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Quenching of spin fluctuations in Sc3In by high magnetic fields
Journal of Magnetism and Magnetic Materials 31-34 (1983) 277-278
277
Q U E N C H I N G O F S P I N F L U C T U A T I O N S I N Sc 3 I n BY H I G H M A G N E T I C F I E L D S K. I K E D A * Department of Metallurgy, Iwate University, Morioka 020, Japan a n d K.A. G S C H N E I D N E R , Jr. Ames Laboratory and Department of Materials Science and Engineering, Iowa State University, Ames, IA 50011, U.S.A.
The effect of magnetic field on the low-temperature heat capacity and electrical resistivity in three Sc3In specimens with Curie temperatures in zero field of T~(0)= 5.5, 6.0 and 6.3 K are systematicallyand reasonably analyzed by assuming that the characteristic spin-fluctuation temperature, Ts, is equal to To(0).
The effect of spin fluctuations in weakly and nearly ferromagnetic metals has been of considerable interest for about two decades because it is connected with the origin of ferromagnetism in metals [1]. If the magnetic field is sufficiently large so that the Zeeman splitting energy is comparable to or larger than the characteristic spin-fluctuation energy, kBT~, the effect of spin fluctuations is quenched. In the typical weak itinerant-electron ferromagnet, Sc3In, actually, a pronounced quenching of spin fluctuations has been observed on the low-temperature heat capacity [2-4] and magnetoresistance [5]. In the present work, the low-temperature heat capacity C and electrical resistivity p were measured in magnetic fields up to 10 and 14 T, respectively, for three Sc3In specimens containing 24.1, 24.3 and 24.4at% In (with the Curie temperatures at zero field of Tc(0) = 5.5, 6.0 and 6.3 K, respectively). The experimental results of the heat capacity and magnetoresistance in Sc3In are analyzed and discussed by assuming T~= To(0). The heat capacity measurements on Sc3In were made between 1.3 and 20 K at magnetic fields of 0, 2.50, 5.39, 7.62, and 9.98 T. The maximum of C around To(0) in zero field becomes significantly smaller with increasing magnetic fields and almost disappears in high fields of > 7 T, as reported in ref. [4]. There is an increase of C / T at temperatures lower than 4 K, which is most remarkable at H = 0. The origin of this up-turn in C / T is concluded to be an intrinsic electronic effect. The apparent values of the electronic specific heat constant and the Debye temperature at 0 K for our Sc3In specimens are estimated as 7 = 10.0,10.8 mJ/g-atom K 2 and 0 D = 288-298 K, respectively, from a least square fit of the 9.98 T data to the equation C / T = y + fiT 2. These 0 o values are 13-16% smaller than the observed value from sound velocity measurements (Or)= (343 4-25 K) by Testardi et al. [2], suggesting the addition of an excess heat capacity with a Ta-dependence at low tern* Present address: Laboratoire de Physique des Solides, Universit6 de Paris-sud, 91405 Orsay, France.
peratures under magnetic fields. This phenomenon, which was also found for the strong Pauli-paramagnets, CeSn 3 [6], Sc [7] and dilute P d - N i alloys by us, is probably due to the induced magnetic moments on Sc atoms of the Sc3In in magnetic fields. Concerning the T~ for the weak ferromagnets, Buschow and van Daal [8] have assumed that the Curie temperature exceeds T~. By assuming T~= To(0), we can analyze the electronic heat capacity of Sc3In at H = 0, because the effective magnetic field sufficient to quench spin fluctuations, Hert = kBTs/lXB, is 8.2, 8.9 and 9.4 T for 24.1, 24.3 and 24.4 at% In, respectively. Therefore,
~ 100 v ~ 80 o ~ 60 ~" /,0
Sc3I n
20 0 100
i
i
i
i
i
i
~ 80 .~. o
60
"~ ~ /,0 ,
,,~
o
"
= 2/*.3
20
24.1
at.%In / This Study J
•
2/*.4
x
24.25
Ref.[3 ]
+ 2/,.18
Ref. [5]
t
J
0.2
0.4
0.1
6
i
i
i
0.8
1.0
1.2
1.4
h
Fig. 1. (a) Lowering of the electronic heat capacity due to spin fluctuations, ACE(H), and (b) the lowering of the coefficient of the T2-term in the electrical resistivity due to spin fluctuations, AA(H), for the Sc3In specimens with different To(0) as a function of the reduced magnetic field, h = #BH/kaT~(O).
0 3 0 4 - 8 8 5 3 / 8 3 / 0 0 0 0 - 0 0 0 0 / $ 0 3 . 0 0 © 1983 N o r t h - H o l l a n d
278
K. Ikeda and K.A. Gschneidner, Jr. / Quenching of spin fluctuations in S%In
the total heat capacity at H = 0 is given by C = 3'T+ flL T3 + AC E + CM,
(1)
where fie T3 is the true lattice contribution to C [2] and AC E is the electronic heat capacity due to spin fluctuations. The magnetic heat capacity C ~ is assumed to be C M / T = 8T (where 8 is constant) at T < To(0). Below - 3 K the AC E values estimated in this way are expressed by ACE./T = A T + a T 2 l n ( T / T s ) .
(2)
In eq. (2) a = a0/T~ 2, where a 0 is the constant containing the electronic specific heat constant determined from the band-structure density of states. According to this interpretation, the ratio of mass enhancement factor for ScaIn is Xs/(1 + ~p) = A 7 / 7 = 1.1-1.2, where Xsand }kp are the contributions due to the spin fluctuation and to the e l e c t r o n - p h o n o n interaction, respectively. Fig. la shows the value of [1 - [ACE(H)/ACE(O)] at 2 K as a function of the reduced field h = #BH/kaT~(O) for our three ScaIn specimens and for the sample of Takeuchi and Masuda [3] with To(0) -- 5.5 K. Here, T = 2 K was chosen as the lowest temperature because any superparamagnetic a n d / o r nuclear contributions to the heat capacity, which are expected to be enhanced by high magnetic fields, are believed to be negligibly small. All of the analyzed points in fig. l a seem to lie on the same curve, which appears to be linear for h < 0.2 and to saturate at h ~ 1.0. The electrical-resistivity measurements on Sc 3In were made between 1.5 and 40 K at magnetic fields of 0, 1.0, 2.5, 5.0, 7.5, 8.5, 10.0, 12.0, and 14.0 T. In all p - T curves at H = 0, a change in slope is observed around T¢(0). With increasing magnetic fields, this ferromagnetic anomaly around To(0) disappears and at H > 5 T the p vs. T curves become similar to those of usual paramagnetic metal. These results of magnetoresistance on Scaln correspond with the above-mentioned results of heat capacity, and both are caused by the quenching of spin fluctuations under high fields. The difference between the electrical resistivities with and without magnetic field, zap(H, T ) = p(H, T ) - p ( O , T), is always negative. The temperature variation of Ap(H, T)
values has a m i n i m u m at Tmi,, which increase with higher magnetic fields. The extrapolated Tmln at H = 0 equals To(0) and thus it appears that Tmi. may be the Curie temperature at high magnetic fields T~(H). A n applied magnetic field not only reduces the residual resistivity p0(H) but also the coefficient of the T2-term in the electrical resistivity, A ( H ) , which becomes almost constant at H - 5 T. The A ( H ) is expressed as A ( H ) = A o + AA(H), where A 0 and AA(H) are due to the electron-phonon interaction and to spin fluctuations, respectively. Fig. lb shows the value of 1 - [ A A ( H ) / A A ( 0 ) ] as a function of h for our Sc3In specimens and for the sample of Masuda et al. [5] with Tc(0) = 5.5 K. All of the analyzed points in fig. l b seem to lie on the same curve, which tends to saturate at lower fields (h - 0.6) than the case of ACE(H ). These analyzed results of the effect of magnetic field on the heat capacity and electrical resistivity in Sc3In strongly suggest that the characteristic spin-fluctuation temperature T~ is equal to the Curie temperature at H - 0. The authors are indebted to Prof. Y. Muto, The Research Institute for Iron, Steel and Other Metals, Tohoku University, for allowing the use of the apparatus and superconducting magnets for the magnetoresistance measurements. References [1] T. Moriya, J. Magn. Magn. Mat. 14 (1979) 1. [2] L.R. Testardi, L.M. Holmes, W.A. Reed and F.S.L. Hsu, Phys. Rev. B6 (1972) 3365. [3] J. Takeuchi and Y. Masuda, J. Phys. Soc. Japan 46 (1979) 468. [4] K. Ikeda and K.A. Gschneidner, Jr., J. Magn. Magn. Mat. 22 (1981) 207; J. Magn. Magn. Mat. 30 (1983) in press. [5] Y. Masuda, T. Hioki and A. Oota, Physica 91B (1977) 291; T. Hioki and Y. Masuda, J. Phys. Soc. Japan 43 (1977) 1200. [6] K. Ikeda and K.A. Gschneidner, Jr., Phys. Rev. B25 (1982) 4623. [7] K. Ikeda, K.A. Gschneidner, Jr., T.-W.E. Tsang and F.A. Schmidt, Solid State Commun. 41 (1982) 889. [8] K.H.J. Buschow and H.J. van Daal, Magnetism and Magnetic Materials, AIP Conf. Proc. No. 5, eds. C.D. Graham and J.J. Rhyne (1972) p. 1464.
277
Q U E N C H I N G O F S P I N F L U C T U A T I O N S I N Sc 3 I n BY H I G H M A G N E T I C F I E L D S K. I K E D A * Department of Metallurgy, Iwate University, Morioka 020, Japan a n d K.A. G S C H N E I D N E R , Jr. Ames Laboratory and Department of Materials Science and Engineering, Iowa State University, Ames, IA 50011, U.S.A.
The effect of magnetic field on the low-temperature heat capacity and electrical resistivity in three Sc3In specimens with Curie temperatures in zero field of T~(0)= 5.5, 6.0 and 6.3 K are systematicallyand reasonably analyzed by assuming that the characteristic spin-fluctuation temperature, Ts, is equal to To(0).
The effect of spin fluctuations in weakly and nearly ferromagnetic metals has been of considerable interest for about two decades because it is connected with the origin of ferromagnetism in metals [1]. If the magnetic field is sufficiently large so that the Zeeman splitting energy is comparable to or larger than the characteristic spin-fluctuation energy, kBT~, the effect of spin fluctuations is quenched. In the typical weak itinerant-electron ferromagnet, Sc3In, actually, a pronounced quenching of spin fluctuations has been observed on the low-temperature heat capacity [2-4] and magnetoresistance [5]. In the present work, the low-temperature heat capacity C and electrical resistivity p were measured in magnetic fields up to 10 and 14 T, respectively, for three Sc3In specimens containing 24.1, 24.3 and 24.4at% In (with the Curie temperatures at zero field of Tc(0) = 5.5, 6.0 and 6.3 K, respectively). The experimental results of the heat capacity and magnetoresistance in Sc3In are analyzed and discussed by assuming T~= To(0). The heat capacity measurements on Sc3In were made between 1.3 and 20 K at magnetic fields of 0, 2.50, 5.39, 7.62, and 9.98 T. The maximum of C around To(0) in zero field becomes significantly smaller with increasing magnetic fields and almost disappears in high fields of > 7 T, as reported in ref. [4]. There is an increase of C / T at temperatures lower than 4 K, which is most remarkable at H = 0. The origin of this up-turn in C / T is concluded to be an intrinsic electronic effect. The apparent values of the electronic specific heat constant and the Debye temperature at 0 K for our Sc3In specimens are estimated as 7 = 10.0,10.8 mJ/g-atom K 2 and 0 D = 288-298 K, respectively, from a least square fit of the 9.98 T data to the equation C / T = y + fiT 2. These 0 o values are 13-16% smaller than the observed value from sound velocity measurements (Or)= (343 4-25 K) by Testardi et al. [2], suggesting the addition of an excess heat capacity with a Ta-dependence at low tern* Present address: Laboratoire de Physique des Solides, Universit6 de Paris-sud, 91405 Orsay, France.
peratures under magnetic fields. This phenomenon, which was also found for the strong Pauli-paramagnets, CeSn 3 [6], Sc [7] and dilute P d - N i alloys by us, is probably due to the induced magnetic moments on Sc atoms of the Sc3In in magnetic fields. Concerning the T~ for the weak ferromagnets, Buschow and van Daal [8] have assumed that the Curie temperature exceeds T~. By assuming T~= To(0), we can analyze the electronic heat capacity of Sc3In at H = 0, because the effective magnetic field sufficient to quench spin fluctuations, Hert = kBTs/lXB, is 8.2, 8.9 and 9.4 T for 24.1, 24.3 and 24.4 at% In, respectively. Therefore,
~ 100 v ~ 80 o ~ 60 ~" /,0
Sc3I n
20 0 100
i
i
i
i
i
i
~ 80 .~. o
60
"~ ~ /,0 ,
,,~
o
"
= 2/*.3
20
24.1
at.%In / This Study J
•
2/*.4
x
24.25
Ref.[3 ]
+ 2/,.18
Ref. [5]
t
J
0.2
0.4
0.1
6
i
i
i
0.8
1.0
1.2
1.4
h
Fig. 1. (a) Lowering of the electronic heat capacity due to spin fluctuations, ACE(H), and (b) the lowering of the coefficient of the T2-term in the electrical resistivity due to spin fluctuations, AA(H), for the Sc3In specimens with different To(0) as a function of the reduced magnetic field, h = #BH/kaT~(O).
0 3 0 4 - 8 8 5 3 / 8 3 / 0 0 0 0 - 0 0 0 0 / $ 0 3 . 0 0 © 1983 N o r t h - H o l l a n d
278
K. Ikeda and K.A. Gschneidner, Jr. / Quenching of spin fluctuations in S%In
the total heat capacity at H = 0 is given by C = 3'T+ flL T3 + AC E + CM,
(1)
where fie T3 is the true lattice contribution to C [2] and AC E is the electronic heat capacity due to spin fluctuations. The magnetic heat capacity C ~ is assumed to be C M / T = 8T (where 8 is constant) at T < To(0). Below - 3 K the AC E values estimated in this way are expressed by ACE./T = A T + a T 2 l n ( T / T s ) .
(2)
In eq. (2) a = a0/T~ 2, where a 0 is the constant containing the electronic specific heat constant determined from the band-structure density of states. According to this interpretation, the ratio of mass enhancement factor for ScaIn is Xs/(1 + ~p) = A 7 / 7 = 1.1-1.2, where Xsand }kp are the contributions due to the spin fluctuation and to the e l e c t r o n - p h o n o n interaction, respectively. Fig. la shows the value of [1 - [ACE(H)/ACE(O)] at 2 K as a function of the reduced field h = #BH/kaT~(O) for our three ScaIn specimens and for the sample of Takeuchi and Masuda [3] with To(0) -- 5.5 K. Here, T = 2 K was chosen as the lowest temperature because any superparamagnetic a n d / o r nuclear contributions to the heat capacity, which are expected to be enhanced by high magnetic fields, are believed to be negligibly small. All of the analyzed points in fig. l a seem to lie on the same curve, which appears to be linear for h < 0.2 and to saturate at h ~ 1.0. The electrical-resistivity measurements on Sc 3In were made between 1.5 and 40 K at magnetic fields of 0, 1.0, 2.5, 5.0, 7.5, 8.5, 10.0, 12.0, and 14.0 T. In all p - T curves at H = 0, a change in slope is observed around T¢(0). With increasing magnetic fields, this ferromagnetic anomaly around To(0) disappears and at H > 5 T the p vs. T curves become similar to those of usual paramagnetic metal. These results of magnetoresistance on Scaln correspond with the above-mentioned results of heat capacity, and both are caused by the quenching of spin fluctuations under high fields. The difference between the electrical resistivities with and without magnetic field, zap(H, T ) = p(H, T ) - p ( O , T), is always negative. The temperature variation of Ap(H, T)
values has a m i n i m u m at Tmi,, which increase with higher magnetic fields. The extrapolated Tmln at H = 0 equals To(0) and thus it appears that Tmi. may be the Curie temperature at high magnetic fields T~(H). A n applied magnetic field not only reduces the residual resistivity p0(H) but also the coefficient of the T2-term in the electrical resistivity, A ( H ) , which becomes almost constant at H - 5 T. The A ( H ) is expressed as A ( H ) = A o + AA(H), where A 0 and AA(H) are due to the electron-phonon interaction and to spin fluctuations, respectively. Fig. lb shows the value of 1 - [ A A ( H ) / A A ( 0 ) ] as a function of h for our Sc3In specimens and for the sample of Masuda et al. [5] with Tc(0) = 5.5 K. All of the analyzed points in fig. l b seem to lie on the same curve, which tends to saturate at lower fields (h - 0.6) than the case of ACE(H ). These analyzed results of the effect of magnetic field on the heat capacity and electrical resistivity in Sc3In strongly suggest that the characteristic spin-fluctuation temperature T~ is equal to the Curie temperature at H - 0. The authors are indebted to Prof. Y. Muto, The Research Institute for Iron, Steel and Other Metals, Tohoku University, for allowing the use of the apparatus and superconducting magnets for the magnetoresistance measurements. References [1] T. Moriya, J. Magn. Magn. Mat. 14 (1979) 1. [2] L.R. Testardi, L.M. Holmes, W.A. Reed and F.S.L. Hsu, Phys. Rev. B6 (1972) 3365. [3] J. Takeuchi and Y. Masuda, J. Phys. Soc. Japan 46 (1979) 468. [4] K. Ikeda and K.A. Gschneidner, Jr., J. Magn. Magn. Mat. 22 (1981) 207; J. Magn. Magn. Mat. 30 (1983) in press. [5] Y. Masuda, T. Hioki and A. Oota, Physica 91B (1977) 291; T. Hioki and Y. Masuda, J. Phys. Soc. Japan 43 (1977) 1200. [6] K. Ikeda and K.A. Gschneidner, Jr., Phys. Rev. B25 (1982) 4623. [7] K. Ikeda, K.A. Gschneidner, Jr., T.-W.E. Tsang and F.A. Schmidt, Solid State Commun. 41 (1982) 889. [8] K.H.J. Buschow and H.J. van Daal, Magnetism and Magnetic Materials, AIP Conf. Proc. No. 5, eds. C.D. Graham and J.J. Rhyne (1972) p. 1464.