- Email: [email protected]
Magnetic susceptibility of LaxNd1−xF3 single crystals
~
ELSEVIER
Journalof magnetism and magnetic materials
Journal of Magnetism and Magnetic Materials 166 (1997) 231-236
Magnetic susceptibility of LaxNdl_xF3 single crystals M.L. Paradowski
a,*,
A.W. Pacyna
b,
A. Bombik c, W. Korczak
a,d,
S.Z. Korczak
a
a Institute of Physics, Maria Curie-Sktodowska University, Pl. Marii Curie-Sktodowskiej I, PL-20-031 Lublin, Poland b Henryk Niewodniczahski Institute of Nuclear Physics, W.E. Radzikowskiego 152, PL-31-342 Krakdw, Poland c Department of Physics and Nuclear Techniques, Academy of Mining and Metallurgy, Al. A. Mickiewicza 30, PL-30-059 Krak6w, Poland d Centre de Recherches sur les Tr~s Basses Temperatures, CNRS, BP 166X, F-38042 Grenoble Cedex, France
Received 6 July 1995; revised 25 January 1996
Abstract The ac susceptibility of La~Ndj_xF3 single crystals, for 0 < x < 0.1, has been measured from 1.5 up to 40 K and their dc susceptibility for 0 < x < 1 has been measured from 3 up to 300 K in magnetic fields up to 0.2 T. In both susceptibilities the magnetic fields were applied parallel to the crystallographic a-axis (perpendicular to the c-axis). The effective Bohr magneton number Peff and paramagnetic Curie temperature 0p have been obtained, using the Curie-Weiss law in the temperature range 100-300 K. Also the g-values corresponding to the five Kramers doublets in the 4•9/2 ground multiplet of Nd 3+ ion in La~Ndl_xF3 have been determined in the direction perpendicular to the c-axis, using the Van Vleck theory of paramagnetic susceptibility. The effect of the dilution of the paramagnetic Nd 3+ ions with diamagnetic La 3÷ ions is also discussed. Keywords: Effective magnetic moment; Paramagnetic Curie temperature; g-factor; Magnetic susceptibility; Rare-earth trifluorides
I. Introduction Mixed LaxNd l_xF3 single crystals have been investigated previously with optical [1-3] and electron paramagnetic resonance (EPR) [4,5] methods. LaF 3 and NdF 3 single crystals have the D4d trigonal symmetry with a hexamolecular unit cell [6]. The site symmetry of the Nd 3+ is C 2 . The second-order axis is perpendicular to the threefold axis C 3 in the unit cell. The crystallographic a-axis forms an angle of 30 ° with respect to one of the three C 2 axes, and the two remaining C 2 axes form angles of 90 ° and 150 ° with respect to the a-axis. The crystallographic c-axis is parallel to the C 3 axis, and perpendicular to the
* Corresponding author. Email: [email protected]; fax: +48-81-376191.
three C 2 axes. There are six molecules per unit cell. The 419/2 ground multiplet of the Nd 3+ ion in LaF 3 single crystals is split by the crystalline electric field into five Kramers doublets at 0, 45, 136, 296 and 500 cm - t , as given by Caspers et al. [1]. Lyon et al. [7] pointed out that the electronic energy levels for Nd 3+ in NdF 3 are similar to those of Nd 3+ in LaF 3. Caro et al. [8] measured the energy levels in the 419/2 ground multiplet of Nd 3+ in NdF 3 single crystals to be 0, 38, 142, 331, and 522 cm -~. Carnall et al. [9] obtained the energy levels in the 419/2 ground multiplet of Nd 3+ (0.1-2%) in LaF 3 the same as those in Ref. [1], whereas Leiteritz and Schaack [10] found them to be 0, 46.5, 147.5, 309.5 and 528 cm -1 for Nd 3+ in NdF 3 single crystals. Baker and Rubins [5] made EPR measurements on Nd 3+ (0.3 mol%) in LaF 3 single crystals; they mea-
0304-8853/97/$17.00 Copyright © 1997 Elsevier Science B.V, All rights reserved. PII S0304-885 3(96)00437-4
232
M.L. Paradowski et al. / Journal of Magnetism and Magnetic Materials 166 (1997) 231-236
sured the g-factor for Nd 3+ in LaF 3 at 4.2 K, which corresponds to the ground Kramers doublet. Their results give g~ = 2.40 + 0.02 for the direction along the crystallographic a-axis. It is not possible to determine the g-factor for Nd 3+ ions at temperatures above 20 K using EPR because the spin-lattice relaxation time of Nd 3+ ions is very short and the linewidths are very broad. Macfarlane and Vial [2] determined the g-value for the ground Kramers doublet in the 419/2 term of Nd 3+ (0.005 at%) in LaF 3 single crystals in the direction parallel to the crystallographic c-axis, using optical techniques. Their experiments were carried out at 1.6 K in an external field of about 0.01 T and the g-value obtained, gl = 2.41, is not in good agreement with the value of 1.72 obtained by B~iuerle et al. [ 11 ] for NdF 3 single crystals using far-infrared techniques and magnetic fields up to 10 T applied parallel to the c-axis. Magnetic susceptibility measurements on NdF 3 single crystals yield information about the effective Bohr magneton number Peff, the paramagnetic Curie temperature 0p, and the spectroscopic splitting g-factor of the Nd 3+ host ions. At low temperatures (T < 100 K) the five Kramers doublets are so differently occupied that large deviations from the CurieWeiss law are observed. These deviations were observed by Kern and Raccah [12] for NdF 3 powder in a magnetic field of I T; by Leycuras et al. [3] for NdF 3 single crystals in magnetic fields up to 1.6 T applied along the c-axis; and by Caro et al. [8] for NdF 3 single crystals in magnetic fields applied parallel and perpendicular to the trigonal axis in the unit cell C 3. The magnetic susceptibility of NdF 3 has also been calculated theoretically for the temperature ranges 4.2-300 K by Neogy and Purohit [13], and 40-300 K by Xu and Duan [14,15]. In the present paper we discuss the results of magnetic susceptibility measurements on paramagnetic NdF 3 single crystals diluted with diamagnetic La 3+ ions.
2. Experimental procedures The mixed LaxNdl_xF3 single crystals doped with Gd 3+ (0.1 mol%) were grown by a modified Bridgman-Stockbarger method for x = 0, 0.01, 0.02, 0.05, 0.1, 0.9, 0.95, 0.98, 0.99 and 1. We used
anhydrous trifluorides (99.9% pure) powders of La, Nd and Gd (from Ventron-Alfa Products, USA). Details of the crystal growth are given in Ref. [16]. All the single crystals were found to be transparent and they are easily cleaved in the cleavage planes (002) and (110) obtained by dropping the crystals into liquid nitrogen and breaking them. The (002) plane reflects light in an almost metallic manner. The dimensions and mass of these single crystals were of about 3 × 2 × 1.5 mm 3 and 40 mg, respectively. The composition x of the samples was confirmed using the PIXE method [17]. The magnetic susceptibility was measured using two methods: an alternating current (ac), and a direct current (dc). The ac susceptibility of LaxNd 1 xF3 single crystals for x = 0, 0.02, 0.05 and 0.10 was measured in the temperature range 1.5-40 K by the mutual inductance method with a frequency of 119 Hz in low magnetic fields B < 0.4 mT applied parallel to the crystallographic a-axis. The EPR investigations were performed in the same direction [4]. The dc susceptibilities of the single crystals with x = 0, 0.02, 0.05, 0.10, 0.90 and 1 were measured in the temperature range 3-300 K by the Faraday method, on a Faraday-type Cahn RG electrobalance equipped with a flow liquid helium cryostat, in magnetic fields B -- 0.2 T applied in the crystallographic plane (002) perpendicular to the caxis. In both methods the single crystals were oriented with an accuracy of 2 °. The temperatures of the single crystals were measured and stabilized to within _+0.5 K by means of a temperature controller with carbon resistor (ac susceptibility), and a temperature controller with an Au + 0.3 at%Fe-NiCr thermocouple (de susceptibility).
3. Results and discussion In the investigated temperature range (1.5-300 K) the Lax Ndl - xF3 single crystals remain paramagnetic for all values of x. The results of dc susceptibility X measurements for temperatures T > 100 K follow a Curie-Weiss law in the form C x=
-
-
T - Op
+Xo,
(I)
where C is the Curie constant (C = NtXZeff/3k), N is Avogadro's number, /z~ff is the effective magnetic moment (/x~ff = p~ff IxB), p~ff is the effective Bohr
M.L Paradowski et al. / Journal of Magnetism and Magnetic Materials 166 (1997) 231-236
magneton number, tz B is the Bohr magneton, k is Boltzmann's constant, 0p is the paramagnetic Curie temperature, and X0 is the constant susceptibility term. The parameters for Nd 3+ in LaxNdl_xF3 estimated from the Curie-Weiss law (l) are given in Table 1. The temperature dependence of the reciprocal dc susceptibility ( X - X0) - l is shown in Fig. 1. The value of the constant susceptibility term X0 is of the order of l0 -4 cm3/mol for all values of x (see Table 1). For LaF 3 (x = 1), which also was doped with Gd 3+ ions (0.1 mol%), the value of X0 is of the same order and equal to 2.118 × l 0 - 4 cma/mol, and this sample is also paramagnetic. Pure LaF 3 is diamagnetic and its magnetic susceptibility is in the range - 3 3 to - 3 7 × 10 - 6 c m a / m o l in the temperature range 77-500 K [6]. Thus X0 is a result of the presence of Gd 3+ impurity ions in the investigated single crystals. The contribution from the Gd 3+ impurity ions covers up the diamagnetism and Van Vleck temperature-independent paramagnetism. The dc susceptibility results have been corrected for the Gd 3+ impurity ions in the temperature range 3-300 K. From the results in Table l, it can be seen that both the Curie constant C and the effective Bohr magneton number Peff decrease with increasing x. The Peff values for Nd a+ ion in LaxNd]_xF 3 (x < 0.10) for T > 100 K are close to the theoretical free-ion value Peff = 3.62. The magnetic measurements of Kern and Raccah [12] on NdF 3 for T > 100 K give Peff = 3.60, which is in good agreement with our result for x = 0, whereas the value Peff = 3.71 obtained by Leycuras et al. [3] differs from our result because it was measured in the direction parallel to the c-axis. Caro et al. [8] pointed out experimentally
Table 1 Curie-Weiss law parameters for Nd 3+ in LaxNdl_xF 3 single crystals, determined from the magnetic dc susceptibility measurements in the direction perpendicular to the c-axis
0 0.02 0.05 0.10 0.90
C (cm 3 K/mol)
0p (K)
Xo (cm3/mol)
/zeff (tZB)
1.617 1.599 1.590 1.583 9.160× 10 -2
-33.0 -34.5 - 50.4 -76.7 -9.3
5.125×10 -4 1.792× 10 -4 5.290 × 10 -4 5.086× 10 -4 2.380× 10 -4
3.60 3.58 3.57 3.56 0.86
233
250
LaxNdl.xF3
~
]
200
E t~
15o
0
E !
•
x=O
c~ x = 0 . 0 2
50
u x = 0.05 ;~ x =0.10
i
i
R
i ~ l
i
i
i
I
100
J
i
f
i
L
i
,
150
,
,
i
200
. . . .
i
250
~
i
i
L
300
T [K] Fig. 1. Temperature dependence of the reciprocal dc susceptibility ( X - X0) - ] of LaxNd j _xF3 single crystals in the direction perpendicular to the c-axis. For clarity, only every fifth point is plotted.
and theoretically that the value of the reciprocal perpendicular susceptibility is larger than reciprocal parallel susceptibility for NdF 3 single crystals in the temperature range 4.2-1100 K. This means that the c-axis of the crystal is the easy magnetization direction, and explains our smaller values of Peff (see Table 1). The Land6 spectroscopic splitting g-factor for the free ion is connected with the effective Bohr magneton number Peff by the formula Peff =
g~J(J+ 1 ) ,
(2)
where J is the total angular momentum quantum number of the Nd 3+ ion. The g-values calculated from Eq. (2) using taking Peff values from Table 1 and, for temperatures 100 K < T < 300 K, J = 5 / 2 [4], are equal to (1.20-1.22) for x < 0.10. The g-values are the resultant values from each of five Kramers doublets. The paramagnetic Curie temperature 0p is negative for all values of x, and 10pl increases with x for x _< 0.10, whereas for x = 0.90 the value is smaller (see Table 1). This may be related to the exchange interaction between paramagnetic Nd 3+ ions, which reaches a maximum in the most concentrated samples for 0 < x < 0.10, whereas when the sample is more diluted with diamagnetic La 3+ ions (x = 0.90), the exchange interaction becomes weaker. The nega-
M.L. Paradowski et al. / Journal of Magnetism and Magnetic Materials 166 (1997) 231-236
234
tive value of 0p suggests the existence of antiferromagnetic ordering below 1.5 K. The Nrel temperature for NdF 3 has not been known until now. The Curie temperature for GdF 3 is 1.25 K [6], and the Nrel temperature for HoF 3 is 0.53 K [18]. Below 100 K the results both of the dc and ac susceptibility (X) measurements indicate that the Curie-Weiss law is not followed. The reciprocal ac susceptibility X ~ is plotted against temperature T in Fig. 2, and there is a good agreement between these results and those in Ref. [8] for x = 0 (NdF3). The results of the ac susceptibility measurements have been corrected for the demagnetization factor only. The corrections for diamagnetism, the temperature-independent Van Vleck paramagnetism, and Gd 3+ impurity ions in the temperature range 1.5-40 K do not influence the results, since they are smaller than experimental error due to the strong ac susceptibility of the samples in the investigated range. According to Van Vleck [19], neglecting second-order perturbation (neglecting quadratic Zeeman shifting), the paramagnetic susceptibility is given by the formula N/z2 • g2 exp( - A i / k T ) i
X= 4k~
Y', e x p ( - A , / k T )
'
(3)
i
where gi and A i are the g-value and energy of the ith level, respectively. The X 1 versus T curves can
60
LaxNdl.×F 3
50
,.-..-,
40
o 0
30
~'~
20
f ] i
•
10
~
-0
5
10
15
20
x=O x = 0.02
25
x = 0.10
30
35
40
T [K] Fig. 2. Temperature dependence of the reciprocal ac susceptibility X - i of La~Nd I _xF3 single crystals in the direction parallel to the a-axis. The solid lines represent the least-squares fits. The bars display error values (for clarity, only some of them are shown). A plot for x = 0.05 is also omitted.
be used to calculate the g-values corresponding to the Kramers doublets in t h e 4 1 9 / 2 ground multiplet of the Nd 3+ ions in LaxNd ~_xF3 single crystals. The g-values were determined by fitting the reciprocal of the susceptibility from Eq. (3) to our experimental data in the temperature ranges 3-300 K
Table 2 g-values for five Kramers doublets in the 419/2 ground multiplet of Nd 3+ in L a x N d I xF3 single crystals, determined from the magnetic dc susceptibility measurements in the direction perpendicular to the c-axis. The references from which the A i were taken, are indicated in column 7 g
x= 0
x = 0.02
x = 0.05
x = 0.10
gt
2.49 2.58 2.60 4.91 5.08 5.08 3,91 2.99 2.99 5.59 6.18 6.17 2.23 0.72 0.32
2.45 2.52 2.54 4.83 5.00 5.01 4.05 3.09 3.20 5.46 6.30 5.92 2.08 0.40 1.74
2.37 2.45 2.49 4.71 4.93 4.82 3.01 1.05 1.95 6.90 7.26 7.05 0.07 0.08 0.12
2.37 2,44 2,45 3,70 3,75 3,78 4.72 4,18 4,32 5.86 6.23 6.08 0.56 0.70 0.32
g2
g3
g4
g5
+ 0.01 + 0.01 + 0.01 4- 0.02 + 0.03 _ 0.02 + 0.08 + 0.11 + 0.10 + 0.10 + 0.05 + 0.06 + 0.04 _+ 0.35 4- 0.22
+ 0.01 + 0.01 4-_0.01 + 0.03 + 0.03 + 0.03 _ 0.07 + 0.12 + 0.09 _ 0.09 + 0.06 -t- 0.08 + 0.10 4- 0.15 4- 0.70
4- 0.01 + 0.01 + 0.01 + 0.02 + 0.01 + 0.02 + 0.08 + 0.21 + 0.07 + 0.05 + 0.04 + 0.02 4- 0.27 4- 0.33 -I- 0.32
4- 0.01 -t- 0.01 4- 0.01 + 0.02 + 0.02 + 0.01 + 0.04 + 0.04 + 0.01 + 0.04 + 0.02 + 0.02 + 0.23 + 0.22 + 0.18
x = 0.997 [5] 2.40 + 0.02
Ai [8] [9] [10] [8] [9] [10] [8] [9] [10] [8] [9] [10] [8] [9] [10]
M.L. Paradowski et al. / Journal of Magnetism and Magnetic Materials 166 (1997) 231-236
235
Table 3 g-values for three Kramers doublets in the 419/2 ground multiplet of Nd 3+ in LaxNd I _xF3 single crystals, determined from the magnetic ac susceptibility measurements in the direction parallel to the a-axis. The references from which the Ai were taken, are indicated in column 7 g
x= 0
x = 0.02
x = 0.05
x = 0.10
g~
2.53 2.55 2.55 4.18 4.47 4.54 5.05 4.02 3.91
2.54 2.56 2.56 4.15 4.44 4.51 5.15 4.08 3.99
2.64 2.46 2.70 4.69 5.11 4.90 2.73 0.65 1.03
2.40 2.41 2.41 4.06 4.34 4.46 5.70 4.98 4.70
g2
g3
+ 0.01 + 0.02 + 0.01 4- 0.05 + 0.07 _ 0.05 _ 0.18 4- 0.26 4- 0.19
+ 0.01 + 0.02 + 0.01 4- 0.05 4- 0.05 4- 0.03 _ 0.16 4- 0.21 4- 0.06
___0.01 + 0.02 ___0.01 + 0.03 4- 0.24 4- 0.01 4- 0.14 + 0.48 + 0.10
(dc susceptibility) and 1.5-40 K (ac susceptibility) by the least-squares method. The best fit is for A i obtained by Caro et al. [8]. The results of the fitting are given in Table 2 and 3, where gl, g2, g3, g4 and g5 denote the g-values corresponding to the following Kramers doublets in t h e 419/2 ground multiplet of the Nd 3+ ion in La~Nd 1 xF3 single crystals. In Table 3 only the g-values for gl, g2, and g3 are given because of smaller investigated range (1.5-40 K) in which they can be determined exactly. The g l value determined for the ground Kramers doublet in t h e 419/2 ground multiplet of Nd 3+ in NdF 3 is close to 2.67, the value given by B~iuerle et al. [11] along the a-axis (see Table 3). The gl value for x = 0.10 is close to 2.40 ___0.02, the value given by Baker et al. [5] for x = 0.997 (see Tables 2 and 3). The g-values depend weakly on the concentration of La 3+ ions x. The values of gl, g2 and gs decrease, and those of g3 and g4 increase with increasing x. The weak x dependence of the g-values of each doublet for x < 0.10 can be explained by the small distortion from the D4d trigonal symmetry of the crystal field.
4. Conclusions The magnetic susceptibility of LaxNdl_xF3 single crystals (0 < x < 0.1) follows a Curie-Weiss law for temperatures T > 100 K and we have determined the Curie-Weiss law parameters (see Table 1). At temperatures below 100 K we have used Van Vleck formula to describe the temperature dependence of
_ 0.01 +_ 0.02 _ 0.01 4- 0.03 4- 0.05 4- 0.04 4- 0.07 4- 0.18 4- 0.07
x = 0.997 [5] 2.40 + 0.02
Ai [8] [9] [10] [8] [9] [10] [8] [9] [10]
the magnetic susceptibility. We have determined the g-values for five Kramers doublets of t h e 419/2 ground state of the Nd 3+ ion in LaxNd I_xF3, and they appear to be only weakly dependent on the concentration x.
Acknowledgements The authors are grateful to Dr J.L. Tholence of CNRS, Grenoble, France, for the opportunity to use the experimental arrangement (ac susceptibility).
References [1] H.H. Caspers, H.E. Rast and R.A. Buchanan, J. Chem. Phys. 42 (1965) 3214. [2] R.M. Macfarlane and J.C. Vial, Phys. Rev. B 36 (1987) 3511. [3] C. Leycuras, H. Le Gall, M. Guillot and A. Marchand, J. Appl. Phys. 55 (1984) 2161. [4] W. Korczak, M.L. Paradowski and L.E. Misiak, Phys. Stat. Solidi (b) 165 (1991) 203; M.L. Paradowski, W. Korczak, J. Pierre and M. Subotowicz, Phys. Status Solidi (b) 175 (1993) 135. [5] J.M. Baker and R.S. Rubins, Proc. Phys. Soc. 78 (1961) 1353. [6] L. Gmelin, Handbuch der Anorganischen Chemie, Vol. 39, Part C3 (Springer, Berlin, 1976) pp. 55, 97, 162, 187. [7] W.G. Lyon, D.W. Osborne and H.E. Flotow, J. Chem. Phys. 71 (1979) 4123. [8] P. Caro, J. Derouet, L. Beaury, G. Teste de Sagey, J.P. Chaminade, J. Aride and M. Pouchard, J. Chem. Phys. 74 (1981) 2698. [9] W. T. Carnall, H. Crosswhite and H. M. Crosswhite, Report, Argonne National Laboratory, Argonne, IL (1977).
236
M.L. Paradowski et al./ Journal of Magnetism and Magnetic Materials 166 (1997) 231-236
[10] K. Leiteritz and G. Schaack, J. Raman Spectrosc. 10 (1981) 36. [11] D. B~iuerle, G. Borstel and A. J. Sievers, J. Appl. Phys. 49 (1978) 676. [12] S. Kern and P.M. Raccah, J. Phys. Chem. Solids 26 (1965) 1625. [13] D. Neogy and T. Purohit, Phys. Status Solidi (b) 131 (1985) 329. [14] Ming-qian Duan and You Xu, J. Magn. Magn. Mater. 115 (1992) 1. [15] You Xu and Ming-qian Duan, Phys. Rev. B 46 (1992) 11636.
[16] W. Korczak and P. Mikolajczak, J. Crystal Growth 61 (1983) 601. [17] M. Kulik, M.L. Paradowski, W. Korczak and A.P. Kobzev, to be published. [18] P.J. Brown, J.B. Forsyth, P.C. Hansen, M.J.M. Leask, R.C.C. Ward and M.R. Wells, J. Phys.: Condens. Matter 2 (1990) 4471. [19] J.H. Van Vleck, Theory of Electric and Magnetic Susceptibilities (Oxford University Press, Oxford, 1932) p. 226.
ELSEVIER
Journalof magnetism and magnetic materials
Journal of Magnetism and Magnetic Materials 166 (1997) 231-236
Magnetic susceptibility of LaxNdl_xF3 single crystals M.L. Paradowski
a,*,
A.W. Pacyna
b,
A. Bombik c, W. Korczak
a,d,
S.Z. Korczak
a
a Institute of Physics, Maria Curie-Sktodowska University, Pl. Marii Curie-Sktodowskiej I, PL-20-031 Lublin, Poland b Henryk Niewodniczahski Institute of Nuclear Physics, W.E. Radzikowskiego 152, PL-31-342 Krakdw, Poland c Department of Physics and Nuclear Techniques, Academy of Mining and Metallurgy, Al. A. Mickiewicza 30, PL-30-059 Krak6w, Poland d Centre de Recherches sur les Tr~s Basses Temperatures, CNRS, BP 166X, F-38042 Grenoble Cedex, France
Received 6 July 1995; revised 25 January 1996
Abstract The ac susceptibility of La~Ndj_xF3 single crystals, for 0 < x < 0.1, has been measured from 1.5 up to 40 K and their dc susceptibility for 0 < x < 1 has been measured from 3 up to 300 K in magnetic fields up to 0.2 T. In both susceptibilities the magnetic fields were applied parallel to the crystallographic a-axis (perpendicular to the c-axis). The effective Bohr magneton number Peff and paramagnetic Curie temperature 0p have been obtained, using the Curie-Weiss law in the temperature range 100-300 K. Also the g-values corresponding to the five Kramers doublets in the 4•9/2 ground multiplet of Nd 3+ ion in La~Ndl_xF3 have been determined in the direction perpendicular to the c-axis, using the Van Vleck theory of paramagnetic susceptibility. The effect of the dilution of the paramagnetic Nd 3+ ions with diamagnetic La 3÷ ions is also discussed. Keywords: Effective magnetic moment; Paramagnetic Curie temperature; g-factor; Magnetic susceptibility; Rare-earth trifluorides
I. Introduction Mixed LaxNd l_xF3 single crystals have been investigated previously with optical [1-3] and electron paramagnetic resonance (EPR) [4,5] methods. LaF 3 and NdF 3 single crystals have the D4d trigonal symmetry with a hexamolecular unit cell [6]. The site symmetry of the Nd 3+ is C 2 . The second-order axis is perpendicular to the threefold axis C 3 in the unit cell. The crystallographic a-axis forms an angle of 30 ° with respect to one of the three C 2 axes, and the two remaining C 2 axes form angles of 90 ° and 150 ° with respect to the a-axis. The crystallographic c-axis is parallel to the C 3 axis, and perpendicular to the
* Corresponding author. Email: [email protected]; fax: +48-81-376191.
three C 2 axes. There are six molecules per unit cell. The 419/2 ground multiplet of the Nd 3+ ion in LaF 3 single crystals is split by the crystalline electric field into five Kramers doublets at 0, 45, 136, 296 and 500 cm - t , as given by Caspers et al. [1]. Lyon et al. [7] pointed out that the electronic energy levels for Nd 3+ in NdF 3 are similar to those of Nd 3+ in LaF 3. Caro et al. [8] measured the energy levels in the 419/2 ground multiplet of Nd 3+ in NdF 3 single crystals to be 0, 38, 142, 331, and 522 cm -~. Carnall et al. [9] obtained the energy levels in the 419/2 ground multiplet of Nd 3+ (0.1-2%) in LaF 3 the same as those in Ref. [1], whereas Leiteritz and Schaack [10] found them to be 0, 46.5, 147.5, 309.5 and 528 cm -1 for Nd 3+ in NdF 3 single crystals. Baker and Rubins [5] made EPR measurements on Nd 3+ (0.3 mol%) in LaF 3 single crystals; they mea-
0304-8853/97/$17.00 Copyright © 1997 Elsevier Science B.V, All rights reserved. PII S0304-885 3(96)00437-4
232
M.L. Paradowski et al. / Journal of Magnetism and Magnetic Materials 166 (1997) 231-236
sured the g-factor for Nd 3+ in LaF 3 at 4.2 K, which corresponds to the ground Kramers doublet. Their results give g~ = 2.40 + 0.02 for the direction along the crystallographic a-axis. It is not possible to determine the g-factor for Nd 3+ ions at temperatures above 20 K using EPR because the spin-lattice relaxation time of Nd 3+ ions is very short and the linewidths are very broad. Macfarlane and Vial [2] determined the g-value for the ground Kramers doublet in the 419/2 term of Nd 3+ (0.005 at%) in LaF 3 single crystals in the direction parallel to the crystallographic c-axis, using optical techniques. Their experiments were carried out at 1.6 K in an external field of about 0.01 T and the g-value obtained, gl = 2.41, is not in good agreement with the value of 1.72 obtained by B~iuerle et al. [ 11 ] for NdF 3 single crystals using far-infrared techniques and magnetic fields up to 10 T applied parallel to the c-axis. Magnetic susceptibility measurements on NdF 3 single crystals yield information about the effective Bohr magneton number Peff, the paramagnetic Curie temperature 0p, and the spectroscopic splitting g-factor of the Nd 3+ host ions. At low temperatures (T < 100 K) the five Kramers doublets are so differently occupied that large deviations from the CurieWeiss law are observed. These deviations were observed by Kern and Raccah [12] for NdF 3 powder in a magnetic field of I T; by Leycuras et al. [3] for NdF 3 single crystals in magnetic fields up to 1.6 T applied along the c-axis; and by Caro et al. [8] for NdF 3 single crystals in magnetic fields applied parallel and perpendicular to the trigonal axis in the unit cell C 3. The magnetic susceptibility of NdF 3 has also been calculated theoretically for the temperature ranges 4.2-300 K by Neogy and Purohit [13], and 40-300 K by Xu and Duan [14,15]. In the present paper we discuss the results of magnetic susceptibility measurements on paramagnetic NdF 3 single crystals diluted with diamagnetic La 3+ ions.
2. Experimental procedures The mixed LaxNdl_xF3 single crystals doped with Gd 3+ (0.1 mol%) were grown by a modified Bridgman-Stockbarger method for x = 0, 0.01, 0.02, 0.05, 0.1, 0.9, 0.95, 0.98, 0.99 and 1. We used
anhydrous trifluorides (99.9% pure) powders of La, Nd and Gd (from Ventron-Alfa Products, USA). Details of the crystal growth are given in Ref. [16]. All the single crystals were found to be transparent and they are easily cleaved in the cleavage planes (002) and (110) obtained by dropping the crystals into liquid nitrogen and breaking them. The (002) plane reflects light in an almost metallic manner. The dimensions and mass of these single crystals were of about 3 × 2 × 1.5 mm 3 and 40 mg, respectively. The composition x of the samples was confirmed using the PIXE method [17]. The magnetic susceptibility was measured using two methods: an alternating current (ac), and a direct current (dc). The ac susceptibility of LaxNd 1 xF3 single crystals for x = 0, 0.02, 0.05 and 0.10 was measured in the temperature range 1.5-40 K by the mutual inductance method with a frequency of 119 Hz in low magnetic fields B < 0.4 mT applied parallel to the crystallographic a-axis. The EPR investigations were performed in the same direction [4]. The dc susceptibilities of the single crystals with x = 0, 0.02, 0.05, 0.10, 0.90 and 1 were measured in the temperature range 3-300 K by the Faraday method, on a Faraday-type Cahn RG electrobalance equipped with a flow liquid helium cryostat, in magnetic fields B -- 0.2 T applied in the crystallographic plane (002) perpendicular to the caxis. In both methods the single crystals were oriented with an accuracy of 2 °. The temperatures of the single crystals were measured and stabilized to within _+0.5 K by means of a temperature controller with carbon resistor (ac susceptibility), and a temperature controller with an Au + 0.3 at%Fe-NiCr thermocouple (de susceptibility).
3. Results and discussion In the investigated temperature range (1.5-300 K) the Lax Ndl - xF3 single crystals remain paramagnetic for all values of x. The results of dc susceptibility X measurements for temperatures T > 100 K follow a Curie-Weiss law in the form C x=
-
-
T - Op
+Xo,
(I)
where C is the Curie constant (C = NtXZeff/3k), N is Avogadro's number, /z~ff is the effective magnetic moment (/x~ff = p~ff IxB), p~ff is the effective Bohr
M.L Paradowski et al. / Journal of Magnetism and Magnetic Materials 166 (1997) 231-236
magneton number, tz B is the Bohr magneton, k is Boltzmann's constant, 0p is the paramagnetic Curie temperature, and X0 is the constant susceptibility term. The parameters for Nd 3+ in LaxNdl_xF3 estimated from the Curie-Weiss law (l) are given in Table 1. The temperature dependence of the reciprocal dc susceptibility ( X - X0) - l is shown in Fig. 1. The value of the constant susceptibility term X0 is of the order of l0 -4 cm3/mol for all values of x (see Table 1). For LaF 3 (x = 1), which also was doped with Gd 3+ ions (0.1 mol%), the value of X0 is of the same order and equal to 2.118 × l 0 - 4 cma/mol, and this sample is also paramagnetic. Pure LaF 3 is diamagnetic and its magnetic susceptibility is in the range - 3 3 to - 3 7 × 10 - 6 c m a / m o l in the temperature range 77-500 K [6]. Thus X0 is a result of the presence of Gd 3+ impurity ions in the investigated single crystals. The contribution from the Gd 3+ impurity ions covers up the diamagnetism and Van Vleck temperature-independent paramagnetism. The dc susceptibility results have been corrected for the Gd 3+ impurity ions in the temperature range 3-300 K. From the results in Table l, it can be seen that both the Curie constant C and the effective Bohr magneton number Peff decrease with increasing x. The Peff values for Nd a+ ion in LaxNd]_xF 3 (x < 0.10) for T > 100 K are close to the theoretical free-ion value Peff = 3.62. The magnetic measurements of Kern and Raccah [12] on NdF 3 for T > 100 K give Peff = 3.60, which is in good agreement with our result for x = 0, whereas the value Peff = 3.71 obtained by Leycuras et al. [3] differs from our result because it was measured in the direction parallel to the c-axis. Caro et al. [8] pointed out experimentally
Table 1 Curie-Weiss law parameters for Nd 3+ in LaxNdl_xF 3 single crystals, determined from the magnetic dc susceptibility measurements in the direction perpendicular to the c-axis
0 0.02 0.05 0.10 0.90
C (cm 3 K/mol)
0p (K)
Xo (cm3/mol)
/zeff (tZB)
1.617 1.599 1.590 1.583 9.160× 10 -2
-33.0 -34.5 - 50.4 -76.7 -9.3
5.125×10 -4 1.792× 10 -4 5.290 × 10 -4 5.086× 10 -4 2.380× 10 -4
3.60 3.58 3.57 3.56 0.86
233
250
LaxNdl.xF3
~
]
200
E t~
15o
0
E !
•
x=O
c~ x = 0 . 0 2
50
u x = 0.05 ;~ x =0.10
i
i
R
i ~ l
i
i
i
I
100
J
i
f
i
L
i
,
150
,
,
i
200
. . . .
i
250
~
i
i
L
300
T [K] Fig. 1. Temperature dependence of the reciprocal dc susceptibility ( X - X0) - ] of LaxNd j _xF3 single crystals in the direction perpendicular to the c-axis. For clarity, only every fifth point is plotted.
and theoretically that the value of the reciprocal perpendicular susceptibility is larger than reciprocal parallel susceptibility for NdF 3 single crystals in the temperature range 4.2-1100 K. This means that the c-axis of the crystal is the easy magnetization direction, and explains our smaller values of Peff (see Table 1). The Land6 spectroscopic splitting g-factor for the free ion is connected with the effective Bohr magneton number Peff by the formula Peff =
g~J(J+ 1 ) ,
(2)
where J is the total angular momentum quantum number of the Nd 3+ ion. The g-values calculated from Eq. (2) using taking Peff values from Table 1 and, for temperatures 100 K < T < 300 K, J = 5 / 2 [4], are equal to (1.20-1.22) for x < 0.10. The g-values are the resultant values from each of five Kramers doublets. The paramagnetic Curie temperature 0p is negative for all values of x, and 10pl increases with x for x _< 0.10, whereas for x = 0.90 the value is smaller (see Table 1). This may be related to the exchange interaction between paramagnetic Nd 3+ ions, which reaches a maximum in the most concentrated samples for 0 < x < 0.10, whereas when the sample is more diluted with diamagnetic La 3+ ions (x = 0.90), the exchange interaction becomes weaker. The nega-
M.L. Paradowski et al. / Journal of Magnetism and Magnetic Materials 166 (1997) 231-236
234
tive value of 0p suggests the existence of antiferromagnetic ordering below 1.5 K. The Nrel temperature for NdF 3 has not been known until now. The Curie temperature for GdF 3 is 1.25 K [6], and the Nrel temperature for HoF 3 is 0.53 K [18]. Below 100 K the results both of the dc and ac susceptibility (X) measurements indicate that the Curie-Weiss law is not followed. The reciprocal ac susceptibility X ~ is plotted against temperature T in Fig. 2, and there is a good agreement between these results and those in Ref. [8] for x = 0 (NdF3). The results of the ac susceptibility measurements have been corrected for the demagnetization factor only. The corrections for diamagnetism, the temperature-independent Van Vleck paramagnetism, and Gd 3+ impurity ions in the temperature range 1.5-40 K do not influence the results, since they are smaller than experimental error due to the strong ac susceptibility of the samples in the investigated range. According to Van Vleck [19], neglecting second-order perturbation (neglecting quadratic Zeeman shifting), the paramagnetic susceptibility is given by the formula N/z2 • g2 exp( - A i / k T ) i
X= 4k~
Y', e x p ( - A , / k T )
'
(3)
i
where gi and A i are the g-value and energy of the ith level, respectively. The X 1 versus T curves can
60
LaxNdl.×F 3
50
,.-..-,
40
o 0
30
~'~
20
f ] i
•
10
~
-0
5
10
15
20
x=O x = 0.02
25
x = 0.10
30
35
40
T [K] Fig. 2. Temperature dependence of the reciprocal ac susceptibility X - i of La~Nd I _xF3 single crystals in the direction parallel to the a-axis. The solid lines represent the least-squares fits. The bars display error values (for clarity, only some of them are shown). A plot for x = 0.05 is also omitted.
be used to calculate the g-values corresponding to the Kramers doublets in t h e 4 1 9 / 2 ground multiplet of the Nd 3+ ions in LaxNd ~_xF3 single crystals. The g-values were determined by fitting the reciprocal of the susceptibility from Eq. (3) to our experimental data in the temperature ranges 3-300 K
Table 2 g-values for five Kramers doublets in the 419/2 ground multiplet of Nd 3+ in L a x N d I xF3 single crystals, determined from the magnetic dc susceptibility measurements in the direction perpendicular to the c-axis. The references from which the A i were taken, are indicated in column 7 g
x= 0
x = 0.02
x = 0.05
x = 0.10
gt
2.49 2.58 2.60 4.91 5.08 5.08 3,91 2.99 2.99 5.59 6.18 6.17 2.23 0.72 0.32
2.45 2.52 2.54 4.83 5.00 5.01 4.05 3.09 3.20 5.46 6.30 5.92 2.08 0.40 1.74
2.37 2.45 2.49 4.71 4.93 4.82 3.01 1.05 1.95 6.90 7.26 7.05 0.07 0.08 0.12
2.37 2,44 2,45 3,70 3,75 3,78 4.72 4,18 4,32 5.86 6.23 6.08 0.56 0.70 0.32
g2
g3
g4
g5
+ 0.01 + 0.01 + 0.01 4- 0.02 + 0.03 _ 0.02 + 0.08 + 0.11 + 0.10 + 0.10 + 0.05 + 0.06 + 0.04 _+ 0.35 4- 0.22
+ 0.01 + 0.01 4-_0.01 + 0.03 + 0.03 + 0.03 _ 0.07 + 0.12 + 0.09 _ 0.09 + 0.06 -t- 0.08 + 0.10 4- 0.15 4- 0.70
4- 0.01 + 0.01 + 0.01 + 0.02 + 0.01 + 0.02 + 0.08 + 0.21 + 0.07 + 0.05 + 0.04 + 0.02 4- 0.27 4- 0.33 -I- 0.32
4- 0.01 -t- 0.01 4- 0.01 + 0.02 + 0.02 + 0.01 + 0.04 + 0.04 + 0.01 + 0.04 + 0.02 + 0.02 + 0.23 + 0.22 + 0.18
x = 0.997 [5] 2.40 + 0.02
Ai [8] [9] [10] [8] [9] [10] [8] [9] [10] [8] [9] [10] [8] [9] [10]
M.L. Paradowski et al. / Journal of Magnetism and Magnetic Materials 166 (1997) 231-236
235
Table 3 g-values for three Kramers doublets in the 419/2 ground multiplet of Nd 3+ in LaxNd I _xF3 single crystals, determined from the magnetic ac susceptibility measurements in the direction parallel to the a-axis. The references from which the Ai were taken, are indicated in column 7 g
x= 0
x = 0.02
x = 0.05
x = 0.10
g~
2.53 2.55 2.55 4.18 4.47 4.54 5.05 4.02 3.91
2.54 2.56 2.56 4.15 4.44 4.51 5.15 4.08 3.99
2.64 2.46 2.70 4.69 5.11 4.90 2.73 0.65 1.03
2.40 2.41 2.41 4.06 4.34 4.46 5.70 4.98 4.70
g2
g3
+ 0.01 + 0.02 + 0.01 4- 0.05 + 0.07 _ 0.05 _ 0.18 4- 0.26 4- 0.19
+ 0.01 + 0.02 + 0.01 4- 0.05 4- 0.05 4- 0.03 _ 0.16 4- 0.21 4- 0.06
___0.01 + 0.02 ___0.01 + 0.03 4- 0.24 4- 0.01 4- 0.14 + 0.48 + 0.10
(dc susceptibility) and 1.5-40 K (ac susceptibility) by the least-squares method. The best fit is for A i obtained by Caro et al. [8]. The results of the fitting are given in Table 2 and 3, where gl, g2, g3, g4 and g5 denote the g-values corresponding to the following Kramers doublets in t h e 419/2 ground multiplet of the Nd 3+ ion in La~Nd 1 xF3 single crystals. In Table 3 only the g-values for gl, g2, and g3 are given because of smaller investigated range (1.5-40 K) in which they can be determined exactly. The g l value determined for the ground Kramers doublet in t h e 419/2 ground multiplet of Nd 3+ in NdF 3 is close to 2.67, the value given by B~iuerle et al. [11] along the a-axis (see Table 3). The gl value for x = 0.10 is close to 2.40 ___0.02, the value given by Baker et al. [5] for x = 0.997 (see Tables 2 and 3). The g-values depend weakly on the concentration of La 3+ ions x. The values of gl, g2 and gs decrease, and those of g3 and g4 increase with increasing x. The weak x dependence of the g-values of each doublet for x < 0.10 can be explained by the small distortion from the D4d trigonal symmetry of the crystal field.
4. Conclusions The magnetic susceptibility of LaxNdl_xF3 single crystals (0 < x < 0.1) follows a Curie-Weiss law for temperatures T > 100 K and we have determined the Curie-Weiss law parameters (see Table 1). At temperatures below 100 K we have used Van Vleck formula to describe the temperature dependence of
_ 0.01 +_ 0.02 _ 0.01 4- 0.03 4- 0.05 4- 0.04 4- 0.07 4- 0.18 4- 0.07
x = 0.997 [5] 2.40 + 0.02
Ai [8] [9] [10] [8] [9] [10] [8] [9] [10]
the magnetic susceptibility. We have determined the g-values for five Kramers doublets of t h e 419/2 ground state of the Nd 3+ ion in LaxNd I_xF3, and they appear to be only weakly dependent on the concentration x.
Acknowledgements The authors are grateful to Dr J.L. Tholence of CNRS, Grenoble, France, for the opportunity to use the experimental arrangement (ac susceptibility).
References [1] H.H. Caspers, H.E. Rast and R.A. Buchanan, J. Chem. Phys. 42 (1965) 3214. [2] R.M. Macfarlane and J.C. Vial, Phys. Rev. B 36 (1987) 3511. [3] C. Leycuras, H. Le Gall, M. Guillot and A. Marchand, J. Appl. Phys. 55 (1984) 2161. [4] W. Korczak, M.L. Paradowski and L.E. Misiak, Phys. Stat. Solidi (b) 165 (1991) 203; M.L. Paradowski, W. Korczak, J. Pierre and M. Subotowicz, Phys. Status Solidi (b) 175 (1993) 135. [5] J.M. Baker and R.S. Rubins, Proc. Phys. Soc. 78 (1961) 1353. [6] L. Gmelin, Handbuch der Anorganischen Chemie, Vol. 39, Part C3 (Springer, Berlin, 1976) pp. 55, 97, 162, 187. [7] W.G. Lyon, D.W. Osborne and H.E. Flotow, J. Chem. Phys. 71 (1979) 4123. [8] P. Caro, J. Derouet, L. Beaury, G. Teste de Sagey, J.P. Chaminade, J. Aride and M. Pouchard, J. Chem. Phys. 74 (1981) 2698. [9] W. T. Carnall, H. Crosswhite and H. M. Crosswhite, Report, Argonne National Laboratory, Argonne, IL (1977).
236
M.L. Paradowski et al./ Journal of Magnetism and Magnetic Materials 166 (1997) 231-236
[10] K. Leiteritz and G. Schaack, J. Raman Spectrosc. 10 (1981) 36. [11] D. B~iuerle, G. Borstel and A. J. Sievers, J. Appl. Phys. 49 (1978) 676. [12] S. Kern and P.M. Raccah, J. Phys. Chem. Solids 26 (1965) 1625. [13] D. Neogy and T. Purohit, Phys. Status Solidi (b) 131 (1985) 329. [14] Ming-qian Duan and You Xu, J. Magn. Magn. Mater. 115 (1992) 1. [15] You Xu and Ming-qian Duan, Phys. Rev. B 46 (1992) 11636.
[16] W. Korczak and P. Mikolajczak, J. Crystal Growth 61 (1983) 601. [17] M. Kulik, M.L. Paradowski, W. Korczak and A.P. Kobzev, to be published. [18] P.J. Brown, J.B. Forsyth, P.C. Hansen, M.J.M. Leask, R.C.C. Ward and M.R. Wells, J. Phys.: Condens. Matter 2 (1990) 4471. [19] J.H. Van Vleck, Theory of Electric and Magnetic Susceptibilities (Oxford University Press, Oxford, 1932) p. 226.