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Spin reorientations in Er2Fe14Si3
ARTICLE IN PRESS
Journal of Magnetism and Magnetic Materials 316 (2007) e383–e386 www.elsevier.com/locate/jmmm
Spin reorientations in Er2Fe14Si3 A.V. Andreev Institute of Physics, Academy of Sciences, Na Slovance 2, Prague 18221, Czech Republic Available online 1 March 2007
Abstract Fe–Si substitution in Er2Fe17 leads to a spin reorientation (SR) because the uniaxial anisotropy of the Er sublattice starts to dominate at low temperatures. In order to investigate the SR in detail, the magnetization measurements were performed on a single crystal of Er2Fe14Si3. K1 changes sign at 116 K. Since K2 is found to be negative at this temperature, the SR is a first-order ‘‘axis–plane’’ phase transition. A second SR was observed at low temperatures and the ground state of Er2Fe14Si3 is characterized by a very low ‘‘cone of easy axes’’ anisotropy with angle 301 between the magnetic moment and the c-axis. With increasing temperature, the cone closes gradually and transforms by a second-order transition to the easy c-axis at about 50 K. r 2007 Elsevier B.V. All rights reserved. PACS: 75.30.m; 75.30.Gw Keywords: R2Fe17; Ferrimagnetism; Magnetic anisotropy; Spin reorientation
1. Introduction
2. Experimental
Er2Fe17 is a representative of the rare-earth intermetallics series R2Fe17 (R ¼ Ce–Lu). It is a collinear ferrimagnet with TC ¼ 310 K. As found from single-crystal measurements, the spontaneous magnetic moment Ms ¼ 19 mB (at 4.2 K) is located in the basal plane of the hexagonal crystal structure of the Th2Ni17 type [1–3]. The Er and Fe sublattices have competitive magnetic anisotropies and the Fe-sublattice anisotropy of the easy-plane type dominates in whole temperature range of ferrimagnetic order. A weakening of the Fe-sublattice anisotropy by dilution with non-magnetic Si leads to a spin-reorientation (SR) phase transition at about 125 K in Er2Fe14Si3 [4] because the uniaxial anisotropy of the Er sublattice starts to dominate at low temperatures. In the present work, a magnetization study was performed on a single crystal of Er2Fe14Si3 in order to investigate the SR in detail, in particular, to determine the order of this phase transition.
A single crystal of Er2Fe14Si3 of 20 mm length and 4 mm diameter has been grown by a modified Czochralski method in a tri-arc furnace from the stoichiometric melt. The magnetization was measured at 2–500 K in fields up to 9 T applied along the main crystallographic axes using PPMS-9 and SQUID cryomagnetic installations (Quantum Design). The magnetization curves presented below are corrected for demagnetizing field.
Tel.: +420 221912772; fax: +420 221911351.
E-mail address: [email protected]. 0304-8853/$ - see front matter r 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2007.02.156
3. Results and discussion X-ray powder-diffraction analysis confirmed the hexagonal crystal structure of the Th2Ni17 type. The lattice parameters a ¼ 840.9 pm, c ¼ 823.2 pm differ slightly from the values in Ref. [4], pointing to a possible small difference in the Si content. This may explain the slightly lower SR temperature (116 K, see below). In addition to this phase transition reported in Ref. [4], a second SR (denoted as SR2, to distinguish from SR1 at 116 K) was observed at low temperatures. Figs. 1 and 2 show the evolution of the magnetization isotherms below 80 K in fields applied along the principal axes /1 0 0S(a), /1 2 0S(b)
ARTICLE IN PRESS A.V. Andreev / Journal of Magnetism and Magnetic Materials 316 (2007) e383–e386
e384
12 K1, 10K2 (MJ m-3)
0.4
8 a b c
Er2Fe14Si3
4
T=5K 0
0.2 0.0 K1 10K2
-0.2 -0.4
a b c
4
(degree)
M (µB/f.u.)
-0.6 8
T = 20 K 0
0
a b c T = 30 K 0
1
2
3
µ0Hi (T) Fig. 1. Magnetization of a Er2Fe14Si3 single crystal in fields applied along the principal axes at 5, 20 and 30 K.
16 Er2Fe14Si3
12
a b c
8 4
T = 40 K
0 M (µB/f.u.)
Er2Fe14Si3
0
4
12 a b c
8 4
T = 60 K
0 12 a b c T = 80 K
8 4 0
60 30
8
0
90
0
1
µ0Hi (T)
2
3
Fig. 2. Same as Fig. 1, but here for 40, 60 and 80 K.
and /0 0 1S(c). One can see that the ground state of Er2Fe14Si3 is characterized by a surprisingly low anisotropy between the basal plane and the c-axis. The a- and c-axis curves at 5 K are practically the same and saturate at the value 9 mB/f.u. in a field of 0.2 T. The b-axis curve is clearly below the a-axis curve, pointing to a considerable anisotropy within the basal plane, the anisotropy field being about 3 T.
50
100
150 200 T (K)
250
300
Fig. 3. Top: the temperature dependence of anisotropy constants K1 and K2 determined by the Sucksmith–Tompson method. For better presentation, the K2 values are multiplied by factor of 10. Bottom: the temperature dependence of angle between the easy-magnetization axis and the c-axis.
Due to the very low anisotropy at 5 K, it is difficult to measure the projections of Ms on the a- and c-axis and thus to determine the direction of Ms. However, it is possible to extrapolate them from the temperature interval 20–40 K because the anisotropy starts to increase rapidly with increasing temperature. At 20 K, the projection of Ms on the basal plane is about 4.5 mB, decreasing with increasing temperature and vanishing above 50 K. No basal-plane component of Ms is observed at 60 K (Fig. 2). The temperature dependence of the angle Y between the easy-magnetization direction and the c-axis (Fig. 3) shows that in the ground state Er2Fe14Si3 has a cone of easy axes with half-opening angle of 301. The ‘‘cone-axis’’ spin reorientation SR2 occurs at 50 K as a second-order phase transition, and the uniaxial magnetic anisotropy extends up to 116 K. At low temperatures, the magnetization curves along the a- and b-axis exhibit a field-induced phase transition with a non-negligible hysteresis (0.1 T at 20 K) pointing to a firstorder type. The anisotropy within the basal plane is reflected in the fact that the transition field Bc defined as an inflection point on the M(H) curve is larger along the b-axis than along the a-axis. This anisotropy vanishes above 90 K. The a- and c-axis magnetization curves at 110–120 K, similar to at 5 K, are practically the same and saturate at very low field. Above this temperature interval, the easyplane anisotropy is seen clearly. A question is if the transformation of the anisotropy from the easy axis to the easy plane occurs by a first-order transition or by two second-order transitions (‘‘axis-cone’’ and ‘‘cone-plane’’) with a narrow range of stability of the ‘‘cone-type’’ anisotropy. Absence of noticeable hysteresis in both the temperature and field dependences of the magnetization is in favor of the second possibility. But the crucial point is
ARTICLE IN PRESS A.V. Andreev / Journal of Magnetism and Magnetic Materials 316 (2007) e383–e386
e385
20
16
M(µB/f.u.)
110 K 120 K 130 K 140 K 150 K 160 K 180 K 200 K
8
Ms(µB/f.u.)
16 12
from a-axis from c-axis from projections
12
8 Er2Fe14Si3
4
Er2Fe14Si3
4
easy axis
TC = 474 K
H // c-axis 0 0.0
0 0.4
0.8 µ0Hi (T)
1.2
Fig. 4. Temperature evolution of the magnetization curve along the c-axis above the ‘‘axis–plane’’ spin reorientation.
the sign of the second anisotropy constant K2 at the temperature where the first anisotropy constant K1 changes its sign [5]. The complicated shape of the magnetization curves at low temperatures with clear evidence of a strong contribution of the high-order anisotropy constants does not allow us to determine properly the K1 and K2 values. Nevertheless, this contribution vanishes above 80 K and the hard-axis magnetization curves can be treated by the Sucksmith–Tompson method and K1 and K2 can be determined with high accuracy. Fig. 4 shows that, in the vicinity of SR1 (just above SR1) the c-axis curve has positive curvature, which corresponds to a negative K2. The same is observed for the a-axis curve just below SR1 where this axis is the hard axis. The temperature dependences of K1 and K2 are presented in Fig. 3. It is found that K1 changes sign at 116 K. Since K2 is negative at this temperature, this SR is an ‘‘axis-plane’’ first-order phase transition, and no range of the ‘‘conetype’’ anisotropy exists. SR1 is accompanied by a pronounced anomaly in the specific heat, whereas the effect of SR2 on specific heat is almost negligible. The specific-heat behavior of Er2Fe14Si3 at the SR will be discussed elsewhere. The clear origin of SR1 is the competition of the easyaxis anisotropy of the Er sublattice, which rapidly decreases with increasing temperature, and the easy-plane anisotropy of the Fe sublattice which has much smoother temperature dependence. T ¼ 116 K is the temperature Fe where KEr 1 ¼ K1 . As regards to K2, it also changes sign at 160 K (see the change from positive to negative curvature of the c-axis magnetization curve in Fig. 4). This is not a phase transition and shows only that the Fe-sublattice anisotropy finally dominates above this temperature (K240 for the Fe sublattice in R2Fe17, [1–3]). SR2 does not originate from the Fe sublattice. The nonmonotonous evolution of anisotropy at low temperatures is
0
100
200
300
400
500
T (K) Fig. 5. Temperature dependence of the spontaneous magnetic moment Ms determined from magnetization data along the easy-magnetization direction.
connected with the Er sublattice and can be explained in two ways. The fact that the low-temperature hard-direction curves cannot be fitted by the Sucksmith–Tompson method points to large terms of order higher than four in the description of the anisotropy. They give a negative contribution to the anisotropy, which practically compensates a positive second-order term in the ground state. Another possible explanation is based on the two nonequivalent positions of Er atoms in the Th2Ni17-type crystal structure. The complicated behavior of the magnetic anisotropy can be caused by considerably different and competitive anisotropies of the two Er sublattices. 4. Conclusions Er2Fe14Si3 is a ferrimagnet with TC ¼ 474 K and Ms ¼ 9.6 mB (Fig. 5). Assuming MEr ¼ 9 mB (as for the free 3+ ion) and a collinear magnetic structure, the average MFe is equal to 1.97 mB (compared with 2.16 mB in Er2Fe17). This is slightly lower than in Tb2Fe14Si3 (2.04 mB, [6]), the only other R2Fe14Si3 compound studied in single-crystalline form. Above 116 K, an easy-plane magnetic anisotropy of the Fe sublattice dominates. Upon cooling, a first-order SR to the easy-axis type occurs at this temperature due to enhancement of the Er-sublattice anisotropy. However, below 50 K the easy axis deviates from the c axis up to 301 at 5 K. Despite of a moderate anisotropy at elevated temperatures, in the ground state the anisotropy of Er2Fe14Si3 is very weak. Acknowledgments The author thanks Dr. E. Sˇantava´ for the help in experiments. This work is a part of the research project AVOZ10100520 and has been supported by Grants GACR 202/06/0185 and GAAV IAA100100530.
ARTICLE IN PRESS e386
A.V. Andreev / Journal of Magnetism and Magnetic Materials 316 (2007) e383–e386
References [1] A.V. Andreev, A.V. Deryagin, S.M. Zadvorkin, N.V. Kudrevatykh, V.N. Moskalev, R.Z. Levitin, Y.F. Popov, R.Y. Yumaguzhin, in: D.D. Mishin (Ed.), Fizika Magnithykh (Physics of Magnetic Materials), Kalinin, 1985, pp. 21–49 (in Russian). [2] S. Sinnema, Ph.D. Thesis, University of Amsterdam, 1988. [3] B. Garcia-Landa, P.A. Algarabel, M.R. Ibarra, P.E. Kaizel, T.H. Ahn, J.J.M. Franse, J. Magn. Magn. Mater. 144 (1995) 1085.
[4] B.G. Shen, B. Liang, Z.H. Cheng, T.Y. Gong, H. Tang, F.R. de Boer, K.H.J. Buschow, Solid State Commun. 103 (1997) 71. [5] K.P. Belov, A.K. Zvezdin, A.M. Kadomtseva, R.Z. Levitin, Sov. Phys. Uspekhi 19 (1976) 574. [6] J. Du, G.H. Wu, C.C. Tang, Y.X. Li, W.S. Zhan, J. Appl. Phys. 84 (1998) 3305.
Journal of Magnetism and Magnetic Materials 316 (2007) e383–e386 www.elsevier.com/locate/jmmm
Spin reorientations in Er2Fe14Si3 A.V. Andreev Institute of Physics, Academy of Sciences, Na Slovance 2, Prague 18221, Czech Republic Available online 1 March 2007
Abstract Fe–Si substitution in Er2Fe17 leads to a spin reorientation (SR) because the uniaxial anisotropy of the Er sublattice starts to dominate at low temperatures. In order to investigate the SR in detail, the magnetization measurements were performed on a single crystal of Er2Fe14Si3. K1 changes sign at 116 K. Since K2 is found to be negative at this temperature, the SR is a first-order ‘‘axis–plane’’ phase transition. A second SR was observed at low temperatures and the ground state of Er2Fe14Si3 is characterized by a very low ‘‘cone of easy axes’’ anisotropy with angle 301 between the magnetic moment and the c-axis. With increasing temperature, the cone closes gradually and transforms by a second-order transition to the easy c-axis at about 50 K. r 2007 Elsevier B.V. All rights reserved. PACS: 75.30.m; 75.30.Gw Keywords: R2Fe17; Ferrimagnetism; Magnetic anisotropy; Spin reorientation
1. Introduction
2. Experimental
Er2Fe17 is a representative of the rare-earth intermetallics series R2Fe17 (R ¼ Ce–Lu). It is a collinear ferrimagnet with TC ¼ 310 K. As found from single-crystal measurements, the spontaneous magnetic moment Ms ¼ 19 mB (at 4.2 K) is located in the basal plane of the hexagonal crystal structure of the Th2Ni17 type [1–3]. The Er and Fe sublattices have competitive magnetic anisotropies and the Fe-sublattice anisotropy of the easy-plane type dominates in whole temperature range of ferrimagnetic order. A weakening of the Fe-sublattice anisotropy by dilution with non-magnetic Si leads to a spin-reorientation (SR) phase transition at about 125 K in Er2Fe14Si3 [4] because the uniaxial anisotropy of the Er sublattice starts to dominate at low temperatures. In the present work, a magnetization study was performed on a single crystal of Er2Fe14Si3 in order to investigate the SR in detail, in particular, to determine the order of this phase transition.
A single crystal of Er2Fe14Si3 of 20 mm length and 4 mm diameter has been grown by a modified Czochralski method in a tri-arc furnace from the stoichiometric melt. The magnetization was measured at 2–500 K in fields up to 9 T applied along the main crystallographic axes using PPMS-9 and SQUID cryomagnetic installations (Quantum Design). The magnetization curves presented below are corrected for demagnetizing field.
Tel.: +420 221912772; fax: +420 221911351.
E-mail address: [email protected]. 0304-8853/$ - see front matter r 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2007.02.156
3. Results and discussion X-ray powder-diffraction analysis confirmed the hexagonal crystal structure of the Th2Ni17 type. The lattice parameters a ¼ 840.9 pm, c ¼ 823.2 pm differ slightly from the values in Ref. [4], pointing to a possible small difference in the Si content. This may explain the slightly lower SR temperature (116 K, see below). In addition to this phase transition reported in Ref. [4], a second SR (denoted as SR2, to distinguish from SR1 at 116 K) was observed at low temperatures. Figs. 1 and 2 show the evolution of the magnetization isotherms below 80 K in fields applied along the principal axes /1 0 0S(a), /1 2 0S(b)
ARTICLE IN PRESS A.V. Andreev / Journal of Magnetism and Magnetic Materials 316 (2007) e383–e386
e384
12 K1, 10K2 (MJ m-3)
0.4
8 a b c
Er2Fe14Si3
4
T=5K 0
0.2 0.0 K1 10K2
-0.2 -0.4
a b c
4
(degree)
M (µB/f.u.)
-0.6 8
T = 20 K 0
0
a b c T = 30 K 0
1
2
3
µ0Hi (T) Fig. 1. Magnetization of a Er2Fe14Si3 single crystal in fields applied along the principal axes at 5, 20 and 30 K.
16 Er2Fe14Si3
12
a b c
8 4
T = 40 K
0 M (µB/f.u.)
Er2Fe14Si3
0
4
12 a b c
8 4
T = 60 K
0 12 a b c T = 80 K
8 4 0
60 30
8
0
90
0
1
µ0Hi (T)
2
3
Fig. 2. Same as Fig. 1, but here for 40, 60 and 80 K.
and /0 0 1S(c). One can see that the ground state of Er2Fe14Si3 is characterized by a surprisingly low anisotropy between the basal plane and the c-axis. The a- and c-axis curves at 5 K are practically the same and saturate at the value 9 mB/f.u. in a field of 0.2 T. The b-axis curve is clearly below the a-axis curve, pointing to a considerable anisotropy within the basal plane, the anisotropy field being about 3 T.
50
100
150 200 T (K)
250
300
Fig. 3. Top: the temperature dependence of anisotropy constants K1 and K2 determined by the Sucksmith–Tompson method. For better presentation, the K2 values are multiplied by factor of 10. Bottom: the temperature dependence of angle between the easy-magnetization axis and the c-axis.
Due to the very low anisotropy at 5 K, it is difficult to measure the projections of Ms on the a- and c-axis and thus to determine the direction of Ms. However, it is possible to extrapolate them from the temperature interval 20–40 K because the anisotropy starts to increase rapidly with increasing temperature. At 20 K, the projection of Ms on the basal plane is about 4.5 mB, decreasing with increasing temperature and vanishing above 50 K. No basal-plane component of Ms is observed at 60 K (Fig. 2). The temperature dependence of the angle Y between the easy-magnetization direction and the c-axis (Fig. 3) shows that in the ground state Er2Fe14Si3 has a cone of easy axes with half-opening angle of 301. The ‘‘cone-axis’’ spin reorientation SR2 occurs at 50 K as a second-order phase transition, and the uniaxial magnetic anisotropy extends up to 116 K. At low temperatures, the magnetization curves along the a- and b-axis exhibit a field-induced phase transition with a non-negligible hysteresis (0.1 T at 20 K) pointing to a firstorder type. The anisotropy within the basal plane is reflected in the fact that the transition field Bc defined as an inflection point on the M(H) curve is larger along the b-axis than along the a-axis. This anisotropy vanishes above 90 K. The a- and c-axis magnetization curves at 110–120 K, similar to at 5 K, are practically the same and saturate at very low field. Above this temperature interval, the easyplane anisotropy is seen clearly. A question is if the transformation of the anisotropy from the easy axis to the easy plane occurs by a first-order transition or by two second-order transitions (‘‘axis-cone’’ and ‘‘cone-plane’’) with a narrow range of stability of the ‘‘cone-type’’ anisotropy. Absence of noticeable hysteresis in both the temperature and field dependences of the magnetization is in favor of the second possibility. But the crucial point is
ARTICLE IN PRESS A.V. Andreev / Journal of Magnetism and Magnetic Materials 316 (2007) e383–e386
e385
20
16
M(µB/f.u.)
110 K 120 K 130 K 140 K 150 K 160 K 180 K 200 K
8
Ms(µB/f.u.)
16 12
from a-axis from c-axis from projections
12
8 Er2Fe14Si3
4
Er2Fe14Si3
4
easy axis
TC = 474 K
H // c-axis 0 0.0
0 0.4
0.8 µ0Hi (T)
1.2
Fig. 4. Temperature evolution of the magnetization curve along the c-axis above the ‘‘axis–plane’’ spin reorientation.
the sign of the second anisotropy constant K2 at the temperature where the first anisotropy constant K1 changes its sign [5]. The complicated shape of the magnetization curves at low temperatures with clear evidence of a strong contribution of the high-order anisotropy constants does not allow us to determine properly the K1 and K2 values. Nevertheless, this contribution vanishes above 80 K and the hard-axis magnetization curves can be treated by the Sucksmith–Tompson method and K1 and K2 can be determined with high accuracy. Fig. 4 shows that, in the vicinity of SR1 (just above SR1) the c-axis curve has positive curvature, which corresponds to a negative K2. The same is observed for the a-axis curve just below SR1 where this axis is the hard axis. The temperature dependences of K1 and K2 are presented in Fig. 3. It is found that K1 changes sign at 116 K. Since K2 is negative at this temperature, this SR is an ‘‘axis-plane’’ first-order phase transition, and no range of the ‘‘conetype’’ anisotropy exists. SR1 is accompanied by a pronounced anomaly in the specific heat, whereas the effect of SR2 on specific heat is almost negligible. The specific-heat behavior of Er2Fe14Si3 at the SR will be discussed elsewhere. The clear origin of SR1 is the competition of the easyaxis anisotropy of the Er sublattice, which rapidly decreases with increasing temperature, and the easy-plane anisotropy of the Fe sublattice which has much smoother temperature dependence. T ¼ 116 K is the temperature Fe where KEr 1 ¼ K1 . As regards to K2, it also changes sign at 160 K (see the change from positive to negative curvature of the c-axis magnetization curve in Fig. 4). This is not a phase transition and shows only that the Fe-sublattice anisotropy finally dominates above this temperature (K240 for the Fe sublattice in R2Fe17, [1–3]). SR2 does not originate from the Fe sublattice. The nonmonotonous evolution of anisotropy at low temperatures is
0
100
200
300
400
500
T (K) Fig. 5. Temperature dependence of the spontaneous magnetic moment Ms determined from magnetization data along the easy-magnetization direction.
connected with the Er sublattice and can be explained in two ways. The fact that the low-temperature hard-direction curves cannot be fitted by the Sucksmith–Tompson method points to large terms of order higher than four in the description of the anisotropy. They give a negative contribution to the anisotropy, which practically compensates a positive second-order term in the ground state. Another possible explanation is based on the two nonequivalent positions of Er atoms in the Th2Ni17-type crystal structure. The complicated behavior of the magnetic anisotropy can be caused by considerably different and competitive anisotropies of the two Er sublattices. 4. Conclusions Er2Fe14Si3 is a ferrimagnet with TC ¼ 474 K and Ms ¼ 9.6 mB (Fig. 5). Assuming MEr ¼ 9 mB (as for the free 3+ ion) and a collinear magnetic structure, the average MFe is equal to 1.97 mB (compared with 2.16 mB in Er2Fe17). This is slightly lower than in Tb2Fe14Si3 (2.04 mB, [6]), the only other R2Fe14Si3 compound studied in single-crystalline form. Above 116 K, an easy-plane magnetic anisotropy of the Fe sublattice dominates. Upon cooling, a first-order SR to the easy-axis type occurs at this temperature due to enhancement of the Er-sublattice anisotropy. However, below 50 K the easy axis deviates from the c axis up to 301 at 5 K. Despite of a moderate anisotropy at elevated temperatures, in the ground state the anisotropy of Er2Fe14Si3 is very weak. Acknowledgments The author thanks Dr. E. Sˇantava´ for the help in experiments. This work is a part of the research project AVOZ10100520 and has been supported by Grants GACR 202/06/0185 and GAAV IAA100100530.
ARTICLE IN PRESS e386
A.V. Andreev / Journal of Magnetism and Magnetic Materials 316 (2007) e383–e386
References [1] A.V. Andreev, A.V. Deryagin, S.M. Zadvorkin, N.V. Kudrevatykh, V.N. Moskalev, R.Z. Levitin, Y.F. Popov, R.Y. Yumaguzhin, in: D.D. Mishin (Ed.), Fizika Magnithykh (Physics of Magnetic Materials), Kalinin, 1985, pp. 21–49 (in Russian). [2] S. Sinnema, Ph.D. Thesis, University of Amsterdam, 1988. [3] B. Garcia-Landa, P.A. Algarabel, M.R. Ibarra, P.E. Kaizel, T.H. Ahn, J.J.M. Franse, J. Magn. Magn. Mater. 144 (1995) 1085.
[4] B.G. Shen, B. Liang, Z.H. Cheng, T.Y. Gong, H. Tang, F.R. de Boer, K.H.J. Buschow, Solid State Commun. 103 (1997) 71. [5] K.P. Belov, A.K. Zvezdin, A.M. Kadomtseva, R.Z. Levitin, Sov. Phys. Uspekhi 19 (1976) 574. [6] J. Du, G.H. Wu, C.C. Tang, Y.X. Li, W.S. Zhan, J. Appl. Phys. 84 (1998) 3305.