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Ambient-pressure specific heat of single-crystal UGe2
ARTICLE IN PRESS
Physica B 378–380 (2006) 961–962 www.elsevier.com/locate/physb
Ambient-pressure specific heat of single-crystal UGe2 J.C. Lashleya, R.A. Fisherb, J. Flouquetc, F. Hardyb, A. Huxleyc, N.E. Phillipsb, a
Los Alamos National Laboratory, Los Alamos, NM 87545, USA Lawrence Berkeley National Laboratory, University of California, Berkeley, CA 94720, USA c De´partement de la Recherche Fondamentale sur la Matie`re Condense´e, SPSMS, CEA Grenoble, 38054 Grenoble Cedex 9, France b
Abstract Measurements of the specific heat of UGe2 at ambient pressure show a feature in the 18–23 K region that is suggestive of a CDW transition. The magnetic field dependence of the specific heat shows the presence of structure in the electron density of states and an unusual nature of the ferromagnetic ordering at the Curie temperature. r 2006 Elsevier B.V. All rights reserved. PACS: 71.20.Gj; 71.45.Lr; 75.30.Fv; 75.40.Cp; 75.50.Cc Keywords: UGe2 ; Heat capacity; Ferromagnetism; CDW
The Curie temperature ðT C Þ of UGe2 , 53 K at ambient pressure, is driven to 0 K at a pressure of 1.6 GPa. The superconductivity [1] occurs within the ferromagnetic phase, at the 0 K limit, near 1.2 GPa, of another phase boundary ðT x Þ. The transition at T x is first order at high pressure [2], but not well defined below approximately 0.5 GPa. There has been speculation that it is a CDW transition. Neutron-scattering measurements have not shown the extra reflections that would be expected, but in heavy-fermion compounds small changes in lattice parameters can induce large electronic changes. There is a well established series of CDW transitions in a-U. The incommensurate–commensurate transition near 23 K is hysteretic and is observed only after slow cooling. Similarities with a-U prompted a search for a similar transition in UGe2 . Specific-heat measurements were made in a Quantum Design PPMS at LANL on a UGe2 crystal grown at Grenoble. As shown in Fig. 1, there is a hysteretic transition in the 18–23 K region that is remarkably similar to that in a-U. It is reasonable to take this feature in the specific heat of UGe2 as a manifestation of the T x
Corresponding author. Tel.: +1 510 642 4855; fax: +1 510 642 2835.
E-mail address: [email protected] (N.E. Phillips). 0921-4526/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2006.01.367
transition, and possibly an indication of CDW ordering. Fig. 2 shows the low-temperature specific-heat data in fields to 14 T along the easy a-axis. The data have been fitted with the expression shown in the figure, which includes a T-proportional term, gðBÞT for the electron contribution, a T 3 term for the phonon contribution, and an exponential term, which probably includes the low-T side of an Einstein function for optical phonons (see below) and possibly a CDW contribution. The strong decrease of gðBÞ with increasing B shows that the Fermi level in the majority spin band is on the high-energy side of a peak in the density of states, which is in at least qualitative agreement with band-structure calculations [3]. The B dependence of the specific heat in the vicinity of T C (see Fig. 3) shows that the ferromagnetic ordering is unusual. Normally an applied field flattens and broadens the specific-heat anomaly without shifting it in temperature; in this case it is shifted to higher temperature. Analogous behavior has been seen, e.g., in a manganite [4], which is also an itinerant-electron ferromagnet. In that case, the nature of the specific-heat anomaly has been explained by a bipolaron model [5]. The heat capacity over a wide range of T below T C can be separated into a smoothly varying magnetic contribution and a phonon contribution. The phonon contribution is represented by a sum of a Debye function for acoustic
ARTICLE IN PRESS J.C. Lashley et al. / Physica B 378–380 (2006) 961–962
962
0.9 +
UGe2 slowcool B=0
UGe2 B || a-axis
UGe2 fastcool B=0 + UGe2 slowcool 1T
C/T (mJK-2 mol-1)
α-U slowcool B=0 400
++
+ + +
+
+
+
+
+
+ + +
+ + + +
C/T ( J K -2 mol-1)
500
UGe2
300
200 + +
+
+
+
+ + +
+
+ + +
0.7
0.5 TC = 52.8 K α-U
100 15
18
21 T(K)
B=0 9T 14T
24
0.3 20
27
40
60
80
100
120
T ( K) Fig. 1. Temperature dependence of C=T of UGe2 for different magnetic fields at different cooling rates, and for a-U. UGe2 data were taken after cooling at 1:2 K h1 (slow cool) or 20 K min1 (fast cool).
+
C(B)/T = γ(B) + B3T2 + [a(B)/T]e-b/T
+
γ(0) = 33.2
+
γ( 9) = 27.9
+
C/T (mJK-2 mol-1)
γ(14) = 26.0
+ + +
B3 = 0.332 [ΘD = 260 K] b = 61.5K
150
+
a(0) = 5.34x104 +
a(14) = 4.01x104 50 +++
+ +++
+
+ +
+
+
TC = 52.8K
+
UGe2 B || a-axis B=0
0.0
8
12
10
100
9T
T (K)
14T
3
Fig. 4. The anomaly in (C-gTÞ=T , centered at 20 K, occurs at a temperature corresponding to the frequencies of optical modes.
0 4
B3
+
+ 1T 0
0.4
0.2
+
a(9) = 4.36x104
+ ++
+ +
+
a(1) = 5.28x104 100
B=0
+
γ(1) = 32.8 200
UGe2
0.6
+
(C-γT)/T3 (mJK-4 mol-1)
250
Fig. 3. Temperature dependence of C=T of UGe2 in the vicinity of the ferromagnetic transition for different magnetic fields applied along the aaxis.
16
20
T (K) Fig. 2. Temperature dependence of C=T of UGe2 for different magnetic fields applied along the a-axis. Solid lines represent numerical fits obtained with the expression given in the figure.
modes, and Einstein functions for optical modes, as shown in Fig. 4, with Einstein frequencies of the order of those seen in recent neutron-scattering measurements [6].
References [1] [2] [3] [4] [5]
S.S. Saxena, et al., Nature (London) 406 (2000) 587. C. Pfleiderer, A. Huxley, Phys. Rev. Lett. 89 (2002) 147005. H. Yamagami, J. Phys.: Condens. Matter 15 (2003) S2271. J.E. Gordon, et al., Phys. Rev. B 65 (2002) 24441. A.S. Alexandrov, A.M. Bratkovsky, J. Phys.: Condens. Matter 115 (1999) 1989. [6] S. Raymond, A. Huxley, to appear.
Physica B 378–380 (2006) 961–962 www.elsevier.com/locate/physb
Ambient-pressure specific heat of single-crystal UGe2 J.C. Lashleya, R.A. Fisherb, J. Flouquetc, F. Hardyb, A. Huxleyc, N.E. Phillipsb, a
Los Alamos National Laboratory, Los Alamos, NM 87545, USA Lawrence Berkeley National Laboratory, University of California, Berkeley, CA 94720, USA c De´partement de la Recherche Fondamentale sur la Matie`re Condense´e, SPSMS, CEA Grenoble, 38054 Grenoble Cedex 9, France b
Abstract Measurements of the specific heat of UGe2 at ambient pressure show a feature in the 18–23 K region that is suggestive of a CDW transition. The magnetic field dependence of the specific heat shows the presence of structure in the electron density of states and an unusual nature of the ferromagnetic ordering at the Curie temperature. r 2006 Elsevier B.V. All rights reserved. PACS: 71.20.Gj; 71.45.Lr; 75.30.Fv; 75.40.Cp; 75.50.Cc Keywords: UGe2 ; Heat capacity; Ferromagnetism; CDW
The Curie temperature ðT C Þ of UGe2 , 53 K at ambient pressure, is driven to 0 K at a pressure of 1.6 GPa. The superconductivity [1] occurs within the ferromagnetic phase, at the 0 K limit, near 1.2 GPa, of another phase boundary ðT x Þ. The transition at T x is first order at high pressure [2], but not well defined below approximately 0.5 GPa. There has been speculation that it is a CDW transition. Neutron-scattering measurements have not shown the extra reflections that would be expected, but in heavy-fermion compounds small changes in lattice parameters can induce large electronic changes. There is a well established series of CDW transitions in a-U. The incommensurate–commensurate transition near 23 K is hysteretic and is observed only after slow cooling. Similarities with a-U prompted a search for a similar transition in UGe2 . Specific-heat measurements were made in a Quantum Design PPMS at LANL on a UGe2 crystal grown at Grenoble. As shown in Fig. 1, there is a hysteretic transition in the 18–23 K region that is remarkably similar to that in a-U. It is reasonable to take this feature in the specific heat of UGe2 as a manifestation of the T x
Corresponding author. Tel.: +1 510 642 4855; fax: +1 510 642 2835.
E-mail address: [email protected] (N.E. Phillips). 0921-4526/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2006.01.367
transition, and possibly an indication of CDW ordering. Fig. 2 shows the low-temperature specific-heat data in fields to 14 T along the easy a-axis. The data have been fitted with the expression shown in the figure, which includes a T-proportional term, gðBÞT for the electron contribution, a T 3 term for the phonon contribution, and an exponential term, which probably includes the low-T side of an Einstein function for optical phonons (see below) and possibly a CDW contribution. The strong decrease of gðBÞ with increasing B shows that the Fermi level in the majority spin band is on the high-energy side of a peak in the density of states, which is in at least qualitative agreement with band-structure calculations [3]. The B dependence of the specific heat in the vicinity of T C (see Fig. 3) shows that the ferromagnetic ordering is unusual. Normally an applied field flattens and broadens the specific-heat anomaly without shifting it in temperature; in this case it is shifted to higher temperature. Analogous behavior has been seen, e.g., in a manganite [4], which is also an itinerant-electron ferromagnet. In that case, the nature of the specific-heat anomaly has been explained by a bipolaron model [5]. The heat capacity over a wide range of T below T C can be separated into a smoothly varying magnetic contribution and a phonon contribution. The phonon contribution is represented by a sum of a Debye function for acoustic
ARTICLE IN PRESS J.C. Lashley et al. / Physica B 378–380 (2006) 961–962
962
0.9 +
UGe2 slowcool B=0
UGe2 B || a-axis
UGe2 fastcool B=0 + UGe2 slowcool 1T
C/T (mJK-2 mol-1)
α-U slowcool B=0 400
++
+ + +
+
+
+
+
+
+ + +
+ + + +
C/T ( J K -2 mol-1)
500
UGe2
300
200 + +
+
+
+
+ + +
+
+ + +
0.7
0.5 TC = 52.8 K α-U
100 15
18
21 T(K)
B=0 9T 14T
24
0.3 20
27
40
60
80
100
120
T ( K) Fig. 1. Temperature dependence of C=T of UGe2 for different magnetic fields at different cooling rates, and for a-U. UGe2 data were taken after cooling at 1:2 K h1 (slow cool) or 20 K min1 (fast cool).
+
C(B)/T = γ(B) + B3T2 + [a(B)/T]e-b/T
+
γ(0) = 33.2
+
γ( 9) = 27.9
+
C/T (mJK-2 mol-1)
γ(14) = 26.0
+ + +
B3 = 0.332 [ΘD = 260 K] b = 61.5K
150
+
a(0) = 5.34x104 +
a(14) = 4.01x104 50 +++
+ +++
+
+ +
+
+
TC = 52.8K
+
UGe2 B || a-axis B=0
0.0
8
12
10
100
9T
T (K)
14T
3
Fig. 4. The anomaly in (C-gTÞ=T , centered at 20 K, occurs at a temperature corresponding to the frequencies of optical modes.
0 4
B3
+
+ 1T 0
0.4
0.2
+
a(9) = 4.36x104
+ ++
+ +
+
a(1) = 5.28x104 100
B=0
+
γ(1) = 32.8 200
UGe2
0.6
+
(C-γT)/T3 (mJK-4 mol-1)
250
Fig. 3. Temperature dependence of C=T of UGe2 in the vicinity of the ferromagnetic transition for different magnetic fields applied along the aaxis.
16
20
T (K) Fig. 2. Temperature dependence of C=T of UGe2 for different magnetic fields applied along the a-axis. Solid lines represent numerical fits obtained with the expression given in the figure.
modes, and Einstein functions for optical modes, as shown in Fig. 4, with Einstein frequencies of the order of those seen in recent neutron-scattering measurements [6].
References [1] [2] [3] [4] [5]
S.S. Saxena, et al., Nature (London) 406 (2000) 587. C. Pfleiderer, A. Huxley, Phys. Rev. Lett. 89 (2002) 147005. H. Yamagami, J. Phys.: Condens. Matter 15 (2003) S2271. J.E. Gordon, et al., Phys. Rev. B 65 (2002) 24441. A.S. Alexandrov, A.M. Bratkovsky, J. Phys.: Condens. Matter 115 (1999) 1989. [6] S. Raymond, A. Huxley, to appear.