J. Phys. Soc. Jpn. 83, 093702 (2014)
Letters
H. Kotegawa et al.
the effective electron mass is enhanced by magnetic corre-
lations near Pc. n is close to 2 in the low-pressure region and
(
c)
has its minimum just above P , followed by a gradual
c
increase under higher pressures. We obtained n ¼ 1:4 ꢅ 0:1
1
)
near P , which is close to n ¼ 1:5 ꢅ 0:1 shown by Wu et al.
c
(
(
b)
a)
The highest Tc of 2.17 K is achieved at 1.00 GPa,
accompanied by the increase in A and the deviation from
the FL behavior. This behavior is reminiscent of a typical
11)
case of heavy-fermion superconductors,
which have a
quantum critical point of magnetic origin. It is conjectured
that magnetic fluctuations play a vital role in inducing
superconductivity in CrAs. However, the difference of CrAs
from heavy-fermion systems is the first-order separation of
the magnetic and PM phases in CrAs. This situation is
reminiscent of the Fe-based superconductor SrFe As , where
2
2
a Tc of 34 K is achieved in the vicinity of the magnetic phase,
but the magnetic and PM phases are separated by a first-order
1
2)
transition. In this case, the coexistence of magnetism and
superconductivity is not simple, and the hybrid state of both
1
3)
phases has been reported in SrFe As . It is an intriguing
2
2
issue whether superconductivity can coexist with the
helimagnetic state in CrAs. Another interesting similarity to
Fe-based superconductors is that the magnetic transition is
accompanied by the structural phase transition. The con-
tribution of orbital fluctuations to superconductivity might be
an interesting issue to be considered in CrAs.
Fig. 3. (Color online) (a) Pressure–temperature phase diagram of CrAs.
The helimagnetic phase disappears above Pc ꢀ 0:7 GPa, and super-
conductivity appears in the PM phase. The closed (open) squares represent
TN obtained during cooling (warming). The observation of hysteresis up to
Pc indicates that helimagnetic-paramagnetic transition is of the first order
even under pressure. (b) The pressure dependence of the coefficient A, which
is estimated from the resistivity below 4 K. Above Pc, A decreases gradually
Wu et al. have reported zero resistance below ³1.5 K,1)
whereas we observed it below ³2.2 K. The RRR range of
their samples is 240–327, and thus there is no significant
difference from that of our sample #2. The pressure-
transmitting media used are different from each other, but
we consider that the properties of the media used, i.e.,
Daphne 7474 (our study) and glycerol (Wu et al.’s study) are
similar. A possible reason for this is the experience of the
magnetic transition with a large magnetostriction, although
we do not know the experimental procedure used by Wu
et al. A systematic study is required to clarify the cause of the
2
with increasing pressure. The estimated 1=ðꢃ0TcÞ is also plotted, showing
good scaling with A. (c) Pressure dependence of n estimated from the
resistivity between Tc and 10 K. The clear deviation from the FL behavior is
confirmed. The highest Tc of 2.17 K is achieved at 1.00 GPa, accompanied by
the increase in A and the deviation from the FL behavior.
increases from 0.73 GPa close to Pc, reaches its maximum difference in Tc.
at approximately 1.00 GPa, and decreases with increasing
Figures 4(a)–4(c) show the temperature dependence of the
pressure. At 3.06 GPa, the onset of superconductivity can be resistivity under different magnetic fields along the a-axis.
confirmed in the measured temperature range. The Tc for zero For 1.00, 1.40, and 1.88 GPa, the field dependences of Tc
resistance is significantly higher than that for sample #1, are obtained and displayed in Fig. 4(d). The initial slope of
orb
orb
where the onset of superconductivity is observed below ðꢃdH =dTÞ gives the orbital field Hc2 through H ð0Þ ¼
c2
Tc
c2
1
4)
³
1.6 K at 0.73 GPa, as shown in the inset of Fig. 1(b). 0:727ðꢃdH =dTÞ T in the clean limit. The slopes are
c2
T
c
c
2
Figure 2(c) shows the T vs µ plot. The resistivity obeys the estimated to be 0.91 T/K (1.00 GPa), 0.80 T/K (1.40 GPa),
2
orb
Fermi liquid (FL) form of ꢂðTÞ ¼ ꢂ0 þ AT in a narrow and 0.62 T/K (1.88 GPa), giving Hc2 ð0Þ of 1.44 T (1.00
temperature range, and its temperature range is likely to GPa), 1.22 T (1.40 GPa), and 0.85 T (1.88 GPa), respectively.
extend slightly under higher pressures. The slope corresponds These values correspond to the Ginzburg–Landau coherence
orb
2
0
to the coefficient A, which represents the inelastic scattering length ꢃ0, through Hc2 ð0Þ ¼ ꢁ0=2ꢀꢃ where ꢁ0 is the
between electrons and is generally proportional to the square quantum fluxoid. ꢃ0 along the bc-plane is estimated to be
of the effective electron mass. A clearly decreases with 151 Å (1.00 GPa), 164 Å (1.40 GPa), and 197 Å (1.88 GPa).
increasing pressure.
We perform a simple comparison between the pressure
The pressure–temperature phase diagram of CrAs up to dependences of Hc2 and A, which corresponds to the effective
2
ꢂ
³
3 GPa is shown in Fig. 3(a). The helimagnetic phase electron mass. ꢃ0 is given by ꢃ0 ’ hꢂ vF=ꢀꢀ0 ¼ hꢂ kF=ꢀꢀ0m ,
ꢂ
disappears above Pc ꢀ 0:7 GPa. The SC phase appears in the where vF, kF, ꢀ0, and m are Fermi velocity, Fermi wave
PM state, extending to relatively high pressures. Figures 3(b) number, SC gap size, and effective electron mass, respec-
and 3(c) show the pressure dependence of A, which is tively. If we assume for simplicity that kF and ꢀ0=kBTc
2
estimated using ꢂðTÞ ¼ ꢂ0 þ AT for the data between Tc are independent of pressure, we obtain the relation
2
and 4 K, and the pressure dependence of n, which is A / 1=ðꢃ T Þ , which is plotted in Fig. 3(b). The good
0
c
0
n
2
evaluated using ꢂðTÞ ¼ ꢂ þ A T between T and 10 K. A scaling between A and 1=ðꢃ T Þ strongly suggests that
0
c
0 c
decreases gradually with increasing pressure, indicating that the superconductivity in CrAs is mediated by electronic
0
93702-3
©2014 The Physical Society of Japan