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Spin reorientation transition in mixed (Dy, Gd)Fe11Ti alloys
Journal of Magnetism and Magnetic Materials 104-107 (1992) 1277-1278 North-Holland
AI41
Spin reorientation transition in mixed (Dy, Gd)Fel Ti alloys L.C.C.M. Nagamine and H.R. Rechenberg Instituto de F[sica, Universidade de Sdo Paulo, C.P. 20516, 01498 Sdo Paulo, Brazil The spin reorientation temperature of (Dy 1 xGdx)FellTi alloys was determined from ac susceptibility measurements in the 80-300 K temperature range. The reorientation was theoretically analyzed with the help of a single-ion model for the rare-earth crystal-field and exchange interactions. The TSR vs x dependence was calculated by using the CEF parameters of Hu et al. (ref. [10]) as a starting point. With a slight adjustment an excellent agreement with our data was obtained. Iron-rich ternary alloys RFe12 xM~ (R = rare earth, M = Ti, V, Cr, Si . . . , x > 1) have recently received attention as potentially useful materials for permanent-magnet applications [1]. In the tetragonal ThMn12 structure, crystalline electric field (CEF) interactions at the R site favor an easy magnetization along the c axis for rare-earth ions with a positive secondorder Stevens coefficient a j (i.e. Sin, Er, Tm, Yb); the Fe sublattice anisotropy also is uniaxial. For R ions with a j < 0 (Nd, Tb, Dy, Ho), a spin reorientation (SR) away from the c axis is then expected to occur on cooling, as a consequence of competing R and Fe anisotropies, which is indeed observed [2-6]. However, a SR was also observed to occur in Er compounds [4,7,8], which can only be explained as an effect of C E F terms of order higher than 2. A detailed study of SR transitions appears to be worthwhile for a proper understanding of the crystal-field interactions in these materials. Our approach is to partially substitute a second rare earth in a given compound in order to vary the R anisotropy in a controlled manner. If a set of C E F parameters is known for a given R, the parameters for the substituent R ' can be obtained by appropriate scaling; thus one gains in experimental latitude without introducing any additional free parameters [9]. The spontaneous magnetization direction n(O, ~o) at a given temperature is calculated in a single-ion model by diagonalizing the R-site Hamiltonian
Y R = Y'~B~ Gn --gJl~BBmolJ'n( O, ~)
(1)
and calculating the free energy "~R as a function of n. For an alloy (R1_xR'x)Fe12_yMy, the angular dependent part of the free energy is given by 9 - = (1 - x ) 5 ~ - R + x g - R, + K ~ e sin2O,
(2)
where the experimental Fe-sublattice anisotropy energy per unit cell has been added. Minimization of eq. (2) with respect to angles yields the equilibrium n. The spin reorientation temperature TSR can be defined as the highest one below which 0 4= 0 o A complete set of parameters pertinent to eqs. (1) and (2) (i.e. C E F coefficients B °, B °, B 4, B ° and B 4,
in addition to molecular field Bmol(T) and Fe anisotropy K~e(T)) has been determined for DyFellTi from an analysis of single-crystal magnetization curves [10]. These data are a good starting point for the study of other alloys with the 1-12 structure. In the mixed system (Dy I xGdx)Fe11Ti, the Gd 3+ ion does not contribute to the average rare-earth anisotropy, which goes smoothly to zero at x = 1, and a decreasing TSR vs x is expected. Experimental data on this system, which quantitatively confirm the expected behavior, are reported in this paper. (Dy l_xGdx)FellTi samples with x = 0, 0.2, 0.4, 0.6 and 0.8 were prepared by arc melting near-stoichiometric amounts of the pure metals in argon atmosphere. All samples were wrapped in Ta foil, sealed in quartz tube with argon and annealed at 900 o C for 10 d. X-ray powder patterns confirmed the ThMna2 structure; only the x = 0.4 sample contained a small amount of TiFe 2, probably due to some rare-earth losses. The Curie temperature was measured with help of a vibrating-sample magnetometer. To good accuracy, T c showed a linear variation with concentration x. A C susceptibility was measured by placing the powdered sample inside a system of coaxial coils coupled to a lock-in amplifier operating at 50 Hz frequency. The sample temperature, measured with a thermocouple, could be varied by first cooling the sample down to nearly 80 K in a cold nitrogen gas flow, and then letting it warm up naturally. A vacuum shield allowed the warm-up to be slow enough to ensure thermal equilibrium across the sample holder. Susceptibility vs temperature curves are plotted in fig. 1. A broad peak marks the SR transition. Following ref. [8], we take TSR at the right-hand inflection point, obtained by numerical differentiation of each curve. For DyFe11Ti we thus obtain TSR = 210 K, in excellent agreement with published data [4]. Fig. 2 displays TSR vs x for our samples, with the exception of DY0.2Gd0.sFeliTi which had a TsR below 80 K. The dashed curve in fig. 2 is the theoretical TSR vs x, calculated according to eq. (2) (where the second term on the right-hand side, corresponding to Gd, is zero), and using the crystal-field parameters given in
0312-8853/92/$05.00 © 1992 - Elsevier Science Publishers B.V. All rights reserved
1278
L.C.C.M. Nagamine, H.R. Rechenberg / Spin reorientation transition in (Dy, Gd)Fe l~Ti alloys
~,1.25 or) ,r-. X=0.6
0.4
0,2
0.0
I.O0
/22 <~ ~0.75
>0.50 FEL II
(f) 0.25
cf) <~ O.O0
100
50
260
150
TEMPERATURE
30
250 (K)
Fig. 1. AC susceptibility of (DY1_xGdx)FellTi alloys as a function of temperature (normalized to 1 at peak value).
ref. [10]. Our data follow the predicted trend quite well. The agreement can be improved by adjusting some parameters to which TSR is most sensitive, specifically B~~ and B ° (nonaxial terms have only a minor effect, and B6° was shown in ref. [10] to be important only at temperatures below 100 K). The TsR(X) func-
Ld
F-<~ 150-
\
ILl Z
0 lOO<~
\\\y\
Z L,d 500
Ld E~
0 0.0
This work is part of the first author's doctoral thesis, under preparation with financial support from CNPq. Support from F A P E S P is also acknowledged. References
~.~250
rY Ld 0_
tion calculated with B~) = 0.14 K and B4° = 0.0016 K (instead of 0.16 and 0.0011 K, respectively, cf. ref. [10]) is shown in fig. 2 as a full curve, illustrating the very good agreement with experiment that can be achieved. The sensitivity of Tsa with respect to B4°, even at comparatively high temperatures, is to be noted, in contrast to many other intermetallic systems in which magnetic anisotropy effects are largely dominated by the B ° term. Our results confirm that the study of spin reorientation p h e n o m e n a in intermetallic compounds with a mixture of two rare earths, their concentration being an additional experimental variable, is a sensitive means of obtaining information on crystal-field parameters. This may be particularly useful when no magnetization measurements on single crystal are available. On the other hand, this work demonstrates the feasibility of varying the anisotropy of rare-earth-based alloys, in a perfectly predictable way, by substitutionally mixing two rare earths. Experiments on other (Dy, R')FeI1Ti alloys, in which R' are rare earths with actively competing anisotropies, are in progress.
0/2
0.6
0:4
0.8
1.0
×
Fig. 2. Experimental spin reorientation temperatures of (Dyl__xGdx)Fe11Ti alloys (circles). Theoretical TsR vs x dependence, calculated with CEF parameters of ref. [10] (dashed curve) and with readjusted parameters (full curve).
[1] D.B. de Mooij and K.H.J. Buschow, Philips J. Res. 42 (1987) 246. [2] H.S. Li, B.P. Hu and J.M.D. Coey, Solid State Commun. 66 (1988) 133. [3] L.Y. Zhang, E.B. Boltich, V.K. Sinha and W.E. Wallace, IEEE Trans. Magn. MAG-25 (1980) 3303. [4] B.P. Hu, H.S. Li, J.P. Gavigan and J.M.D. Coey, J. Phys.: Condens. Matter 1 (1989) 755. [5] P.A. AIgarabel and M.R. Ibarra, Solid State Commun. 74 (1990) 231. [6] P. Stefanski, A. Kowalczyk and A. Wrzeciono, J. Magn. Magn. Mater. 83 (1990) 145. [7] O. Moze, P.A. Algarabel, M.R. Ibarra, M. Solzi and L. Pareti, Solid State Commun. 68 (1988) 711. [8] P. Stefanski and A. Kowalczyk, Solid State Commun. 77 (1991) 397. [9] H.R. Rechenberg, J.P. Sanchez, P. L'H&itier and R. Fruchart, Phys. Rev. B 36 (1987) 1865. [10] B.P. Hu, H.S. Li, J.M.D. Coey and J.P. Gavigan, Phys. Rev. B 41 (1990) 2221.
AI41
Spin reorientation transition in mixed (Dy, Gd)Fel Ti alloys L.C.C.M. Nagamine and H.R. Rechenberg Instituto de F[sica, Universidade de Sdo Paulo, C.P. 20516, 01498 Sdo Paulo, Brazil The spin reorientation temperature of (Dy 1 xGdx)FellTi alloys was determined from ac susceptibility measurements in the 80-300 K temperature range. The reorientation was theoretically analyzed with the help of a single-ion model for the rare-earth crystal-field and exchange interactions. The TSR vs x dependence was calculated by using the CEF parameters of Hu et al. (ref. [10]) as a starting point. With a slight adjustment an excellent agreement with our data was obtained. Iron-rich ternary alloys RFe12 xM~ (R = rare earth, M = Ti, V, Cr, Si . . . , x > 1) have recently received attention as potentially useful materials for permanent-magnet applications [1]. In the tetragonal ThMn12 structure, crystalline electric field (CEF) interactions at the R site favor an easy magnetization along the c axis for rare-earth ions with a positive secondorder Stevens coefficient a j (i.e. Sin, Er, Tm, Yb); the Fe sublattice anisotropy also is uniaxial. For R ions with a j < 0 (Nd, Tb, Dy, Ho), a spin reorientation (SR) away from the c axis is then expected to occur on cooling, as a consequence of competing R and Fe anisotropies, which is indeed observed [2-6]. However, a SR was also observed to occur in Er compounds [4,7,8], which can only be explained as an effect of C E F terms of order higher than 2. A detailed study of SR transitions appears to be worthwhile for a proper understanding of the crystal-field interactions in these materials. Our approach is to partially substitute a second rare earth in a given compound in order to vary the R anisotropy in a controlled manner. If a set of C E F parameters is known for a given R, the parameters for the substituent R ' can be obtained by appropriate scaling; thus one gains in experimental latitude without introducing any additional free parameters [9]. The spontaneous magnetization direction n(O, ~o) at a given temperature is calculated in a single-ion model by diagonalizing the R-site Hamiltonian
Y R = Y'~B~ Gn --gJl~BBmolJ'n( O, ~)
(1)
and calculating the free energy "~R as a function of n. For an alloy (R1_xR'x)Fe12_yMy, the angular dependent part of the free energy is given by 9 - = (1 - x ) 5 ~ - R + x g - R, + K ~ e sin2O,
(2)
where the experimental Fe-sublattice anisotropy energy per unit cell has been added. Minimization of eq. (2) with respect to angles yields the equilibrium n. The spin reorientation temperature TSR can be defined as the highest one below which 0 4= 0 o A complete set of parameters pertinent to eqs. (1) and (2) (i.e. C E F coefficients B °, B °, B 4, B ° and B 4,
in addition to molecular field Bmol(T) and Fe anisotropy K~e(T)) has been determined for DyFellTi from an analysis of single-crystal magnetization curves [10]. These data are a good starting point for the study of other alloys with the 1-12 structure. In the mixed system (Dy I xGdx)Fe11Ti, the Gd 3+ ion does not contribute to the average rare-earth anisotropy, which goes smoothly to zero at x = 1, and a decreasing TSR vs x is expected. Experimental data on this system, which quantitatively confirm the expected behavior, are reported in this paper. (Dy l_xGdx)FellTi samples with x = 0, 0.2, 0.4, 0.6 and 0.8 were prepared by arc melting near-stoichiometric amounts of the pure metals in argon atmosphere. All samples were wrapped in Ta foil, sealed in quartz tube with argon and annealed at 900 o C for 10 d. X-ray powder patterns confirmed the ThMna2 structure; only the x = 0.4 sample contained a small amount of TiFe 2, probably due to some rare-earth losses. The Curie temperature was measured with help of a vibrating-sample magnetometer. To good accuracy, T c showed a linear variation with concentration x. A C susceptibility was measured by placing the powdered sample inside a system of coaxial coils coupled to a lock-in amplifier operating at 50 Hz frequency. The sample temperature, measured with a thermocouple, could be varied by first cooling the sample down to nearly 80 K in a cold nitrogen gas flow, and then letting it warm up naturally. A vacuum shield allowed the warm-up to be slow enough to ensure thermal equilibrium across the sample holder. Susceptibility vs temperature curves are plotted in fig. 1. A broad peak marks the SR transition. Following ref. [8], we take TSR at the right-hand inflection point, obtained by numerical differentiation of each curve. For DyFe11Ti we thus obtain TSR = 210 K, in excellent agreement with published data [4]. Fig. 2 displays TSR vs x for our samples, with the exception of DY0.2Gd0.sFeliTi which had a TsR below 80 K. The dashed curve in fig. 2 is the theoretical TSR vs x, calculated according to eq. (2) (where the second term on the right-hand side, corresponding to Gd, is zero), and using the crystal-field parameters given in
0312-8853/92/$05.00 © 1992 - Elsevier Science Publishers B.V. All rights reserved
1278
L.C.C.M. Nagamine, H.R. Rechenberg / Spin reorientation transition in (Dy, Gd)Fe l~Ti alloys
~,1.25 or) ,r-. X=0.6
0.4
0,2
0.0
I.O0
/22 <~ ~0.75
>0.50 FEL II
(f) 0.25
cf) <~ O.O0
100
50
260
150
TEMPERATURE
30
250 (K)
Fig. 1. AC susceptibility of (DY1_xGdx)FellTi alloys as a function of temperature (normalized to 1 at peak value).
ref. [10]. Our data follow the predicted trend quite well. The agreement can be improved by adjusting some parameters to which TSR is most sensitive, specifically B~~ and B ° (nonaxial terms have only a minor effect, and B6° was shown in ref. [10] to be important only at temperatures below 100 K). The TsR(X) func-
Ld
F-<~ 150-
\
ILl Z
0 lOO<~
\\\y\
Z L,d 500
Ld E~
0 0.0
This work is part of the first author's doctoral thesis, under preparation with financial support from CNPq. Support from F A P E S P is also acknowledged. References
~.~250
rY Ld 0_
tion calculated with B~) = 0.14 K and B4° = 0.0016 K (instead of 0.16 and 0.0011 K, respectively, cf. ref. [10]) is shown in fig. 2 as a full curve, illustrating the very good agreement with experiment that can be achieved. The sensitivity of Tsa with respect to B4°, even at comparatively high temperatures, is to be noted, in contrast to many other intermetallic systems in which magnetic anisotropy effects are largely dominated by the B ° term. Our results confirm that the study of spin reorientation p h e n o m e n a in intermetallic compounds with a mixture of two rare earths, their concentration being an additional experimental variable, is a sensitive means of obtaining information on crystal-field parameters. This may be particularly useful when no magnetization measurements on single crystal are available. On the other hand, this work demonstrates the feasibility of varying the anisotropy of rare-earth-based alloys, in a perfectly predictable way, by substitutionally mixing two rare earths. Experiments on other (Dy, R')FeI1Ti alloys, in which R' are rare earths with actively competing anisotropies, are in progress.
0/2
0.6
0:4
0.8
1.0
×
Fig. 2. Experimental spin reorientation temperatures of (Dyl__xGdx)Fe11Ti alloys (circles). Theoretical TsR vs x dependence, calculated with CEF parameters of ref. [10] (dashed curve) and with readjusted parameters (full curve).
[1] D.B. de Mooij and K.H.J. Buschow, Philips J. Res. 42 (1987) 246. [2] H.S. Li, B.P. Hu and J.M.D. Coey, Solid State Commun. 66 (1988) 133. [3] L.Y. Zhang, E.B. Boltich, V.K. Sinha and W.E. Wallace, IEEE Trans. Magn. MAG-25 (1980) 3303. [4] B.P. Hu, H.S. Li, J.P. Gavigan and J.M.D. Coey, J. Phys.: Condens. Matter 1 (1989) 755. [5] P.A. AIgarabel and M.R. Ibarra, Solid State Commun. 74 (1990) 231. [6] P. Stefanski, A. Kowalczyk and A. Wrzeciono, J. Magn. Magn. Mater. 83 (1990) 145. [7] O. Moze, P.A. Algarabel, M.R. Ibarra, M. Solzi and L. Pareti, Solid State Commun. 68 (1988) 711. [8] P. Stefanski and A. Kowalczyk, Solid State Commun. 77 (1991) 397. [9] H.R. Rechenberg, J.P. Sanchez, P. L'H&itier and R. Fruchart, Phys. Rev. B 36 (1987) 1865. [10] B.P. Hu, H.S. Li, J.M.D. Coey and J.P. Gavigan, Phys. Rev. B 41 (1990) 2221.