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Stability of the non-Fermi liquid state in UCoAl
Physica B 281&282 (2000) 379}380
Stability of the non-Fermi liquid state in UCoAl L. Havela!,*, A. Kolomiets!, F. Honda", A.V. Andreev!, V. Sechovsky!, L.E. DeLong#, Y. Shiokawa$, T. Kagayama", G. Oomi" !Department of Electronic Structures and Joint Laboratory for Magnetic Studies, Charles University, Ke Karlovu 5, 121 16 Prague 2, Czech Republic "Department of Engineering and Materials Science, Kumamoto University, Japan #Department of Physics and Astronomy, University of Kentucky, Lexington, USA $Institute for Materials Research, Tohoku University, Sendai, Japan
Abstract A non-Fermi liquid (NFL) power law behaviour of the resistivity with exponent n"5 was found in the low-"eld state 3 of the band metamagnet UCoAl. This characteristic is rather robust, with weak dependence on magnetic "eld lower than the critical metamagnetic "eld. The critical "eld increases, while the anomaly at the metamagnetic transition is gradually reduced, with applied pressure. ( 2000 Elsevier Science B.V. All rights reserved. Keywords: UCoAl; Itinerant electron metamagnetism; Non-Fermi liquid behaviour
UCoAl crystallizes in the hexagonal ZrNiAl structure and is characterized by a proximity to magnetic order. Its ground state is non-magnetic, but a weak magnetic state with an ordered moment around 0.3 l /f.u. can be inB duced by magnetic "eld less than 1 T. It can be phenomeologically classi"ed as a band metamagnet, with the critical metamagnetic "eld increasing with temperature as ¹2 [1]. Here we describe results of more detailed study performed on a high-quality UCoAl single crystal. Susceptibility measurements detected a sharp metamagnetic transition at a critical "eld l H "0.65 T (at ¹"4.5 K), 0 # which is a somewhat lower value compared with samples studied previously [2,3]. The electrical resistivity for current i along the c-axis (Fig. 1) resembles previous results, with the residual resistivity reduced to 7.9 l) cm for the present sample. A non-Fermi liquid (NFL) type of resistivity, o&b¹n, n(2, was observed in the low-"eld state, whereas the Fermi liquid dependence o&a¹2 is established in the high-"eld state [2,3].
* Corresponding author. Tel./fax: #420-2-21911351. E-mail address: [email protected]!.cuni.cz (L. Havela)
A careful analysis of the low-¹ part for UCoAl clearly shows that a power law with n"5 yields an excellent 3 description of the data in the temperature range from 1.8 K (the lowest temperature in the experiment) up to about 17 K (12 K) for current applied along the c- (a-axis). A higher low-¹ slope for i DD a is re#ected by a coe$cient b"0.43 l) cm/K5@3, whereas b"0.081 l) cm/K5@3 for i DD c. Due to the increase of H with increasing temperature, # the non-magnetic NFL state is preserved in magnetic "elds even somewhat higher than 0.65 T in a limited intermediate temperature range, and can be observed up to about 2 T. The character of the resistivity behaviour with n"5 is preserved in all the non-magnetic state. The 3 weak "eld dependence of the coe$cient b (see Fig. 2) indicates that the observed NFL behaviour covers an extended range of "eld and temperature dominated by spin #uctuations in the non-magnetic state. This is consistent with the fact that magnetic "eld couples to the magnetic order parameter, but contrasts with the case of a `quantum critical pointa, with NFL behaviour observable over a restricted range of parameters. It is thus suggestive of a breakdown of the Fermi-liquid theory for the whole low-"eld phase. In Ref. [4], it was shown that the metamagnetic transition induces a magnetovolume anomaly. We have
0921-4526/00/$ - see front matter ( 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 1 1 4 1 - 2
380
L. Havela et al. / Physica B 281&282 (2000) 379}380
Fig. 1. Temperature dependence of electrical resistivity in various magnetic "elds. An increase of o occurs at H for i DD c, 0 # whereas it decreases for i DD a. This e!ect is attributed to the Fermi surface reconstruction. Full lines represent the "ts with n"5 for 0 T and n"2 for 5 T. 3
found a step-like lattice expansion by a factor of 0.160]10~3 in the basal plane (a-axis), whereas the lattice parameter c contracts by about 0.133]10~3 at the critical "eld for ¹"2.0 K. The higher multiplicity of the a-axis leads to an overall positive volume e!ect *
Fig. 2. Residual resistivity o (full symbols, left scale) and the 0 coe$cient b (open symbols, right scale) versus magnetic "eld applied along the c-axis. Lines are guides to the eye. The variations of o can be attributed to the Fermi surface reconstruc0 tion at the transition.
Acknowledgements This work was supported by the Grant Agency of the Czech Republic under grant No. 106/99/0183. One of us (L.H.) is indebted to the Japanese Society for Promotion of Science for the support during his stay in Japan. Research at the University of Kentucky was supported by US NSF Grant INT-9515504.
References [1] L. Havela, A.V. Andreev, V. Sechovsky, I.K. Kozlovskaya, K. Prokes, P. Javorsky, M.I. Bartashevich, T. Goto, K. Kamishima, Physica B 230}232 (1997) 98. [2] A.V. Kolomiets, L. Havela, V. Sechovsky, L.E. DeLong, D.B. Watkins, A.V. Andreev, J. Appl. Phys. 83 (1998) 6435. [3] A.V. Kolomiets, L. Havela, V. Sechovsky, L.E. DeLong, D.B. Watkins, A.V. Andreev, Physica B 259}261 (1999) 415. [4] A.V. Andreev, R.Z. Levitin, Yu.F. Popov, R.Yu. Yumaguzhin, Sov. Phys. Solid State 27 (1985) 1145.
Stability of the non-Fermi liquid state in UCoAl L. Havela!,*, A. Kolomiets!, F. Honda", A.V. Andreev!, V. Sechovsky!, L.E. DeLong#, Y. Shiokawa$, T. Kagayama", G. Oomi" !Department of Electronic Structures and Joint Laboratory for Magnetic Studies, Charles University, Ke Karlovu 5, 121 16 Prague 2, Czech Republic "Department of Engineering and Materials Science, Kumamoto University, Japan #Department of Physics and Astronomy, University of Kentucky, Lexington, USA $Institute for Materials Research, Tohoku University, Sendai, Japan
Abstract A non-Fermi liquid (NFL) power law behaviour of the resistivity with exponent n"5 was found in the low-"eld state 3 of the band metamagnet UCoAl. This characteristic is rather robust, with weak dependence on magnetic "eld lower than the critical metamagnetic "eld. The critical "eld increases, while the anomaly at the metamagnetic transition is gradually reduced, with applied pressure. ( 2000 Elsevier Science B.V. All rights reserved. Keywords: UCoAl; Itinerant electron metamagnetism; Non-Fermi liquid behaviour
UCoAl crystallizes in the hexagonal ZrNiAl structure and is characterized by a proximity to magnetic order. Its ground state is non-magnetic, but a weak magnetic state with an ordered moment around 0.3 l /f.u. can be inB duced by magnetic "eld less than 1 T. It can be phenomeologically classi"ed as a band metamagnet, with the critical metamagnetic "eld increasing with temperature as ¹2 [1]. Here we describe results of more detailed study performed on a high-quality UCoAl single crystal. Susceptibility measurements detected a sharp metamagnetic transition at a critical "eld l H "0.65 T (at ¹"4.5 K), 0 # which is a somewhat lower value compared with samples studied previously [2,3]. The electrical resistivity for current i along the c-axis (Fig. 1) resembles previous results, with the residual resistivity reduced to 7.9 l) cm for the present sample. A non-Fermi liquid (NFL) type of resistivity, o&b¹n, n(2, was observed in the low-"eld state, whereas the Fermi liquid dependence o&a¹2 is established in the high-"eld state [2,3].
* Corresponding author. Tel./fax: #420-2-21911351. E-mail address: [email protected]!.cuni.cz (L. Havela)
A careful analysis of the low-¹ part for UCoAl clearly shows that a power law with n"5 yields an excellent 3 description of the data in the temperature range from 1.8 K (the lowest temperature in the experiment) up to about 17 K (12 K) for current applied along the c- (a-axis). A higher low-¹ slope for i DD a is re#ected by a coe$cient b"0.43 l) cm/K5@3, whereas b"0.081 l) cm/K5@3 for i DD c. Due to the increase of H with increasing temperature, # the non-magnetic NFL state is preserved in magnetic "elds even somewhat higher than 0.65 T in a limited intermediate temperature range, and can be observed up to about 2 T. The character of the resistivity behaviour with n"5 is preserved in all the non-magnetic state. The 3 weak "eld dependence of the coe$cient b (see Fig. 2) indicates that the observed NFL behaviour covers an extended range of "eld and temperature dominated by spin #uctuations in the non-magnetic state. This is consistent with the fact that magnetic "eld couples to the magnetic order parameter, but contrasts with the case of a `quantum critical pointa, with NFL behaviour observable over a restricted range of parameters. It is thus suggestive of a breakdown of the Fermi-liquid theory for the whole low-"eld phase. In Ref. [4], it was shown that the metamagnetic transition induces a magnetovolume anomaly. We have
0921-4526/00/$ - see front matter ( 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 1 1 4 1 - 2
380
L. Havela et al. / Physica B 281&282 (2000) 379}380
Fig. 1. Temperature dependence of electrical resistivity in various magnetic "elds. An increase of o occurs at H for i DD c, 0 # whereas it decreases for i DD a. This e!ect is attributed to the Fermi surface reconstruction. Full lines represent the "ts with n"5 for 0 T and n"2 for 5 T. 3
found a step-like lattice expansion by a factor of 0.160]10~3 in the basal plane (a-axis), whereas the lattice parameter c contracts by about 0.133]10~3 at the critical "eld for ¹"2.0 K. The higher multiplicity of the a-axis leads to an overall positive volume e!ect *
Fig. 2. Residual resistivity o (full symbols, left scale) and the 0 coe$cient b (open symbols, right scale) versus magnetic "eld applied along the c-axis. Lines are guides to the eye. The variations of o can be attributed to the Fermi surface reconstruc0 tion at the transition.
Acknowledgements This work was supported by the Grant Agency of the Czech Republic under grant No. 106/99/0183. One of us (L.H.) is indebted to the Japanese Society for Promotion of Science for the support during his stay in Japan. Research at the University of Kentucky was supported by US NSF Grant INT-9515504.
References [1] L. Havela, A.V. Andreev, V. Sechovsky, I.K. Kozlovskaya, K. Prokes, P. Javorsky, M.I. Bartashevich, T. Goto, K. Kamishima, Physica B 230}232 (1997) 98. [2] A.V. Kolomiets, L. Havela, V. Sechovsky, L.E. DeLong, D.B. Watkins, A.V. Andreev, J. Appl. Phys. 83 (1998) 6435. [3] A.V. Kolomiets, L. Havela, V. Sechovsky, L.E. DeLong, D.B. Watkins, A.V. Andreev, Physica B 259}261 (1999) 415. [4] A.V. Andreev, R.Z. Levitin, Yu.F. Popov, R.Yu. Yumaguzhin, Sov. Phys. Solid State 27 (1985) 1145.