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Irreversibility lines of the heavy fermion spin glass URh2Ge2
Physica B 312–313 (2002) 289–291
Irreversibility lines of the heavy fermion spin glass URh2Ge2 I. Maksimova,*, F.J. Littersta, D. Menzelb, J. Schoenesb, A.A. Menovskyc, c J.A. Mydoshc, S. Sullow . a
Institut fur Mendelssohnstr. 3, 38106 Braunschweig, Germany . Metallphysik und Nukleare Festkorperphysik, . b Institut fur . Halbleiterphysik und Optik, TU Braunschweig, Germany c Kamerlingh Onnes Laboratory, Leiden University, Netherlands
Abstract We present a study of the field dependence of the frozen-in state in the 3D Ising-like heavy fermion spin glass URh2Ge2. From DC-susceptibility experiments in field-cooled and zero-field-cooled mode along the crystallographic a and c axes of the tetragonal unit cell, we determine the crossover temperatures associated with the occurrence of weak and strong irreversibilities in the magnetic behaviour. In low fields, we observe single-ion anisotropy with a c axes susceptibility larger by a factor of 5–6 than along a; and a transition into a spin-glass state at Tf ¼ 9:38 K. In higher fields, we observe two characteristic temperatures: the upper one, Tf ; indicates the onset of spin freezing, while the lower one, Tirr ; reflects increased irreversibility of the frozen state. From our data, we construct the B2T phase diagram, revealing anisotropy of the freezing process for fields applied along a-and c-axis, respectively, which we discuss in terms of the magnetic irreversibility in m-vector spin glasses. r 2002 Elsevier Science B.V. All rights reserved. Keywords: Heavy fermion; Spin glass; Magnetic irreversibility
1. Introduction In recent years, the interplay of local-moment magnetism and disordered electronic transport has been a topic of major interest for uranium heavy-fermion compounds like UCu5xPdx, U2RhSi3 or URh2Ge2 [1– 3]. Here, we present a study on one of these compounds, tetragonal URh2Ge2 [3], which has been established as the first 3D random-bond Ising-like heavy-fermion spin glass. Crystallographic disorder in URh2Ge2 is believed to arise from a mixing of Rh and Ge atoms, while the U ions are translational invariantly positioned on a BCT tetragonal sublattice. This disorder can be viewed as a random stacking of unit cells with I4=mmm and P4=mmm symmetry along the tetragonal c axis. For this material, it has been possible to establish the anisotropy of the freezing process by means of susceptibility studies on single crystalline specimens, which revealed a preferred orientation of the spins along the c-axis of the system. So far, however, neither for *Corresponding author. Fax: +49-531-391-5129. E-mail address: [email protected] (I. Maksimov).
URh2Ge2 nor for any other disordered uranium compound, the dynamics of the freezing process has been studied. In contrast, for canonical spin glasses, this topic has been investigated in detail, both from the theoretical [4,5] as well as the experimental [6] side. Nevertheless, the physics behind the observations of strong and weak irreversibilities in the magnetic behaviour of spin glasses remains incompletely understood [7]. Our study was performed on an as-grown single crystal of URh2Ge2 prepared in the same way as in Ref. [3]. DC-susceptibility experiments wDC (not shown), performed on a SQUID magnetometer, at low temperatures closely resemble the behaviour reported in Ref. [3]. We observe single-ion anisotropy along the crystallographic a and c axes by a factor of 5–6. The temperature dependence of wDC measured in low fields in the zero-field-cooled mode (ZFC) exhibits a sharp cusp, indicating the freezing transition at Tf into the spin-glass state. In contrast, in field-cooled (FC) measurements, we observe a temperature (T) independent wDC below the freezing temperature Tf usual for spin glasses.
0921-4526/02/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 0 1 ) 0 1 3 0 1 - 1
I. Maksimov et al. / Physica B 312–313 (2002) 289–291
290
(a)
45
0.1
(b)
200
d χ dc /dT (memu/mole K)
B // c B // a
1
B (T)
χ dc(memu/mole)
50
0.01 4
Tf
8
10
12
10
Fig. 2. The B2Tirr;f phase diagram of URh2Ge2 for fields applied along the crystallographic a and c axes.
0
6
8
T (K)
ZF C FC
Tirr
6
14
T (K ) Fig. 1. The DC-susceptibility wDC (a) and its derivative dwDC =dT (b) as a function of temperature T in FC and ZFC modes in a magnetic field of B ¼ 0:3 T along the c-axis of URh2Ge2. Dotted lines illustrate the construction used to determine Tirr from dwDC =dT:
Application of external magnetic fields leads to a smearing out of the cusp, and separates the crossover temperatures of the occurrence of weak and strong irreversibility in the magnetic behaviour. From our FC and ZFC experiments, we determine these crossover temperatures: the upper one is related to the onset of spin freezing at Tf ; the lower one, Tirr ; defines the onset of strong irreversibility in the frozen-in state (Fig. 1). The value of Tf has been defined as temperature derivative dwdc =dT ¼ 0; Tirr represents the temperature at which FC and ZFC experiments deviate from each other, and has been quantified from dwDC =dT via a line construction as indicated in Fig. 1b (dotted lines) [8]. From the field dependence of Tf and Tirr ; we establish a B2T phase diagram (Fig. 2). In the zero-field limit, Tf is determined to be 9.38 K. For finite magnetic fields, the phase diagram reveals the anisotropy of Tf and Tirr for fields applied along the a and c axes, respectively. The field dependence of Tirr ; commonly associated with the Almeida–Thouless line [4], shows a behaviour qualitatively similar to that of canonical spin glasses like CuMn [7,8]. A fit to the data for 0:8pT=Tf p1; employing ½1 T=Tf0 pðmB gB=kB Tf0 Þx [5,8] yields x ¼ 0:5670:03 for B8a and 0.4770.02 for B8c axes. These values are significantly smaller than expected for the Ising case,
x ¼ 2=3: Furthermore, Tf ; which is associated with the Gabay–Toulouse crossover line [5], exhibits a highly unusual field dependence: instead of the typical observed decrease with field [9], Tf increases monotonously for B8a; and passes through the maximum at about 1 T for B8c: This behaviour is qualitatively different from that predicted in Ref. [5]. Recently, it has been proposed that such field dependencies of the GT line might be the result of the freezing process in an m-vector spin glass in an external field: Vieira and co-workers [10] calculated that for such a system, the low-field GT line for a Heisenberg spin glass should exhibit a re-entrant behaviour, with a maximum of Tf ðBÞ at a finite field as the result of a finite single-ion anisotropy. Our data are in qualitative agreement with these predictions, suggesting that the URh2Ge2 might be a model compound to test the predictions of Ref. [10] for the m-vector spin glass. In summary, we have examined the irreversibility lines of the 3D Ising-like heavy-fermion spin glass URh2Ge2 in fields up to 3 T. Our B2T phase diagram shows the anisotropy of the irreversibility behaviour between the crystallographic a- and c-directions. The temperature dependence of the GT line exhibits re-entrant behaviour, which is remnant of predictions presented for an mvector spin glass. This work was supported by the Deutsche Forschungsgemeinschaft DFG under Grant No. SU 229/11/2.
References [1] B. Andraka, G.R. Stewart, Phys. Rev. B 47 (1993) 3208; C.H. Booth, et al., Phys. Rev. B 81 (1998) 3960. [2] D.X. Li, et al., J. Phys.: Condens. Matter 11 (1999) 8263.
I. Maksimov et al. / Physica B 312–313 (2002) 289–291 S. Sullow, . et al., Phys. Rev. Lett. 78 (1997) 354. J.R.L. de Almeida, D.J. Thouless, J. Phys. A 11 (1978) 983. M. Gabay, G. Toulouse, Phys. Rev. Lett. 47 (1981) 201. U. Atzmony, et al., Phys. Rev. Lett. 43 (1979) 782.H. Albrecht, et al., Phys. Rev. Lett. 48 (1982) 819. [7] J.A. Mydosh, Spin Glasses: An Experimental Introduction, Taylor & Francis, London, 1993; [3] [4] [5] [6]
291
D. Chu, G.G. Kenning, R. Orbach, Phys. Rev. Lett. 72 (1994) 3270. [8] R.V. Chamberlin, et al., Phys. Rev. B 25 (1982) 6720. [9] M.A. Girtu, et al., Phys. Rev. B 57 (1998) 11058.D.H. Ryan, et al., Phys. Rev. B 63 (2001) 140405(R). [10] S.R. Vieira, F.D. Nobre, F.A. da Costa, J. Magn. Magn. Mater. 210 (2000) 390.
Irreversibility lines of the heavy fermion spin glass URh2Ge2 I. Maksimova,*, F.J. Littersta, D. Menzelb, J. Schoenesb, A.A. Menovskyc, c J.A. Mydoshc, S. Sullow . a
Institut fur Mendelssohnstr. 3, 38106 Braunschweig, Germany . Metallphysik und Nukleare Festkorperphysik, . b Institut fur . Halbleiterphysik und Optik, TU Braunschweig, Germany c Kamerlingh Onnes Laboratory, Leiden University, Netherlands
Abstract We present a study of the field dependence of the frozen-in state in the 3D Ising-like heavy fermion spin glass URh2Ge2. From DC-susceptibility experiments in field-cooled and zero-field-cooled mode along the crystallographic a and c axes of the tetragonal unit cell, we determine the crossover temperatures associated with the occurrence of weak and strong irreversibilities in the magnetic behaviour. In low fields, we observe single-ion anisotropy with a c axes susceptibility larger by a factor of 5–6 than along a; and a transition into a spin-glass state at Tf ¼ 9:38 K. In higher fields, we observe two characteristic temperatures: the upper one, Tf ; indicates the onset of spin freezing, while the lower one, Tirr ; reflects increased irreversibility of the frozen state. From our data, we construct the B2T phase diagram, revealing anisotropy of the freezing process for fields applied along a-and c-axis, respectively, which we discuss in terms of the magnetic irreversibility in m-vector spin glasses. r 2002 Elsevier Science B.V. All rights reserved. Keywords: Heavy fermion; Spin glass; Magnetic irreversibility
1. Introduction In recent years, the interplay of local-moment magnetism and disordered electronic transport has been a topic of major interest for uranium heavy-fermion compounds like UCu5xPdx, U2RhSi3 or URh2Ge2 [1– 3]. Here, we present a study on one of these compounds, tetragonal URh2Ge2 [3], which has been established as the first 3D random-bond Ising-like heavy-fermion spin glass. Crystallographic disorder in URh2Ge2 is believed to arise from a mixing of Rh and Ge atoms, while the U ions are translational invariantly positioned on a BCT tetragonal sublattice. This disorder can be viewed as a random stacking of unit cells with I4=mmm and P4=mmm symmetry along the tetragonal c axis. For this material, it has been possible to establish the anisotropy of the freezing process by means of susceptibility studies on single crystalline specimens, which revealed a preferred orientation of the spins along the c-axis of the system. So far, however, neither for *Corresponding author. Fax: +49-531-391-5129. E-mail address: [email protected] (I. Maksimov).
URh2Ge2 nor for any other disordered uranium compound, the dynamics of the freezing process has been studied. In contrast, for canonical spin glasses, this topic has been investigated in detail, both from the theoretical [4,5] as well as the experimental [6] side. Nevertheless, the physics behind the observations of strong and weak irreversibilities in the magnetic behaviour of spin glasses remains incompletely understood [7]. Our study was performed on an as-grown single crystal of URh2Ge2 prepared in the same way as in Ref. [3]. DC-susceptibility experiments wDC (not shown), performed on a SQUID magnetometer, at low temperatures closely resemble the behaviour reported in Ref. [3]. We observe single-ion anisotropy along the crystallographic a and c axes by a factor of 5–6. The temperature dependence of wDC measured in low fields in the zero-field-cooled mode (ZFC) exhibits a sharp cusp, indicating the freezing transition at Tf into the spin-glass state. In contrast, in field-cooled (FC) measurements, we observe a temperature (T) independent wDC below the freezing temperature Tf usual for spin glasses.
0921-4526/02/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 0 1 ) 0 1 3 0 1 - 1
I. Maksimov et al. / Physica B 312–313 (2002) 289–291
290
(a)
45
0.1
(b)
200
d χ dc /dT (memu/mole K)
B // c B // a
1
B (T)
χ dc(memu/mole)
50
0.01 4
Tf
8
10
12
10
Fig. 2. The B2Tirr;f phase diagram of URh2Ge2 for fields applied along the crystallographic a and c axes.
0
6
8
T (K)
ZF C FC
Tirr
6
14
T (K ) Fig. 1. The DC-susceptibility wDC (a) and its derivative dwDC =dT (b) as a function of temperature T in FC and ZFC modes in a magnetic field of B ¼ 0:3 T along the c-axis of URh2Ge2. Dotted lines illustrate the construction used to determine Tirr from dwDC =dT:
Application of external magnetic fields leads to a smearing out of the cusp, and separates the crossover temperatures of the occurrence of weak and strong irreversibility in the magnetic behaviour. From our FC and ZFC experiments, we determine these crossover temperatures: the upper one is related to the onset of spin freezing at Tf ; the lower one, Tirr ; defines the onset of strong irreversibility in the frozen-in state (Fig. 1). The value of Tf has been defined as temperature derivative dwdc =dT ¼ 0; Tirr represents the temperature at which FC and ZFC experiments deviate from each other, and has been quantified from dwDC =dT via a line construction as indicated in Fig. 1b (dotted lines) [8]. From the field dependence of Tf and Tirr ; we establish a B2T phase diagram (Fig. 2). In the zero-field limit, Tf is determined to be 9.38 K. For finite magnetic fields, the phase diagram reveals the anisotropy of Tf and Tirr for fields applied along the a and c axes, respectively. The field dependence of Tirr ; commonly associated with the Almeida–Thouless line [4], shows a behaviour qualitatively similar to that of canonical spin glasses like CuMn [7,8]. A fit to the data for 0:8pT=Tf p1; employing ½1 T=Tf0 pðmB gB=kB Tf0 Þx [5,8] yields x ¼ 0:5670:03 for B8a and 0.4770.02 for B8c axes. These values are significantly smaller than expected for the Ising case,
x ¼ 2=3: Furthermore, Tf ; which is associated with the Gabay–Toulouse crossover line [5], exhibits a highly unusual field dependence: instead of the typical observed decrease with field [9], Tf increases monotonously for B8a; and passes through the maximum at about 1 T for B8c: This behaviour is qualitatively different from that predicted in Ref. [5]. Recently, it has been proposed that such field dependencies of the GT line might be the result of the freezing process in an m-vector spin glass in an external field: Vieira and co-workers [10] calculated that for such a system, the low-field GT line for a Heisenberg spin glass should exhibit a re-entrant behaviour, with a maximum of Tf ðBÞ at a finite field as the result of a finite single-ion anisotropy. Our data are in qualitative agreement with these predictions, suggesting that the URh2Ge2 might be a model compound to test the predictions of Ref. [10] for the m-vector spin glass. In summary, we have examined the irreversibility lines of the 3D Ising-like heavy-fermion spin glass URh2Ge2 in fields up to 3 T. Our B2T phase diagram shows the anisotropy of the irreversibility behaviour between the crystallographic a- and c-directions. The temperature dependence of the GT line exhibits re-entrant behaviour, which is remnant of predictions presented for an mvector spin glass. This work was supported by the Deutsche Forschungsgemeinschaft DFG under Grant No. SU 229/11/2.
References [1] B. Andraka, G.R. Stewart, Phys. Rev. B 47 (1993) 3208; C.H. Booth, et al., Phys. Rev. B 81 (1998) 3960. [2] D.X. Li, et al., J. Phys.: Condens. Matter 11 (1999) 8263.
I. Maksimov et al. / Physica B 312–313 (2002) 289–291 S. Sullow, . et al., Phys. Rev. Lett. 78 (1997) 354. J.R.L. de Almeida, D.J. Thouless, J. Phys. A 11 (1978) 983. M. Gabay, G. Toulouse, Phys. Rev. Lett. 47 (1981) 201. U. Atzmony, et al., Phys. Rev. Lett. 43 (1979) 782.H. Albrecht, et al., Phys. Rev. Lett. 48 (1982) 819. [7] J.A. Mydosh, Spin Glasses: An Experimental Introduction, Taylor & Francis, London, 1993; [3] [4] [5] [6]
291
D. Chu, G.G. Kenning, R. Orbach, Phys. Rev. Lett. 72 (1994) 3270. [8] R.V. Chamberlin, et al., Phys. Rev. B 25 (1982) 6720. [9] M.A. Girtu, et al., Phys. Rev. B 57 (1998) 11058.D.H. Ryan, et al., Phys. Rev. B 63 (2001) 140405(R). [10] S.R. Vieira, F.D. Nobre, F.A. da Costa, J. Magn. Magn. Mater. 210 (2000) 390.