Feb 2, 2008 - ferromagnetism (W-FM) and SC was discov- ... nal magnetic field from the FM magnetiza- ..... in the superconducting phase clearly demon-.
arXiv:cond-mat/0311245v1 [cond-mat.supr-con] 11 Nov 2003
The internal magnetic field in superconducting ferromagnets Grigory I. Leviev∗ , Menachem I. Tsindlekht, Edouard B. Sonin, and Israel Felner The Racah Institute of Physics, The Hebrew University of Jerusalem, 91904 Jerusalem, Israel (February 2, 2008)
Abstract We have measured the nonlinear response to the ac magnetic field in the superconducting weak ferromagnet Ru-1222, at different regimes of sample cooling which provides unambiguous evidence of the interplay of the domain structure and the vorticity in the superconducting state. This is direct proof of coexistence of ferromagnetic and superconductive order parameters in high-Tc ruthenocuprates.
Typeset using REVTEX The problem of coexistence of supercon- the W-FM is related to the Ru layers. In ductivity (SC) and ferromagnetism (FM) both systems, the magnetic order does not has been studied for almost 50 years start- vanish when SC sets in at Tc , and remains uning from the theoretical work by Ginzburg changed and coexists with the SC state. The [1] (see also [2]).
Coexistence of weak- Ru-1222 materials (for R=Eu and Gd) dis-
ferromagnetism (W-FM) and SC was discov- play a magnetic transition at TN = 125 − 180 ered some time ago in RuSr2 R2−x Cex Cu2 O10 K and bulk SC below Tc = 25-50 K (TN > (R=Eu and Gd, Ru-1222) layered cuprate Tc ) depending on the oxygen concentration systems [3],
and more recently [4] in and sample preparation. This discovery has
RuSr2 GdCu2 O8 (Ru-1212). The SC charge launched a new wave of investigations in this carriers originate from the CuO2 planes and field [5]. The problem is of general inter1
est for condensed matter physics and is rele- the spontaneous magnetization, is a source vant for many materials, in particular uncon- of an internal magnetic field inside a samventional superconductors (including some ple even without an external magnetic field heavy fermions) with triplet pairing [6].
H. On the other hand, the superconducting
Despite a lot of work done in the past and properties of type-II superconductors depend recently, debates concerning whether such strongly on whether the sample was cooled to coexistence is genuine are still continuing. the SC state in zero magnetic field (ZFC) or Evidence in favor of coexistence is mostly in a finite magnetic field (FC). Here a “field” indirect and refers to some peculiarities of is supposed to be an external magnetic field. the magnetization curve. One of the most We show here that these properties depend pronounced manifestations of SC-FM coex- also on the internal magnetic field during the istence is the spontaneous vortex phase (su- cooling process. We exploited the procedure, perconducting vortices induced by the inter- which we shall call the internal-field coolnal magnetic field from the FM magnetiza- ing (IFC): The sample was cooled down to tion).
It explains well the magnetization TIF C under an external magnetic field HIF C ,
curve of these materials (see [7] and refer- (TIF C < TN ). At TIF C , HIF C was turned off ences therein). However, this phase has not and further cool-down to T = 5 K was done yet been observed experimentally (visualized at H = 0. It appears that, by using the IFC as the more common mixed state of type II procedure, the properties of the SC state were different from those measured after the reg-
superconductors).
In the past the evidence of the FM-SC ular ZFC process from temperatures above coexistence referred mostly to the magnetic TN . Thus, in the SC state, the sample senses properties of the materials affected by the the internal magnetic field evolved from the presence of superconductivity. In this letter remanent magnetization, which was formed we present the first experimental evidence of in the normal ferromagnetic phase and then the effect of the ferromagnetic order parame- frozen at further cooling. We measured the nonlinear response to
ter, on the superconducting order parameter.
The ferromagnetic order parameter, namely the ac magnetic field, which is a sensi2
tional to the time derivative of M(t). Our home made experimental setup was adapted '
, h =0.4 Oe
1
200
A
0
to a commercial MPMS SQUID magnetome-
, h =2 Oe 0
ter. An ac field h(t) at a frequency of ω/2π =
T
c
100
T
N
3
(a.u.)
3
1
'
& A
1.5 kHz and an amplitude up to the h0 = 3 0
Oe was generated by a copper solenoid ex-
T
m
0
50
100
isting inside the SQUID magnetometer. The
Temperature (K)
temperature, dc magnetic field, and ampli′
FIG. 1. Temperature dependencies of χ1 and tude dependencies of the fundamental and A3ω
third harmonic signals presented here have been measured by the two coils method [9] .
tive probe of superconducting vorticity, as
In the present letter the results for the first
demonstrated by numerous investigations in the past [8–10].
and third harmonics will be discussed.
Ceramic sample of
Figure 1 shows the temperature depen-
Gd1.5 Ce0.5 Ru2 Sr2 Cu2 O10 (Ru-1222) with di-
′
dencies of the in-phase susceptibility χ1 and
mensions 8 × 2 × 2 mm3 was prepared by a
of the amplitude of the third harmonic A3ω ∝
solid-state reaction as described in Ref. 2. In
′
′′
h0 |χ3 − iχ3 |, measured after the ZFC process
a nonlinear medium, magnetization oscilla-
at H = 0. The temperature dependence of
tions, induced by an ac magnetic field h(t) =
′
χ1 is typical for superconducting ferromag-
h0 sin ωt, may be expanded in a Fourier se-
nets [3]. This plot reveals three transitions:
ries:
(i) the paramagnetic-antiferromagnetic tran-
M(t) = h0
X
′ ′′ χn sin(nωt) − χn cos(nωt) (1) sition at TN ≈ 125 K, (ii) the most pro-
n>0 ′
nounced transition, which corresponds to the ′′
where χn and χn (n = 1, 2, 3...) are the in-
peak at Tm ≈ 78 K, and (iii) the transition
phase and out-of-phase components of the
into the SC state at Tc ≈ 28 K. The na-
harmonic susceptibility. In all experiments
ture of the second transition, which is ev-
described here we measured the voltage drop
ident both in the linear and the nonlinear
induced in a pickup coil, which is propor-
response, is not yet completely clear and is 3
unobservable under our experimental conditions. For T < Tc the third harmonic grows 15
very fast with temperature decreasing (Fig.
T = 62 K
(a.u.)
1), and its dependence on the ac field am-
0.5
3
10
ZFC
A
(a.u.)
1.0
A3
0.0
5
0
1
2
plitude (Fig.
3
Excitaion amplitude, h (Oe)
2) is different from that at
T = 5 K
0
T > Tc , as evident from the saturation for the
ZFC
0 1E-3
0.01
0.1
nonlinear response at high amplitude of ex-
1
Excitation amplitude, h
0
(Oe)
citation, instead of a quadratic growth. The FIG. 2. Amplitude dependencies of A3ω at growth of the nonlinear response in the suT = 5K. Inset: amplitude dependence of A3ω in perconducting materials was revealed in numagnetic phase at T = 62 K.
merous previous experimental investigations [8–10]. Various mechanisms were suggested
discussed elsewhere [3,11]. Ambiguity is con-
for this nonlinear response based on the crit-
nected with the magnetic phase between Tm
ical state model [8] and the presence of weak
and TN , which is characterized by low coer-
links [10]. In particular, the response shown
civity. On the other hand, the Tc < T < Tm
in Fig. 2 is well described by the Josephson-
temperature region definitely corresponds to
media model. We do not have to discuss these
the weak ferromagnetic phase [3].
models, since all of them relate the response
The third harmonic behavior is different
to the penetration of the magnetic flux (vor-
for T > Tc and T < Tc . For T > Tc the
tices) into the sample, and only this fact is
behavior is typical for ferromagnetic materi-
essential for the present investigation. Thus
als and was known already from Rayleigh’s investigation on iron [12].
it seems reasonable that the A3ω at T < Tc
The third har-
is an effective probe of the superconducting
monic response demonstrates a quadratic de-
vorticity.
pendence on h0 (inset in Fig. 2), which di-
Figure 3 demonstrates ZFC dependence
rectly derived from the oscillatory motion of
of A3ω on the external magnetic field. One
the domain walls [13]. This signal should de-
can see that A3ω decreases with the mag-
crease at low temperatures and it becomes
netic field. At high magnetic fields A3ω is 4
can be extremely small, and the peak is not observable. Moreover, we deal with the su-
15 T = 5 K h
A
3
( V)
0
10
perconducting ferromagnets, where the spon-
= 0.2 Oe
q = 0.8
taneous vortex phase can replace the Meiss-
-q
ner state at H = 0. Altogether this explains
H
5
why we observe the maximum value of A3ω
0 0
50
100
150
at H = 0.
Magnetic field (Oe)
Now let us consider the experimental reFIG. 3. Magnetic field dependence of A3ω at sults in the IFC process. After turning off the T = 5 K after ZFC
magnetic field HIF C at temperature TIF C , the sample was cooled in H = 0 down to
a power function of the H: A3ω ∝ H −q , with
T = 5 K and the signal of the third har-
q ≈ 0.8. Suppression of the A3ω by the mag-
monic at T = 5 K was measured. Figure 4
netic field applied after ZFC was observed
shows A3ω (HIF C ) dependence for TIF C = 40
in the previous nonlinear studies and agrees
K and 70 K. It is evident that the field HIF C
with all suggested models of the nonlinear re-
suppresses the A3ω signal similarly to the ex-
sponse. The nonlinearity under discussion is
ternal field after ZFC Fig. 3 even though
connected with a nonhomogeneous distribu-
HIF C was turned off before the onset of su-
tion of the magnetic flux, which penetrated
perconductivity. Turning off HIF C at T = 40
into the sample, and the magnetic flux dis-
K affects A3ω more strongly than for T = 70
tribution becomes more and more uniform,
K due to larger remanent magnetization at
when the vortex density increases. On the
T = 40 K. This behavior is typical for the
other hand, in the Meissner state the non-
FM materials [13].
linear response must be quite weak, and the
Figure 5 presents the signal of the third
magnetic field dependence of A3ω should have
harmonic A3ω (T = 5K) as a function of
a peak at some H, as was observed in some
TIF C after cooling in HIF C = 30 Oe. The
materials [8]. But in ceramics with numerous
signal of the A3ω (T = 5K) decreases for
weak links, such as our material, this field
TIF C < Tm . This demonstrates that the sup5
h
0
15
= 0.2 Oe
H = 30 Oe h
V)
T
= 70 K
0
= 0.2 Oe
10
A
A
3
3
(
IFC
(a.u.)
10
5 T
IFC
5
= 40 K
0 0
50
100
Magnetic field, H
IFC
0
150 (Oe)
20
40
60
80
Temperature, T
IFC
FIG. 4. A3ω (T = 5K) as a function of HIF C
100
(K)
FIG. 5. Amplitude of the third harmonic
for TIF C = 40 K and 70 K
A3ω at H = 0 and T = 5 K vs TIF C
pression of the third harmonic response by value of A3ω from the plot in Fig. 4, find the the internal magnetic field takes place only if value of H, which corresponds to this value of the field cooling continues down to the weakly A3ω in Fig 3, and assume that this value of H ferromagnetic phase with essential coerciv- gives a reasonable estimation of HI . Figure ity. It is known [7] that in idealized single- 6 presents the dependence of HI on HIF C . domain superconducting ferromagnets the in-
The internal magnetic field arises from
~i ternal magnetic field from the spontaneous the frozen remanent magnetization 4πhM ~ has the same effect on after field cooling down to T magnetization 4π M IF C . We have the phase diagram, i.e., on the magnetic flux compared obtained in Fig. 6 with direct dc penetrating into the sample, as the external remanent magnetization measured in our prefield. This can be generalized in the more vious studies [15]. It appears that there is a realistic case of a multi-domain sample with reasonable agreement (with an accuracy of ~ nonzero average internal field 4πhMi. On ±20%) between the two methods, and conthe basis of this argument we can use plot firms our scenario. of A3ω (H) (Fig. 3) as a calibration curve to
The phenomenon revealed in our exper-
estimate the magnitude of the frozen inter- iment is possible if the domain structure nal magnetic field (HI ). Namely, we take the formed in the ferromagnetic phase can be 6
~ i, frozen down to the superconducting state. tribute to the average internal field ∼ 4πhM On the other hand, as was noted in the pio- studied here. This vortex tangle is expected neering paper by Ginzburg [1] and confirmed to exist even after the ZFC process and conby the detailed analysis in Ref. [14], super- tributes to the initial value of the third harconductivity should strongly affect the equi- monic, which was detected without external librium domain structure: Its period should or internal magnetic field. These arguments grow, and in equilibrium any sample in the illustrate that the vorticity (magnetic flux) Meissner state is a single domain. But in our distribution in a real (especially ceramic) sucase we deal with a non-equilibrium domain perconducting ferromagnet can be very comstructure, which is a metastable state due to plicated. Genuinely zero field cooling is praccoercivity.
tically impossible: if one cools a sample in
The presence of the frozen internal field zero external field, one cannot avoid internal in the superconducting phase clearly demon- magnetic fields from the spontaneous magnestrates that the sample is in the mixed state tization, even if these fields vanish on averwith many vortices.
One cannot call this age but still remain inside the domains. A
state the spontaneous vortex phase because more detailed analysis of the magnetic-flux the latter refers to the equilibrium state, but distribution would become possible if further we deal with a metastable state. We have an- investigations provided more information on alyzed here the nonlinear response, which is the structure of the material: sizes of grains ~ sensitive to the average internal field 4πhMi. and domains, data on crystal anisotropy etc. The absolute value of the average magnetiza-
In summary, our measurements of the
~ is less than the saturation magne- nonlinear response unambiguously demontion hMi tization M, which can determine the vortex strate the coexistence of the superconductdensity in a single-domain sample [7]. How- ing and ferromagnetic order parameter in Ruever, the saturation magnetization may cre- 1222 samples below the superconducting crit~ changes ical temperature. Coexistence is manifested ate vortices inside domains. Since M its direction from domain to domain, we ob- by the clear effect on the domain structure tain the vortex tangle, which does not con7
50
[1] V. L. Ginzburg, Zh. Eksp. Teor. Fiz.
I
Internal magnetic field, H (Oe)
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