Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Please use the sample manuscript starting from the next page to prepare your manuscript. Notes: 1) Contact information after % are for editors’ use only, not for publishing. 2) For PACS Codes see: https://www.aip.org/publishing/pacs/pacs-2010-regular-edition 3) Financial support should be indicated as the footnotes on the first page, whereas the scientific contributions from other people or groups should be acknowledged after the main body of text. 4) Captions of figures and tables should be presented in text format. 5) Do not create links for citations, and close attention should be paid to the author format in the bibliography. 1 Magnetic Pair-Breaking in Y1-xHoxNi2B2C (x=0, 0.25, 0.5, 0.75) Single Crystals* Song-Rui Zhao(赵松睿)1, Jin-Qin Shen(沈静琴)1, Zhu-An Xu(许祝安)1**, H. Takeya2, K. Hirata2 1 2 Department of Physics, Zhejiang University, Hangzhou 310027 National Institute for Materials Science, 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, Japan *Supported by the National Natural Science Foundation of China under Grant No 10225417, and National Basic Research Program of China of China under Grant No 2006CB601003. **To whom correspondence should be addressed. Email: [email protected] %Email: [email protected]; [email protected]; [email protected]; [email protected] (这些是备用邮箱,发清样用) %Tel. 0571-87953345 13588186458 (Received 22 November 2005) Abstract Temperature-dependent resistivity and magnetic susceptibility were studied for quaternary borocarbide intermetallic compounds Y1-xHoxNi2B2C (x = 0, 0.25, 0.5, 0.75), which show coexistence of superconductivity with magnetism. In a normal state, the compounds exhibit conventional metallic behaviour. The Debye temperature θD is derived by fitting the temperature dependence of resistivity to the Bloch-Gruneisen expression, i.e. θD scales with M-0.5 (M is the averaged atomic mass on the Y3+ site), which means that the acoustic mode of the lattice vibrating spectrum is influenced by the Y3+ site atoms. Fitting the temperature-dependent magnetic susceptibility above TN to the Curie--Weiss law, effective magnetic moment μeff is deduced, and then de Gennes factor dG is calculated. It is found that as Ho content increases, μeff as well as dG increases and TC decreases. Moreover, the decrease of TC scales with dG, i.e., TC nI 2 N ( F )dG , which is consistent with the prediction of 2 the Abrikosov--Gor’kov theory. We suggest that the depression of TC could be mainly ascribed to the magnetic pair-breaking effect of magnetic Ho3+ ions. The change of Debye temperature with Ho content may not have significant impact on TC. PACS: 74.70.Dd, 74.25.Fy, 74.25.Ha, 74.62.-c Usually superconductivity does not coexist with magnetism due to magnetic pair-breaking effect. However, the discovery of the coexistence of superconducting order and magnetic order in RMo6S8 and RRh4B4 compounds[1] has stimulated enormous interests to seek for new compounds which allow the coexistence of superconductivity with magnetism. The recently discovered rare-earth nickel boride carbides, RNi2B2C (R = rare-earth elements, Y and Sc), become attractive because they show the coexistence of superconductivity with magnetism[2-4] and they are ideal candidates for the study of two competing orders. HoNi2B2C is a magnetic superconductor with superconducting transition temperature TC of 7--8K, and antiferromagnetic (AFM) transition temperature TN of about 5 K. The abundance of the magnetic structure of HoNi2B2C has been reported.[5-9] The most exotic property of HoNi2B2C is that under applied magnetic field, it re-enters normal state just above TN (<TC), and goes back to a superconducting state below TN.[10,11] Compared to HoNi2B2C, YNi2B2C is a non-magnetic superconductor with a higher superconducting transition temperature TC of 15.5 K (LuNi2B2C shows the highest TC of 16.6K in the RNi2B2C family). In order to study more details about the interplay between superconducting order and magnetic order and to investigate how it affects the transport properties, in this study, Ho-doped superconducting Y1-xHoxNi2B2C (x = 0, 0.25, 0.5, 0.75) single crystals are prepared and the measurements of resistivity and magnetic susceptibility are performed. The results give strong evidence for the competing mechanism between superconducting order and antiferromagnetic order. The suppression of TC is consistent with the prediction of the Abrikosov--Gor’kov theory.[12] 3 A series of Y1-xHoxNi2B2C (x=0, 0.25, 0.5, 0.75) single crystals were synthesized by floating-zone technique. The details of the sample growth were reported elsewhere.[13] Standard four-probe method was used to measure in-plane resistivity. The dc magnetic susceptibility was measured by the Quantum Design PPMS-9 system and the magnetic field was applied along the c-axis direction. The weight of the samples for magnetic susceptibility measurements is about 1 mg. Figure 1 shows the temperature dependence of in-plane resistivity of Y1-xHoxNi2B2C single crystals for different Ho content under zero applied magnetic field, where the solid lines are the fitting curves with the Bloch-Gruneisen expression which will be discussed in the following. The zero point of superconducting transition temperature TC0 is 15, 12.8, 11.4, and 7.6 K for x = 0, 0.25, 0.5, and 0.75, respectively. We define TC(x) as the zero point of superconducting transition temperature for different Ho contents. Significant increase of residual resistivity for Ho doped samples is observed, indicating that the disorder is enhanced by Ho doping. The temperature dependence of resistivity is linear from 100 K to room temperature (RT), but it becomes nearly quadratic at low temperature, that is, (T ) T n , (1) where n is around 2.0 for all the samples. Generally speaking, the linear temperature dependence of high temperature resistivity is caused by electron-phonon interaction. Allen et al.[15,16] developed a “modernized” Bloch--Gruneisen theory for the phonon-scattering dominated ρ(T). This theory leads to the classical Bloch--Gruneisen formula with a model employing Debye phonons, spherical Fermi surface and electron-phonon coupling via longitudinal phonons only.[17] Thus, we fit our ρ(T) data with the Bloch--Gruneisen expression for normal state resistivity, viz., (T ) 0 (m 1) ' D ( Jm( T D D ) 0 T T D )m J m ( T D x m dx , (e x 1)(1 e x ) 4 ), (2) (3) where θD is the Debye temperature, ρ’ is the temperature coefficient of resistivity and m=2~5. Equation (2) degenerates into Eq. (1) for T < 0.1θD.We take m=2.1 for x = 0 and m=2.0 for x=0, 0.25, 0.5, and 0.75 (m in Eqs. (2) and (3) should be almost the same as n in Eq. (1)), and the best fitting generates θD = (480±10)K, (425±10)K, (395±10)K, and (375±10)K for x = 0, 0.25, 0.5, and 0.75 respectively. The inset of Fig. 1 shows the x dependence of θD. The θD value for x =0 is consistent with the value in the previous report.[18] All the Debye temperatures fit well to the equation M ( x) D ( x) D (0) M ( 0 ) 0.5 (4) , where M(x) = (1-x)M(0) + x M(Ho) denotes the averaged atomic mass on the Y3+ site, θD(0) ( = 480 K) is the Debye temperature for x = 0, M(0) is the atomic mass of Y atom, and M(1) is the atomic mass of the Ho atom. By extrapolating the θD curve to x = 1, we can deduce that θD of pure HoNi2B2C is 352 K, which agrees with the θD value reported in Ref. [14]. The fact that θD scales with M-0.5 means that the acoustic mode of lattice vibrating spectrum is influenced by the Y3+ site atoms. 60 500 450 (.cm) D (K) 50 40 400 0.25 350 300 0.00 30 0.5 0.25 0.50 0.75 1.00 Ho content, x 0 20 0.75 10 0 0 50 100 150 200 250 300 T (K) Fig. 1. Temperature dependence of resistivity for Y1-xHoxNi2B2C. The solid circles present the experimental data, and the solid lines are the fitting curves with the Bloch--Gruneisen expression. The numbers denote the Ho content x. Inset: Plot of Debye temperature vs Ho content. The Debye temperature for x =1 (open squares in the inset) is taken from Ref. [14]. The dashed line is the theoretic curve calculated based on Eq. (4). 5 Low temperature magnetic susceptibility measurements under small applied magnetic field (10 Oe) show that sharp superconducting transition and TC values are consistent with those determined by resistivity measurements. In order to study the normal state susceptibility and magnetic order, a higher magnetic field of 1 k Oe is applied along the c-direction. Figure 2 shows the temperature dependence of the inverse of magnetic susceptibility under applied magnetic field of 1 kOe, which fits well to the Cure--Weiss law for the temperatures above TN. Effective magnetic moments were derived for different doping levels: 5.9 B, 7.25B, and 8.77B for x = 0.25, 0.5, and 0.75, respectively. For YNi2B2C (x=0),eff = 0. For HoNi2B2C (x=1), eff =10.4B has been reported in Ref. [19]. The effective magnetic moment increases monotonously with increasing Ho content. Usually, de Gennes factor dG is defined as dG ( g 1) 2 J ( J 1) , where g is the Landé factor and can be calculated by the formula g 1 J ( J 1) S ( S 1) L( L 1) for the L-S coupling, J is the total 2 J ( J 1) angular momentum. The effective magnetic moment can be calculated by the formula eff g J ( J 1) B , therefore the dG factor for all the Ho doped samples can be derived from the experimental results of eff . The inset of Fig. 2 shows the plots of eff and dG versus Ho content. Both eff and dG increase with x monotonously. Our dG values are close to the results reported in Ref. [20]. The Abrikosov--Gor’kov theory[12] predicts a linear decrease of TC with magnetic impurities. Depression of TC scales with dG via the expression: TC nI 2 N ( F )dG , (5) where n is the number of magnetic moments, I is the exchange constant, N ( F ) is the density of states at the Fermi level. From the inset of Fig. 3, it can be found that TC scales inversely with dG, consistent with the Abrikosov—Gor’kov theory. It should be noted that the Abrikosov--Gor’kov theory was derived for non-interacting magnetic impurities, thus the linear relationship between TC and dG factor is valid only in the 6 case that TC is higher than the Neel temperature TN. -1 6 8 4 4 2 0.25 dG 60 12 eff (B) 1/ (emu .Oe.mol) 80 0 0 0.00 0.25 0.50 0.75 1.00 40 x 0.5 20 0 0.75 0 50 100 150 200 250 300 T (K) Fig. 2. The temperature dependence of the inverse of susceptibility under magnetic field H = 1 kOe. The solid lines are the fitting curves by the Cure--Weiss law. The arrows denote the deviation from linearity. The numbers denote the Ho content x. Inset: Plots of effective magnetic moment eff and dG vs Ho content x. The dashed straight line is guide for the eyes. The data for x = 1 (open symbols in the inset) were taken from Ref. [19]. Finally, the variations of superconducting transition temperatures with x are summarized in Fig. 3. TC is the experimental data, i.e., TC(x) TC(x) – TC(0). TC1 is defined as the calculated variation of TC assuming that the depression of TC is determined by the M ( x) TC1 ( x) TC (0) M ( 0 ) change of Debye temperature, i.e., 0.5 TC (0) . TC2 is defined as the theoretical depression of TC due to the effect of magnetic pair-breaking induced by Ho doping, i.e., TC 2 ( x) kdG , where k = 1.44 calculated from Ref. [20], TC3 TC1 + TC2, which includes both the effect of Debye temperature and the effect of magnetic pair-breaking. From Fig. 3, we can find that the experimental value of TC is almost the same as that of TC2 except for the case at x=0.75. This result indicates that the decrease of superconducting transition temperature with the increasing Ho content is 7 almost attributed to the magnetic pair-breaking of Ho3+, and the change of Debye temperature has little impact on TC. 0 -4 TC2 6 12 4 TC (K) -8 16 -12 0.00 8 2 TC dG TC (K) TC1 TC3 4 0 0.00 0.25 0.50 0.75 1.00 x 0.25 0.50 0.75 1.00 Ho content, x Fig. 3. The variation of TC with Ho content x. Solid circles were our data and the open circle is from Ref. [20]. TC is the experimental data. TC1 is the calculated variation of TC assuming that the depression of TC is determined by the change of Debye temperature, and TC2 is the theoretical depression of TC due to magnetic pair-breaking effect, and TC3 TC1 + TC2. Inset: Plots of TC and dG vs Ho content. The TC (open square) and dG (open triangle) values for x =1 were taken from Ref. [19] and [20]. The dashed straight line is guide for the eyes. In summery, by fitting the temperature dependence of in-plane resistivity to the Bloch--Gruneisen expression for Y1-xHoxNi2B2C (x = 0, 0.25, 0.5, 0.75) system, we have found that the Debye temperature θD decreases with Ho content, and θD M-0.5, indicating that the acoustic mode of the lattice vibrating spectrum is influenced by the Y3+ site atoms. However, the change of θD only has little impact on TC. A nearly linear depression of superconducting transition temperature with increasing Ho3+ content is found, and strong magnetic pair-breaking effect induced by Ho3+ ions is observed. Our results imply that there exists strong competition between superconductivity and magnetism in this system. This behaviour can be interpreted in the framework of the Abrikosov--Gor’kov theory. References [1] Maple M B and Fischer O 1982 Superconductivity in Ternary Compounds III (Berlin: Springer) [2] Nagarajan R, Mazumdar C, Hossain Z et al 1994 Phys. Rev. Lett. 72 274 [3] Cava R J, Takagi H, Zandbergen H W et al 1994 Nature 367 252 8 [4] Fisher I R and Cooper J R 1995 Phys. Rev. B 52 15086 [5] Lin M S, Shieh J H, You Y B et al 1995 Phys. Rev. B 52 1181 [6] Goldman A I, Stassis C, Canfield P C et al 1994 Phys. Rev. B 50 9668 [7] Grigereit T E, Lynn J W, Huang Q et al 1994 Phys. Rev. Lett. 73 2756 [8] Huang Q, Santoro A, Grigereit T E et al 1995 Phys. Rev. B 51 3701 [9] Dewhurst C D, Doyle R A, Zeldov E et al 1999 Phys. Rev. Lett. 82.827 [10] Krug K, Heinecke M and Winzer M 1996 Physica C 267 321 [11] Rathnayaka K D D, Naugle D G, Cho B K et al 1996 Phys. Rev. B 53 5688 [12] Abrikosov A A and Gor’kov L P 1961 Sov. Phys. JETP 12 1243 [13] Takeya H, Hirano T and Kadowaki K 1996 Physica C 256 220 [14] Bhatnagar A K, Rathnayaka K D D, Naugle D G et al 1997 Phys. Rev. B 56 437 [15] Allen P B 1971 Phys. Rev. B 3 305 [16] Allen P B and Butler W H 1978 Phys. Today 31 44 [17] Pinski F J, Allen P B and Butler W H 1981 Phys. Rev. B 23 5080 [18] Rathnayaka K D D, Bhatnagar A K, Parasiris A et al 1997 Phys. Rev. B 55 8506 [19] Eisaki H and Takagi H 1994 Phys. Rev. B 50 647 [20] Eversmann K, Handstein A, Fuchs G et al 1996 Physica C 266 27 9