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Magnetic part of specific heat in high-purity Dy single crystal
26
Journal
of Magnetism
and Magnetic
Materials
96 (1991) 26-28 North-Holland
Magnetic
part of specific heat in high-purity
S.A. N&tin, A.M. Tishin, S.F. Savchenkova, Yu.1. Spichkin, S.V. Red’ko and Yu.A. Nesterov lleparrmen~ of Physics, Moscow State University, 119899 Moscow, USSR Received
24 September
1990; in revised form 24 October
Dy single crystal O.D. Chistykov,
1990
The specific heat and spontaneous magnetization of high-purity Dy single crystal are measured in the temperature range 4.2-300 K. The magnetic contribution to the specific heat is determined and the magnetic part of the entropy is calculated. The magnetic ordering in the paramagnetic region above the Neel temperature is discussed.
1. Introduction The magnetic and elastic properties of Dy single crystal have been studied in ref. [l] and the temperature hysteresis of elasticity modulus E and dynamic susceptibility x have been observed in the paramagnetic region above the NCel temperature 0,=179 K up to r,=290 K (at T=T, hysteresis vanishes). The maximum of internal friction Q -i at T, has also been observed. Earlier, in ref. [2], the hysteresis of intensity of magnetic reflex, the angle of helicoid and the factor of neutron depolarization have been studied using the neutron diffraction method. This hysteresis was still present tens of degrees Celsius above O2 (0, - the point of phase transition from antiferromagnetic to paramagnetic state). The authors of ref. [3] pointed out that the magnetic part of the entropy of Dy increased for temperatures well above 0,. In ref. [4] the magnetic contribution of specific heat of Dy was found above 0,. Observed phenomena can be explained by the existence in the paramagnetic region of short-range magnetic ordering as clusters of ordered spins which concentration is different under heating and cooling. The authors of the theoretical work [5] have shown that in the paramagnetic region the “local phase transformation” with reconstruction of short-range ordering may exist. Obviously this transformation 0304-8853/91/$03.50
0 1991 - Elsevier Science Publishers
may cause the peak on the Q-’ temperature dependence at TH, In connection with many papers about shortrange magnetic ordering in the paramagnetic region [l-4] the investigation of the properties of transformation of magnetic ordering of high-purity Dy single crystal is important. In such a crystal the effects caused by impurity and crystal imperfections are negligible. In the present paper the specific heat cP and spontaneous magnetization us of Dy single crystal are measured. The obtained results allow us to study the experimental temperature dependence of the magnetic part of specific heat (c,,,,) and compare it with values calculated from molecular-field theory [6]. The parameter cM is sensitive to transformation of magnetic structure and its disordering.
2. Experimental
details
We use samples of Dy single crystal with a ratio of specific resistance at 4.2 and 300 K of p3,,0/p4.2 = 200. The samples are refined by vacuum sublimation in a resistance furnace with a graphite heater under a residual pressure of 10P6 Torr. The refined metal is deposited on the watercooled copper condenser forming druses with orientation along one of three crystallographic directions
B.V. (North-Holland)
S.A. Nikitin et al. / Specific heat in Dy single crystal
[1124], [ll?O], [lOiO]. The impurity content of samples is determined by spark mass-spectrometry and vacuum extraction. The concentration of 20 elements is investigated. The Na, Ca and Mn in the range of 10m3 at%, Fe, Si, Cu and the other elements 10P4-10-5 at%. After refining the concentration of oxygen is decreased tenfold, carbon twentyfold and nitrogen twofold compared to before refining. The measurement of specific heat cp is carried out by adiabatic calorimetry over the temperature range 4.2-300 K. The mean error of measurement of cP is less than 1%. The spontaneous magnetization us is determined using the specific magnetization measured with a vibration magnetometer with a superconductive solenoid [7].
3. Results and discussion The observed temperature dependence of specific heat cP and spontaneous magnetization u, are shown in fig. 1. The maxima on the c,(T) curve correspond with paramagnetic-antiferromagnetic (180.3 K) and antiferromagnetic-ferromagnetic (90.4 K) transitions. The magnetization a, is determined by extrapolation of the linear part of the a(H) curve from a 60 kOe field to a zero field. The determination of lattice (c,,,,), electronic ( ce) and magnetic ( c~) contributions to the specific heat is carried out as follows. At first we found the parameter y and /3 from the equation cP = yT + j3T3 using a straight-line fitting of c,/T
Spmflc
heat, ~lmol K
magnetlzatlon. emu/g
Spontaneous
ao~400 ji
60
‘I 1 40
h\:
01 0
\ 50
100
160
Temperature,
Fig. 1. Temperature
'0
I
200
250
300
K
dependences of specific heat and spontaneous magnetization in Dy.
21
C,,l/molK
60
0
50
100
150
Temperature,
200
250
300
K
Fig. 2. Temperature dependences of the magnetic part of the specific heat in Dy single crystal (curve 1 - experimental data; curve 2 - data calculated with the molecular field theory).
versus T2. Obtained results correspond with experimental data very well. The parameter y is used for the determination of the electronic part of c,,, and /I is used for calculation of the Debye temperature 0, and the lattice part of cP: clatt = 3kND(x,), CltW= 2kN[l-
T < 0,. & (0,/T)*],
T> O,,
(1)
where 0(x,,) is the Debye function of specific heat, N is the number of atoms and k is the Boltzmann constant. The magnetic contribution to C~ is determined with the formula CM = cp - Clatt - c,.
(2)
The experimental (curve 1) and calculated (based on molecular field theory; curve 2) dependencies of cM(T) are shown in fig. 2 and c,(T), cM(T), c,,,,(T) in the temperature range 200-300 K in fig. 3. C~ does not vanish at 0, but monotonously decreases to zero when approaching to room temperature. This phenomenon indicates the absence of a transformation of magnetic structure at T < 300 K. In our opinion such behavior of C~ confirms the suggestion about conservation of clusters with short-range magnetic ordering over the temperature range 0,-T,. The concentration and size of these clusters decrease with increasing temperature. The area under the cM(T) curve is equal to the energy (&) which necessary to
S.A. Nikitin
28
c
et al. / Specific heat in Dy single crvstal
23 200
150
250
Temperature,
360
300
K
Fig. 3. Dependences of electron (curve l), magnetic (curve 2) and lattice (curve 3) parts of the specific heat versus temperature above 0,.
transfer the system from a magneto-ordering state (T -c 0,) to a magneto-disordering state (T > 0, ). The integration of experimental cM(T) data between 0 K and 0, gives a value of 2188.4 J/mol, between 0, and 300 K - 180.7 J/mol. Based on experimental and theoretical cM( T) dependencies we plot the c,(T)-T curve and calculate the magnetic part of the entropy (fig. 4) with the
Over the temperature range 0 K-O, the magnetic part of the entropy equals 22 J/mol K, above O2 1 J/molK. Thus the total value of S, is equal to 23 J/mol K in agreement with the theoretical values S, = R ln(2j + 1) (23 J/mol K for Dy). Comparing the magnetic part of the entropy below and above 0, we conclude that in the paramagnetic region only 5% of the entropy caused by magnetic ordering at T < 0, is conserved. It is interesting to compare the experimental values of and S, with data from molecular-field theQM ory. Calculated values of QM and S, are equal to 1946.5 J/mol and 18.5 J/mol K, respectively. Note the proximity of theoretical and experimental maxima of cM in the 0, point (fig. 2). As in the molecular-field theory the existence of magnetic ordering is suggested, we conclude that the ferromagnetic ordering within basal planes gives the main contribution to the magnetic part of the specific heat. The contribution of the helicoidal structure is small.
References (3)
7 I
(
0” 0
1 50
I 100
Temperature,
150
200
250
K
Fig. 4. Experimental and calculated dependences of the magnetic part of the entropy versus temperature.
[l] G.I. Kataev, S.V. Kortov, M.R. Sattarov and A.M. Tishm. Proc. 2nd All-Union Conf. Magnetic Phase Transition and Critical Phenomena, Mahachkala, 1989. p. 125 (in Russian). PI N.G. Baazov and A.G. Mandjavidze, in: Investigation of Rare-Earth Magnets by Neutron Methods (Metsniereha. Tbilisi, 1983) p. 96 (in Russian). Physics of Rare-Earth C‘om[31 K. Teylor and M. Darby, pounds (Mir, Moscow. 1974) p. 374 (in Russian). and F.H. Spedding, J. <‘hem. [41 M. Griffel, R.E. Skochodopole Phys. 25 (1956) 75. [51 T.I. Kostina, V.N. Menshov and V.V. Tugushev. Fir. Met. Metalloved. 59 (1985) 430 (in Ruwan). [61 S.V. Vonsovski. Magnetism (Nauka. Moscow. 1971) p. 1032 (in Russian). USSR [71 A.M. Tishin. PhD thesis, Moscow State Ciniversitv, (1988) (in Russian). PI L. Girifalko, Statistical Physics of Solid State (Mir. Moscow. 1975) p. 382 (in Russtan).
Journal
of Magnetism
and Magnetic
Materials
96 (1991) 26-28 North-Holland
Magnetic
part of specific heat in high-purity
S.A. N&tin, A.M. Tishin, S.F. Savchenkova, Yu.1. Spichkin, S.V. Red’ko and Yu.A. Nesterov lleparrmen~ of Physics, Moscow State University, 119899 Moscow, USSR Received
24 September
1990; in revised form 24 October
Dy single crystal O.D. Chistykov,
1990
The specific heat and spontaneous magnetization of high-purity Dy single crystal are measured in the temperature range 4.2-300 K. The magnetic contribution to the specific heat is determined and the magnetic part of the entropy is calculated. The magnetic ordering in the paramagnetic region above the Neel temperature is discussed.
1. Introduction The magnetic and elastic properties of Dy single crystal have been studied in ref. [l] and the temperature hysteresis of elasticity modulus E and dynamic susceptibility x have been observed in the paramagnetic region above the NCel temperature 0,=179 K up to r,=290 K (at T=T, hysteresis vanishes). The maximum of internal friction Q -i at T, has also been observed. Earlier, in ref. [2], the hysteresis of intensity of magnetic reflex, the angle of helicoid and the factor of neutron depolarization have been studied using the neutron diffraction method. This hysteresis was still present tens of degrees Celsius above O2 (0, - the point of phase transition from antiferromagnetic to paramagnetic state). The authors of ref. [3] pointed out that the magnetic part of the entropy of Dy increased for temperatures well above 0,. In ref. [4] the magnetic contribution of specific heat of Dy was found above 0,. Observed phenomena can be explained by the existence in the paramagnetic region of short-range magnetic ordering as clusters of ordered spins which concentration is different under heating and cooling. The authors of the theoretical work [5] have shown that in the paramagnetic region the “local phase transformation” with reconstruction of short-range ordering may exist. Obviously this transformation 0304-8853/91/$03.50
0 1991 - Elsevier Science Publishers
may cause the peak on the Q-’ temperature dependence at TH, In connection with many papers about shortrange magnetic ordering in the paramagnetic region [l-4] the investigation of the properties of transformation of magnetic ordering of high-purity Dy single crystal is important. In such a crystal the effects caused by impurity and crystal imperfections are negligible. In the present paper the specific heat cP and spontaneous magnetization us of Dy single crystal are measured. The obtained results allow us to study the experimental temperature dependence of the magnetic part of specific heat (c,,,,) and compare it with values calculated from molecular-field theory [6]. The parameter cM is sensitive to transformation of magnetic structure and its disordering.
2. Experimental
details
We use samples of Dy single crystal with a ratio of specific resistance at 4.2 and 300 K of p3,,0/p4.2 = 200. The samples are refined by vacuum sublimation in a resistance furnace with a graphite heater under a residual pressure of 10P6 Torr. The refined metal is deposited on the watercooled copper condenser forming druses with orientation along one of three crystallographic directions
B.V. (North-Holland)
S.A. Nikitin et al. / Specific heat in Dy single crystal
[1124], [ll?O], [lOiO]. The impurity content of samples is determined by spark mass-spectrometry and vacuum extraction. The concentration of 20 elements is investigated. The Na, Ca and Mn in the range of 10m3 at%, Fe, Si, Cu and the other elements 10P4-10-5 at%. After refining the concentration of oxygen is decreased tenfold, carbon twentyfold and nitrogen twofold compared to before refining. The measurement of specific heat cp is carried out by adiabatic calorimetry over the temperature range 4.2-300 K. The mean error of measurement of cP is less than 1%. The spontaneous magnetization us is determined using the specific magnetization measured with a vibration magnetometer with a superconductive solenoid [7].
3. Results and discussion The observed temperature dependence of specific heat cP and spontaneous magnetization u, are shown in fig. 1. The maxima on the c,(T) curve correspond with paramagnetic-antiferromagnetic (180.3 K) and antiferromagnetic-ferromagnetic (90.4 K) transitions. The magnetization a, is determined by extrapolation of the linear part of the a(H) curve from a 60 kOe field to a zero field. The determination of lattice (c,,,,), electronic ( ce) and magnetic ( c~) contributions to the specific heat is carried out as follows. At first we found the parameter y and /3 from the equation cP = yT + j3T3 using a straight-line fitting of c,/T
Spmflc
heat, ~lmol K
magnetlzatlon. emu/g
Spontaneous
ao~400 ji
60
‘I 1 40
h\:
01 0
\ 50
100
160
Temperature,
Fig. 1. Temperature
'0
I
200
250
300
K
dependences of specific heat and spontaneous magnetization in Dy.
21
C,,l/molK
60
0
50
100
150
Temperature,
200
250
300
K
Fig. 2. Temperature dependences of the magnetic part of the specific heat in Dy single crystal (curve 1 - experimental data; curve 2 - data calculated with the molecular field theory).
versus T2. Obtained results correspond with experimental data very well. The parameter y is used for the determination of the electronic part of c,,, and /I is used for calculation of the Debye temperature 0, and the lattice part of cP: clatt = 3kND(x,), CltW= 2kN[l-
T < 0,. & (0,/T)*],
T> O,,
(1)
where 0(x,,) is the Debye function of specific heat, N is the number of atoms and k is the Boltzmann constant. The magnetic contribution to C~ is determined with the formula CM = cp - Clatt - c,.
(2)
The experimental (curve 1) and calculated (based on molecular field theory; curve 2) dependencies of cM(T) are shown in fig. 2 and c,(T), cM(T), c,,,,(T) in the temperature range 200-300 K in fig. 3. C~ does not vanish at 0, but monotonously decreases to zero when approaching to room temperature. This phenomenon indicates the absence of a transformation of magnetic structure at T < 300 K. In our opinion such behavior of C~ confirms the suggestion about conservation of clusters with short-range magnetic ordering over the temperature range 0,-T,. The concentration and size of these clusters decrease with increasing temperature. The area under the cM(T) curve is equal to the energy (&) which necessary to
S.A. Nikitin
28
c
et al. / Specific heat in Dy single crvstal
23 200
150
250
Temperature,
360
300
K
Fig. 3. Dependences of electron (curve l), magnetic (curve 2) and lattice (curve 3) parts of the specific heat versus temperature above 0,.
transfer the system from a magneto-ordering state (T -c 0,) to a magneto-disordering state (T > 0, ). The integration of experimental cM(T) data between 0 K and 0, gives a value of 2188.4 J/mol, between 0, and 300 K - 180.7 J/mol. Based on experimental and theoretical cM( T) dependencies we plot the c,(T)-T curve and calculate the magnetic part of the entropy (fig. 4) with the
Over the temperature range 0 K-O, the magnetic part of the entropy equals 22 J/mol K, above O2 1 J/molK. Thus the total value of S, is equal to 23 J/mol K in agreement with the theoretical values S, = R ln(2j + 1) (23 J/mol K for Dy). Comparing the magnetic part of the entropy below and above 0, we conclude that in the paramagnetic region only 5% of the entropy caused by magnetic ordering at T < 0, is conserved. It is interesting to compare the experimental values of and S, with data from molecular-field theQM ory. Calculated values of QM and S, are equal to 1946.5 J/mol and 18.5 J/mol K, respectively. Note the proximity of theoretical and experimental maxima of cM in the 0, point (fig. 2). As in the molecular-field theory the existence of magnetic ordering is suggested, we conclude that the ferromagnetic ordering within basal planes gives the main contribution to the magnetic part of the specific heat. The contribution of the helicoidal structure is small.
References (3)
7 I
(
0” 0
1 50
I 100
Temperature,
150
200
250
K
Fig. 4. Experimental and calculated dependences of the magnetic part of the entropy versus temperature.
[l] G.I. Kataev, S.V. Kortov, M.R. Sattarov and A.M. Tishm. Proc. 2nd All-Union Conf. Magnetic Phase Transition and Critical Phenomena, Mahachkala, 1989. p. 125 (in Russian). PI N.G. Baazov and A.G. Mandjavidze, in: Investigation of Rare-Earth Magnets by Neutron Methods (Metsniereha. Tbilisi, 1983) p. 96 (in Russian). Physics of Rare-Earth C‘om[31 K. Teylor and M. Darby, pounds (Mir, Moscow. 1974) p. 374 (in Russian). and F.H. Spedding, J. <‘hem. [41 M. Griffel, R.E. Skochodopole Phys. 25 (1956) 75. [51 T.I. Kostina, V.N. Menshov and V.V. Tugushev. Fir. Met. Metalloved. 59 (1985) 430 (in Ruwan). [61 S.V. Vonsovski. Magnetism (Nauka. Moscow. 1971) p. 1032 (in Russian). USSR [71 A.M. Tishin. PhD thesis, Moscow State Ciniversitv, (1988) (in Russian). PI L. Girifalko, Statistical Physics of Solid State (Mir. Moscow. 1975) p. 382 (in Russtan).