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Magnetovolume effects and magnetic transitions in the invar systems Fe65Ni35 and Er2Fe14B at high hydrostatic pressure
Journal of Magnetism North-Holland
and Magnetic
Materials
A M A
129 (1994) 356-360
journal of magnetism and magnetic materials
Magnetovolume systems Fe,,Ni,,
effects and magnetic transitions in the invar and Er,Fe,,B at high hydrostatic pressure
V.A.
Khvostantsev
Sidorov
and
L.G.
L.F. Vereshchagin Institute of High Pressure Physics, Academy of Sciences of Russia, 142092 Troitsk, Moscow region, Russia Received
10 December
1992
The relative volume change and the initial ac-susceptibility have been measured for Fe,SNi,, and Er*Fe,,B under hydrostatic pressure up to 8.5 GPa at room temperature. The bulk modulus of Fe,,Ni,, begins to rise and the susceptibility begins to drop at 3.5-4 GPa, indicating the continuous disappearance of ferromagnetism at high pressure. The transition from ferromagnetic to paramagnetic state in ErzFe,,B at 5.7 GPa is more abrupt and the giant (order of magnitude) softening of the bulk modulus is observed before this transition. The spin reorientation (SR) transition in Er,Fe,,B shifts under pressure to lower temperatures (dTsR /dP = - 19 K/GPa).
1. Introduction The invar effect is now one of the most interesting problems in modern physics of magnetic phenomena. Even though the invar effect (nearly zero thermal expansion in a wide temperature range) has been discovered for Fe,,Ni,, alloy many years ago and much efforts has been done to its theoretical investigation, the theory capable of describing microscopically various specific properties of invar systems is still in progress [l]. The anomalous physical properties of invar materials include the temperature dependences of thermal expansion, heat capacity and magnetization, and the pressure dependences of the lattice constant and Curie temperature. The latter of the effects listed were investigated earlier for the classic invar Fe,,Ni,, [2-41. It was found that the compressibility and the pressure derivative of the Curie temperature dT,-/dP are much higher for Fe-Ni alloys near the invar composition Fe,,Ni,, then the values, common for magnetic 3d-metals. Correspondence to: V.A. Sidorov, L.F. Vereshchagin Institute of High Pressure Physics, Academy of Sciences of Russia, 142092 Troitsk, Moscow Region, Russia. 0304-8853/94/$07.00 0 1994 - Elsevier SSDI 0304-8853(93)E0208-T
Science
A new class of materials, exhibiting the invar properties with the tetragonal structure of the Nd,Fe,,B-type is studied extensively during the last few years. Some review articles devoted to these materials have already been written (see for example [5]). The superior magnetic properties, notably the energy product, make them the very useful objects for permanent magnet applications. The invar properties of R,Fe,,B compounds (R is a rare earth) are the most prominent in measurements of thermal expansion [6,71 and the pressure dependence of the Curie temperature [8,9]. The Curie temperature of the R,Fe,,B compounds investigated (R = Nd, Y, Ce) decreases strongly at high pressure from T, - 600 K at ambient pressure to T, = 300 K at a pressure of a few gigapascals. No experimental data are now available concerning the volume contraction under pressure of the R,Fe,,B materials, though everyone who discussed the pressure dependence of T, 1%101 mentioned some speculations to estimate its compressibility. It is also interesting to study the behavior of the bulk modulus of R,Fe,,B near the Curie point under pressure in comparison with that of the classic invar Fe,,Ni,,. A number of the R,Fe,,B mate-
B.V. All rights reserved
VIA. Sidoroc, L.G. Khuostantsel: /Journal
of Magnetism and Magnetic Materials 129 (1994) 356-360
rials exhibit the so called spin-reorientation (SR) transition: the change in the direction of the easy magnetization axis and spin orientation at some temperature and pressure conditions. Especially the SR transition occurs in Er,Fe,,B near 320 K at ambient pressure, where the easy magnetization axis is being turned by 90” from the (10 0) to the (00 1) direction [5]. It is known that a pressure of about 1.5 GPa shifts the SR transition to room temperature [ll]. It is of interest to search the possible magnetovolume effects in this range of pressure and temperature. This paper presents the results of experimental study of the relative volume change and the initial ac-susceptibility of invar compounds and Er,Fe,,B under hydrostatic presFe,,Ni,, sure up to 8.5 GPa at room temperature, including the region of magnetic transitions.
2. Experiment High hydrostatic pressure was generated in the 1-2 cm3 teflon container filled with liquid and placed in compressible gasket of ‘toroid’ device [121. Mixtures of methanol and ethanol 4: 1 or pentan and petroleum ether 1: 1 were used as pressure transmitting media with a hydrostatic limit of 10 and 6.5 GPa respectively. The pressure inside the container was determined by means of a calibrated manganin gauge [13]. The relative volume change was determined by a strain gauge technique, with the use of miniature strain gauges glued onto the 2 X 3 X 4 mm3 sample [14]. The initial magnetic susceptibility was measured with the use of a Hartshorn bridge circuit. The sample was placed inside a part of the secondary coil, connected in series with its true copy, but wound in opposite direction. The primary coil, excited by a 2000 Hz and 20-70 mA ac, was wound over this two-sectioned secondary coil. The coil system was placed in the middle part of a teflon container and the output signal was detected by a lock-in amplifier. The number of turns in the coils varied from 5-6 to 20-40 because of the limited volume of the teflon container, the sample dimensions varying from 1X1X0.1 mm3 to 2~3x4 mm3 and the output signal being in the microvolt range.
Fig. 1. Pressure
dependence of the relative volume Fe,,Ni3s CO-[3], 0 - [15]).
change
of
The samples of Fe,,Ni,, and Er,Fe,,B were obtained by arc melting in the inert gas and annealed for a long time. The Curie temperature of Fe,,Ni,, at ambient pressure is 495 K, the SR temperature of Er,Fe,,B is 320 K.
3. Results and discussion The results of the measurements of the relative volume changes of Fe,,Ni,, and Er,Fe,,B
Fig. 2. Pressure dependence of the relative volume change Er,Fe,,B at increase (+) and decrease (0) of pressure.
of
358
V.A. SidoroL: L.C. Khcostantseu /Journal
of Magnetism and Magnetic Materials 129 (1994) 356-360
Er2Fe14B
Fig. 3. Pressure
dependence of the bulk modulus (0) and Er,Fe,,B (0).
of Fe,,Ni,,
are shown in figs. 1 and 2 and the bulk moduli dependences, calculated by differentiating numerically AW>/V,, are shown in fig. 3. The results obtained for Fe,,Ni,, are in general agreement with those published earlier [3,151. The employment of a strain gauge technique and hydrostatic pressure conditions enable us to reduce the scattering of experimental points in the measurements of AV(P>/V, in comparison with Oomi and Mori [31 and to study more carefully the lattice compressibility in the region of magnetic transition. The disappearance of the ferromagnetic state under pressure appears as a progressive decrease of the lattice compressibility and an increase of the bulk modulus starting from 3.5-4 GPa. The bulk modulus increases in a wide pressure range above 4 GPa and gradually saturates near 8 GPa, which indicates that the magnetic transition is nearly complete at this pressure. The value of the bulk modulus of ferromagnetic phase B,= 110-120 GPa is in good agreement with the result of [3] (B, = 119 + 5 GPa). The value of the bulk modulus of paramagnetic phase B, = 180 GPa (taken at P = 8 GPa) is also in good agreement with the data of [31, where B, = 180 + 8 GPa is an average value in the range of pressure from 5 to 12 GPa. Generally it should be mentioned that hardening of the bulk modulus in the region where
ferromagnetic state disappears goes rather smoothly, indicating the coexistence of ferromagnetic and paramagnetic regions in the sample in a wide range of pressures. Since the pressure dependences AV(P)/V, obtained at the increase and decrease of the pressure coincide well and no hysteresis or kinetic phenomena are found, the transition from ferromagnetic to paramagnetic state is not of the first order and the coexistence of phases should be treated as a fluctuation process. (The data obtained at the pressure decrease are not depicted in fig. 1, simply for clarity of figure). The spread nature of the magnetic transi. . tion m a Fe,,Nr,, invar alloy has already been established in a number of papers [16,17], where the temperature dependences of the elastic constants were studied by an ultrasonic method. So the temperature dependence of the bulk modulus is very similar to the pressure dependence shown in fig. 3. The authors of refs. [17,18] have explained the spread temperature dependence of the bulk modulus by the thermal volume fluctuations, leading to pronounced fluctuations of the magnetization and the Curie temperature, but not by chemical inhomogeneity. It means that ferromagnetic and paramagnetic regions of small dimensions coexist and fluctuate very rapidly. Our results are in line with these ideas. Extrapolation of the AI’(P)/V,, dependence from the region of high pressure, where the samis mainly paramagnetic to ambiple of Fe,,Ni,, ent pressure, allows one to estimate the value of spontaneous volume magnetostriction ws, i.e. the lattice volume change due to spontaneous magnetization of ferromagnetic phase. The value of w, (293 K) is 1.3%, as can be seen in fig. 1, in good agreement with the results of [4]. The pressure-volume dependence for Er, Fe,,B is shown in fig. 2. One can see that volume decreases in a nearly linear manner up to P - 3.5 GPa. No appreciable magnetovolume effects were found in the region of SR transition near 1.5 GPa. Those effects were not found earlier in the thermal expansion studies at ambient pressure [7], though the related compound Nd,Fe,,B exhibits jumps of the lattice constants and volume at the SR transition [6]. The value of the bulk modulus of Er,Fe,,B coincides practically with
VIA. Sidorou, L.G. Khcostantseu /Journal
of Magnetism and Magnetic Materials 129 (1994) 356-360
invar in this range of pressure that of Fe,,Ni,, (fig. 3). However, the bulk modulus of Er,Fe,,B begins to soften at P 2: 3.5-4 GPa and this softening becomes ‘catastrophic’ at further increase of pressure. The value of the modulus is an order of magnitude lower at P = 5.78 GPa than the initial one. An increase of the pressure above 5.78 GPa results in a drastic increase of the bulk modulus to a value in excess of initial one. Generally the pressure dependence of the bulk modulus (and the compressibility) appears as a typical h-anomaly, that is apparently due to the magnetic transition (disappearance of ferromagnetism) in Er,Fe,,B at a pressure near 5.78 GPa. The solid lines in fig. 3 put upon the data points for Er,Fe,,B are the result of computer fitting through the critical scaling formula: B= (a/b)]1
-P/PJb+c,
applied usually for analysis of critical phenomena. The fitting parameters for the ferromagnetic and paramagnetic phases are: b, = 0.88, b, = 0.82, Pcf = 5.78 and Pep = 5.77. Similar results concerning the A-anomalies of the bulk modulus were obtained in refs. [16,19] for related materials Y,Fe,,B and Nd,Fe,,B in the course of ultrasonic measurements at high temperature and ambient pressure. The dependences AV(P)/V,, for Er,Fe,,B obtained at the increase and decrease of the pressure coincide well and no hysteresis phenomena are found (fig. 2). So the volume anomaly at high pressure should be treated as a result of magnetoelastic interactions at the second order (magnetic) transition but not as the first order transition. Note that the magnetic transition in the invar system Er,Fe,,B has the features of a second order transition close to the first order one, as evidenced by the giant (in order of magnitude) softening of the bulk modulus before the transition. However, the lattice seems to retain its stability and no structural change takes place. The pressure derivative of the Curie temperature dT,/dP for Er,Fe,,B can be estimated on the basis of known values of T, at ambient pressure CT, = 554 K [5]) and the transition pressure
359
P, = 5.78 GPa as dT,/dP = CT, - T,,,,)/P, = -44.6 K/GPa. The data available in literature on dT,_dP for related compounds Y,Fe,,B and Nd 2Fe ,4 B are contradictory. Kamarad and Arnold [81 have found dT,/dP to be - 26.5 K/GPa for Nd,Fe,,B at pressures up to 4 GPa. On the other hand Nagata et al. have found the T,(P) dependences for Y,Fe,,B, Ce,Fe,,B and Nd,Fe,,B up to 8 GPa to be non-linear, dT,/d P being - 100 K/GPa at low pressures and -35 K/GPa at higher pressure. Our estimation for Er,Fe,,B is closer to the results of Nagata et al. Studies of the P-T diagram of the magnetic transitions at hydrostatic pressure are required to obtain more reliable data for dT,/dP. Extrapolation of the AV(P)/V, dependence from the region of paramagnetic phase to ambient pressure allows one to estimate spontaneous volume magnetostriction w, as in the case of Fe,,Ni,,. The value obtained is w, = 2.8% (fig. 2), in close agreement with the values for Y2Fe,, B and Nd,Fe,,B [6]. Measurements of the initial magnetic susceptibility (Fig. 4) allow one to compare the behavior of magnetic and elastic properties of Er,Fe,,B and Fe,,Ni,, at the magnetic transitions. The SR transition in Er,Fe,,B is indistinguishable in the
Fig. 4. Pressure dependence bility of Fe,sNi,,
of the initial magnetic (+) and ErZFe,,B (0).
suscepti-
360
V.A. Sidorov, L.G. Khvostantsec /Journal
of Magnetism and Magnetic Materials 129 (1994) 356-360
volume change measurements but it is very pronounced in the ac-susceptibility measurements and looks like a typical A-anomaly. The anomaly was observed in two pressure runs: at 288 K (1.64 GPa) and 296 K (1.3 GPa). Taking into account the ambient pressure value (TSR = 320 K), we obtain dTs,/dP = - 19 K/GPa, in good agreement with the result of Arnold and Kamarad (-20 K/ GPa) [ll]. The second magnetic transition (disappearance of ferromagnetism) manifests itself as a distinct drop of susceptibility in a narrow pressure range. The ferromagnetism disappears essentially at pressure 5.8 GPa, after finishing the anomalous contraction of the lattice. In contrast to Er,Fe,,B, where the ac-susceptibility drops in a rather narrow pressure range, the susceptibility of Fe,,Ni,, decrease gradually in a wide pressure range above 3 GPa in accordance with the bulk modulus data (figs. 3 and 4). This result confirms the spread nature of the ferroparamagnetic transition in Fe,,Ni,, and the existence of magnetic fluctuations in a wide range of hydrostatic pressures at room temperature. The comparison of two invar systems Fe,,Ni,, and Er,Fe,,B shows that the disappearance of ferromagnetism in the latter occurs in a more narrow pressure range and is not so spread as in the former. It is probable that magnetic fluctuations in Er,Fe,,B are not so pronounced as in Fe,,Ni,,. The hydrostatic pressure range used (8.5 GPa) exceeds essentially pressures of ferro to paramagnetic transitions. This enables one to perform a back extrapolation of volume-pressure dependences and to estimate the spontaneous volume magnetostriction w, of both compounds studied, which is in good agreement with the earlier published data.
Acknowledgement
We would like to thank Dr. I.V. Medvedeva for helpful discussion and kindly providing samples for this investigation.
References [l] Mohn P, Schwartz K. and Wagner D., Phys. Rev. B 43 (1991) 3318. [2] J.M. Leger, C. Loriers-Susse and B. Vodar, Phys. Rev. B6 (1972) 42.50. [3] G. Oomi and N. Mori, J. Phys. Sot. Jpn. 50 (1981) 2917. [4] G. Oomi and N. Mori, J. Phys. Sot. Jpn. 50 (1981) 2924. [5] J.F. Herbs& Rev. Mod. Phys. 63 (1991) 819. [6] A.V. Andreev, A.V. Deryagin, S.M. Zadvorkin and S.V. Terent’ev, Fiz. Tverd. Tela 27 (198.5) 1641. [7] K.H.J. Buschow, J. Less-Common. Met. 118 (1986) 349. [8] J. Kamarad and Z. Arnold, J. Magn. Magn. Mater. 67 (1987) 29. [9] H. Nagata, S. Hirosawa, M. Sagawa, A. Ishibashi and S. Endo, J. Magn. Magn. Mater. 70 (1987) 334. [lOI J.P. Gavigan, D. Givord, H.S. Li and J. Voiron, Physica B + C 149 (1988) 345. [ll] Z. Arnold and J. Kamarad, High Press. Res. 7-8 (1991) 265. [12] L.G. Khvostantsev, L.F. Vereshchagin and A.P. Novikov, High Temp.-High Press. 9 (1977) 637. [13] L.G. Khvostantsev and V.A. Sidorov, Phys. Stat. Solidi (a) 64 (1981) 379. [14] O.B. Tsiok, V.V. Bredikhin, V.A. Sidorov and L.G. Khvostantsev, High Press. Res. 10 (1992) 523. [15] P.W. Bridgman, Collected Experimental Papers, Vol. 6 (Harvard Univ. Press, Cambridge, MA 1964), p. 3933. [16] M. Shiga and Y. Nakamura, J. Magn. Magn. Mater. 90-91 (1990) 733. [17] G.P. Renaud and S.G. Steinemann, Physica B 161 (1989) 75. [18] G.P. Renaud and S.G. Steinemann, Physica B 149 (1988) 217. [19] M. Shiga, Y. Kusakaba, Y. Nakamura, K. Makita and M. Sagawa, Physica B 161 (1989) 206.
and Magnetic
Materials
A M A
129 (1994) 356-360
journal of magnetism and magnetic materials
Magnetovolume systems Fe,,Ni,,
effects and magnetic transitions in the invar and Er,Fe,,B at high hydrostatic pressure
V.A.
Khvostantsev
Sidorov
and
L.G.
L.F. Vereshchagin Institute of High Pressure Physics, Academy of Sciences of Russia, 142092 Troitsk, Moscow region, Russia Received
10 December
1992
The relative volume change and the initial ac-susceptibility have been measured for Fe,SNi,, and Er*Fe,,B under hydrostatic pressure up to 8.5 GPa at room temperature. The bulk modulus of Fe,,Ni,, begins to rise and the susceptibility begins to drop at 3.5-4 GPa, indicating the continuous disappearance of ferromagnetism at high pressure. The transition from ferromagnetic to paramagnetic state in ErzFe,,B at 5.7 GPa is more abrupt and the giant (order of magnitude) softening of the bulk modulus is observed before this transition. The spin reorientation (SR) transition in Er,Fe,,B shifts under pressure to lower temperatures (dTsR /dP = - 19 K/GPa).
1. Introduction The invar effect is now one of the most interesting problems in modern physics of magnetic phenomena. Even though the invar effect (nearly zero thermal expansion in a wide temperature range) has been discovered for Fe,,Ni,, alloy many years ago and much efforts has been done to its theoretical investigation, the theory capable of describing microscopically various specific properties of invar systems is still in progress [l]. The anomalous physical properties of invar materials include the temperature dependences of thermal expansion, heat capacity and magnetization, and the pressure dependences of the lattice constant and Curie temperature. The latter of the effects listed were investigated earlier for the classic invar Fe,,Ni,, [2-41. It was found that the compressibility and the pressure derivative of the Curie temperature dT,-/dP are much higher for Fe-Ni alloys near the invar composition Fe,,Ni,, then the values, common for magnetic 3d-metals. Correspondence to: V.A. Sidorov, L.F. Vereshchagin Institute of High Pressure Physics, Academy of Sciences of Russia, 142092 Troitsk, Moscow Region, Russia. 0304-8853/94/$07.00 0 1994 - Elsevier SSDI 0304-8853(93)E0208-T
Science
A new class of materials, exhibiting the invar properties with the tetragonal structure of the Nd,Fe,,B-type is studied extensively during the last few years. Some review articles devoted to these materials have already been written (see for example [5]). The superior magnetic properties, notably the energy product, make them the very useful objects for permanent magnet applications. The invar properties of R,Fe,,B compounds (R is a rare earth) are the most prominent in measurements of thermal expansion [6,71 and the pressure dependence of the Curie temperature [8,9]. The Curie temperature of the R,Fe,,B compounds investigated (R = Nd, Y, Ce) decreases strongly at high pressure from T, - 600 K at ambient pressure to T, = 300 K at a pressure of a few gigapascals. No experimental data are now available concerning the volume contraction under pressure of the R,Fe,,B materials, though everyone who discussed the pressure dependence of T, 1%101 mentioned some speculations to estimate its compressibility. It is also interesting to study the behavior of the bulk modulus of R,Fe,,B near the Curie point under pressure in comparison with that of the classic invar Fe,,Ni,,. A number of the R,Fe,,B mate-
B.V. All rights reserved
VIA. Sidoroc, L.G. Khuostantsel: /Journal
of Magnetism and Magnetic Materials 129 (1994) 356-360
rials exhibit the so called spin-reorientation (SR) transition: the change in the direction of the easy magnetization axis and spin orientation at some temperature and pressure conditions. Especially the SR transition occurs in Er,Fe,,B near 320 K at ambient pressure, where the easy magnetization axis is being turned by 90” from the (10 0) to the (00 1) direction [5]. It is known that a pressure of about 1.5 GPa shifts the SR transition to room temperature [ll]. It is of interest to search the possible magnetovolume effects in this range of pressure and temperature. This paper presents the results of experimental study of the relative volume change and the initial ac-susceptibility of invar compounds and Er,Fe,,B under hydrostatic presFe,,Ni,, sure up to 8.5 GPa at room temperature, including the region of magnetic transitions.
2. Experiment High hydrostatic pressure was generated in the 1-2 cm3 teflon container filled with liquid and placed in compressible gasket of ‘toroid’ device [121. Mixtures of methanol and ethanol 4: 1 or pentan and petroleum ether 1: 1 were used as pressure transmitting media with a hydrostatic limit of 10 and 6.5 GPa respectively. The pressure inside the container was determined by means of a calibrated manganin gauge [13]. The relative volume change was determined by a strain gauge technique, with the use of miniature strain gauges glued onto the 2 X 3 X 4 mm3 sample [14]. The initial magnetic susceptibility was measured with the use of a Hartshorn bridge circuit. The sample was placed inside a part of the secondary coil, connected in series with its true copy, but wound in opposite direction. The primary coil, excited by a 2000 Hz and 20-70 mA ac, was wound over this two-sectioned secondary coil. The coil system was placed in the middle part of a teflon container and the output signal was detected by a lock-in amplifier. The number of turns in the coils varied from 5-6 to 20-40 because of the limited volume of the teflon container, the sample dimensions varying from 1X1X0.1 mm3 to 2~3x4 mm3 and the output signal being in the microvolt range.
Fig. 1. Pressure
dependence of the relative volume Fe,,Ni3s CO-[3], 0 - [15]).
change
of
The samples of Fe,,Ni,, and Er,Fe,,B were obtained by arc melting in the inert gas and annealed for a long time. The Curie temperature of Fe,,Ni,, at ambient pressure is 495 K, the SR temperature of Er,Fe,,B is 320 K.
3. Results and discussion The results of the measurements of the relative volume changes of Fe,,Ni,, and Er,Fe,,B
Fig. 2. Pressure dependence of the relative volume change Er,Fe,,B at increase (+) and decrease (0) of pressure.
of
358
V.A. SidoroL: L.C. Khcostantseu /Journal
of Magnetism and Magnetic Materials 129 (1994) 356-360
Er2Fe14B
Fig. 3. Pressure
dependence of the bulk modulus (0) and Er,Fe,,B (0).
of Fe,,Ni,,
are shown in figs. 1 and 2 and the bulk moduli dependences, calculated by differentiating numerically AW>/V,, are shown in fig. 3. The results obtained for Fe,,Ni,, are in general agreement with those published earlier [3,151. The employment of a strain gauge technique and hydrostatic pressure conditions enable us to reduce the scattering of experimental points in the measurements of AV(P>/V, in comparison with Oomi and Mori [31 and to study more carefully the lattice compressibility in the region of magnetic transition. The disappearance of the ferromagnetic state under pressure appears as a progressive decrease of the lattice compressibility and an increase of the bulk modulus starting from 3.5-4 GPa. The bulk modulus increases in a wide pressure range above 4 GPa and gradually saturates near 8 GPa, which indicates that the magnetic transition is nearly complete at this pressure. The value of the bulk modulus of ferromagnetic phase B,= 110-120 GPa is in good agreement with the result of [3] (B, = 119 + 5 GPa). The value of the bulk modulus of paramagnetic phase B, = 180 GPa (taken at P = 8 GPa) is also in good agreement with the data of [31, where B, = 180 + 8 GPa is an average value in the range of pressure from 5 to 12 GPa. Generally it should be mentioned that hardening of the bulk modulus in the region where
ferromagnetic state disappears goes rather smoothly, indicating the coexistence of ferromagnetic and paramagnetic regions in the sample in a wide range of pressures. Since the pressure dependences AV(P)/V, obtained at the increase and decrease of the pressure coincide well and no hysteresis or kinetic phenomena are found, the transition from ferromagnetic to paramagnetic state is not of the first order and the coexistence of phases should be treated as a fluctuation process. (The data obtained at the pressure decrease are not depicted in fig. 1, simply for clarity of figure). The spread nature of the magnetic transi. . tion m a Fe,,Nr,, invar alloy has already been established in a number of papers [16,17], where the temperature dependences of the elastic constants were studied by an ultrasonic method. So the temperature dependence of the bulk modulus is very similar to the pressure dependence shown in fig. 3. The authors of refs. [17,18] have explained the spread temperature dependence of the bulk modulus by the thermal volume fluctuations, leading to pronounced fluctuations of the magnetization and the Curie temperature, but not by chemical inhomogeneity. It means that ferromagnetic and paramagnetic regions of small dimensions coexist and fluctuate very rapidly. Our results are in line with these ideas. Extrapolation of the AI’(P)/V,, dependence from the region of high pressure, where the samis mainly paramagnetic to ambiple of Fe,,Ni,, ent pressure, allows one to estimate the value of spontaneous volume magnetostriction ws, i.e. the lattice volume change due to spontaneous magnetization of ferromagnetic phase. The value of w, (293 K) is 1.3%, as can be seen in fig. 1, in good agreement with the results of [4]. The pressure-volume dependence for Er, Fe,,B is shown in fig. 2. One can see that volume decreases in a nearly linear manner up to P - 3.5 GPa. No appreciable magnetovolume effects were found in the region of SR transition near 1.5 GPa. Those effects were not found earlier in the thermal expansion studies at ambient pressure [7], though the related compound Nd,Fe,,B exhibits jumps of the lattice constants and volume at the SR transition [6]. The value of the bulk modulus of Er,Fe,,B coincides practically with
VIA. Sidorou, L.G. Khcostantseu /Journal
of Magnetism and Magnetic Materials 129 (1994) 356-360
invar in this range of pressure that of Fe,,Ni,, (fig. 3). However, the bulk modulus of Er,Fe,,B begins to soften at P 2: 3.5-4 GPa and this softening becomes ‘catastrophic’ at further increase of pressure. The value of the modulus is an order of magnitude lower at P = 5.78 GPa than the initial one. An increase of the pressure above 5.78 GPa results in a drastic increase of the bulk modulus to a value in excess of initial one. Generally the pressure dependence of the bulk modulus (and the compressibility) appears as a typical h-anomaly, that is apparently due to the magnetic transition (disappearance of ferromagnetism) in Er,Fe,,B at a pressure near 5.78 GPa. The solid lines in fig. 3 put upon the data points for Er,Fe,,B are the result of computer fitting through the critical scaling formula: B= (a/b)]1
-P/PJb+c,
applied usually for analysis of critical phenomena. The fitting parameters for the ferromagnetic and paramagnetic phases are: b, = 0.88, b, = 0.82, Pcf = 5.78 and Pep = 5.77. Similar results concerning the A-anomalies of the bulk modulus were obtained in refs. [16,19] for related materials Y,Fe,,B and Nd,Fe,,B in the course of ultrasonic measurements at high temperature and ambient pressure. The dependences AV(P)/V,, for Er,Fe,,B obtained at the increase and decrease of the pressure coincide well and no hysteresis phenomena are found (fig. 2). So the volume anomaly at high pressure should be treated as a result of magnetoelastic interactions at the second order (magnetic) transition but not as the first order transition. Note that the magnetic transition in the invar system Er,Fe,,B has the features of a second order transition close to the first order one, as evidenced by the giant (in order of magnitude) softening of the bulk modulus before the transition. However, the lattice seems to retain its stability and no structural change takes place. The pressure derivative of the Curie temperature dT,/dP for Er,Fe,,B can be estimated on the basis of known values of T, at ambient pressure CT, = 554 K [5]) and the transition pressure
359
P, = 5.78 GPa as dT,/dP = CT, - T,,,,)/P, = -44.6 K/GPa. The data available in literature on dT,_dP for related compounds Y,Fe,,B and Nd 2Fe ,4 B are contradictory. Kamarad and Arnold [81 have found dT,/dP to be - 26.5 K/GPa for Nd,Fe,,B at pressures up to 4 GPa. On the other hand Nagata et al. have found the T,(P) dependences for Y,Fe,,B, Ce,Fe,,B and Nd,Fe,,B up to 8 GPa to be non-linear, dT,/d P being - 100 K/GPa at low pressures and -35 K/GPa at higher pressure. Our estimation for Er,Fe,,B is closer to the results of Nagata et al. Studies of the P-T diagram of the magnetic transitions at hydrostatic pressure are required to obtain more reliable data for dT,/dP. Extrapolation of the AV(P)/V, dependence from the region of paramagnetic phase to ambient pressure allows one to estimate spontaneous volume magnetostriction w, as in the case of Fe,,Ni,,. The value obtained is w, = 2.8% (fig. 2), in close agreement with the values for Y2Fe,, B and Nd,Fe,,B [6]. Measurements of the initial magnetic susceptibility (Fig. 4) allow one to compare the behavior of magnetic and elastic properties of Er,Fe,,B and Fe,,Ni,, at the magnetic transitions. The SR transition in Er,Fe,,B is indistinguishable in the
Fig. 4. Pressure dependence bility of Fe,sNi,,
of the initial magnetic (+) and ErZFe,,B (0).
suscepti-
360
V.A. Sidorov, L.G. Khvostantsec /Journal
of Magnetism and Magnetic Materials 129 (1994) 356-360
volume change measurements but it is very pronounced in the ac-susceptibility measurements and looks like a typical A-anomaly. The anomaly was observed in two pressure runs: at 288 K (1.64 GPa) and 296 K (1.3 GPa). Taking into account the ambient pressure value (TSR = 320 K), we obtain dTs,/dP = - 19 K/GPa, in good agreement with the result of Arnold and Kamarad (-20 K/ GPa) [ll]. The second magnetic transition (disappearance of ferromagnetism) manifests itself as a distinct drop of susceptibility in a narrow pressure range. The ferromagnetism disappears essentially at pressure 5.8 GPa, after finishing the anomalous contraction of the lattice. In contrast to Er,Fe,,B, where the ac-susceptibility drops in a rather narrow pressure range, the susceptibility of Fe,,Ni,, decrease gradually in a wide pressure range above 3 GPa in accordance with the bulk modulus data (figs. 3 and 4). This result confirms the spread nature of the ferroparamagnetic transition in Fe,,Ni,, and the existence of magnetic fluctuations in a wide range of hydrostatic pressures at room temperature. The comparison of two invar systems Fe,,Ni,, and Er,Fe,,B shows that the disappearance of ferromagnetism in the latter occurs in a more narrow pressure range and is not so spread as in the former. It is probable that magnetic fluctuations in Er,Fe,,B are not so pronounced as in Fe,,Ni,,. The hydrostatic pressure range used (8.5 GPa) exceeds essentially pressures of ferro to paramagnetic transitions. This enables one to perform a back extrapolation of volume-pressure dependences and to estimate the spontaneous volume magnetostriction w, of both compounds studied, which is in good agreement with the earlier published data.
Acknowledgement
We would like to thank Dr. I.V. Medvedeva for helpful discussion and kindly providing samples for this investigation.
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