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The magnetic phase transitions in (Tb, Ho)Co2 and (Tb, Y)Co2 compounds
Physica B 160 (1989) 199-203 North-Holland, Amsterdam
THE MAGNETIC PHASE TRANSITIONS IN (Tb, Ho)Co, AND (Tb, Y)Co, COMPOUNDS N.H. DUC’, T.D. HIEN’, P.P. MAI’, N.H.K. J.J.M. FRANSE Natuurkundig
Laboratorium
NGAN’, N.H. SINH’, P.E. BROMMER
der Universiteit van Amsterdam,
Valckenierstraat 6.5, 1018 XE, Amsterdam,
and
The Netherlands
Received 10 March 1989
The type of the magnetic phase transitions in a series of Tb,Ho,_xCo, and Tb,Y,_,Co, compounds is studied by means of magnetization, electrical-resistivity and specific-heat measurements. In both systems the Tc values decrease with decreasing Tb content. At about x = 0.7 the type of the magnetic transition changes from second order to first order. An explanation is offered in terms of the Inoue-Shim&u model by taking into account the strong temperature dependence of the magnetic susceptibility of the 3d itinerant electrons.
1. Introduction
such as the total molar magnetic moment M:
The order of the magnetic phase transition in the cubic Laves phase compounds RECo, (RE: heavy rare earth) is related to the metamagnetism of the itinerant d-electrons. The occurrence of metamagnetism in YCo, follows from electronic-structure calculations (e.g., ref. [l]) and can be connected with a negative sign of the coefficient a3 in the expansion of the free energy of the itinerant-electron subsystem in terms of the magnetic molar moment on the Co atoms M,
F(M)
PI: Fd(Md)= &@4; + &z,h4;+ $Q4f;. The temperature imated as a,(T) =
dependence
(1)
of u3( T) is approx-
a,(O)[l - (TIQ21 3
(2)
u,(O) is negative.
Bloch et al. [2] deduced T3 = 250 K from the temperature dependence of the susceptibility of YCo,. Inoue and Shimizu [3] stressed the importance of an expansion of the total free energy in terms of a proper thermodynamical variable ’ Permanent address: Cryogenic Laboratory, Hanoi, SR Vietnam.
University
of
= F,, + +c,M* + $c,M4 + ;c,M6.
(3)
The order of the magnetic transition is now determined by the sign of c3(Tc). In practice, however, this sign is very much governed by the sign of u,(T,). Notice, that T, is defined as the temperature at which c1 vanishes: c,(T,) = 0. In comparison with experiment T, is taken to indicate not only the critical temperature for a second order transition, but to be a measure for the transition temperature for a first order transition as well. On the basis of the Inoue-Shimizu model Due et al. [4] offered a satisfactory explanation for the observed behaviour in the RECo, compounds. It appeared to be necessary to adopt a value T3 = 178 K in order to explain the change in type of the transition: going from Er to Gd the transition changes from a first-order one for RE = Er, Ho and Dy (with Tc equal to 32.6, 75 and 140 K, respectively, all below T3 = 178 K) to a second-order one for RE = Tb and Gd (with T, equal to 227 and 395 K, respectively, all above T3). Obviously, TbCo, is near the borderline between a first-order transition and a second-order one. Consequently, a change from second order to first order is expected in case T, is reduced to values below T3 by substituting Tb
0921-4526/89/$03.50 @ Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
200
N.H.
Due et al.
I Magnetic
by a rare-earth ion with lower spin value (Dy, Ho, Er, see T, values given above) or by nonmagnetic Y. Indeed, Franse et al. [5] concluded from ac-susceptibility and thermal-expansion measurements on a series of Tb,Y I_xCoZ compounds, that such a change in type of the magnetic phase transition does occur at about x = 0.7 (see also Levitin et al. [6]). Furthermore, Due et al. [4] concluded from the change of the type of magnetic transition in a series of (Er, Y)Co, compounds, that the appropriate value for a,(O) must be a,(O) = -6.8 T(mol/Am2)3. In this paper we present our studies of the transition in Tb,Ho,_,Co, and magnetic Tb,Y 1_xCo2 by measurements of the magnetization, the electrical resistivity and the specific heat.
2. Experimental The Tb,Ho,_,Co, and Tb,Y,_,Co, compounds were prepared by arc-melting stoichiometric mixtures of rare-earth metals (3N) and cobalt (4N8) under a helium atmosphere in a water-cooled copper container. The ingots were annealed in a quartz tube under vacuum at 700°C during 4 days. The cubic Laves phase structure was verified by X-ray diffraction. The magnetization was measured by an induction method. Using a four-terminal measuring technique on bar-shaped samples (size of about 1 x 1 x 7 mm3) data for the electrical resistivity were obtained quasi-continuously by slowly changing the temperature. Specific heat measurements were performed by an adiabatic method.
phase transitions
40 -i 230 “E ” b 20
10
0 0
100
T(K)
Fig. 1. The temperature dependence an applied field of 0.1 T for TbxHo,
200
300
of the magnetization _,Co,.
in
is observed around T,, whereas for the lower Tb-concentrations a sharp transition is observed. This difference is ascribed to the changeover from a second-order transition to a first-order one. Qualitatively, the same features were observed by Abd El-Aal et al. [7], although these authors report a less sharp transition in the Ho-rich compounds. Figures 3 and 4 show the resistivity data observed on these compounds. For all samples the resistivity tends to saturate at T > T,, whereas around T, a strong change of slope is found. These changes are almost discontinuous in the Tb,Ho,_,Co, compounds with x up to 0.7. This behaviour is indicative for the first-order transition. In the Tb,Y,_,Co, series this first-order
40
T-- 3 N’
3. Experimental
results and discussion
For Tb,Ho,_,Co, and Tb,Y,_,Co, the temperature dependence of the magnetization in an applied field of 0.1 T is shown in fig. 1 and fig. 2. All samples show ferromagnetic (or ferrimagnetic) behaviour. Tc decreases with decreasing Tb content. For the higher Tb-concentrations (x > 0.7) a gradual change of the magnetization
s 20
,,
10
0 0
200
100
3
T(K)
Fig. 2. The temperature dependence of the magnetization an applied field of 0.1 T for Tb,Y ,_,Co,.
in
201
N. H. Due et al. I Magnetic phase transitions
type behaviour is somewhat less clearly seen in the compounds with x =0.3 and x =0.5. The change of type of the phase transition is also confirmed by the specific-heat measurements (see fig. 5). The Curie temperatures of these compounds are determined by ac-susceptibility measurements. The results are listed in table I and II. The T, values are in good agreement with those reported in the literature [5,8,9]. In the Inoue-Shimizu model as generalized by one of us [lo] the Curie temperature can be written as
TC = I
(NApB)2 J2,_,,& 3R
x Od
(T C )
(4)
I
200
100
300 TIKI
Fig. 3. The temperature dependence of the electrical resistivity for the Tb,Ho,_,Co, compounds. The curves for different concentrations are shifted consecutively. For all compounds the maximum resistivity value is about 150 @cm.
where NA (Avogadro’s number), R = A%, (gas constant), p. and pB have their usual meaning. J R-Co 3 the effective exchange constant, represents the interaction between a 4f-spin and a 3dspin, and is connected to the molecular field constant ndi (in the molar interaction energy
400
300 Y _: E 2 u” 200
100
50
100
150
200
250
300
T(K)
Fig. 4. The temperature dependence of the electrical resistivity for the Tb,Y,_,Co, compounds. The curves are shifted (see caption to fig. 3).
0 200
100
300
TIK)
Fig. 5. The specific heat as a function of temperature Tb, ,Y&o, and Tb,,Y&o,.
for
202
lldi
N.H.
=
JR-C,(gi- ‘j/g.
I
9
Due et al. I Magnetic phase transitions
(5)
where gj is the LandC g-factor for the rare earth ion R,. ,yd(T) is the temperature-dependent susceptibility of the 3d electrons, i.e., poxd( T) = 1 la,. G is the averaged De Gennes factor [(G = (_g - l)‘J(J + l)], i.e., for Tb,Y i_+Co2 we have G = xG,, and for Tb,Ho,_,Co, we have: 0
200
200
a3 + c3(Tc)
C,x,b,,(nd,lb,i)4
= q4
ii
( It,,
300
T
where GTb and G,, are the De Gennes factors of Tb and Ho, respectively. From the above expression for T, Due et al. [4] calculated ,yd(Tc) for the heavy rare-earth RECo, compounds and for a series of taking JR_co = 18.5 x (Er, Y)Co, compounds, lo6 mol/m3 (consistent with T, = 395 K for GdCo, combined with ~~(395 K) = 46.5 x 10e9 m3/mol). In fig. 6 it is shown that the resulting temperature dependence appears to be similar to that for YCo, and to be in good agreement with that for LuCo, [ll-141. For the compounds under consideration in this paper an analogous calculation has been carried out. The resulting xd(Tc) values are listed in table I and II, and are plotted in fig. 6 together with the earlier results. For the (Tb, Ho)Co, series a gradual decrease of xd( T,) with decreasing T, is calculated. A similar decrease was calculated for the RECo, series, in good agreement with the behaviour of x,(T) for LuCo,. For the (Tb, Y)Co, compounds xd( T,) increases initially and decreases only for T, values below 170 K. An analogous behaviour was found in the (Gd, Y)Co, series [4]. The difference in behaviour might be related to a slight change in the density of states due to a decrease of the atomic d-level of the rare-earth ions. In the generalized Inoue-Shimizu model [lo] the coefficient cl(T) can be expressed as:
* .
t:,
Yi
[;rJ;,
I lo)
c:“;’
400
-
(IO
Fig. 6. The 3d susceptibility xd(T) at T= Tr for (Tb, Ho)Co, and for (Tb, Y)Co,. For comparison, xd(T) at T = Tc for RCo, (R = Gd, Tb, Dy, Ho, Er) and (Gd, Y)Co, are given too (see ref. [4]), as well as the temperature dependence of the susceptibility x(T) for YCo, [2,11] and LuCo, [ll, 121 (drawn curves). At low temperatures the data for LuCo, obtained by Ikeda et al. [14] and Shinogi et al. [13] yield somewhat lower X-values. Shinogi’s extrapolated value at zero temperature is indicated in the figure (x).
Here,
q
is given by
q = 1 + C;Xindrlb,;
.
(8)
In these expressions ndl is given by eq. (5). b,; and b,i are the corresponding coefficients in the expansion of the magnetic free energy of the
Table
I
The calculated results for the TbXY,_,Co, compounds: x.,(Tc) from eq. (4), with J,.,, = 18.5 x lo6 molim’, and using the experimentally determined r, values. cl( T,) from eq. (7), with b,(T,) and b,(T,) from eqs. (9a.b) (for Tb). a,(T,) from eq. (2) with a,(O) = -6.8T(mol/Am2)‘. l/(4 1) = n,,xJT,), with nd, given by eq. (5) (for Tb): x
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
100a3
Tr
xc0cl
100C)
K
10e9 m’imol
T(mol/AmZ)’
38 67 98 128 154 176 197 214 227
33.6 39.4 43.3 45.2 45.3 44.4 43.5 42.0 40.1
-3.02 -6.26 -8.35 -7.35 -3.84 -0.23 2.87 4.66 5.11
-649 -584 -474 -328 -171 -15 153 303 426
ll(q -0.21 -0.24 -0.27 -0.28 -0.28 -0.27 -0.27 -0.26 -0.25
- 1)
N. H. Due et al. I Magnetic phase transitions
Table II The calculated results for the Tb,Ho,_,Co, compounds: xd(Tc) from eq. (4), with J,_,, = 18.5 x lo6 mol/m3, and using the experimentally determined Tc values. c,( Tc) from eq. (7), with b,(Tc) and b,(Tc) from eqs. (9a,b) (for Tb as well as Ho). a,(T,) from eq. (2), with a,(O) = -6.8T(mol/Am*)‘. l/( q - 1) from eq. (8), with n,,, and ndZ given bv eo. (5) (for Tb and Ho, respectivelv). x
0.00 0.10 0.15 0.30 0.70 0.90 1.00
TC- xd(Tc) 10m9 m’/mol
100 c1 100 a3 T(mol/Am*)3
l/(q
K 75 85 94 129 185 210 227
30.9 30.9 32.3 38.0 39.4 39.3 40.1
-0.14 -0.21 -0.29 -0.67 0.37 2.48 5.11
-0.11 -0.12 -0.14 -0.18 -0.22 -0.24 -0.25
-559 -525 -490 -323 55 266 426
- 1)
subsystem of the rare-earth ions Ri in the binary compound Rico,. Explicit expressions are given in ref. [3]. Here, dropping the index i we reproduce the expressions for b, and b,: 3RT b1 = (JY4PB)*{g2J(J + 1)) 9RT b3 =
20
(2J + l)* + 1 J3(J + 1)3( gN*&)4
.
Pb)
Taking the same values as in ref. [4], i.e., a,(O) = -6.8 T(mol/Am2)3 and T3 = 178 K, we calculated the relevant coefficients. The results ar given in tables I and II. Clearly, the sign of c3(Tc) is in accordance with the type of the transition.
4. Concluding
remarks
The magnetic phase transitions in the (Tb, Ho)Co, and the (Tb, Y)Co, compounds are
203
of special interest because TbCo, is quite near the border between a first-order transition and a second-order one in the series of RECoz compounds. At substituting Tb by Ho or Y, the Tc-value of these compounds is reduced as well as xd(T,-J, and the transition changes from second order to first order. The strong temperature dependence of xd( T) is important in the determination of T,, and thus in the sign of the coefficient cg( T,), which determines the type of the magnetic transition. Consequently, a satisfactory description has been provided for the change of type of the magnetic phase transition.
References (11 M. Cyrot and M. Lavagna, J. de Phys. 40 (1979) 763. [2] D. Bloch, D.M. Edwards, M. Shimizu and J. Voiron, J. Phys. F 5 (1975) 1217. [3] J. Inoue and M. Shimizu, J. Phys. F 12 (1982) 1811. [4] N.H. Due, T.D. Hien, P.E. Brommer and J.J.M. Franse, J. Phys. F 18 (1988) 275. [5] J.J.M. Franse, T.D. Hien. N.H.K. Ngan and N.H. Due, J. Magn. _ Magn. _ Mat. 39 (1983) 275. Fl R.Z. Levitin, A.S. Markdsyan ‘and VV Snegirev, Sov. Phys. Solid State 26 (1984) 16. [71 M.M. Abd El-Aal, A.S. Ilyshin and V.I. Chernicov, J. Magn. Magn. Mat. 69 (1987) 325. PI Y. Berthier, D. Gignoux, R. Kuentzler and A. Tari, J. Magn. Magn. Mat. 58 (1986) 265. and A. Tari, J. Magn. Magn. Mat. 61 [91 R. Kuentzler (1986) 29. [lOI P.E. Brommer, Physica B 154 (1989) 197. [Ill R. Lemaire, Cobalt 33 (1966) 210. Solid State Commun. 9 1121 D. Givord and R. Lemaire, (1981) 341. iI31 A. Shinogi, M. Iijima, T. Saito and K. Endo, Physica B 149 (1988) 323. Jr, R.J. Stierman, T.W.E. [I41 K. Ikeda, K.A. Gschneidner Tsang and O.D. Masters, Phys. Rev. B 29 (1984) 5037.
THE MAGNETIC PHASE TRANSITIONS IN (Tb, Ho)Co, AND (Tb, Y)Co, COMPOUNDS N.H. DUC’, T.D. HIEN’, P.P. MAI’, N.H.K. J.J.M. FRANSE Natuurkundig
Laboratorium
NGAN’, N.H. SINH’, P.E. BROMMER
der Universiteit van Amsterdam,
Valckenierstraat 6.5, 1018 XE, Amsterdam,
and
The Netherlands
Received 10 March 1989
The type of the magnetic phase transitions in a series of Tb,Ho,_xCo, and Tb,Y,_,Co, compounds is studied by means of magnetization, electrical-resistivity and specific-heat measurements. In both systems the Tc values decrease with decreasing Tb content. At about x = 0.7 the type of the magnetic transition changes from second order to first order. An explanation is offered in terms of the Inoue-Shim&u model by taking into account the strong temperature dependence of the magnetic susceptibility of the 3d itinerant electrons.
1. Introduction
such as the total molar magnetic moment M:
The order of the magnetic phase transition in the cubic Laves phase compounds RECo, (RE: heavy rare earth) is related to the metamagnetism of the itinerant d-electrons. The occurrence of metamagnetism in YCo, follows from electronic-structure calculations (e.g., ref. [l]) and can be connected with a negative sign of the coefficient a3 in the expansion of the free energy of the itinerant-electron subsystem in terms of the magnetic molar moment on the Co atoms M,
F(M)
PI: Fd(Md)= &@4; + &z,h4;+ $Q4f;. The temperature imated as a,(T) =
dependence
(1)
of u3( T) is approx-
a,(O)[l - (TIQ21 3
(2)
u,(O) is negative.
Bloch et al. [2] deduced T3 = 250 K from the temperature dependence of the susceptibility of YCo,. Inoue and Shimizu [3] stressed the importance of an expansion of the total free energy in terms of a proper thermodynamical variable ’ Permanent address: Cryogenic Laboratory, Hanoi, SR Vietnam.
University
of
= F,, + +c,M* + $c,M4 + ;c,M6.
(3)
The order of the magnetic transition is now determined by the sign of c3(Tc). In practice, however, this sign is very much governed by the sign of u,(T,). Notice, that T, is defined as the temperature at which c1 vanishes: c,(T,) = 0. In comparison with experiment T, is taken to indicate not only the critical temperature for a second order transition, but to be a measure for the transition temperature for a first order transition as well. On the basis of the Inoue-Shimizu model Due et al. [4] offered a satisfactory explanation for the observed behaviour in the RECo, compounds. It appeared to be necessary to adopt a value T3 = 178 K in order to explain the change in type of the transition: going from Er to Gd the transition changes from a first-order one for RE = Er, Ho and Dy (with Tc equal to 32.6, 75 and 140 K, respectively, all below T3 = 178 K) to a second-order one for RE = Tb and Gd (with T, equal to 227 and 395 K, respectively, all above T3). Obviously, TbCo, is near the borderline between a first-order transition and a second-order one. Consequently, a change from second order to first order is expected in case T, is reduced to values below T3 by substituting Tb
0921-4526/89/$03.50 @ Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
200
N.H.
Due et al.
I Magnetic
by a rare-earth ion with lower spin value (Dy, Ho, Er, see T, values given above) or by nonmagnetic Y. Indeed, Franse et al. [5] concluded from ac-susceptibility and thermal-expansion measurements on a series of Tb,Y I_xCoZ compounds, that such a change in type of the magnetic phase transition does occur at about x = 0.7 (see also Levitin et al. [6]). Furthermore, Due et al. [4] concluded from the change of the type of magnetic transition in a series of (Er, Y)Co, compounds, that the appropriate value for a,(O) must be a,(O) = -6.8 T(mol/Am2)3. In this paper we present our studies of the transition in Tb,Ho,_,Co, and magnetic Tb,Y 1_xCo2 by measurements of the magnetization, the electrical resistivity and the specific heat.
2. Experimental The Tb,Ho,_,Co, and Tb,Y,_,Co, compounds were prepared by arc-melting stoichiometric mixtures of rare-earth metals (3N) and cobalt (4N8) under a helium atmosphere in a water-cooled copper container. The ingots were annealed in a quartz tube under vacuum at 700°C during 4 days. The cubic Laves phase structure was verified by X-ray diffraction. The magnetization was measured by an induction method. Using a four-terminal measuring technique on bar-shaped samples (size of about 1 x 1 x 7 mm3) data for the electrical resistivity were obtained quasi-continuously by slowly changing the temperature. Specific heat measurements were performed by an adiabatic method.
phase transitions
40 -i 230 “E ” b 20
10
0 0
100
T(K)
Fig. 1. The temperature dependence an applied field of 0.1 T for TbxHo,
200
300
of the magnetization _,Co,.
in
is observed around T,, whereas for the lower Tb-concentrations a sharp transition is observed. This difference is ascribed to the changeover from a second-order transition to a first-order one. Qualitatively, the same features were observed by Abd El-Aal et al. [7], although these authors report a less sharp transition in the Ho-rich compounds. Figures 3 and 4 show the resistivity data observed on these compounds. For all samples the resistivity tends to saturate at T > T,, whereas around T, a strong change of slope is found. These changes are almost discontinuous in the Tb,Ho,_,Co, compounds with x up to 0.7. This behaviour is indicative for the first-order transition. In the Tb,Y,_,Co, series this first-order
40
T-- 3 N’
3. Experimental
results and discussion
For Tb,Ho,_,Co, and Tb,Y,_,Co, the temperature dependence of the magnetization in an applied field of 0.1 T is shown in fig. 1 and fig. 2. All samples show ferromagnetic (or ferrimagnetic) behaviour. Tc decreases with decreasing Tb content. For the higher Tb-concentrations (x > 0.7) a gradual change of the magnetization
s 20
,,
10
0 0
200
100
3
T(K)
Fig. 2. The temperature dependence of the magnetization an applied field of 0.1 T for Tb,Y ,_,Co,.
in
201
N. H. Due et al. I Magnetic phase transitions
type behaviour is somewhat less clearly seen in the compounds with x =0.3 and x =0.5. The change of type of the phase transition is also confirmed by the specific-heat measurements (see fig. 5). The Curie temperatures of these compounds are determined by ac-susceptibility measurements. The results are listed in table I and II. The T, values are in good agreement with those reported in the literature [5,8,9]. In the Inoue-Shimizu model as generalized by one of us [lo] the Curie temperature can be written as
TC = I
(NApB)2 J2,_,,& 3R
x Od
(T C )
(4)
I
200
100
300 TIKI
Fig. 3. The temperature dependence of the electrical resistivity for the Tb,Ho,_,Co, compounds. The curves for different concentrations are shifted consecutively. For all compounds the maximum resistivity value is about 150 @cm.
where NA (Avogadro’s number), R = A%, (gas constant), p. and pB have their usual meaning. J R-Co 3 the effective exchange constant, represents the interaction between a 4f-spin and a 3dspin, and is connected to the molecular field constant ndi (in the molar interaction energy
400
300 Y _: E 2 u” 200
100
50
100
150
200
250
300
T(K)
Fig. 4. The temperature dependence of the electrical resistivity for the Tb,Y,_,Co, compounds. The curves are shifted (see caption to fig. 3).
0 200
100
300
TIK)
Fig. 5. The specific heat as a function of temperature Tb, ,Y&o, and Tb,,Y&o,.
for
202
lldi
N.H.
=
JR-C,(gi- ‘j/g.
I
9
Due et al. I Magnetic phase transitions
(5)
where gj is the LandC g-factor for the rare earth ion R,. ,yd(T) is the temperature-dependent susceptibility of the 3d electrons, i.e., poxd( T) = 1 la,. G is the averaged De Gennes factor [(G = (_g - l)‘J(J + l)], i.e., for Tb,Y i_+Co2 we have G = xG,, and for Tb,Ho,_,Co, we have: 0
200
200
a3 + c3(Tc)
C,x,b,,(nd,lb,i)4
= q4
ii
( It,,
300
T
where GTb and G,, are the De Gennes factors of Tb and Ho, respectively. From the above expression for T, Due et al. [4] calculated ,yd(Tc) for the heavy rare-earth RECo, compounds and for a series of taking JR_co = 18.5 x (Er, Y)Co, compounds, lo6 mol/m3 (consistent with T, = 395 K for GdCo, combined with ~~(395 K) = 46.5 x 10e9 m3/mol). In fig. 6 it is shown that the resulting temperature dependence appears to be similar to that for YCo, and to be in good agreement with that for LuCo, [ll-141. For the compounds under consideration in this paper an analogous calculation has been carried out. The resulting xd(Tc) values are listed in table I and II, and are plotted in fig. 6 together with the earlier results. For the (Tb, Ho)Co, series a gradual decrease of xd( T,) with decreasing T, is calculated. A similar decrease was calculated for the RECo, series, in good agreement with the behaviour of x,(T) for LuCo,. For the (Tb, Y)Co, compounds xd( T,) increases initially and decreases only for T, values below 170 K. An analogous behaviour was found in the (Gd, Y)Co, series [4]. The difference in behaviour might be related to a slight change in the density of states due to a decrease of the atomic d-level of the rare-earth ions. In the generalized Inoue-Shimizu model [lo] the coefficient cl(T) can be expressed as:
* .
t:,
Yi
[;rJ;,
I lo)
c:“;’
400
-
(IO
Fig. 6. The 3d susceptibility xd(T) at T= Tr for (Tb, Ho)Co, and for (Tb, Y)Co,. For comparison, xd(T) at T = Tc for RCo, (R = Gd, Tb, Dy, Ho, Er) and (Gd, Y)Co, are given too (see ref. [4]), as well as the temperature dependence of the susceptibility x(T) for YCo, [2,11] and LuCo, [ll, 121 (drawn curves). At low temperatures the data for LuCo, obtained by Ikeda et al. [14] and Shinogi et al. [13] yield somewhat lower X-values. Shinogi’s extrapolated value at zero temperature is indicated in the figure (x).
Here,
q
is given by
q = 1 + C;Xindrlb,;
.
(8)
In these expressions ndl is given by eq. (5). b,; and b,i are the corresponding coefficients in the expansion of the magnetic free energy of the
Table
I
The calculated results for the TbXY,_,Co, compounds: x.,(Tc) from eq. (4), with J,.,, = 18.5 x lo6 molim’, and using the experimentally determined r, values. cl( T,) from eq. (7), with b,(T,) and b,(T,) from eqs. (9a.b) (for Tb). a,(T,) from eq. (2) with a,(O) = -6.8T(mol/Am2)‘. l/(4 1) = n,,xJT,), with nd, given by eq. (5) (for Tb): x
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
100a3
Tr
xc0cl
100C)
K
10e9 m’imol
T(mol/AmZ)’
38 67 98 128 154 176 197 214 227
33.6 39.4 43.3 45.2 45.3 44.4 43.5 42.0 40.1
-3.02 -6.26 -8.35 -7.35 -3.84 -0.23 2.87 4.66 5.11
-649 -584 -474 -328 -171 -15 153 303 426
ll(q -0.21 -0.24 -0.27 -0.28 -0.28 -0.27 -0.27 -0.26 -0.25
- 1)
N. H. Due et al. I Magnetic phase transitions
Table II The calculated results for the Tb,Ho,_,Co, compounds: xd(Tc) from eq. (4), with J,_,, = 18.5 x lo6 mol/m3, and using the experimentally determined Tc values. c,( Tc) from eq. (7), with b,(Tc) and b,(Tc) from eqs. (9a,b) (for Tb as well as Ho). a,(T,) from eq. (2), with a,(O) = -6.8T(mol/Am*)‘. l/( q - 1) from eq. (8), with n,,, and ndZ given bv eo. (5) (for Tb and Ho, respectivelv). x
0.00 0.10 0.15 0.30 0.70 0.90 1.00
TC- xd(Tc) 10m9 m’/mol
100 c1 100 a3 T(mol/Am*)3
l/(q
K 75 85 94 129 185 210 227
30.9 30.9 32.3 38.0 39.4 39.3 40.1
-0.14 -0.21 -0.29 -0.67 0.37 2.48 5.11
-0.11 -0.12 -0.14 -0.18 -0.22 -0.24 -0.25
-559 -525 -490 -323 55 266 426
- 1)
subsystem of the rare-earth ions Ri in the binary compound Rico,. Explicit expressions are given in ref. [3]. Here, dropping the index i we reproduce the expressions for b, and b,: 3RT b1 = (JY4PB)*{g2J(J + 1)) 9RT b3 =
20
(2J + l)* + 1 J3(J + 1)3( gN*&)4
.
Pb)
Taking the same values as in ref. [4], i.e., a,(O) = -6.8 T(mol/Am2)3 and T3 = 178 K, we calculated the relevant coefficients. The results ar given in tables I and II. Clearly, the sign of c3(Tc) is in accordance with the type of the transition.
4. Concluding
remarks
The magnetic phase transitions in the (Tb, Ho)Co, and the (Tb, Y)Co, compounds are
203
of special interest because TbCo, is quite near the border between a first-order transition and a second-order one in the series of RECoz compounds. At substituting Tb by Ho or Y, the Tc-value of these compounds is reduced as well as xd(T,-J, and the transition changes from second order to first order. The strong temperature dependence of xd( T) is important in the determination of T,, and thus in the sign of the coefficient cg( T,), which determines the type of the magnetic transition. Consequently, a satisfactory description has been provided for the change of type of the magnetic phase transition.
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