants
a.
rotors
for
different
The critical point appears first at infinitely large value of U0 and T, and then as
a
increases it shifts very rapidly to the values
a » 12, Tc » 1.5. At a = 0.01 (Fig.
of U0 and T characteristic for the QOM. At = 0.009, U0c
3) the critical point lies approximately at the point of minimum of the phase separation line
phase
the
"classical"
separation
"quantum"
part
line
still
part
of
the
disappeared
persists.
The
original but
the
orienta-
tional ordering with rising temperature occurs as a quantum phase transition but the disordering with temperature proceeds continuously. At pears
a » 0.011 a second critical point ap-
at
the
low-temperature
part
or
"quantum" side of the phase separation line and the line turns into a segment which begins and ends with the critical points (Fig. 4) which eventually degenerates into a multicritical point (0.017
0 and the easy-plane orientational state with h < 0.
Data on the variation of the temperature dependencies of the order parameter with the crystal field (Figs. 1-6) can be summarized as evolution of the phase diagram of the system under changes of the crystal field (Fig. 7). For negative and zero crystal fields the phase separation line goes to infinite large U0 and T. At negative crystal fields the depth of the minimum at the phase line increases with
ïaï,
that is the range of U0 which displays the reentrant ordering-disordering behavior in-
creases. At positive crystal fields the phase separation line either ends at a critical point or begins and ends by critical points which degenerates at a certain value of the crystal field. At higher crystal fields there are no phase transitions in the system. No detailed comparison of the theory with experiment has been made so far. But let us note that the reentrant behavior and the existence of the critical point are displayed for the hindering barriers and temperatures which are characteristic of the range of the phase diagram of hydrogen where analogous phenomena allegedly were observed in experiment [3, 4].
REFERENCES
1.
Yu. A. Freiman et al., J. Phys.: Condens. Matt. 3, 3855 (1991); Low Temp. Phys. 19, 368 (1993)
2.
Physics of Cryocrystals, eds. V. G. Manzhelii and Yu. A. Freiman , eds., AIP Press, NY (1997)
3.
H. K. Mao and R. J. Hemley, Rev. Mod. Phys. 66, 671 (1994)
4.
I. F. Silvera, in: Frontiers of High-Pressure Research, H. D. Hochheimer and R. D. Etters, eds., Plenum Press, NY, 101114 (1991)
