~i ELSEVIER
Journal of Magnetism and Magnetic Materials 170 (1997) 223 227
Jewnal of amni~gnellsm nlaglmllc materials
Magnetic method of magnetocaloric effect determination in high pulsed magnetic fields R.Z. Levitin a, V.V. Snegirev a, A.V. Kopylov b, A.S. Lagutin b'*, A.
Gerber c
aMoscow State University, 117234, Moscow, Russia b Russian Research Center 'Kurchatov Institute', 123182, Moscow, Russia c Tel Aviv UniversiO,. 69979, Tel Aviv. Israel
Received 6 September 1996
Abstract A contactless method of magnetocaloric effect measurements is described, based on the comparison of magnetisation curves obtained in adiabatic and isothermal processes. By this method the magnetocaloric effect of paramagnetic garnet Gd3GasO12 is studied in pulsed magnetic fields up to 400 kOe. PACS:
75.20.-g; 75.30.Sg
Kewvords:
Magnetocaloric effect; Paramagnet; Magnetisation curve
The magnetocaloric effect represents by itself the temperature change of a magnetic sample during the process of its adiabatic magnetisation in an external magnetic field. There are several reasons which make this phenomenon of great interest. First of all, the study of the magnetocaloric effect gives important information about the magnetic state of materials under investigation. The best illustration of that is the classical research of Weiss and Forrer [1] on determination of the value of the exchange interactions in ferromagnets. The importance of the magnetocaloric effect investiga-
*Corresponding author. Tel.: + 7-095-196-7604; fax: + 7095-196-1632; e-mail:
[email protected]. 0304-8853/97/$17.00 ~, 1997 Elsevier Science B.V. All Pll S0304-88 53(96)00688-9
tions is caused also by technical applications, linked with using of this phenomenon in refrigerators [2m]. Till now, the magnetocaloric effect magnitude was derived directly by means of temperature measurements of a magnetic sample during its adiabatic magnetisation and demagnetisation. In this paper, another approach is proposed to measure the magnetocaloric effect value without any direct measurements of the sample temperature. The idea of the method is based on a comparison of the magnetisation curves of a sample, obtained in isothermal and adiabatic conditions. It is well known that the temperature of ferro- and paramagnets increases during the adiabatic magnetisation. As a result, the adiabatic magnetisation
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R.Z Levitin et al. / Journal of Magnetism and Magnetic Materials 170 (1997) 223-227
curve of the samples with initial temperature To will intersect the isothermal curves obtained at still higher temperatures TI, T2, ..., T,. The crossing points of the adiabatic curve with the set of isothermal curves determine the fields, in which a studied sample has corresponding temperatures. So, it is possible to construct (from point to point) full field dependence of the sample temperature during its adiabatic magnetisation. The simplest way to realise the proposed method is to compare the data of magnetisation measurements (M(H) curves) in static and pulsed magnetic fields. Typically, the magnetisation measurements in static fields are carried out under isothermal conditions (if no special measures are accepted) practically in all cases. The character of a thermal regime of the magnetisation measurements in pulsed magnetic fields depends on the field sweep rate, thermal parameters of a sample, conditions of the heat exchange between sample and cooling bath and is, normally, polythropic (e.g. intermediate between the isothermal and adiabatic ones). The estimates made by Ponomarev [5] along with our results (see below) have shown that the magnetisation process is close to being adiabatic at the field sweep rate of about 10 4 kOe/s and more, if a sample with dimensions of the order of several millimetres is in good thermal contact with the cooling bath (liquid nitrogen or helium). A decrease of the field sweep rate up to 10-100 kOe/s makes the magnetisation process practically isothermal. There exists a simple way to determine the character of magnetisation in pulsed magnetic fields, because the adiabatic process (as well as the isothermal one) is reversible and the corresponding reversible magnetisation curves do not manifest hysteresis, in other words, M(H) curves coincide for ascending and descending external fields. At the same time, the magnetic hysteresis arises each time, when the magnetisation process is polythropic due to different thermal regimes for increasing and decreasing fields. The aim of this paper is to demonstrate the possibilities of the magnetic method for the measurements of a magnetocaloric effect in the paramagnet Gd3GasO12. The compound has cubic crystal structure of a garnet type. Its magnetic properties are well known [6]: Gd3GasO~2 is anti-
ferromagnetic below 0.7 K and it is a classical paramagnet above this temperature. So, its magnetic properties at T > 2 K are well described in the molecular field approximation for a magnet with the localised magnetic moments. In the framework of this model the magnetisation/2 and the paramagnetic susceptibility 7~ (per one Gd 3+ ion) are as follows: /2 =/2BBs
C Z - T _ 0.
IH + 2/2'1,
(1)
(2)
Here Po = gJ/2B is magnetic moment of saturation (for Gd 3+ these parameters are equal to g = 2, J = S = 3,/2o = 7/2B), Bs is the Brillouin function, 2 is the exchange constant, C is the Curie constant (C = J(J + 1)g2/2~/3k), 0 = cZ is paramagnetic Curie temperature, O = - 2.8 K for Gd3GasO12. Magnetic anisotropy of the garnet is negligibly small, because the Gd 3 + ion is in the s-state (its orbital moment equals zero) and one can compare the adiabatic magnetisation of a Gd3GasO12 garnet, measured experimentally with the calculated isothermal M(H) curve for arbitrary field. That gives an opportunity to get the values of the magnetocaloric effect up to maximum fields, available in the pulsed field experiments. In this work magnetisation measurements of Gd3GasO12 single crystals were performed in pulsed magnetic fields up to 40 T. The pulse duration was around 9 ms and the corresponding field sweep rate was in the range from 150 to 2 MOe/s. The samples in the form of balls with diameters from 1 to 3 mm were immersed in liquid helium. Along with the pulsed measurements some magnetisation experiments were carried out in static fields up to 75 kOe. Fig. 1 shows a comparison of the experimental M(H) curve of a Gd3GasO12 garnet, obtained under isothermal conditions in relatively small static external fields, with the theoretical one, calculated using Eq. (1). It is clear that there is a good coincidence between theory and experiment in this case. It points out that it is possible to use the abovementioned theoretical relations to get realistic
R.Z Levitin et al. /Journal of Magnetism and Magnetic Materials 170 (1997) 223 227
8.00
225
- -
8.00
6 00
T
=
4
y
2
--
4oO2oo
--
~
Calculation
+
4.00
H, kOe ooo F
'
1
20
'
t
I
r
40
60
80
Fig. 1. Magnetisation versus field curves for a Gd3GasO,2 single crystal in static magnetic fields at T = 4.2 K: solid line theory; crosses - experimental data.
isothermal M ( H ) curves of the garnet in a r b i t r a r y magnetic fields, which is necessary to m a k e comparison between experimental adiabatic m a g n e t i s a tion curves a n d the isothermal ones. Fig. 2 illustrates the e x p e r i m e n t a l M ( H ) curves of a G d 3 G a s O l 2 crystal in pulsed m a g n e t i c fields with an average sweep rate a r o u n d 50 M O e / s at an initial t e m p e r a t u r e To = 4.2 K. It is evident that the magnetic hysteresis is practically absent. The latter testifies that the process of m a g n e t i s a t i o n is purely adiabatic. Several isothermal M ( H ) curves, calculated at different t e m p e r a t u r e s by m e a n s of Eq. (1t, are also s h o w n in Fig. 2. As was discussed above, there are intersections between the adiabatic a n d isothermal m a g n e t i s a t i o n curves. The t e m p e r a t u r e d e p e n d e n c e of a G d 3 G a s O 1 2 crystal versus field (T(H) curves) u n d e r adiabatic change of external m a g n e t i c (the m a g n e t o c a l o r i c effect) field is presented in Fig. 3. It is clear from the figure that the sample heating is rather significant: at the m a x i m u m field of 40 T the sample temperature reaches 50 K, e.g. d u r i n g the field pulse a temperature change of a b o u t A T = 46 K takes place at the initial t e m p e r a t u r e T = 4.2 K.
o.oo
'
I
- - ]
'
200
400
Fig. 2. Magnetisation versus field for a Gd3Ga~O12 single crystal in pulsed field (thick line) at initial temperature T, = 4.2 K, obtained in experiments with average sweep rate around 50 MOe/s. Thin solid lines show the set of calculated isothermal MIH) curves, starting with T = 5 K (top curve). The temperature step between the adjacent curves is AT - 5 K.
T, K
60.00
(go = 450 K
~,~.-~-jr
4OOO
H,
~
o0o
0
F
100
F
{
200
kOe '
T
300
w-
400
Fig, 3. Field dependence of temperature of a Gd3GasO t 2 single crystal, obtained in the pulsed field experiment. Thick line illustrates the experimental result, thin lines show the simulation for three different Debye temperatures.
R.Z. Levitin et al. / Journal o f Magnetism and Magnetic Materials 170 (1997) 223 227
226
The literature data concerning the magnetocaloric effect in a Gd3GasO12 garnet [7] do not give opportunity to make a comparison with our results, because they were obtained for another temperature range. To check the derived T(H) curves we have chosen the following approach. From thermodynamics it is known that one can describe the magnetocaloric effect using the relation [-8]
T,K 10,00
8.00 6.00
6.00 4,00"
400
dT = Cm\~T /mdM.
(3)
Here Cm is the heat capacity at constant magnetisation and it does not include the magnetic part of the heat capacity. It contains only the lattice contribution in the case of a garnet (for metals one needs to take into account the electronic contribution also). From Eqs. (3) and (1) after trivial, but cumbersome transformations it is easy to get an integral relation for description of the magnetocaloric effect
I T Clat(Y) d y J
~#/u~ = n
Jo
_ B
t(z) dz.
(4)
Here C~at is the lattice heat capacity per mole of the garnet
C,at = 3RF(T/OD),
(5)
where F is the Debye function, OD is the Debye temperature, n = 3 is the number of Od 3 + ions per formula unit, Bs l(z) is the reversed Brillouin function and R is the gas constant. One can determine the temperature dependence of a sample versus applied field by using Eq. (5) and experimental data on its adiabatic magnetisation, if the Debye temperature is known. The experimental T(H) dependence is shown on Fig. 3 together with the theoretical curves, derived for different Debye temperatures. The best agreement between the simulations and the experimental results was found at OD = 390 K, but in this case some divergences in low-field region still exist. Possibly this is due to the transient process in the sample during the initial stage of pulsed magnetisation process which produces the inhomogeneous sample temperature distribution. This value of the Debye temperature is close to literature data O r ) = 380 K [-9] and OD = 410 K [-73, which points out the adequacy of
2.00 2.00
H, kOe 000
-0.00 50
100
150
200
250
Fig. 4. Field dependenciesof magnetisation (crosses)and temperature (triangles)of a Gd3GasO12 singlecrystalin pulsed field at initial temperature To = 4.2 K, obtained in experimentswith average sweep rate around 0.2 MOe/s.
this method for the measurements of magnetocaloric effect. A possible transformation of the M(H) curve and the corresponding magnetocaloric effect at low sweep rate of external magnetic field is illustrated in Fig. 4. Due to the large pulse duration (of about 0.5 s) the average dH/dt did not exceed 0.2 MOe/s and, as a result, the magnetisation process of a Gd3GasO12 crystal became polythropic. Comparison of Figs. 2 and 4 gives the opportunity to conclude that the border between adiabatic and polythropic regimes of the pulsed magnetisation process (q) is situated in the range 2 > r / > 0.2 MOe/s in the case of the studied garnet. We turn our attention to the fact that the magnetocaloric data enable one to obtain directly the lattice heat capacity, which is difficult in many cases, if the magnetic contribution to heat capacity is large. It is important also to note that our consideration, made for paramagnets, can be easily generalised for ferromagnets. There are no difficulties in expanding the consideration for magnets, which include ions with non-zero orbital moments, if the energetic levels and corresponding wave function of the ions are known. Finally, if these data are not available, it is possible to compare adiabatic experimental curves with the isothermal ones, obtained in experiments also.
R.Z Levitin et al. /Journal of Magnetism and Magnetic: Materials 170 (1997) 223-227
Acknowledgements This work was supported by INTAS (grant No 94-3569) and RFBR (grant No 95-02-0651a). References [1] P. Weiss and R. Forrer, Comptes Rendus 178 (1924) 1670. [2] T. Hashimoto, T, Numasawa, M. Shino and T. Okada, Cryogenics 21 (1981) 647.
227
[3] H. Oesterreicher and F.T. Parker, J. Appl. Phys. 55 (1984) 4334. [4] M.D. Kuz'min and A,M. Tishin, Cryogenics 32 (1992) 545. [57 B.K. Ponomarev, Private communication. [6] Landolt-B6rnstein, New Series, Vol. III/12a (Springer-Verlag, Berlin/Heidelberg, 1978) Section 1.3. [7] J.A. Barclay and W.A. Steyert, Cryogenics 22 (1982) 73. [8] R. Kubo, Thermodynamics (North-Holland, Amsterdam, 1968). [9] D.J. Onn, H. Meier and J.P. Remeika. Phys. Rev. 156 (1967) 663.
