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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, 7.25B, and 8.77B for x =
0.25, 0.5, and 0.75, respectively. For YNi2B2C (x=0),eff = 0. For HoNi2B2C (x=1),
eff =10.4B 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.
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