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Neutron critical scattering and crossover effect at antiferro-ferromagnetic phase transition in Mn1.88Cr0.12Sb
NEUTRON CRITICAL SCAITERING AND CROSSOVER EFFECT AT ANTIFERRO-FERRIMAGNETIC PHASE TRANSITION IN Mn,,s,Cr,,,zSb J. TODOROVIC “Boris Kid&”
Institute of Nuclear Sciences, Vi&,
II001 Belgrade, P.O. Box 522, Yugoslacjia
The intermetallic compound with the tetragonal unit cell has an antiferro-ferrimagnetic phase transition and a change of anisotropy at T, = 318 K. In the report the neutron scattering measurements on magnetic fluctuations are shown and well described by critical exponents /3 and y. The fluctuations get the longest temporal stability at T,.
Mn ,_,Cr,Sb is a typical representative of magnetic phase transition of the type order-order (antiferro-ferrimagnetic). Kittel [l] developed the phenomenological theory for this type of phase transition, assuming a dependence of the effective exchange interaction on the interatomic distances (exchange inversion). This interaction changes sign going through zero for a critical value of the lattice parameter. The phase transition is followed by a discontinuous change of the lattice parametertypical for first order phase transitions. However, Akhiezer and G&burg [2] showed that this type of phase transition is followed by softening of a magnon mode and by critical fluctuations of magnetic moments. The existence of the magnon soft mode has been experimentally proved [3]. The acoustic magnon branch measured in the direction of the c-axis and in the vicinity of the phase transition is very “soft” and appears with a weak dispersion [4]. These experimental facts makes one conjecture the existence of strong fluctuations with a quasi twodimensional character in the immediate vicinity of the transition temperature. In this paper the experimental results obtained from X-ray and neutron measurements on Mn,,,,CrO,,,Sb are presented. By X-ray and elastic neutron scattering the temperature dependence of the lattice parameter c has been measured. Fig. 1 is a typical picture for the coexistence of two magnetic phases: antiferromagnetic (AF) and ferrimagnetic (FIM). Due to a bad resolution, the neutron measurements indicate a smeared phase transition. The temperature dependence of the magnetic intensity for the (001.5) superlattice reflection was measured on the neutron three-axis spectrometer. We tried to fit the experimental result to the conventional continuous phase transition picture (CPT). In the region of relative temperature t critical exponent of the magnetization is Journal of Magnetism
and Magnetic Materials
15-18 (1980) 1159-1160
/3 = 0.12 + 0.01. A calculation for the two-dimensional XY model [5] gives /3 = 0.13, whereas for the two-dimensional Ising model /3 is equal to 0.125. Taking into account that the effective exchange interaction goes through zero at the phase transition, it could be expected that /3 might correspond to the two-dimensional XY model value, as below T, the spins lie in the plane perpendicular to c-axis; above T, spins are oriented in the c-axis direction. In the region t z lo-’ we get /? = 0.53 ? 0.07, which is close to the value of the meanfield theory (MF). In this region of t the X-ray measurements give the same value for p. For the transverse component of the susceptibility (see fig. 2) the critical exponent yl, in the region t x 10p3, is 0.29 ? 0.09. If we take into account the existence of the change of anisotropy, i.e. H c x 0 for the spin flopping in the vicinity of T,, and an assumption that the line of exchange
C,A
6.550 _
+ (001) x X-RAY(006J
6.500
,
,
,
270 280 290 300
,
,
,
,
,
,
,
310 320 330 340 350 360 370 T,
t
Fig. 1. Temperature dependence of parameter c by measured using X-ray and neutron scattering method. Neutrons (A = 2.376 A) were used for measuring the position of magnetic reflexion (001.5) and nuclear reflexion (002). In the region from 287 to 318 K the X-ray reflexion (006) is doubled. It gives two values for lattice parameter at the measuring temperature. Above 318 K the reflexion (006), with a smaller C, has disappeared. The temperature T, = 318 K is adopted as the phase transition temperature.
ONorth Holland
1159
1160
J. Todoro&/
Crossowr
effecr at AF-FIMphase
Fig. 2. Temperatures dependence of the transverse susceptibility and the sublattice magnetization of AF phase.
inversion is the CPT line, then we may assume the existence of a bicritical point for H = 0 near T,. Theoretical bicritical exponent 7 for a system with the two-component order parameter is 0.33 + 0.06 [6]. In the intermediate region of t we find yL = 1.07 & 0.12, in agreement with the MF theory. Finally, in the region t x lop2 we obtain yI = 2.29 + 0.23. Numerically, the latter corresponds to the exponent for 2D XY model, y = 2.4 -+ 0.5 [7]. The change of width of the central peak with the change of temperature (cf. fig. 3) can easily be understood if we accept the existence of AF clusters above T,. The width change below T, is the result either of the magnon soft mode existence or
transition
280
Fig. 3. Temperature
290
300
310
320
330
dependence of the Bragg peak.
of the rather slowly fluctuations the easy axis of magnetization tion.
width
340
T,K
of the
(001.5)
of the direction of during its 90” rota-
References [l] C. Kittel, Phys. Rev. 120 (1960) 335. [2] I. A. Akhiezer and A. E. Ginzburg, Phys. Lett. 37A (1971) 63. [3] J. Todorovic, Solid State Commun. 21 (1977) 919. [4] S. Funahashi and N. Kazama, J. Phys. Sot. Japan 4 I (19’76) 811; J. TodoroviC, Physica 8688B (1977) 977. [5] T. Schneider and E. Stoll, Phys. Rev. Lett. 36 (1976) 1501. [6] W. P. Wolf, Physica 8688B (1977) 550. [7] D. M. Lublin, Phys. Rev. Lett. 34 (1975) 568.
Institute of Nuclear Sciences, Vi&,
II001 Belgrade, P.O. Box 522, Yugoslacjia
The intermetallic compound with the tetragonal unit cell has an antiferro-ferrimagnetic phase transition and a change of anisotropy at T, = 318 K. In the report the neutron scattering measurements on magnetic fluctuations are shown and well described by critical exponents /3 and y. The fluctuations get the longest temporal stability at T,.
Mn ,_,Cr,Sb is a typical representative of magnetic phase transition of the type order-order (antiferro-ferrimagnetic). Kittel [l] developed the phenomenological theory for this type of phase transition, assuming a dependence of the effective exchange interaction on the interatomic distances (exchange inversion). This interaction changes sign going through zero for a critical value of the lattice parameter. The phase transition is followed by a discontinuous change of the lattice parametertypical for first order phase transitions. However, Akhiezer and G&burg [2] showed that this type of phase transition is followed by softening of a magnon mode and by critical fluctuations of magnetic moments. The existence of the magnon soft mode has been experimentally proved [3]. The acoustic magnon branch measured in the direction of the c-axis and in the vicinity of the phase transition is very “soft” and appears with a weak dispersion [4]. These experimental facts makes one conjecture the existence of strong fluctuations with a quasi twodimensional character in the immediate vicinity of the transition temperature. In this paper the experimental results obtained from X-ray and neutron measurements on Mn,,,,CrO,,,Sb are presented. By X-ray and elastic neutron scattering the temperature dependence of the lattice parameter c has been measured. Fig. 1 is a typical picture for the coexistence of two magnetic phases: antiferromagnetic (AF) and ferrimagnetic (FIM). Due to a bad resolution, the neutron measurements indicate a smeared phase transition. The temperature dependence of the magnetic intensity for the (001.5) superlattice reflection was measured on the neutron three-axis spectrometer. We tried to fit the experimental result to the conventional continuous phase transition picture (CPT). In the region of relative temperature t critical exponent of the magnetization is Journal of Magnetism
and Magnetic Materials
15-18 (1980) 1159-1160
/3 = 0.12 + 0.01. A calculation for the two-dimensional XY model [5] gives /3 = 0.13, whereas for the two-dimensional Ising model /3 is equal to 0.125. Taking into account that the effective exchange interaction goes through zero at the phase transition, it could be expected that /3 might correspond to the two-dimensional XY model value, as below T, the spins lie in the plane perpendicular to c-axis; above T, spins are oriented in the c-axis direction. In the region t z lo-’ we get /? = 0.53 ? 0.07, which is close to the value of the meanfield theory (MF). In this region of t the X-ray measurements give the same value for p. For the transverse component of the susceptibility (see fig. 2) the critical exponent yl, in the region t x 10p3, is 0.29 ? 0.09. If we take into account the existence of the change of anisotropy, i.e. H c x 0 for the spin flopping in the vicinity of T,, and an assumption that the line of exchange
C,A
6.550 _
+ (001) x X-RAY(006J
6.500
,
,
,
270 280 290 300
,
,
,
,
,
,
,
310 320 330 340 350 360 370 T,
t
Fig. 1. Temperature dependence of parameter c by measured using X-ray and neutron scattering method. Neutrons (A = 2.376 A) were used for measuring the position of magnetic reflexion (001.5) and nuclear reflexion (002). In the region from 287 to 318 K the X-ray reflexion (006) is doubled. It gives two values for lattice parameter at the measuring temperature. Above 318 K the reflexion (006), with a smaller C, has disappeared. The temperature T, = 318 K is adopted as the phase transition temperature.
ONorth Holland
1159
1160
J. Todoro&/
Crossowr
effecr at AF-FIMphase
Fig. 2. Temperatures dependence of the transverse susceptibility and the sublattice magnetization of AF phase.
inversion is the CPT line, then we may assume the existence of a bicritical point for H = 0 near T,. Theoretical bicritical exponent 7 for a system with the two-component order parameter is 0.33 + 0.06 [6]. In the intermediate region of t we find yL = 1.07 & 0.12, in agreement with the MF theory. Finally, in the region t x lop2 we obtain yI = 2.29 + 0.23. Numerically, the latter corresponds to the exponent for 2D XY model, y = 2.4 -+ 0.5 [7]. The change of width of the central peak with the change of temperature (cf. fig. 3) can easily be understood if we accept the existence of AF clusters above T,. The width change below T, is the result either of the magnon soft mode existence or
transition
280
Fig. 3. Temperature
290
300
310
320
330
dependence of the Bragg peak.
of the rather slowly fluctuations the easy axis of magnetization tion.
width
340
T,K
of the
(001.5)
of the direction of during its 90” rota-
References [l] C. Kittel, Phys. Rev. 120 (1960) 335. [2] I. A. Akhiezer and A. E. Ginzburg, Phys. Lett. 37A (1971) 63. [3] J. Todorovic, Solid State Commun. 21 (1977) 919. [4] S. Funahashi and N. Kazama, J. Phys. Sot. Japan 4 I (19’76) 811; J. TodoroviC, Physica 8688B (1977) 977. [5] T. Schneider and E. Stoll, Phys. Rev. Lett. 36 (1976) 1501. [6] W. P. Wolf, Physica 8688B (1977) 550. [7] D. M. Lublin, Phys. Rev. Lett. 34 (1975) 568.