- Email: [email protected]
Anisotropic magnetic properties of single-crystalline HoNi2B2C at high magnetic fields and high pressure
Physica B 294}295 (2001) 229}233
Anisotropic magnetic properties of single-crystalline HoNi B C at high magnetic "elds and high pressure
G. Oomi *, T. Kagayama, H. Mitamura, T. Goto, B.K. Cho, P.C. Can"eld Department of Physics, Kyushu University, Ropponmatsu, Fukuoka 810-8560, Japan Department of Mechanical Engineering and Materials Science, Kumamoto University, Kumamoto 860-8555, Japan The Institute for Solid State Physics, The University of Tokyo, Minato-ku, Tokyo 106-8666, Japan Ames Laboratory, Iowa State University, Iowa, NM 50011, USA
Abstract Magnetostriction and magnetoresistance of single-crystalline HoNi B C have been measured at ambient pressure. A large anisotropy was found in the "eld dependence of these properties. The magnetoresistance was also measured at high pressure up to 2 GPa at low temperature below the superconducting transition temperature (9 K). Several anomalies were found due to the metamagnetic transitions, in which the transition "elds increased with increasing pressure. These results will be discussed from a thermodynamical point of view and compared with the anisotropy in the lattice compression. 2001 Elsevier Science B.V. All rights reserved. Keywords: High pressure; Boron carbide; Electrical resistance; X-ray di!raction
1. Introduction Borocarbides having the formula RNi B C (R: rare earth elements) were discovered as a new family of superconductors with relatively high transition temperatures ¹ of 10}20 K [1,2]. The ! structure is a variant of the ThCr Si type, which consists of alternating layers of RC planes and Ni B slabs [3]. The physical properties of these compounds are highly anisotropic re#ecting the tetragonal structure. The coexistence of superconductivity and antiferromagnetic ordering below ¹ has been reported through the measurement of !
* Corresponding author. Fax: #81-92-726-4841. E-mail address: [email protected] (G. Oomi).
electrical resistance, speci"c heat, magnetization and so forth [4]. Among these compounds, the most interesting material may be HoNi B C, which becomes super conducting at &9 K, reenters the normal conducting state near 5 K due to antiferromagnetic ordering and then quickly recovers superconductivity below 5 K. Below ¹ , it shows metamagnetic transi, tions indicating a complex magnetic structure [5]. Until now, there have been few data on the magnetostriction and the e!ect of pressure on magnetic properties. In order to examine the complicated phase transitions at high magnetic "eld, we attempted to measure the magnetostriction and magnetoresistance of single-crystalline HoNi B C at ambient pressure. To investigate the phase stability under pressure, we also observed the e!ect of pressure on the magnetoresistance.
0921-4526/01/$ - see front matter 2001 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 0 0 ) 0 0 6 4 8 - 7
230
G. Oomi et al. / Physica B 294}295 (2001) 229}233
2. Experimental procedure A single crystal was grown via high-temperature #ux growth. The details of the preparation were published previously [5]. The pressure dependence of the lattice parameters was measured using a Guinier-type focusing camera. Hydrostatic pressure was generated by tungsten-carbide Bridgmantype anvils using a beryllium gasket and a 4 : 1 mixture of methanol and ethanol as the pressuretransmitting medium up to 10 GPa. The electrical resistance was measured by using the standard four-probe method. The current direction was parallel to the ab-plane and the magnetic "eld was applied parallel or perpendicular to the c-axis. High pressure was generated by using the standard piston-cylinder method. The magnetic "eld was generated by a superconducting magnet. The details of the high-pressure apparatus were reported elsewhere [6]. The magnetostriction was measured by means of the capacitance method.
3. Results
Fig. 1. The relative change in lattice parameters and unit cell volume of HoNi B C as a function of pressure.
3.1. Anisotropic compression of lattice parameters Fig. 1 shows the relative change of the lattice parameters c and a of tetragonal HoNi B C at room temperature as a function of pressure. Since no discontinuous changes in the pressure dependence of the lattice constants and also no new diffraction lines were found, the tetragonal structure is stable up to 10 GPa. The large anisotropy is seen in the compression curves: the c-axis is more compressible than the a-axis. The linear compressibilities are estimated to be 2.6;10} and 1.3; 10} GPa} for c and a axis, respectively. The volume V, also shown in the "gure, was calculated using the formula <"ca. The bulk modulus is estimated to be 192 GPa. 3.2. Magnetoresistance at ambient pressure and high pressure Fig. 2 shows the magnetoresistance (MR) of HoNi B C at ambient pressure for two directions parallel and perpendicular to the magnetic "eld
Fig. 2. Magnetoresistance at 4.2 K at ambient pressure.
B(T) below 1.2 T at 4.2 K. A large anisotropy can be seen depending on the direction of the magnetic "eld B. In the direction perpendicular to the c-axis, the superconducting state is broken near 0.15 T, a discontinuous change occurs at 0.5 T followed by a small maximum near 1 T. This corresponds well
G. Oomi et al. / Physica B 294}295 (2001) 229}233
231
Fig. 3. Magnetoresistance at 4.2 K at ambient pressure.
to the metamagnetic transitions observed in the magnetization measurement [5]. Here, we de"ne these three characteristic magnetic "elds as H , H and H , which are shown by arrows in Fig. 2. On the other hand, there is no such complicated behavior for the "eld in the direction parallel to the c-axis, in which we can only observe a discontinuous change around 0.15 T, corresponding to H . Fig. 3 shows the MR at 2.2 GPa at 4.2 K for both directions below 4 T. There is a clear change in MR around 0.2 T due to the breaking of superconductivity. But the discontinuous change in MR observed at ambient pressure at H seems to be di$cult to "nd. The broad maximum is still observed near 1.2 T. In this "gure a small knee is observed around 1.8 T, which corresponds to the third metamagnetic transition at H . H is not observed at ambient pressure because the maximum "eld was smaller than 1.3 T (H at ambient pressure). H increases also with increasing pressure. For the direction parallel to the c-axis, the MR is almost independent of H above 0.3 T. Fig. 4 shows these three characteristic "elds H , H and H as a function of pressure. It is found that the three (or four) "elds including H increase with increasing pressure, which corresponds to the increase in ¹ at high pressure [7]. The results , suggest an enhancement of the antiferromagnetic interaction at high pressure.
Fig. 4. Upper critical "eld H and metamagnetic transition "elds H , H as a function of pressure.
3.3. Magnetostriction The magnetostriction parallel to the magnetic "eld in the direction of magnetic "elds parallel , to the a-axis is shown in Fig. 5 below 3 T. is , found to have two peaks near 0.5 and 1.4 T. Considering the MR measurements in the foregoing paragraph and the magnetization [5], these correspond to the metamagnetic transition at H and H . There is a clear hysteresis at H indicating a "rst-order phase transition. Since the phase transition at H is second order, there is no anomaly in (H) at H . H may exist , around the minimum between H and H as shown in Fig. 5. It was reported that the metamagnetic transition "eld H is strongly dependent on the direction of G applied "eld for a "eld in the tetragonal ab-plane [8]. In the present work, there is an error in determining the crystal axis and also sample arrangement in the capacitance measurement. Taking into account the present result H &1.4 T and the angular dependence of H , H "0.66(¹)/ sin(45!) where is the angle between [1 1 0] axis and applied "eld [8], the deviation from [1 1 0] axis is estimated to be 10}203.
232
G. Oomi et al. / Physica B 294}295 (2001) 229}233
4. Discussion
Fig. 5. Longitudinal magnetostriction at 4.2 K for Ha. ,
It is interesting to note the relation between lattice compression and the pressure e!ect on ¹ of ! borocarbides. As was seen from Fig. 1, we found a large anisotropy in the compression of the a- and the c-axis. The ¹ of the Ho-borocarbide was ! found to decrease with pressure, R¹ /RP"!0.5 K/ ! GPa [7]. On the other hand, the values of R¹ /RP ! are almost 0 for the Er- and Y-borocarbides, in which the linear compressibility of the a-axis is almost the same as that of the c-axis [9]. This fact implies that the large anisotropic compression is related to the large value of R¹ /RP, i.e., the ! pressure coe$cient of ¹ is closely related to that ! of c/a. Next, we discuss brie#y the present results by using GruK neisen parameters because the metamagnetic transition "elds H are related with the G NeH el temperature ¹ . is de"ned as , R ln E (E)"! , R ln <
(1)
where E is the characteristic energy and V the volume. for H is written as
Fig. 6. Transverse magnetostriction ( c) at 4.2 K for Ha. ,
Fig. 6 shows the magnetostriction (c-axis) , perpendicular to the magnetic "eld below 3 T. is , found to be almost independent of H. Because the metamagnetic transition at H is of "rst-order one, the relation, dP/dH"M/< is valid, where the magnetization jump M at H is around 3 /Ho [5] and the pressure dependence dH /dP is esti mated from Fig. 4 to be 4.7;10} T/GPa. We get the value for the volume jump <" 1.37;10} m.
R ln H 1 RH "B , (H )"! 2 R ln < H RP
(2)
where B is the isothermal bulk modulus. By using 2 the data for pressure dependence of H (see Fig. 4) and P"192 GPa, we obtain "37 for H . H at 4.2 K may be related to the superconducting transition temperature ¹ of the reentrant phase. The GruK neisen parameter for ¹ (¹(¹ ) is about , 12 from the pressure dependence of ¹ . It has been suggested that the GruK neisen parameter of ¹ should not be strongly di!erent from , that of the metamagnetic transition "eld H [10]. + From the pressure dependence of ¹ [8], the value , of (¹ ) is estimated to be about 27. On the other , hand, the values of for H and H are 16 and 25, respectively. These values are comparable with that of ¹ . Thus, it should be emphasized that the , GruK neisen parameter of ¹ , H (i"1, 2, 3) and , G ¹ (¹(¹ ) are all of the same order of magnitude. ,
G. Oomi et al. / Physica B 294}295 (2001) 229}233
We reported previously for ErNi B C that RH /RP"0.1 T/GPa [11], which gives (¹ )" + , 10, which is also comparable with those of the Ho-borocarbide.
References [1] R. Nagarajan, C. Mazumder, Z. Hossain, S.K. Dhar, K.V. Gopalakrishmnan, L.C. Gupta, C. Godart, B.D. Padalia, R. Vijayaraghavan, Phys. Rev. Lett. 72 (1994) 274. [2] R.J. Cava, H. Takagi, B. Battlogg, H.W. Zandbergen, J.J. Krajewski, W.F. Peck Jr., R.B. van Dover, R.J. Felder, T. Siwgrist, K. Mizuhasi, J.O. Lee, H. Eisaki, S.A. Carter, S. Uchida, Nature 367 (1994) 146.
233
[3] T. Siegrist, H.W. Zandbergen, R.J. Cava, J.J. Krajewski, W.F. Peck Jr., Nature 367 (1994) 254. [4] M. El Massalami, S.L. Bud'ko, B. Giordanengo, E.M. Baggio-Saitovitch, Physica C 244 (1995) 41. [5] P.C. Can"eld, B.K. Cho, D.C. Johnston, D.K. Finnemore, M.F. Hundley, Physica C 230 (1994) 397. [6] G. Oomi, T. Kagayama, Physica B 239 (1997) 191. [7] Y. Uwatoko, G. Oomi, P.C. Can"eld, B.K. Cho, Physica B 216 (1996) 329. [8] P.C. Can"eld, S.L. Bud'ko, B.K. Cho, A. Lacerda, D. Farrell, E. Johnstan-Halperin, V.A. Kalatsky, V.L. Pokrovsky, Phys. Rev. B 55 (1997) 970. [9] G. Oomi, H. Takeya, K. Kadowaki, Rev. High Pressure Sci. Technol. 7 (1998) 592. [10] P. Thalmeier, P. Fulde, Europhys. Lett. 1 (1986) 367. [11] T. Ishii, G. Oomi, Y. Uwatoko, P.C. Can"eld, B.K. Cho, Physica B 237}238 (1997) 299.
Anisotropic magnetic properties of single-crystalline HoNi B C at high magnetic "elds and high pressure
G. Oomi *, T. Kagayama, H. Mitamura, T. Goto, B.K. Cho, P.C. Can"eld Department of Physics, Kyushu University, Ropponmatsu, Fukuoka 810-8560, Japan Department of Mechanical Engineering and Materials Science, Kumamoto University, Kumamoto 860-8555, Japan The Institute for Solid State Physics, The University of Tokyo, Minato-ku, Tokyo 106-8666, Japan Ames Laboratory, Iowa State University, Iowa, NM 50011, USA
Abstract Magnetostriction and magnetoresistance of single-crystalline HoNi B C have been measured at ambient pressure. A large anisotropy was found in the "eld dependence of these properties. The magnetoresistance was also measured at high pressure up to 2 GPa at low temperature below the superconducting transition temperature (9 K). Several anomalies were found due to the metamagnetic transitions, in which the transition "elds increased with increasing pressure. These results will be discussed from a thermodynamical point of view and compared with the anisotropy in the lattice compression. 2001 Elsevier Science B.V. All rights reserved. Keywords: High pressure; Boron carbide; Electrical resistance; X-ray di!raction
1. Introduction Borocarbides having the formula RNi B C (R: rare earth elements) were discovered as a new family of superconductors with relatively high transition temperatures ¹ of 10}20 K [1,2]. The ! structure is a variant of the ThCr Si type, which consists of alternating layers of RC planes and Ni B slabs [3]. The physical properties of these compounds are highly anisotropic re#ecting the tetragonal structure. The coexistence of superconductivity and antiferromagnetic ordering below ¹ has been reported through the measurement of !
* Corresponding author. Fax: #81-92-726-4841. E-mail address: [email protected] (G. Oomi).
electrical resistance, speci"c heat, magnetization and so forth [4]. Among these compounds, the most interesting material may be HoNi B C, which becomes super conducting at &9 K, reenters the normal conducting state near 5 K due to antiferromagnetic ordering and then quickly recovers superconductivity below 5 K. Below ¹ , it shows metamagnetic transi, tions indicating a complex magnetic structure [5]. Until now, there have been few data on the magnetostriction and the e!ect of pressure on magnetic properties. In order to examine the complicated phase transitions at high magnetic "eld, we attempted to measure the magnetostriction and magnetoresistance of single-crystalline HoNi B C at ambient pressure. To investigate the phase stability under pressure, we also observed the e!ect of pressure on the magnetoresistance.
0921-4526/01/$ - see front matter 2001 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 0 0 ) 0 0 6 4 8 - 7
230
G. Oomi et al. / Physica B 294}295 (2001) 229}233
2. Experimental procedure A single crystal was grown via high-temperature #ux growth. The details of the preparation were published previously [5]. The pressure dependence of the lattice parameters was measured using a Guinier-type focusing camera. Hydrostatic pressure was generated by tungsten-carbide Bridgmantype anvils using a beryllium gasket and a 4 : 1 mixture of methanol and ethanol as the pressuretransmitting medium up to 10 GPa. The electrical resistance was measured by using the standard four-probe method. The current direction was parallel to the ab-plane and the magnetic "eld was applied parallel or perpendicular to the c-axis. High pressure was generated by using the standard piston-cylinder method. The magnetic "eld was generated by a superconducting magnet. The details of the high-pressure apparatus were reported elsewhere [6]. The magnetostriction was measured by means of the capacitance method.
3. Results
Fig. 1. The relative change in lattice parameters and unit cell volume of HoNi B C as a function of pressure.
3.1. Anisotropic compression of lattice parameters Fig. 1 shows the relative change of the lattice parameters c and a of tetragonal HoNi B C at room temperature as a function of pressure. Since no discontinuous changes in the pressure dependence of the lattice constants and also no new diffraction lines were found, the tetragonal structure is stable up to 10 GPa. The large anisotropy is seen in the compression curves: the c-axis is more compressible than the a-axis. The linear compressibilities are estimated to be 2.6;10} and 1.3; 10} GPa} for c and a axis, respectively. The volume V, also shown in the "gure, was calculated using the formula <"ca. The bulk modulus is estimated to be 192 GPa. 3.2. Magnetoresistance at ambient pressure and high pressure Fig. 2 shows the magnetoresistance (MR) of HoNi B C at ambient pressure for two directions parallel and perpendicular to the magnetic "eld
Fig. 2. Magnetoresistance at 4.2 K at ambient pressure.
B(T) below 1.2 T at 4.2 K. A large anisotropy can be seen depending on the direction of the magnetic "eld B. In the direction perpendicular to the c-axis, the superconducting state is broken near 0.15 T, a discontinuous change occurs at 0.5 T followed by a small maximum near 1 T. This corresponds well
G. Oomi et al. / Physica B 294}295 (2001) 229}233
231
Fig. 3. Magnetoresistance at 4.2 K at ambient pressure.
to the metamagnetic transitions observed in the magnetization measurement [5]. Here, we de"ne these three characteristic magnetic "elds as H , H and H , which are shown by arrows in Fig. 2. On the other hand, there is no such complicated behavior for the "eld in the direction parallel to the c-axis, in which we can only observe a discontinuous change around 0.15 T, corresponding to H . Fig. 3 shows the MR at 2.2 GPa at 4.2 K for both directions below 4 T. There is a clear change in MR around 0.2 T due to the breaking of superconductivity. But the discontinuous change in MR observed at ambient pressure at H seems to be di$cult to "nd. The broad maximum is still observed near 1.2 T. In this "gure a small knee is observed around 1.8 T, which corresponds to the third metamagnetic transition at H . H is not observed at ambient pressure because the maximum "eld was smaller than 1.3 T (H at ambient pressure). H increases also with increasing pressure. For the direction parallel to the c-axis, the MR is almost independent of H above 0.3 T. Fig. 4 shows these three characteristic "elds H , H and H as a function of pressure. It is found that the three (or four) "elds including H increase with increasing pressure, which corresponds to the increase in ¹ at high pressure [7]. The results , suggest an enhancement of the antiferromagnetic interaction at high pressure.
Fig. 4. Upper critical "eld H and metamagnetic transition "elds H , H as a function of pressure.
3.3. Magnetostriction The magnetostriction parallel to the magnetic "eld in the direction of magnetic "elds parallel , to the a-axis is shown in Fig. 5 below 3 T. is , found to have two peaks near 0.5 and 1.4 T. Considering the MR measurements in the foregoing paragraph and the magnetization [5], these correspond to the metamagnetic transition at H and H . There is a clear hysteresis at H indicating a "rst-order phase transition. Since the phase transition at H is second order, there is no anomaly in (H) at H . H may exist , around the minimum between H and H as shown in Fig. 5. It was reported that the metamagnetic transition "eld H is strongly dependent on the direction of G applied "eld for a "eld in the tetragonal ab-plane [8]. In the present work, there is an error in determining the crystal axis and also sample arrangement in the capacitance measurement. Taking into account the present result H &1.4 T and the angular dependence of H , H "0.66(¹)/ sin(45!) where is the angle between [1 1 0] axis and applied "eld [8], the deviation from [1 1 0] axis is estimated to be 10}203.
232
G. Oomi et al. / Physica B 294}295 (2001) 229}233
4. Discussion
Fig. 5. Longitudinal magnetostriction at 4.2 K for Ha. ,
It is interesting to note the relation between lattice compression and the pressure e!ect on ¹ of ! borocarbides. As was seen from Fig. 1, we found a large anisotropy in the compression of the a- and the c-axis. The ¹ of the Ho-borocarbide was ! found to decrease with pressure, R¹ /RP"!0.5 K/ ! GPa [7]. On the other hand, the values of R¹ /RP ! are almost 0 for the Er- and Y-borocarbides, in which the linear compressibility of the a-axis is almost the same as that of the c-axis [9]. This fact implies that the large anisotropic compression is related to the large value of R¹ /RP, i.e., the ! pressure coe$cient of ¹ is closely related to that ! of c/a. Next, we discuss brie#y the present results by using GruK neisen parameters because the metamagnetic transition "elds H are related with the G NeH el temperature ¹ . is de"ned as , R ln E (E)"! , R ln <
(1)
where E is the characteristic energy and V the volume. for H is written as
Fig. 6. Transverse magnetostriction ( c) at 4.2 K for Ha. ,
Fig. 6 shows the magnetostriction (c-axis) , perpendicular to the magnetic "eld below 3 T. is , found to be almost independent of H. Because the metamagnetic transition at H is of "rst-order one, the relation, dP/dH"M/< is valid, where the magnetization jump M at H is around 3 /Ho [5] and the pressure dependence dH /dP is esti mated from Fig. 4 to be 4.7;10} T/GPa. We get the value for the volume jump <" 1.37;10} m.
R ln H 1 RH "B , (H )"! 2 R ln < H RP
(2)
where B is the isothermal bulk modulus. By using 2 the data for pressure dependence of H (see Fig. 4) and P"192 GPa, we obtain "37 for H . H at 4.2 K may be related to the superconducting transition temperature ¹ of the reentrant phase. The GruK neisen parameter for ¹ (¹(¹ ) is about , 12 from the pressure dependence of ¹ . It has been suggested that the GruK neisen parameter of ¹ should not be strongly di!erent from , that of the metamagnetic transition "eld H [10]. + From the pressure dependence of ¹ [8], the value , of (¹ ) is estimated to be about 27. On the other , hand, the values of for H and H are 16 and 25, respectively. These values are comparable with that of ¹ . Thus, it should be emphasized that the , GruK neisen parameter of ¹ , H (i"1, 2, 3) and , G ¹ (¹(¹ ) are all of the same order of magnitude. ,
G. Oomi et al. / Physica B 294}295 (2001) 229}233
We reported previously for ErNi B C that RH /RP"0.1 T/GPa [11], which gives (¹ )" + , 10, which is also comparable with those of the Ho-borocarbide.
References [1] R. Nagarajan, C. Mazumder, Z. Hossain, S.K. Dhar, K.V. Gopalakrishmnan, L.C. Gupta, C. Godart, B.D. Padalia, R. Vijayaraghavan, Phys. Rev. Lett. 72 (1994) 274. [2] R.J. Cava, H. Takagi, B. Battlogg, H.W. Zandbergen, J.J. Krajewski, W.F. Peck Jr., R.B. van Dover, R.J. Felder, T. Siwgrist, K. Mizuhasi, J.O. Lee, H. Eisaki, S.A. Carter, S. Uchida, Nature 367 (1994) 146.
233
[3] T. Siegrist, H.W. Zandbergen, R.J. Cava, J.J. Krajewski, W.F. Peck Jr., Nature 367 (1994) 254. [4] M. El Massalami, S.L. Bud'ko, B. Giordanengo, E.M. Baggio-Saitovitch, Physica C 244 (1995) 41. [5] P.C. Can"eld, B.K. Cho, D.C. Johnston, D.K. Finnemore, M.F. Hundley, Physica C 230 (1994) 397. [6] G. Oomi, T. Kagayama, Physica B 239 (1997) 191. [7] Y. Uwatoko, G. Oomi, P.C. Can"eld, B.K. Cho, Physica B 216 (1996) 329. [8] P.C. Can"eld, S.L. Bud'ko, B.K. Cho, A. Lacerda, D. Farrell, E. Johnstan-Halperin, V.A. Kalatsky, V.L. Pokrovsky, Phys. Rev. B 55 (1997) 970. [9] G. Oomi, H. Takeya, K. Kadowaki, Rev. High Pressure Sci. Technol. 7 (1998) 592. [10] P. Thalmeier, P. Fulde, Europhys. Lett. 1 (1986) 367. [11] T. Ishii, G. Oomi, Y. Uwatoko, P.C. Can"eld, B.K. Cho, Physica B 237}238 (1997) 299.