- Email: [email protected]
μSR study on CDW phase transition in K metal
ARTICLE IN PRESS
Physica B 374–375 (2006) 402–404 www.elsevier.com/locate/physb
mSR study on CDW phase transition in K metal H. Suzukia,, H. Aburanoa, R. Yamauchia, S. Abea, I. Watanabeb a
Department of Physics, Kanazawa University, Kakuma-machi, Kanazawa 920 1192, Japan b Muon Science Laboratory, RIKEN, Wako, Saitama 351 0198, Japan
Abstract Since the prediction of a CDW state in alkali metals by Overhauser in 1962, many groups tried to observe this state. However no clear evidence has been reported. We attempted to observe the phase transition in potassium and observed anomalous behavior at about 20 K in magnetic susceptibility, specific heat and lattice constant. To confirm the phase transition at about 20 K in potassium, a muon-spinrelaxation ðmþ SRÞ experiment was performed between 10 and 50 K. Temperature dependence of the dynamical mþ SR rate increases below about 20 K. r 2005 Elsevier B.V. All rights reserved. Keywords: CDW; Potassium metal; Muon spin depolarization rate
1. Introduction
2. Experimental procedure and results
Since the prediction of a CDW state in alkali metals by Overhauser in 1962 [1], many groups have searched for this state in these metals. However no clear evidence has been reported. Overhauser and his co-workers claimed in many papers they had observed CDW and electron–phason scattering effects. But these experimental results, except for a neutron diffraction experiment, involved only seeing a deviation from the isotropic Fermi sphere in the experiments. There has been no experiment specifically undertaken to observe the CDW phase transition. We attempted to observe the phase transition in potassium and observed anomalous behavior at about 20 K in magnetic susceptibility, specific heat and lattice constant. In Figs. 1–3, the experimental results of the magnetic susceptibility, the specific heat and the lattice constant are shown, respectively [2]. To confirm the phase transition at about 20 K in potassium, a muon-spin-relaxation ðmþ SRÞ experiment was performed between 10 and 50 K. Temperature dependence of the dynamical mþ SR rate increases below about 20 K.
A mþ SR experiment was carried out using a doublepulsed muon beam at the RIKEN–RAL muon facility. A polycrystalline specimen made from commercially available 99.95% pure molten potassium was mounted on the sample holder made of silver. The size of the specimen was 2 mm thick and 30 mm in diameter. The thickness of the crystal, however, was not large enough to trap positive muons in the potassium metal. Two 15 mm silver foils were used as an attenuator to trap muons in the potassium metal. To prevent the oxidation of the specimen surface, thin Apiezon N grease was covered on the specimen surface. The sample was cooled down using a He flow cryostat. In zero-field (ZF) and transverse-field (TF) measurements, the positive muon beam, polarized parallel to beam direction, is stopped in a specimen and the time histograms of muon decay positrons are recorded by forward (F) and backward (B) counters as a function of residence time t for each mþ within the specimen. Since a positron is emitted preferentially toward the muon spin direction, the asymmetry AðtÞ ¼ ðF BÞ=ðF þ BÞ of the two histograms reflects the time evolution of the muon spin polarization. In our experiments the time revolution can be fitted to the equation, AðtÞ ¼ A0 expðltÞ þ C. Here C is a constant value and l is a muon spin depolarization rate.
Corresponding author. Tel.: +81 76 264 5667; fax: +81 72 264 5739.
E-mail address: [email protected] (H. Suzuki). 0921-4526/$ - see front matter r 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2005.11.114
ARTICLE IN PRESS H. Suzuki et al. / Physica B 374–375 (2006) 402–404 26.0
3.7258
25.5
3.7256 3.7254
24.5
(Å)
χ( 10-6 cm3 / mole )
25.0
403
24.0
3.7252 3.7250
23.5 23.0
3.7248
22.5
3.7246
15
22.0 0
50
100 Temperature (K)
150
20 25 Temperature(K)
30
200
Fig. 3. Lattice spacing d of (1 1 0) reflection vs. temperature.
Fig. 1. Temperature dependence of the magnetic susceptibility of potassium metal. 0.30 1.0
Depolarization Rate (10-6 sec) -1
0.29
C/T (J/molK2)
0.80
0.60
0.40
0.20
0.28 0.27 0.26 0.25 0.24 0.23
0.0
0
100
200
300
400
500
T2[K2]
0.22 10
20
30 40 Temperature (K)
50
60
Fig. 2. Temperature dependence of the specific heat of potassium metal. A small but sharp peak was observed at about 18 K.
Fig. 4. Depolarization rate of muon spin vs. temperature. Open circles represent the data for first run, closed circles represent the data for second run.
In Fig. 4, the muon spin depolarization rate which is l in above equation, observed in ZF is plotted against temperature. Depolarization rate decreases till about 20–25 K, then turns up with decreasing temperature. The second run was performed the next day after the first run. The temperature dependence is very similar to each other, but the amount of the change is different. The difference can be due to the difference of the grain structure of the potassium metal. The melting temperature of potassium metal is so low, that is 336.7 K, that the annealing effect progresses even at room temperature. This temperature dependence is very similar to the temperature dependence of the lattice spacing shown in Fig. 3. The origin of this temperature dependence of the spin depolarization rate is not known yet, but a possible explanation can be as follows. A muon implanted in metal is subject to magnetic dipolar interactions with the magnetic moment of the host
metal nuclei which leads to a transverse relaxation in much the same way as it causes a dipolar line broadening in NMR experiments. When a muon is trapped at the interstitial site in metals, it will produce the electric field gradient and also the local distortion of the surrounding host atoms which induces the quadrupole moment of the nuclei in distorted metals [3]. Since the potassium metal is rather soft, the local distortion due to the interstitial muon should be not so small. The interaction between the quadrupole moment and the phonon (the lattice vibration of the host metal) produces the depolarization of the spin (see A. Abragam: The Principle of Nuclear Magnetism, Chapter IX, Clarendon, Oxford, 1961). So this local distortion should contribute to the muon spin depolarization rate. When the specimen cools down, the lattice constant decreases as shown in Fig. 1. The crystal should become harder which should lead to smaller vibration. Then the muon spin depolarization rate decreases with
ARTICLE IN PRESS H. Suzuki et al. / Physica B 374–375 (2006) 402–404
404
lattice through the Debye–Waller factor. The increasing of the intensity with decreasing temperature till about 20 K implies the hardening of the lattice by the thermal effect in the equation kB T sin2 yB I ¼ I 0 exp , (1) Mo2
8600
Int. Intensity (arb. unit)
8500 8400 8300 8200 8100 8000
0
10
20
30 40 Temperature (K)
50
60
Fig. 5. I.I. of the X-ray scattering vs. temperature.
decreasing temperature. If the CDW transition which accompanies with a crystal distortion below about 20 K and the softening of the lattice at the CDW transition temperature, the depolarization rate should increase more rapidly. In Fig. 5, the integrated intensity of the (1 1 0) X-ray reflection peak is plotted against temperature. The intensity of the X-ray reflection is related to the stiffness of the
where yB is the X-ray scattering angle, M is the mass of the atom and o is the frequency of the lattice vibration. From the Fig. 5, it is found that the stiffness of the lattice increases with decreasing temperature down to about 20–25 K. Below about 20 K the intensity of the X-ray spectrum shows rather complicated behavior suggesting the phase transition, may be CDW transition. This result supports the explanation for the depolarization rate shown in Fig. 4. We are going to do the same experiments again to confirm the reproducibility of the experiment in near future. References [1] A.W. Overhauser, Phys. Rev. 128 (1962) 1437. [2] M. Sekine, S. Abe, Y. Tanaka, S. Nakagawa, H. Suzuki, H. Abe, K. Ohshima, T. Nakajima, J. Low Temp. Phys. 101 (1995) 651. [3] M. Camani, F.N. Gygax, W. Ru¨egg, A. Schneck, H. Schilling, Phys. Rev. Lett. 39 (1997) 836.
Physica B 374–375 (2006) 402–404 www.elsevier.com/locate/physb
mSR study on CDW phase transition in K metal H. Suzukia,, H. Aburanoa, R. Yamauchia, S. Abea, I. Watanabeb a
Department of Physics, Kanazawa University, Kakuma-machi, Kanazawa 920 1192, Japan b Muon Science Laboratory, RIKEN, Wako, Saitama 351 0198, Japan
Abstract Since the prediction of a CDW state in alkali metals by Overhauser in 1962, many groups tried to observe this state. However no clear evidence has been reported. We attempted to observe the phase transition in potassium and observed anomalous behavior at about 20 K in magnetic susceptibility, specific heat and lattice constant. To confirm the phase transition at about 20 K in potassium, a muon-spinrelaxation ðmþ SRÞ experiment was performed between 10 and 50 K. Temperature dependence of the dynamical mþ SR rate increases below about 20 K. r 2005 Elsevier B.V. All rights reserved. Keywords: CDW; Potassium metal; Muon spin depolarization rate
1. Introduction
2. Experimental procedure and results
Since the prediction of a CDW state in alkali metals by Overhauser in 1962 [1], many groups have searched for this state in these metals. However no clear evidence has been reported. Overhauser and his co-workers claimed in many papers they had observed CDW and electron–phason scattering effects. But these experimental results, except for a neutron diffraction experiment, involved only seeing a deviation from the isotropic Fermi sphere in the experiments. There has been no experiment specifically undertaken to observe the CDW phase transition. We attempted to observe the phase transition in potassium and observed anomalous behavior at about 20 K in magnetic susceptibility, specific heat and lattice constant. In Figs. 1–3, the experimental results of the magnetic susceptibility, the specific heat and the lattice constant are shown, respectively [2]. To confirm the phase transition at about 20 K in potassium, a muon-spin-relaxation ðmþ SRÞ experiment was performed between 10 and 50 K. Temperature dependence of the dynamical mþ SR rate increases below about 20 K.
A mþ SR experiment was carried out using a doublepulsed muon beam at the RIKEN–RAL muon facility. A polycrystalline specimen made from commercially available 99.95% pure molten potassium was mounted on the sample holder made of silver. The size of the specimen was 2 mm thick and 30 mm in diameter. The thickness of the crystal, however, was not large enough to trap positive muons in the potassium metal. Two 15 mm silver foils were used as an attenuator to trap muons in the potassium metal. To prevent the oxidation of the specimen surface, thin Apiezon N grease was covered on the specimen surface. The sample was cooled down using a He flow cryostat. In zero-field (ZF) and transverse-field (TF) measurements, the positive muon beam, polarized parallel to beam direction, is stopped in a specimen and the time histograms of muon decay positrons are recorded by forward (F) and backward (B) counters as a function of residence time t for each mþ within the specimen. Since a positron is emitted preferentially toward the muon spin direction, the asymmetry AðtÞ ¼ ðF BÞ=ðF þ BÞ of the two histograms reflects the time evolution of the muon spin polarization. In our experiments the time revolution can be fitted to the equation, AðtÞ ¼ A0 expðltÞ þ C. Here C is a constant value and l is a muon spin depolarization rate.
Corresponding author. Tel.: +81 76 264 5667; fax: +81 72 264 5739.
E-mail address: [email protected] (H. Suzuki). 0921-4526/$ - see front matter r 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2005.11.114
ARTICLE IN PRESS H. Suzuki et al. / Physica B 374–375 (2006) 402–404 26.0
3.7258
25.5
3.7256 3.7254
24.5
χ( 10-6 cm3 / mole )
25.0
403
24.0
3.7252 3.7250
23.5 23.0
3.7248
22.5
3.7246
15
22.0 0
50
100 Temperature (K)
150
20 25 Temperature(K)
30
200
Fig. 3. Lattice spacing d of (1 1 0) reflection vs. temperature.
Fig. 1. Temperature dependence of the magnetic susceptibility of potassium metal. 0.30 1.0
Depolarization Rate (10-6 sec) -1
0.29
C/T (J/molK2)
0.80
0.60
0.40
0.20
0.28 0.27 0.26 0.25 0.24 0.23
0.0
0
100
200
300
400
500
T2[K2]
0.22 10
20
30 40 Temperature (K)
50
60
Fig. 2. Temperature dependence of the specific heat of potassium metal. A small but sharp peak was observed at about 18 K.
Fig. 4. Depolarization rate of muon spin vs. temperature. Open circles represent the data for first run, closed circles represent the data for second run.
In Fig. 4, the muon spin depolarization rate which is l in above equation, observed in ZF is plotted against temperature. Depolarization rate decreases till about 20–25 K, then turns up with decreasing temperature. The second run was performed the next day after the first run. The temperature dependence is very similar to each other, but the amount of the change is different. The difference can be due to the difference of the grain structure of the potassium metal. The melting temperature of potassium metal is so low, that is 336.7 K, that the annealing effect progresses even at room temperature. This temperature dependence is very similar to the temperature dependence of the lattice spacing shown in Fig. 3. The origin of this temperature dependence of the spin depolarization rate is not known yet, but a possible explanation can be as follows. A muon implanted in metal is subject to magnetic dipolar interactions with the magnetic moment of the host
metal nuclei which leads to a transverse relaxation in much the same way as it causes a dipolar line broadening in NMR experiments. When a muon is trapped at the interstitial site in metals, it will produce the electric field gradient and also the local distortion of the surrounding host atoms which induces the quadrupole moment of the nuclei in distorted metals [3]. Since the potassium metal is rather soft, the local distortion due to the interstitial muon should be not so small. The interaction between the quadrupole moment and the phonon (the lattice vibration of the host metal) produces the depolarization of the spin (see A. Abragam: The Principle of Nuclear Magnetism, Chapter IX, Clarendon, Oxford, 1961). So this local distortion should contribute to the muon spin depolarization rate. When the specimen cools down, the lattice constant decreases as shown in Fig. 1. The crystal should become harder which should lead to smaller vibration. Then the muon spin depolarization rate decreases with
ARTICLE IN PRESS H. Suzuki et al. / Physica B 374–375 (2006) 402–404
404
lattice through the Debye–Waller factor. The increasing of the intensity with decreasing temperature till about 20 K implies the hardening of the lattice by the thermal effect in the equation kB T sin2 yB I ¼ I 0 exp , (1) Mo2
8600
Int. Intensity (arb. unit)
8500 8400 8300 8200 8100 8000
0
10
20
30 40 Temperature (K)
50
60
Fig. 5. I.I. of the X-ray scattering vs. temperature.
decreasing temperature. If the CDW transition which accompanies with a crystal distortion below about 20 K and the softening of the lattice at the CDW transition temperature, the depolarization rate should increase more rapidly. In Fig. 5, the integrated intensity of the (1 1 0) X-ray reflection peak is plotted against temperature. The intensity of the X-ray reflection is related to the stiffness of the
where yB is the X-ray scattering angle, M is the mass of the atom and o is the frequency of the lattice vibration. From the Fig. 5, it is found that the stiffness of the lattice increases with decreasing temperature down to about 20–25 K. Below about 20 K the intensity of the X-ray spectrum shows rather complicated behavior suggesting the phase transition, may be CDW transition. This result supports the explanation for the depolarization rate shown in Fig. 4. We are going to do the same experiments again to confirm the reproducibility of the experiment in near future. References [1] A.W. Overhauser, Phys. Rev. 128 (1962) 1437. [2] M. Sekine, S. Abe, Y. Tanaka, S. Nakagawa, H. Suzuki, H. Abe, K. Ohshima, T. Nakajima, J. Low Temp. Phys. 101 (1995) 651. [3] M. Camani, F.N. Gygax, W. Ru¨egg, A. Schneck, H. Schilling, Phys. Rev. Lett. 39 (1997) 836.