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Magnetic properties of some rare earth tellurate garnets
ARTICLE IN PRESS
Journal of Physics and Chemistry of Solids 68 (2007) 1756–1761 www.elsevier.com/locate/jpcs
Magnetic properties of some rare earth tellurate garnets Ryan P. Applegate, Yuhua Zong, L.R. Corruccini Physics Department, University of California, Davis, CA 95616, USA Received 10 October 2006; received in revised form 18 April 2007; accepted 24 April 2007
Abstract The magnetic properties of the lanthanide tellurate garnets Ln3Te2Li3O12 for Ln ¼ Pr, Nd, Gd–Er, and Yb are found to exhibit similarities in many cases to the related aluminum or gallium garnet compounds. Magnetic exchange is also roughly comparable in magnitude, despite the systematic difference in exchange pathways. r 2007 Elsevier Ltd. All rights reserved. PACS: 75.30.Cr; 75.50.Dd Keywords: A. Magnetic materials; D. Magnetic properties
1. Introduction The rare earth tellurate garnets Ln3Te2Li3O12 were first described by Kasper [1]. They form for all the rare earths Ln from Pr to Lu. Like the related and more familiar Ln3M5O12 garnet compounds, including M ¼ Al, Ga, and ¯ The lanthanide Fe, they are cubic, with space group Ia3d. ions have orthorhombic point symmetry. However, the TeO6 complexes are more isolated than the continuous M–O–M linkages found in the Ln3M5O12 materials. This results in a more pronounced lanthanide contraction in the tellurate garnets. Superexchange pathways are qualitatively different in the rare earth tellurate garnets, which contain monovalent and hexavalent diamagnetic cations, from those in the rare earth aluminum and gallium garnets, where the diamagnetic cations are all trivalent. The lattice parameters of the Ln3Te2Li3O12 materials are much closer, on average, to those of the rare earth gallium garnets than those containing aluminum or iron. We have investigated the magnetic properties of a number of these materials to see to what extent they resemble the rare earth gallium (LnGG) and aluminum (LnAG) garnets, their closest magnetic analogs. We were also curious to see whether magnetic exchange is measurably affected, and Corresponding author. Tel.: +1 530 752 1023; fax: +1 530 752 4717.
E-mail address: [email protected] (L.R. Corruccini). 0022-3697/$ - see front matter r 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.jpcs.2007.04.022
possibly reduced, by the isolation of the tightly bound TeO6 complexes. 2. Experimental details Polycrystalline samples were made by solid-state reaction in air of the relevant metal oxides or hydroxides in stoichiometric ratio, pressed into pellets, typically at 850 1C for 10 h. After the initial firing, samples were reground, repressed and fired a second time. Powder X-ray diffraction ¯ with no impurity peaks peaks could all be indexed to Ia3d, visible at the 1% level. The lattice parameters are listed in Table 1, in reasonable agreement with those of Kasper [1]. Static magnetic susceptibilities were measured on spherical samples at 500 Oersteds in a quantum design MPMS susceptometer. 3. Data and discussion Magnetic susceptibilities of Ln3Te2Li3O12 containing the Kramers ions Ln3+ ¼ Dy3+, Gd3+, Nd3+, Er3+, and Yb3+, are shown in Figs. 1–6. The low temperature Curie constants and Weiss constants, obtained from a linear fitting of w1 well above any ordering features, are listed in Table 1. In many cases, the Curie constant is within 20% of values ascribed to either the corresponding Ga or Al
ARTICLE IN PRESS R.P. Applegate et al. / Journal of Physics and Chemistry of Solids 68 (2007) 1756–1761
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Table 1 Lattice parameter, Curie and Weiss constants with the temperature range of the linear fit, exchange constant, and lowest-level crystal field splittings for rare earth tellurate garnets, with parameters of some related aluminum and gallium garnets shown for comparison Material
a (A˚)
C (cm3-K/mol)
yW (K)
J (K)
Dy3Te2Li3O12 DyAG DyGG Gd3Te2Li3O12 GdAG GdGG Nd3Te2Li3O12 Nd3+:Y, LuAG NdGG Er3Te2Li3O12 Er3+:Y, LuAG Er3+:Y, LuGG Yb3Te2Li3O12 Yb3+:Y, LuAG Yb3+:Y, LuGG Pr3Te2Li3O12 Tb3Te2Li3O12 Ho3Te2Li3O12
12.2951
11.2470.6 (5–12K) 10.45a 6.6–7.8a,b,c 7.9970.2 (12–20 K) 7.82d 7.82d 0.74070.04 (2.2–5 K) 0.617d 0.586e, 0.598d 6.17370.3 (1.9–4 K) 4.00–4.254d 4.79–5.61d,f 1.15970.05 (5–14 K) 1.106–1.108d 1.094–1.109c,d
0.7870.3 0.20a (0.05)–(0.436)a,b,c 2.6670.3 3.0d 2.3d 0.9170.3
0.45
0.2870.1
0.22
0.30f 0.06270.03
0.03
10.070.5 (6–10 K)
0.01770.1
12.3722
12.5402
12.2266
12.1623
12.5921 12.3354 12.2563
D (K)
0.063
0.47
0.045c 20.872, 160720 5.771
a
Ref. [2]. Ref. [7]. c Ref. [9]. d Ref. [6]. e Ref. [17]. f Ref. [5]. b
25
45
1 Dy3Te2Li3O12
1.5
Gd3Te2Li3O12
40 1
0.5 20
35
0
15
5
0.5
30
10
1/ χ (mol-RE / cm3)
1 / χ (mol-RE/cm3)
0
10
5
0 0
5
10
25 20 15 10 5
0 0
50
100
150
200
250
300
Temperature (K)
0 0
50
100
150
200
250
300
Temperature (K) Fig. 1. Inverse susceptibility of Dy3Te2Li3O12 versus temperature from 1.9 to 300 K. The solid line is the free-ion prediction. The inset shows expanded data at the lowest temperature. An ordering feature at T 2 K is visible.
Fig. 2. Susceptibility of Gd3Te2Li3O12 versus temperature, from 1.9 to 300 K. Solid line is the predicted free-ion susceptibility.
garnet, or both. This suggests that the ground state of the lanthanide ion may be related in the two materials. The Curie constant of Dy3Te2Li3O12, in particular, is close to that of Dy aluminum garnet, in which the Dy3+
ions have the rather large axial moment gjj mB S eff ffi 9mB , where S eff ¼ 12 for the doublet ground state of Dy3+, so that gjj ¼ gz ffi 18, gx ¼ gy ffi 0 [2]. The susceptibility of Dy3Te2Li3O12 is shown in Fig. 1. Assuming the ground
ARTICLE IN PRESS R.P. Applegate et al. / Journal of Physics and Chemistry of Solids 68 (2007) 1756–1761
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0.75
30
Gd3Te2Li3O12
3
Er3Te2Li3O12
2 25
1/ χ (mol-RE/ cm3)
0.7 1/ χ (mol-RE/ cm3)
1
squid data 500 Oersted FC 100 Oersted FC 10 Oersted FC 10 Oersted ZFC
0.65
0
20
0
10
20
15
10 0.6 5
0.55 0
1
2
0
3
0
Temperature (K)
50
100
150
200
250
300
Temperature (K) Fig. 3. Susceptibility of Gd3Te2Li3O12 from 0.02 to 3 K. An apparent ordering feature at T 0:25 K is visible.
250
30
Fig. 5. Susceptibility of Er3Te2Li3O12 versus temperature from 1.9 to 300 K.
Nd3Te2Li3O12
20 10
140
10
Yb3Te2Li3O12
0 0
0 0
150
20
120
10
1 /χ χ (mol-RE / cm3)
1/χ χ (mol-RE / cm3)
200
160
20
100
10
20
100 80 60 40
50 20
0 0
50
100 150 200 Temperature (K)
250
300
0 0
50
100 150 200 Temperature (K)
250
300
Fig. 4. Susceptibility of Nd3Te2Li3O12 versus temperature, from 1.9 to 300 K, with solid line the free-ion prediction.
Fig. 6. Susceptibility of Yb3Te2Li3O12 versus temperature from 1.9 to 300 K.
state of Dy3+ in Dy3Te2Li3O12 is also axial, its Curie constant predicts an axial moment of 9.5mB or gz ¼ 19.0 (close to the maximum possible value of 20). The susceptibility of Dy3Te2Li3O12 also exhibits an antiferromagnetic ordering feature at approximately 2 K, reminiscent of that in dysprosium aluminum garnet at
TN ¼ 2.53 K [3]. Although the lattice constant of Dy3Te2 Li3O12 is much closer to that of Dy gallium garnet, its magnetic properties resemble Dy aluminum garnet more closely. yW contains contributions from both exchange and magnetic dipole–dipole interactions. For a spherical sample these contributions are additive, yW ¼ yex þ yd ,
ARTICLE IN PRESS R.P. Applegate et al. / Journal of Physics and Chemistry of Solids 68 (2007) 1756–1761
For Dy3Te2Li3O12, assuming gx gy 0, we obtain yd ¼ 0.126 K, which is not negligible in comparison to the measured yW. From yex we obtain a value of the exchange constant J (assumed isotropic) shown in Table 1, from the mean-field result yex ¼ 2JnS(S+1)/3kB. Here the number of nearest magnetic neighbors n is four for the garnet structure, and S is the effective spin of the ion’s ground state. Gd3Te2Li3O12 exhibits a susceptibility similar to that observed in both gadolinium gallium and aluminum garnets above 2 K, namely Curie–Weiss behavior above 12 K with a Curie constant close to the theoretical free-ion value of 7.875 mol K cm3, a Weiss constant between 2 and 3 K, and a gradual deviation of the susceptibility from the Curie–Weiss extrapolation at lower temperatures [6–8]. This is shown in Fig. 2. From yW we obtain J ¼ 0.063 K directly, since yd vanishes for the isotropic moment of Gd3+. Gadolinium gallium garnet (GGG) is known to display strong magnetic frustration, undergoing a spin glass transition at 0.1 K [8], with no evidence of long-range order in zero field. A sample of Gd3Te2Li3O12 cooled to lower temperatures in a dilution refrigerator exhibits an apparent ordering feature in the static susceptibility at approximately 0.25 K, shown in Fig. 3. This measurement was taken in a smaller field of 10 Oe. There is a small amount of history dependence in the susceptibility, but it commences well below the ordering feature, so the behavior of Gd3Te2Li3O12 appears distinct from GGG, and frustration, while present, does not appear to be as strong in this material. The susceptibility of Nd3Te2Li3O12, shown in Fig. 4, obeys a Curie–Weiss law below 5 K which yields a Curie constant about 20% larger than that predicted by the g factors of Nd3+ in yttrium aluminum and yttrium gallium garnets, both about 0.6 mol K cm3 [6]. If we assume the elements of the g tensor are proportional to an average of the values measured for Nd3+ in diamagnetic aluminum and gallium garnet hosts [6], we obtain an estimated ydE0.025 K. This is small compared to yW, in consequence of the relatively small size of the moment of Nd3+, and yields the estimate of J shown in Table 1. The susceptibility of Er3Te2Li3O12, shown in Fig. 5, yields a Curie constant in the region 1.9–4 K of 6.17 mol K cm3, which exceeds values calculated from paramagnetic resonance determinations of the g tensor of Er3+ in YAG (4.0 mol K cm3), LuAG (4.25 mol K cm3), YGG (4.8 mol K cm3), and LuGG (5.6 mol K cm3) [6]. The difference is substantially less in the last case, which
has by far the most axial g tensor. If we assume the g tensor of Er3Te2Li3O12 resembles that of Er3+ in LuGG, we obtain the estimate J ¼ 0.22 K from the Weiss constant. Yb3Te2Li3O12, shown in Fig. 6, obeys a Curie–Weiss law accurately in the interval 2–4 K, with a Curie constant within 5% of the value measured in YbGG [9], as well as values calculated from magnetic resonance data in YAG, LuAG, YGG, and LuGG [6]. The close similarity of the Yb3+ g tensors obtained by magnetic resonance suggests that the Yb3+ ground state is not very different in Yb3Te2Li3O12. The small moment of Yb3+, together with its near-isotropy in LnAG and LnGG [5], implies yex yW with the resulting J ¼ 0.03 K. The magnitude of yW in the Kramers ion Ln3Te2Li3O12 compounds, shown in Table 1, does not appear markedly different overall from values measured in the corresponding aluminum and gallium garnets, where available. Thus it seems unlikely that the differences in chemical bonding in these materials, due to the presence of hexavalent Te+6 and monovalent Li+, result in a qualitative difference in the magnitude of exchange. The derived exchange is antiferromagnetic in all cases. The susceptibilities of Ln3Te2Li3O12 containing the non-Kramers ions Pr3+, Tb3+, and Ho3+ are shown in Figs. 7–9. Both the Pr and Ho compounds exhibit Van Vleck paramagnetism at the lowest temperatures. In both PrGG and PrAG the ground state of the Pr3+ ion is a singlet derived from a G5 triplet in cubic symmetry. The other components of the triplet lie higher by splittings which have been determined to lie in the range
40
250
Pr3Te2Li3O12
20 200 0 0 1/ χ (mol-RE/ cm3)
and the dipolar contribution can be calculated [4]. For the garnet structure, from the results of Capel [5] we obtain ( m2B yd ¼ 2:809g2x 86:243g2y þ 10:373g2z 4kB a3 ) 125:455g2x g2y þ 90:418g2x g2z þ 1:3656g2y g2z þ . ð1Þ g2x þ g2y þ g2z
1759
10
20
150
100
50
0 0
50
100
150 200 Temperature (K)
250
300
Fig. 7. Susceptibility of Pr3Te2Li3O12 versus temperature from 1.9 to 300 K. Van Vleck paramagnetism is evident below 10 K. The curved line is a two-parameter fit to the data, yielding splittings D1 ¼ 20:8 K, D2 ¼ 160 K (see text). Straight line is the free-ion prediction.
ARTICLE IN PRESS R.P. Applegate et al. / Journal of Physics and Chemistry of Solids 68 (2007) 1756–1761
1760
25
Ho3Te2Li3O12
0.6 0.4 20
1 / χ (mol-RE/cm3)
0.2 0 0
15
2
4
10
5
0 0
50
100 150 200 Temperature (K)
250
300
Fig. 8. Susceptibility of Ho3Te2Li3O12 versus temperature from 1.9 to 300 K. The onset of temperature-independent paramagnetism is visible in the inset.
30 Tb3Te2Li3O12
1/ χ (mol-RE / cm3)
2 25
1
20
0 0
10
20
15
10
5
higher states to the susceptibility by a constant. A fit to the susceptibility of Pr3Te2Li3O12 using the Van Vleck formula, similar to the procedure of Belorizky and Ayant [11] and shown in Fig. 7, then yields D1 ¼ 20.8 K, D2 ¼ 160 K. A consistency check can be obtained by observing that D2 is sufficiently large that the temperature dependence of the susceptibility should be described below 100 K by the lowest two singlets only. In this ‘‘twosinglet’’ model [7], which omits interactions, the susceptibility is given simply by w ¼ 2N 0 ðgJ mB Þ2 tanhðD1 =2TÞ ~ 2 =D1 where J~ is the total angular momentum. This h0jJj1i predicts that the point of maximum slope of the susceptibility as a function of temperature is at T ¼ D1 =2:4. For the data shown in Fig. 7, the maximum in jdw=dTj occurs at 9.5 K, implying D1 ¼ 22:8 K, in reasonable agreement with the two-parameter fit. Tb3+ and Ho3+ in both the aluminum and gallium garnets possess two low-lying singlets split by less than 10 K, well-separated from higher states [7,12–15]. Under these conditions the susceptibility is described accurately at the lowest temperatures by the two-singlet model. If we assume that the lowest states are arranged similarly in Ho3Te2Li3O12 and Tb3Te2Li3O12, the maximum in jdw=dTj occurring at 2.38 K in Ho3Te2Li3O12 implies a splitting D ¼ 5:7 K between the Ho3+ singlets, some 23% smaller than the value of 7.4 K in HoGG [12] but rather close to the value of D ¼ 5:96 K measured in HoAG [15]. jdw=dTj for Tb3Te2Li3O12 increases monotonically down to the lowest temperature of 1.9 K, implying Do4:6 K. Overall, its susceptibility resembles that of TbGG (D ¼ 2:87 K) more closely than TbAG (D ¼ 2:5 K), which deviates from the prediction of the two-singlet model at the lowest temperatures due to interactions, exhibiting an inflection around 2 K and magnetic order at 1.35 K [6,14,16]. In conclusion, we find that in each case the magnetic properties of the rare earth tellurate garnets show some resemblance to one or both of the corresponding aluminum or gallium garnets. The magnitude of exchange also does not appear to be qualitatively different between this series of compounds and the LnAG and LnGG, in those cases where it can be determined, despite the systematic difference in superexchange pathways. References
0 0
50
100 150 200 Temperature (K)
250
300
Fig. 9. Susceptibility of Tb3Te2Li3O12 versus temperature from 1.9 to 300 K.
D1 ¼ 20.7–32 K and D2 ¼ 55–130 K for PrGG and Pr3+:YGG, and D1 ¼ 32 K, D2 ¼ 72 K in Pr3+:YAG [10]. The next higher state is a G1 singlet at least 400 K above ground in Pr3+:YGG and 700 K in Pr3+:YAG. Here we assume that the low-lying levels in Pr3Te2Li3O12 are qualitatively similar, and approximate the contribution of
[1] H.M. Kasper, Inorg. Chem. 8 (1969) 1000. [2] W.P. Wolf, B. Schneider, D.P. Landau, B.E. Keen, Phys. Rev. B 5 (1972) 4472. [3] D.P. Landau, B.E. Keen, B. Schneider, W.P. Wolf, Phys. Rev. B 3 (1971) 2310. [4] J.M. Daniels, Proc. Phys. Soc. A 66 (1953) 673. [5] H.W. Capel, Physica 31 (1965) 1152. [6] W.P. Wolf, M. Ball, M.T. Hutchings, M.J.M. Leask, A.F.G. Wyatt, J. Phys. Soc. Japan 17 (Suppl. B-I) (1962) 443. [7] A.H. Cooke, T.L. Thorp, M.R. Wells, Proc. Phys. Soc. 92 (1967) 400. [8] P. Schiffer, A.P. Ramirez, D.A. Huse, P.L. Gammel, U. Yaron, D.J. Bishop, A.J. Valentino, Phys. Rev. Lett. 74 (1995) 2379. [9] J. Filippi, J.C. Lasjaunias, B. Hebral, J. Rossat-Mignod, F. Tcheou, J. Mag. Magn. Mat. 15–18 (1980) 527.
ARTICLE IN PRESS R.P. Applegate et al. / Journal of Physics and Chemistry of Solids 68 (2007) 1756–1761 [10] D.P. Goshorn, D.G. Onn, J.P. Remeika, Phys. Rev. B 15 (1977) 3527 and references therein. [11] E. Belorizky, Y. Ayant, in: W. Low (Ed.), Paramagnetic Resonance, vol. 1, Academic, New York, 1963, p. 290. [12] D.G. Onn, H. Meyer, J.P. Remeika, Phys. Rev. 156 (1967) 663. [13] J. Hammann, P. Manneville, J. Phys. 34 (1973) 615. [14] A. Gavignet-Tillard, J. Hammann, L. de Seze, J. Phys. 34 (1973) 27.
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[15] S. Nagata, H. Sasaki, K. Suzuki, J. Kiuchi, N. Wada, J. Phys. Chem. Solids 62 (2001) 1123. [16] J. Hammann, P. Manneville, in: K.D. Timmerhaus, W.J. O’Sullivan, E.F. Hammel (Eds.), Proceedings of the 13th International Conference on Low Temperature Physics, vol. 2, 1974, p. 328. [17] M. Guillot, X. Wei, D. Hall, Y. Xu, J.H. Yang, F. Zhang, J. Appl. Phys. 93 (2003) 8005.
Journal of Physics and Chemistry of Solids 68 (2007) 1756–1761 www.elsevier.com/locate/jpcs
Magnetic properties of some rare earth tellurate garnets Ryan P. Applegate, Yuhua Zong, L.R. Corruccini Physics Department, University of California, Davis, CA 95616, USA Received 10 October 2006; received in revised form 18 April 2007; accepted 24 April 2007
Abstract The magnetic properties of the lanthanide tellurate garnets Ln3Te2Li3O12 for Ln ¼ Pr, Nd, Gd–Er, and Yb are found to exhibit similarities in many cases to the related aluminum or gallium garnet compounds. Magnetic exchange is also roughly comparable in magnitude, despite the systematic difference in exchange pathways. r 2007 Elsevier Ltd. All rights reserved. PACS: 75.30.Cr; 75.50.Dd Keywords: A. Magnetic materials; D. Magnetic properties
1. Introduction The rare earth tellurate garnets Ln3Te2Li3O12 were first described by Kasper [1]. They form for all the rare earths Ln from Pr to Lu. Like the related and more familiar Ln3M5O12 garnet compounds, including M ¼ Al, Ga, and ¯ The lanthanide Fe, they are cubic, with space group Ia3d. ions have orthorhombic point symmetry. However, the TeO6 complexes are more isolated than the continuous M–O–M linkages found in the Ln3M5O12 materials. This results in a more pronounced lanthanide contraction in the tellurate garnets. Superexchange pathways are qualitatively different in the rare earth tellurate garnets, which contain monovalent and hexavalent diamagnetic cations, from those in the rare earth aluminum and gallium garnets, where the diamagnetic cations are all trivalent. The lattice parameters of the Ln3Te2Li3O12 materials are much closer, on average, to those of the rare earth gallium garnets than those containing aluminum or iron. We have investigated the magnetic properties of a number of these materials to see to what extent they resemble the rare earth gallium (LnGG) and aluminum (LnAG) garnets, their closest magnetic analogs. We were also curious to see whether magnetic exchange is measurably affected, and Corresponding author. Tel.: +1 530 752 1023; fax: +1 530 752 4717.
E-mail address: [email protected] (L.R. Corruccini). 0022-3697/$ - see front matter r 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.jpcs.2007.04.022
possibly reduced, by the isolation of the tightly bound TeO6 complexes. 2. Experimental details Polycrystalline samples were made by solid-state reaction in air of the relevant metal oxides or hydroxides in stoichiometric ratio, pressed into pellets, typically at 850 1C for 10 h. After the initial firing, samples were reground, repressed and fired a second time. Powder X-ray diffraction ¯ with no impurity peaks peaks could all be indexed to Ia3d, visible at the 1% level. The lattice parameters are listed in Table 1, in reasonable agreement with those of Kasper [1]. Static magnetic susceptibilities were measured on spherical samples at 500 Oersteds in a quantum design MPMS susceptometer. 3. Data and discussion Magnetic susceptibilities of Ln3Te2Li3O12 containing the Kramers ions Ln3+ ¼ Dy3+, Gd3+, Nd3+, Er3+, and Yb3+, are shown in Figs. 1–6. The low temperature Curie constants and Weiss constants, obtained from a linear fitting of w1 well above any ordering features, are listed in Table 1. In many cases, the Curie constant is within 20% of values ascribed to either the corresponding Ga or Al
ARTICLE IN PRESS R.P. Applegate et al. / Journal of Physics and Chemistry of Solids 68 (2007) 1756–1761
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Table 1 Lattice parameter, Curie and Weiss constants with the temperature range of the linear fit, exchange constant, and lowest-level crystal field splittings for rare earth tellurate garnets, with parameters of some related aluminum and gallium garnets shown for comparison Material
a (A˚)
C (cm3-K/mol)
yW (K)
J (K)
Dy3Te2Li3O12 DyAG DyGG Gd3Te2Li3O12 GdAG GdGG Nd3Te2Li3O12 Nd3+:Y, LuAG NdGG Er3Te2Li3O12 Er3+:Y, LuAG Er3+:Y, LuGG Yb3Te2Li3O12 Yb3+:Y, LuAG Yb3+:Y, LuGG Pr3Te2Li3O12 Tb3Te2Li3O12 Ho3Te2Li3O12
12.2951
11.2470.6 (5–12K) 10.45a 6.6–7.8a,b,c 7.9970.2 (12–20 K) 7.82d 7.82d 0.74070.04 (2.2–5 K) 0.617d 0.586e, 0.598d 6.17370.3 (1.9–4 K) 4.00–4.254d 4.79–5.61d,f 1.15970.05 (5–14 K) 1.106–1.108d 1.094–1.109c,d
0.7870.3 0.20a (0.05)–(0.436)a,b,c 2.6670.3 3.0d 2.3d 0.9170.3
0.45
0.2870.1
0.22
0.30f 0.06270.03
0.03
10.070.5 (6–10 K)
0.01770.1
12.3722
12.5402
12.2266
12.1623
12.5921 12.3354 12.2563
D (K)
0.063
0.47
0.045c 20.872, 160720 5.771
a
Ref. [2]. Ref. [7]. c Ref. [9]. d Ref. [6]. e Ref. [17]. f Ref. [5]. b
25
45
1 Dy3Te2Li3O12
1.5
Gd3Te2Li3O12
40 1
0.5 20
35
0
15
5
0.5
30
10
1/ χ (mol-RE / cm3)
1 / χ (mol-RE/cm3)
0
10
5
0 0
5
10
25 20 15 10 5
0 0
50
100
150
200
250
300
Temperature (K)
0 0
50
100
150
200
250
300
Temperature (K) Fig. 1. Inverse susceptibility of Dy3Te2Li3O12 versus temperature from 1.9 to 300 K. The solid line is the free-ion prediction. The inset shows expanded data at the lowest temperature. An ordering feature at T 2 K is visible.
Fig. 2. Susceptibility of Gd3Te2Li3O12 versus temperature, from 1.9 to 300 K. Solid line is the predicted free-ion susceptibility.
garnet, or both. This suggests that the ground state of the lanthanide ion may be related in the two materials. The Curie constant of Dy3Te2Li3O12, in particular, is close to that of Dy aluminum garnet, in which the Dy3+
ions have the rather large axial moment gjj mB S eff ffi 9mB , where S eff ¼ 12 for the doublet ground state of Dy3+, so that gjj ¼ gz ffi 18, gx ¼ gy ffi 0 [2]. The susceptibility of Dy3Te2Li3O12 is shown in Fig. 1. Assuming the ground
ARTICLE IN PRESS R.P. Applegate et al. / Journal of Physics and Chemistry of Solids 68 (2007) 1756–1761
1758
0.75
30
Gd3Te2Li3O12
3
Er3Te2Li3O12
2 25
1/ χ (mol-RE/ cm3)
0.7 1/ χ (mol-RE/ cm3)
1
squid data 500 Oersted FC 100 Oersted FC 10 Oersted FC 10 Oersted ZFC
0.65
0
20
0
10
20
15
10 0.6 5
0.55 0
1
2
0
3
0
Temperature (K)
50
100
150
200
250
300
Temperature (K) Fig. 3. Susceptibility of Gd3Te2Li3O12 from 0.02 to 3 K. An apparent ordering feature at T 0:25 K is visible.
250
30
Fig. 5. Susceptibility of Er3Te2Li3O12 versus temperature from 1.9 to 300 K.
Nd3Te2Li3O12
20 10
140
10
Yb3Te2Li3O12
0 0
0 0
150
20
120
10
1 /χ χ (mol-RE / cm3)
1/χ χ (mol-RE / cm3)
200
160
20
100
10
20
100 80 60 40
50 20
0 0
50
100 150 200 Temperature (K)
250
300
0 0
50
100 150 200 Temperature (K)
250
300
Fig. 4. Susceptibility of Nd3Te2Li3O12 versus temperature, from 1.9 to 300 K, with solid line the free-ion prediction.
Fig. 6. Susceptibility of Yb3Te2Li3O12 versus temperature from 1.9 to 300 K.
state of Dy3+ in Dy3Te2Li3O12 is also axial, its Curie constant predicts an axial moment of 9.5mB or gz ¼ 19.0 (close to the maximum possible value of 20). The susceptibility of Dy3Te2Li3O12 also exhibits an antiferromagnetic ordering feature at approximately 2 K, reminiscent of that in dysprosium aluminum garnet at
TN ¼ 2.53 K [3]. Although the lattice constant of Dy3Te2 Li3O12 is much closer to that of Dy gallium garnet, its magnetic properties resemble Dy aluminum garnet more closely. yW contains contributions from both exchange and magnetic dipole–dipole interactions. For a spherical sample these contributions are additive, yW ¼ yex þ yd ,
ARTICLE IN PRESS R.P. Applegate et al. / Journal of Physics and Chemistry of Solids 68 (2007) 1756–1761
For Dy3Te2Li3O12, assuming gx gy 0, we obtain yd ¼ 0.126 K, which is not negligible in comparison to the measured yW. From yex we obtain a value of the exchange constant J (assumed isotropic) shown in Table 1, from the mean-field result yex ¼ 2JnS(S+1)/3kB. Here the number of nearest magnetic neighbors n is four for the garnet structure, and S is the effective spin of the ion’s ground state. Gd3Te2Li3O12 exhibits a susceptibility similar to that observed in both gadolinium gallium and aluminum garnets above 2 K, namely Curie–Weiss behavior above 12 K with a Curie constant close to the theoretical free-ion value of 7.875 mol K cm3, a Weiss constant between 2 and 3 K, and a gradual deviation of the susceptibility from the Curie–Weiss extrapolation at lower temperatures [6–8]. This is shown in Fig. 2. From yW we obtain J ¼ 0.063 K directly, since yd vanishes for the isotropic moment of Gd3+. Gadolinium gallium garnet (GGG) is known to display strong magnetic frustration, undergoing a spin glass transition at 0.1 K [8], with no evidence of long-range order in zero field. A sample of Gd3Te2Li3O12 cooled to lower temperatures in a dilution refrigerator exhibits an apparent ordering feature in the static susceptibility at approximately 0.25 K, shown in Fig. 3. This measurement was taken in a smaller field of 10 Oe. There is a small amount of history dependence in the susceptibility, but it commences well below the ordering feature, so the behavior of Gd3Te2Li3O12 appears distinct from GGG, and frustration, while present, does not appear to be as strong in this material. The susceptibility of Nd3Te2Li3O12, shown in Fig. 4, obeys a Curie–Weiss law below 5 K which yields a Curie constant about 20% larger than that predicted by the g factors of Nd3+ in yttrium aluminum and yttrium gallium garnets, both about 0.6 mol K cm3 [6]. If we assume the elements of the g tensor are proportional to an average of the values measured for Nd3+ in diamagnetic aluminum and gallium garnet hosts [6], we obtain an estimated ydE0.025 K. This is small compared to yW, in consequence of the relatively small size of the moment of Nd3+, and yields the estimate of J shown in Table 1. The susceptibility of Er3Te2Li3O12, shown in Fig. 5, yields a Curie constant in the region 1.9–4 K of 6.17 mol K cm3, which exceeds values calculated from paramagnetic resonance determinations of the g tensor of Er3+ in YAG (4.0 mol K cm3), LuAG (4.25 mol K cm3), YGG (4.8 mol K cm3), and LuGG (5.6 mol K cm3) [6]. The difference is substantially less in the last case, which
has by far the most axial g tensor. If we assume the g tensor of Er3Te2Li3O12 resembles that of Er3+ in LuGG, we obtain the estimate J ¼ 0.22 K from the Weiss constant. Yb3Te2Li3O12, shown in Fig. 6, obeys a Curie–Weiss law accurately in the interval 2–4 K, with a Curie constant within 5% of the value measured in YbGG [9], as well as values calculated from magnetic resonance data in YAG, LuAG, YGG, and LuGG [6]. The close similarity of the Yb3+ g tensors obtained by magnetic resonance suggests that the Yb3+ ground state is not very different in Yb3Te2Li3O12. The small moment of Yb3+, together with its near-isotropy in LnAG and LnGG [5], implies yex yW with the resulting J ¼ 0.03 K. The magnitude of yW in the Kramers ion Ln3Te2Li3O12 compounds, shown in Table 1, does not appear markedly different overall from values measured in the corresponding aluminum and gallium garnets, where available. Thus it seems unlikely that the differences in chemical bonding in these materials, due to the presence of hexavalent Te+6 and monovalent Li+, result in a qualitative difference in the magnitude of exchange. The derived exchange is antiferromagnetic in all cases. The susceptibilities of Ln3Te2Li3O12 containing the non-Kramers ions Pr3+, Tb3+, and Ho3+ are shown in Figs. 7–9. Both the Pr and Ho compounds exhibit Van Vleck paramagnetism at the lowest temperatures. In both PrGG and PrAG the ground state of the Pr3+ ion is a singlet derived from a G5 triplet in cubic symmetry. The other components of the triplet lie higher by splittings which have been determined to lie in the range
40
250
Pr3Te2Li3O12
20 200 0 0 1/ χ (mol-RE/ cm3)
and the dipolar contribution can be calculated [4]. For the garnet structure, from the results of Capel [5] we obtain ( m2B yd ¼ 2:809g2x 86:243g2y þ 10:373g2z 4kB a3 ) 125:455g2x g2y þ 90:418g2x g2z þ 1:3656g2y g2z þ . ð1Þ g2x þ g2y þ g2z
1759
10
20
150
100
50
0 0
50
100
150 200 Temperature (K)
250
300
Fig. 7. Susceptibility of Pr3Te2Li3O12 versus temperature from 1.9 to 300 K. Van Vleck paramagnetism is evident below 10 K. The curved line is a two-parameter fit to the data, yielding splittings D1 ¼ 20:8 K, D2 ¼ 160 K (see text). Straight line is the free-ion prediction.
ARTICLE IN PRESS R.P. Applegate et al. / Journal of Physics and Chemistry of Solids 68 (2007) 1756–1761
1760
25
Ho3Te2Li3O12
0.6 0.4 20
1 / χ (mol-RE/cm3)
0.2 0 0
15
2
4
10
5
0 0
50
100 150 200 Temperature (K)
250
300
Fig. 8. Susceptibility of Ho3Te2Li3O12 versus temperature from 1.9 to 300 K. The onset of temperature-independent paramagnetism is visible in the inset.
30 Tb3Te2Li3O12
1/ χ (mol-RE / cm3)
2 25
1
20
0 0
10
20
15
10
5
higher states to the susceptibility by a constant. A fit to the susceptibility of Pr3Te2Li3O12 using the Van Vleck formula, similar to the procedure of Belorizky and Ayant [11] and shown in Fig. 7, then yields D1 ¼ 20.8 K, D2 ¼ 160 K. A consistency check can be obtained by observing that D2 is sufficiently large that the temperature dependence of the susceptibility should be described below 100 K by the lowest two singlets only. In this ‘‘twosinglet’’ model [7], which omits interactions, the susceptibility is given simply by w ¼ 2N 0 ðgJ mB Þ2 tanhðD1 =2TÞ ~ 2 =D1 where J~ is the total angular momentum. This h0jJj1i predicts that the point of maximum slope of the susceptibility as a function of temperature is at T ¼ D1 =2:4. For the data shown in Fig. 7, the maximum in jdw=dTj occurs at 9.5 K, implying D1 ¼ 22:8 K, in reasonable agreement with the two-parameter fit. Tb3+ and Ho3+ in both the aluminum and gallium garnets possess two low-lying singlets split by less than 10 K, well-separated from higher states [7,12–15]. Under these conditions the susceptibility is described accurately at the lowest temperatures by the two-singlet model. If we assume that the lowest states are arranged similarly in Ho3Te2Li3O12 and Tb3Te2Li3O12, the maximum in jdw=dTj occurring at 2.38 K in Ho3Te2Li3O12 implies a splitting D ¼ 5:7 K between the Ho3+ singlets, some 23% smaller than the value of 7.4 K in HoGG [12] but rather close to the value of D ¼ 5:96 K measured in HoAG [15]. jdw=dTj for Tb3Te2Li3O12 increases monotonically down to the lowest temperature of 1.9 K, implying Do4:6 K. Overall, its susceptibility resembles that of TbGG (D ¼ 2:87 K) more closely than TbAG (D ¼ 2:5 K), which deviates from the prediction of the two-singlet model at the lowest temperatures due to interactions, exhibiting an inflection around 2 K and magnetic order at 1.35 K [6,14,16]. In conclusion, we find that in each case the magnetic properties of the rare earth tellurate garnets show some resemblance to one or both of the corresponding aluminum or gallium garnets. The magnitude of exchange also does not appear to be qualitatively different between this series of compounds and the LnAG and LnGG, in those cases where it can be determined, despite the systematic difference in superexchange pathways. References
0 0
50
100 150 200 Temperature (K)
250
300
Fig. 9. Susceptibility of Tb3Te2Li3O12 versus temperature from 1.9 to 300 K.
D1 ¼ 20.7–32 K and D2 ¼ 55–130 K for PrGG and Pr3+:YGG, and D1 ¼ 32 K, D2 ¼ 72 K in Pr3+:YAG [10]. The next higher state is a G1 singlet at least 400 K above ground in Pr3+:YGG and 700 K in Pr3+:YAG. Here we assume that the low-lying levels in Pr3Te2Li3O12 are qualitatively similar, and approximate the contribution of
[1] H.M. Kasper, Inorg. Chem. 8 (1969) 1000. [2] W.P. Wolf, B. Schneider, D.P. Landau, B.E. Keen, Phys. Rev. B 5 (1972) 4472. [3] D.P. Landau, B.E. Keen, B. Schneider, W.P. Wolf, Phys. Rev. B 3 (1971) 2310. [4] J.M. Daniels, Proc. Phys. Soc. A 66 (1953) 673. [5] H.W. Capel, Physica 31 (1965) 1152. [6] W.P. Wolf, M. Ball, M.T. Hutchings, M.J.M. Leask, A.F.G. Wyatt, J. Phys. Soc. Japan 17 (Suppl. B-I) (1962) 443. [7] A.H. Cooke, T.L. Thorp, M.R. Wells, Proc. Phys. Soc. 92 (1967) 400. [8] P. Schiffer, A.P. Ramirez, D.A. Huse, P.L. Gammel, U. Yaron, D.J. Bishop, A.J. Valentino, Phys. Rev. Lett. 74 (1995) 2379. [9] J. Filippi, J.C. Lasjaunias, B. Hebral, J. Rossat-Mignod, F. Tcheou, J. Mag. Magn. Mat. 15–18 (1980) 527.
ARTICLE IN PRESS R.P. Applegate et al. / Journal of Physics and Chemistry of Solids 68 (2007) 1756–1761 [10] D.P. Goshorn, D.G. Onn, J.P. Remeika, Phys. Rev. B 15 (1977) 3527 and references therein. [11] E. Belorizky, Y. Ayant, in: W. Low (Ed.), Paramagnetic Resonance, vol. 1, Academic, New York, 1963, p. 290. [12] D.G. Onn, H. Meyer, J.P. Remeika, Phys. Rev. 156 (1967) 663. [13] J. Hammann, P. Manneville, J. Phys. 34 (1973) 615. [14] A. Gavignet-Tillard, J. Hammann, L. de Seze, J. Phys. 34 (1973) 27.
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[15] S. Nagata, H. Sasaki, K. Suzuki, J. Kiuchi, N. Wada, J. Phys. Chem. Solids 62 (2001) 1123. [16] J. Hammann, P. Manneville, in: K.D. Timmerhaus, W.J. O’Sullivan, E.F. Hammel (Eds.), Proceedings of the 13th International Conference on Low Temperature Physics, vol. 2, 1974, p. 328. [17] M. Guillot, X. Wei, D. Hall, Y. Xu, J.H. Yang, F. Zhang, J. Appl. Phys. 93 (2003) 8005.