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Metamagnetic transition based on the quadrupole moment in PrCu2
Physica B 223&224 (1996) 389-391
ELSEVIER
Metamagnetic transition based on the quadrupole moment in PrCu2 R. Settai a, P. Ahmet a, M. Abliz a, K. Sugiyama a, Y. Onuki a'*, K. Kindo b, S. Takayanagi c aFaculty of Science, Osaka University, Toyonaka, Osaka 560, Japan bResearch Centerfor Extreme Materials, Osaka University, Toyonaka, Osaka 560, Japan CHokkaido University of Education, Sapporo Campus, Sapporo 002, Japan
Abstract The metamagnetic transition of PrCu 2 brings about the crystal distortion based on the magnetoelastic effect. We have studied in detail this transition through the magnetostriction, magnetoresistance and magnetization measurements.
1. Introduction Characteristic metamagnetic behaviors are observed in the f electron systems such as CeRuzSi2, UPt3 and RCo2 (R = rare earth). PrCu2 is another paramagnetic system, where we have recently found a new type of metamagnetic transition [1, 2]. It crystallizes in the orthorhombic structure which corresponds to the distorted hexagonal AIB2 structure. The previous experiments indicated that there is a cooperative Jahn-Teller effect occurring below 8 K I-3]. The ninefold multiplet 3H 4 is split into nine singlets under the orthorhombic crystalline electric field (CEF). An interesting feature is that the easy (a-) and hard (c-) magnetizations are switched through the metamagnetic transition. Namely, the hard magnetization Mc is changed into the easy (a- axis like) one, which is denoted by M,,. Alternatively, the easy magnetization M, is changed into the hard (c-axis like) one Me,. Moreover, with increasing field Me,, is changed into Ma, or M, through the transition. These features were found to repeat in PrCu2 samples in different field runs.
* Corresponding author.
We have continued to study the metamagnetic transition through the magnetostriction, mangetoresistance and magnetization measurements.
2. Experimental results Fig. 1 shows the field dependence of the relative magnetostriction Al/l along the a-axis in the field along the c-axis at 1.5 K. The magnetostriction decreases steeply at 10 T, reaching - 1 % in magnitude and furthermore shows a sharp drop at 12 T. On decreasing the field the magnetostriction increases almost linearly, and a large hysteresis occurs. The sample is thus found to possess a large residual strain, - 0.5% in magnitude. Namely, the magnetostriction of - 1% is extremely large in magnitude and therefore becomes no more an elastic strain. This result is consistent with the previous de Haas-van Alphen results [1], showing that the scattering lifetime of the conduction electron is reduced by a factor of two by this transition. Next we show in Fig. 2 the magnetoresistance in the current along the b-axis at 2.2 K. First we have increased the field along the c-axis. The magnetoresistance increases in magnitude due to the cyclotron motion of the
0921-4526/96/$15.00 ~,~': 1996 Elsevier Science B.V. All rights reserved Pll S 0 9 2 1 - 4 5 2 6 ( 9 6 ) 0 0 1 3 1-7
390
R. Settai et al./Physica B 223&224 (1996) 389-391
l
.
.
.
.
I
.
.
.
.
J
.
.
.
.
PrCu2 #11 T=1.5K
PrCu 2 #11
7- 2~tB/Pr ion
±
H//c-axis -- CEF calc. ~"
0 ~
---
v-
~
_ 1.3K
........
1
4.2
--'"""
-10
8.0
_.
........ . . . . . . . .
I
. . . . 15
MagneticField(T)
~ ~
15 18
........
22
~ _ , ~ .,_ - ---" ~
3
1
Fig. 1. Field dependence of the relative magnetostriction along the a-axis for the field along the c-axis in PrCu2.
4°
_...c~__50 ~
10L
/
~77
PrCu 2#6 T=2.2K J//b-axis
0 ~
~
10 20 3'0 Magnetic Field (T)
4'0
Fig. 3. Magnetization at various temperatures for the field along the c-axis in PrCu 2.
.
H//c-axis
,-.
5
:zl.
Q,
a-axis 3
0
0
5 10 Magnetic Field (T)
15
Fig. 2. Magnetoresistance for the current along the b-axis in PrCu2.
conduction electrons but increases steeply above 10 T, reflecting the metamagnetic transition mentioned above. On decreasing the field the magnetoresistance decreases monotonously, and a large hysteresis is observed. The
residual resistivity increases from 1.0 to 2.21.ff]cm through this metamagnetic transition. The large residual strain mentioned above corresponds to the large residual resistivity. We have furthermore rotated the sample by 90 °, namely applying the field along the a-axis. Here, the easy magnetization Ma is changed into the hard (c-axis like) one Me,, as mentioned in the Introduction. Therefore, we expect a similar metamagnetic transition when the field is applied along the a-axis. As shown in Fig. 2, the magnetoresistance along the a-axis is found to decrease around 7 T, showing the metamagnetic transition. On decreasing the field the magnetoresistance shows hysteresis. The residual resistivity does not have the initial value of 1.0 ~ cm but has about 2.0 ~ cm. There remains a residual strain in the sample, although it should have returned to the initial state. These behaviors of the magnetoresistance correspond to switching between the easy and hard magnetizations. Lastly, we have studied the metamagnetic transition in the wide temperature range in fields up to 37 T, as shown in Fig. 3. Here the solid lines indicate the magnetization measured in the pulsed field, while the broken lines correspond to the results of CEF calculations. The details of the 4f levels in PrCu2 and the CEF calculations will be published elsewhere [4]. The magnetization deviates from the CEF curve, which indicates the metamagnetic
R. Settai et al. /Physica B 223&224 (1996) 389-391
transition. The metamagnetic transition is found to be clearly observed even at high temperatures. Note the magnetization curve at 22 K. The transition field increases almost linearly from 10 to 32 T with increasing temperature from 1.3 to 50 K.
3. Discussions PrCu2 is in the single ground state, showing no magnetic ordering. The origin of the present metamagnetic transition is not the spin flop of the magnetic moment but most likely switching of the quadrupole moment, although the magnitude of magnetization itself is due to the magnetic moment of the 4f levels. A value of 10 T roughly corresponds to 20 K in PrCuz. Three excited states of the 4f levels, separated by 15 K from the ground state, contribute to the magnetic moment and most likely the quadrupole moment. The quadrupole moment couples to the lattice through the strain and brings about the crystal distortion and/or lowers the symmetry of the crystal through the metamagnetic transition. A linear temperature dependence of the transition field should be related to the lattice through the quadrupole moment. The previous result on the reduction of the scattering lifetime for the conduction electrons and the present result of the steep increase of the magnetoresistance are the result of the large magnetostriction of - 1%.
391
The switching of the magnetic moment could also be ascribed to the switching of the direction of the quadrupole moment. This switching seems to be closely related to the crystal structure because the orthorhombic CeCu2 structure can be thought of as the distorted hexagonal A1B2 one; the orthorhombic a- and c-axis corresponds to the hexagonal basal plane; therefore, the quadrupole moment could rotate in the a - c plane easily.
Acknowledgements This work was supported by Grant-in-Aid for the Scientific Research from Ministry of Education, Science and Culture.
References [I] R. Settai, M. Abliz, P. Ahmet, K. Motoki, N. Kimura, H. Ikezawa, T. Ebihara, H. Sugawara, K. Sugiyama and Y. t)nuki, J. Phys. Soc. Japan 64 (1995) 383. [2] K. Sugiyama, P. Ahmet, M. Abliz, H. Azuma, T. Takeuchi, K. Kindo, H. Sugawara, K. Motoki, H. Ikezawa, T. Ebihara, R. Settai and Y. Onuki, Physica B 211 (1995) 145. [3-1 K. Andres, P.S. Wang, Y.H. Wong, B. Liithi and H.R. Ott, AIP Conf. Proc. 34 (1976) 222. [4] P. Ahmet, M. Abliz, R. Settai, K. Sugiyama, Y. Onuki, T. Takeuchi, K. Kindo and S. Takayanagi, J. Phys. Soc. Japan 65 (1996).
ELSEVIER
Metamagnetic transition based on the quadrupole moment in PrCu2 R. Settai a, P. Ahmet a, M. Abliz a, K. Sugiyama a, Y. Onuki a'*, K. Kindo b, S. Takayanagi c aFaculty of Science, Osaka University, Toyonaka, Osaka 560, Japan bResearch Centerfor Extreme Materials, Osaka University, Toyonaka, Osaka 560, Japan CHokkaido University of Education, Sapporo Campus, Sapporo 002, Japan
Abstract The metamagnetic transition of PrCu 2 brings about the crystal distortion based on the magnetoelastic effect. We have studied in detail this transition through the magnetostriction, magnetoresistance and magnetization measurements.
1. Introduction Characteristic metamagnetic behaviors are observed in the f electron systems such as CeRuzSi2, UPt3 and RCo2 (R = rare earth). PrCu2 is another paramagnetic system, where we have recently found a new type of metamagnetic transition [1, 2]. It crystallizes in the orthorhombic structure which corresponds to the distorted hexagonal AIB2 structure. The previous experiments indicated that there is a cooperative Jahn-Teller effect occurring below 8 K I-3]. The ninefold multiplet 3H 4 is split into nine singlets under the orthorhombic crystalline electric field (CEF). An interesting feature is that the easy (a-) and hard (c-) magnetizations are switched through the metamagnetic transition. Namely, the hard magnetization Mc is changed into the easy (a- axis like) one, which is denoted by M,,. Alternatively, the easy magnetization M, is changed into the hard (c-axis like) one Me,. Moreover, with increasing field Me,, is changed into Ma, or M, through the transition. These features were found to repeat in PrCu2 samples in different field runs.
* Corresponding author.
We have continued to study the metamagnetic transition through the magnetostriction, mangetoresistance and magnetization measurements.
2. Experimental results Fig. 1 shows the field dependence of the relative magnetostriction Al/l along the a-axis in the field along the c-axis at 1.5 K. The magnetostriction decreases steeply at 10 T, reaching - 1 % in magnitude and furthermore shows a sharp drop at 12 T. On decreasing the field the magnetostriction increases almost linearly, and a large hysteresis occurs. The sample is thus found to possess a large residual strain, - 0.5% in magnitude. Namely, the magnetostriction of - 1% is extremely large in magnitude and therefore becomes no more an elastic strain. This result is consistent with the previous de Haas-van Alphen results [1], showing that the scattering lifetime of the conduction electron is reduced by a factor of two by this transition. Next we show in Fig. 2 the magnetoresistance in the current along the b-axis at 2.2 K. First we have increased the field along the c-axis. The magnetoresistance increases in magnitude due to the cyclotron motion of the
0921-4526/96/$15.00 ~,~': 1996 Elsevier Science B.V. All rights reserved Pll S 0 9 2 1 - 4 5 2 6 ( 9 6 ) 0 0 1 3 1-7
390
R. Settai et al./Physica B 223&224 (1996) 389-391
l
.
.
.
.
I
.
.
.
.
J
.
.
.
.
PrCu2 #11 T=1.5K
PrCu 2 #11
7- 2~tB/Pr ion
±
H//c-axis -- CEF calc. ~"
0 ~
---
v-
~
_ 1.3K
........
1
4.2
--'"""
-10
8.0
_.
........ . . . . . . . .
I
. . . . 15
MagneticField(T)
~ ~
15 18
........
22
~ _ , ~ .,_ - ---" ~
3
1
Fig. 1. Field dependence of the relative magnetostriction along the a-axis for the field along the c-axis in PrCu2.
4°
_...c~__50 ~
10L
/
~77
PrCu 2#6 T=2.2K J//b-axis
0 ~
~
10 20 3'0 Magnetic Field (T)
4'0
Fig. 3. Magnetization at various temperatures for the field along the c-axis in PrCu 2.
.
H//c-axis
,-.
5
:zl.
Q,
a-axis 3
0
0
5 10 Magnetic Field (T)
15
Fig. 2. Magnetoresistance for the current along the b-axis in PrCu2.
conduction electrons but increases steeply above 10 T, reflecting the metamagnetic transition mentioned above. On decreasing the field the magnetoresistance decreases monotonously, and a large hysteresis is observed. The
residual resistivity increases from 1.0 to 2.21.ff]cm through this metamagnetic transition. The large residual strain mentioned above corresponds to the large residual resistivity. We have furthermore rotated the sample by 90 °, namely applying the field along the a-axis. Here, the easy magnetization Ma is changed into the hard (c-axis like) one Me,, as mentioned in the Introduction. Therefore, we expect a similar metamagnetic transition when the field is applied along the a-axis. As shown in Fig. 2, the magnetoresistance along the a-axis is found to decrease around 7 T, showing the metamagnetic transition. On decreasing the field the magnetoresistance shows hysteresis. The residual resistivity does not have the initial value of 1.0 ~ cm but has about 2.0 ~ cm. There remains a residual strain in the sample, although it should have returned to the initial state. These behaviors of the magnetoresistance correspond to switching between the easy and hard magnetizations. Lastly, we have studied the metamagnetic transition in the wide temperature range in fields up to 37 T, as shown in Fig. 3. Here the solid lines indicate the magnetization measured in the pulsed field, while the broken lines correspond to the results of CEF calculations. The details of the 4f levels in PrCu2 and the CEF calculations will be published elsewhere [4]. The magnetization deviates from the CEF curve, which indicates the metamagnetic
R. Settai et al. /Physica B 223&224 (1996) 389-391
transition. The metamagnetic transition is found to be clearly observed even at high temperatures. Note the magnetization curve at 22 K. The transition field increases almost linearly from 10 to 32 T with increasing temperature from 1.3 to 50 K.
3. Discussions PrCu2 is in the single ground state, showing no magnetic ordering. The origin of the present metamagnetic transition is not the spin flop of the magnetic moment but most likely switching of the quadrupole moment, although the magnitude of magnetization itself is due to the magnetic moment of the 4f levels. A value of 10 T roughly corresponds to 20 K in PrCuz. Three excited states of the 4f levels, separated by 15 K from the ground state, contribute to the magnetic moment and most likely the quadrupole moment. The quadrupole moment couples to the lattice through the strain and brings about the crystal distortion and/or lowers the symmetry of the crystal through the metamagnetic transition. A linear temperature dependence of the transition field should be related to the lattice through the quadrupole moment. The previous result on the reduction of the scattering lifetime for the conduction electrons and the present result of the steep increase of the magnetoresistance are the result of the large magnetostriction of - 1%.
391
The switching of the magnetic moment could also be ascribed to the switching of the direction of the quadrupole moment. This switching seems to be closely related to the crystal structure because the orthorhombic CeCu2 structure can be thought of as the distorted hexagonal A1B2 one; the orthorhombic a- and c-axis corresponds to the hexagonal basal plane; therefore, the quadrupole moment could rotate in the a - c plane easily.
Acknowledgements This work was supported by Grant-in-Aid for the Scientific Research from Ministry of Education, Science and Culture.
References [I] R. Settai, M. Abliz, P. Ahmet, K. Motoki, N. Kimura, H. Ikezawa, T. Ebihara, H. Sugawara, K. Sugiyama and Y. t)nuki, J. Phys. Soc. Japan 64 (1995) 383. [2] K. Sugiyama, P. Ahmet, M. Abliz, H. Azuma, T. Takeuchi, K. Kindo, H. Sugawara, K. Motoki, H. Ikezawa, T. Ebihara, R. Settai and Y. Onuki, Physica B 211 (1995) 145. [3-1 K. Andres, P.S. Wang, Y.H. Wong, B. Liithi and H.R. Ott, AIP Conf. Proc. 34 (1976) 222. [4] P. Ahmet, M. Abliz, R. Settai, K. Sugiyama, Y. Onuki, T. Takeuchi, K. Kindo and S. Takayanagi, J. Phys. Soc. Japan 65 (1996).