Ferromagnetic 0-pi Junctions as Classical Spins

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by  M. L. Della Rocca

Ferromagnetic 0−π Junctions as Classical Spins
M.L. Della Rocca,1,2,∗ M. Aprili,1,3 T. Kontos,4 A. Gomez,1 and P. Spatkis1
1Ecole Sup`erieure de Physique et Chimie Industrielles (ESPCI), 10 rue Vauquelin, 75005 Paris, France
2Dipartimento di Fisica ”E.R. Caianiello”, Universit`a degli Studi di Salerno, via S.Allende, 84081 Baronissi (Salerno), Italy
3CSNSM-CNRS, Bˆat.108 Universit´e Paris-Sud, 91405 Orsay, France
5
4Institute of Physics, University of Basel, Klingelbergstrasse, 82, CH-4056 Basel, Switzerland
0
0 (Dated: February 2, 2008)
2 The ground state of highly damped PdNi based 0−π ferromagnetic Josephson junctions shows

n aspontaneoushalfquantumvortex,sustained byasupercurrentofundeterminedsign. Thissuper-
a current flows in the electrode of a Josephson junction used as a detector and producesa φ0/4 shift
J initsmagnetic diffraction pattern. Wehavemeasured thestatistics of thepositiveornegativesign

9 shift occurring at the superconducting transition of such a junction. The randomness of the shift
1 sign, the reproducibility of its magnitude and the possibility of achieving exact flux compensation
upon field cooling: all these features show that 0−π junctions behave as classical spins, just as

] magnetic nanoparticles with uniaxial anisotropy.
n
o
PACSnumbers: 74.50.+r,74.45.+j,85.25.Cp
c
-
r
p Macroscopicdevices formed by a large number of par- part and its minimum is reached for a zero total flux
u
ticles can behave as a quantum two-level system pro- enclosed in the loop. The system maintains a constant
s
t. vided phase coherence is conserved at the macroscopic phase everywhere and a shift of φ0/2 in the Ic(φ) re-
a scale [1, 2]. One example is the rf-SQUID, i.e. a su- lationship is expected [14, 15]. When 2πLI >>φ , the
c 0
m
perconducting ring interrupted by a Josephsonjunction. Josephsonpartofthe free energydominates anda phase
- In a rf−SQUID quantum tunneling between two differ- gradientthroughoutthe loop favoredthereby generating
d
ent macroscopic states corresponding to either zero or aspontaneousfluxof±φ /2. Thespontaneoussupercur-
n 0
o one quantum flux in the ring has been observed in the rent can circulate clockwise and counterclockwise with
c past [3, 4]. More recently, it was shown that when exactly the same energy [13]. Applying a small mag-
[ threeJosephsonjunctions areintroducedinthe ring,the netic field can lift this degeneracy and defines an easy

1 ground state is two-fold degenerate for an applied half magnetizationdirection. The existence of a spontaneous
v quantum flux [5]. These two macroscopic configurations supercurrent sustaining half a quantum flux in π−rings
9 correspond to clockwise or anticlockwise circulating su- has been recently shown in Nb loops interrupted by a
5 percurrent. Coherent superposition between these two ferromagnetic (PdNi) π−junction [16]. Direct scanning
4
stateshasalsobeenobserved,makingthisdeviceofgreat SQUIDmicroscopeimagingofthehalf-integervortexhas
1
0 interest for quantum electronics [6, 7, 8]. However, as also been reported in HTSC grain boundary junctions
5 shown below, clockwise or anticlockwise circulating su- [17, 18]. Analogously, a highly damped single Josephson
0 percurrent can occur spontaneously (i.e. in zero applied junction fabricated with a 0 and a π region in parallel
/
t magnetic field) when the three junctions in the ring are shoulddisplayaspontaneoushalfquantumvortexatthe
a replaced by one π−junction (π−SQUID). 0−π boundary [13].
m
We detect a spontaneous supercurrent by measuring
In this Letter, we show that the macroscopic ground
-
thephasegradientwithanotherJosephsonjunction. The
d state ofaferromagneticJosephsonjunction shortedby a
n 0weaklinkmimicsthatofasuperconductingπ−SQUID. ferromagnetic junction (source) and the detection junc-
o tion(detector)arecoupled,asshowninFig.1(a),byshar-
Specifically, it is doubly degenerate,so that half a quan-
c ing an electrode. I.e., the top electrode of the conven-
: tumvortexφ0/2orhalfaquantumantivortex−φ0/2ap-
v tional Josephson junction is simultaneously the bottom
pearsinthejunction. Weinvestigatetheclassicallimitof
i electrode of the ferromagnetic one. If half a quantum
X this two-level system, which behaves macroscopically as
vortex is spontaneously generated in the ferromagnetic
r a magnetic nanoparticle of quantized flux, the magnetic
a junction, the spontaneous supercurrent that sustains it
anisotropy axis being defined by the junction plane.
circulates in the common electrode [Nb2, Fig.1(a)] pro-
π−junctions can be viewed as weak links character- ducing a phase variation equal to π/2. A φ /4−shift of
0
ized by an intrinsic phase difference across them equal
the detection junction’s diffraction pattern is thus pro-
to π [9, 10, 11, 12]. As a consequence, a π−junction
duced. When an external magnetic field is applied, the
in a superconducting loop is a phase bias generator that
diffractionpatternofthe detectionjunction is givenby:
produces a spontaneous current and hence a magnetic
flux [13]. In the limit 2πLIc<φ0, where Ic is the junc- sinhφπ0(ksJs+k′φ′+φ)i
tion critical current and L is the self-inductance of the I(B)=I(0) (1)
loop, the free energy is dominated by its magnetostatic hφπ0(ksJs+k′φ′+φ)i
2
Thisprocedureresultsinajunctioncriticaltemperature,
T , equal to 8.5K. Typical junction normal state resis-
cj
tances are of the order of 0.1−1Ω and critical current
valuesareof1−10mAat4.2K.Theresultingcriticalcur-
rentdensity is ∼1−10−1 A/cm2 leading to a Josephson
penetration depth λ ≥ 1mm, i.e. larger than the size
j
of the junction (small limit). The I-V characteristic of
a typical detector is shown in Fig.1(b). The Nb2 layer
actsasboththecounterelectrodeofthebottomdetection
junction and the base electrode of the top ferromagnetic
junction. Its thickness is comparable to the Nb pene-
tration depth to insure good coupling between the two
junctions. The same procedure is used to prepare the
top planar Nb/PdNi/Nb/Al junction. Specifically, af-
ter defining the same junction area by evaporating 500˚A
thickSiOlayers,aPdNilayerwasevaporateddirectlyon
the Nb layer, without any Al-oxide barrier. This results
FIG.1: (a)Schematiccrosssectionofthedevice: aNbbased in a very large critical current and very small junction
Josephson junction (detector) is coupled to a ferromagnetic resistance [19]. An estimate of the critical current den-
(PdNi)junction(source)bysharingoneelectrode(Nb2). The
sity is 104 −105 A/cm2, so the Josephson penetration
red-colored closed loop indicates the half quantum vortex’s depth λ < 10−2mm≪D. Hence the ”source” ferro-
location. (b)I-Vcharacteristicofthedetectorat1.5Kinzero jf
magnetic junction is in the ”large limit” with a large
appliedexternalfield. (c)Scanningelectronmicroscopeimage
of the ferromagnetic junction edge area. The black spots are screening capability. The junction was closed by a 100˚A
inhomogeneitieswhichpreventPdNicontinuityinducinga0- thick Nb layer backed by a 750˚A thick Al layer, result-
coupling region. inginacriticaltemperature,T ,of3.6K.Asthecritical
cf
temperature of the detector was higher than that of the
source, its diffraction pattern could be measured with
′ ′
where φ = BDt and φ = BDt are the magnetic fluxes and without spontaneous supercurrents. The Ni concen-
throughtheferromagneticanddetectionjunctionrespec- tration was checked by Rutherford backscattering spec-
′
tively, with D the junction width, t and t the effective trometryonPdNisamplesevaporatedinthesamerunas
barrier thickness. Js is the spontaneous supercurrent the junctions and was equal to 9%, corresponding to an
density, k = (µ0λL(T)2)D and k′ = (µ0λL(T)2) D , exchangeenergy,E ,of10.5meVanda0toπ−coupling
s 2 L wdNb2 ex
with µ0 the vacuum permittivity, λL(T) the Nb London transition for d0−π ∼75˚A.
penetration depth, L the ferromagnetic junction induc- An intrinsic feature of our fabricationtechnique is the
tance, w the junction length and d the thickness of formationofinhomogeneities atthe window edges of the
Nb2
the commonelectrode,assumedto be of the orderofthe ferromagnetic junction [see Fig.1(c)]. SEM images and
London penetrationdepth. The term k J generates the AFM analysis [20] have revealed bubbles [black spots in
s s
shift due to the spontaneous supercurrent contribution, Fig.1(c)] with diameter of about 2 − 3µm and rough-
while the term k′φ′ reduces the diffraction pattern pe- ness up to 1000˚A much higher than the PdNi thickness.
riod as a result of the contribution due to the screening These inhomogeneities have been observed in all sam-
current in the ferromagnetic junction. ples andthey may produceshortsthroughthe ferromag-
Samples are fabricated by e-gun evaporation in an ul- neticlayerresultingina0−couplingatthejunctionedge,
trahighvacuum(UHV)systeminatypicalbasepressure independently from the PdNi layer thickness. There-
of 10−9mbar. The whole device is fabricated completely fore, 0−junctions and 0−π junctions are obtained with
in situ by shadow masks. The maximum degree of mis- PdNi layer thickness corresponding to 0−coupling and
alignmentis100µm. Depositionratesaremonitoredbya π−coupling, respectively.
quartz balance with 0.1˚A/s resolution. First the bottom Measurements were made in a 4He flow cryostat.
planar Nb/Al/Al O /Nb detection junction is made. A Residual fields were screened by cryoperm and µ-metal
2 3
1000˚A thick Nb strip [Nb1, Fig.1(a))] is evaporated and shields. All measurements showed comparable residual
backed by 500˚A of Al. An Al O oxide layer is achieved fields at 4.2K of some tenths of mG. Depending on the
2 3
byoxygenplasmaoxydationduring12min,completedin PdNi layer thickness, the ferromagnetic junction is ei-
a 10 mbar O partial pressure during 10 min. A square ther 0 or π while a spontaneous half quantum vortex
2
window of 0.6× 0.8mm2 (D × w), obtained by evapo- or antivortex is expected only for π−coupling. This is
rating 500˚A thick SiO layers, defines the junction area. the main result of our experiment as reported in Fig.2,
Then,a500˚AthickNblayer[Nb2,Fig.1(a)]isevaporated where we show the diffraction patterns of three samples
perpendicular to the Nb/Al strip to close the junction. for PdNi thickness equal respectively to 40˚A, 100˚A and
3
16
4 ψ a 14 a
a dPdNi = 40A
3 b c %) 12
mA) dPdNi age ( 10
I ( 2 ent 8
c 6
1 per
4
0 2
φ
0 b 0
4 4 dPdNi = 100A b
2 dPdNi=40A
mA) 3 T (K) 3 ddPPddNNii==120000AA
I ( 2
4 Tcf
1
-0.4 -0.2 0.0 0.2 0.4
0 shift (φ0)
3 c
dPdNi = 200A FIG. 3: (a) Amplitude histograms (red bars) of the sponta-
neous shift for 26 different cooldowns from room tempera-
A) 2 ture of different samples, and their best Gaussian fits (black
m curves). The Gaussians have mean values of +0.24φ0 and
(
I −0.26φ0, with dispersions equal to ±0.03φ0. (b) Temper-
1 ature dependence of the spontaneous shift for the samples
of Fig.2: d ≃ 40˚A (black circles), d ≃ 100˚A (red
PdNi PdNi
square) and d ≃ 200˚A (open circles). The spontaneous
PdNi
0
half quantum flux appears below the ferromagnetic junction
-2 -1 0 1 2
φ/φ superconductingtransition temperature, Tcf.
0
FIG. 2: Detector diffraction patterns for sources with
sourceandthedetectorweredecoupledbyathininsulat-
d ∼ 40˚A−100˚A−200˚A, corresponding respectively to
PdNi inglayer. Thisindicatesthatordinaryinductivecoupling
0−coupling (a)−(c) and π−coupling (b). Measurements are
between the two junctions is negligible. Regarding the
taken at T = 4.2K>T (red data) and T = 2K<T (bleu
cf cf
data). Aφ0/4−shiftofthemaximumcriticalcurrentappears possible effect of an external residual field or the mag-
in the (b) case, where a 0−π coupling region is realized at netic layer itself on the spontaneous supercurrents, it is
theferromagneticjunctionedge. Inset: Oscillatingbehaviour importanttostressthattheshifts arealwaysaboutφ /4
0
of the order parameter as function of dPdNi. for π−coupling and zero for 0−coupling. Since this de-
pendsneitherontheresidualfieldnor,for0−coupling,on
the thicknessofthe ferromagneticlayer,anyeffectofthe
200˚A at T = 4.2K (red data) and T = 2K (bleu data). PdNi magnetic moment on the amplitude of the sponta-
For0−coupling[40˚Aand200˚A,Fig.2(a)andFig.2(c)re- neous supercurrents can be ruled out. The PdNi mag-
spectively]atT <T ,the periodisreducedbutnoshift netic structure only lifts the degeneracy of the ground
cf
occurs in the detector diffraction pattern. The magnetic state andpolarizesthe supercurrents. As a consequence,
field corresponding to a quantum flux is 300mG. On the thesignshiftisalwaysthesamebelowtheCurietemper-
other hand, for π−coupling [100˚A, Fig.2(b)] the period ature(∼100K),indicatingthesamespontaneouscurrent
reductionis accompaniedby a shiftof φ /4 inthe detec- polarization.
0
tor,asexpectedforaspontaneoushalfquantumvortexin Whencoolingdownfromroomtemperatureto2K,the
the ferromagnetic junction. The period reduction at the shift, while reproducible in magnitude, becomes random
lowest temperature (2K) for all the samples was about in sign as shown in Fig.3(a). The gaussian distribution
15%. This value results from two competing effects: a functions used to approximate these distributions show
smaller period is expected because of screening in the mean values of +0.24φ and −0.26φ with equal disper-
0 0
ferromagneticjunction asshownineq.1,whereasthe de- sions of ±0.03φ . This is the expected behavior of a
0
crease in the penetration depth, λ(T), at lower temper- two−fold degenerate ground state corresponding to ei-
atures should increase the modulation period. We found ther half a quantum flux or half a quantum antiflux in
no period reductionor diffractionpatternshift when the theferromagneticjunction. Thesamedistributionwould
4
In conclusion, we have probed the ground state of
0.3 highly damped ferromagnetic 0−π junctions by a phase
sensitive technique. The samples were directly coupled
0.2
toadetectionjunctionwithahighercriticaltemperature
0.1 via a shared electrode. The spontaneous supercurrent,
φhift ()0 0.0 psursotdauinceindgahφalf/4a−qsuhainfttuinmthvoerdteexteicntiothneju0n−ctπionjudnicfftrioanc-,
s 0
-0.1 tionpatternbelowtheferromagneticjunctiontransition.
Although equal in magnitude, the shifts were random in
-0.2
directionfordifferentcooldowns,asaresultofthedoubly
-0.3 degenerategroundstateofthe0−πjunction,correspond-
ing to equal vortex or antivortex probabilities. Thus a
-1.0 0.0 1.0
0−π Josephson junction is a macroscopic realization of
applied magnetic field (φ)
0 a two-level system and behaves in the classical limit as
a single magnetic domain with uniaxial anisotropy. It
FIG. 4: Field cooled measurements for a half and an integer
wouldbe interesting to investigate the quantumlimit by
quantumfluxappliedtotheferromagneticjunctioninthedi-
reducingthetemperatureandthebarrierheightbetween
rectionoppositetothespontaneoushalfquantumfluxduring
the two potential wells.
cooldown through T .
cf
We are indebted to A. Bauer and C. Strunk for sug-
gesting the field-cooled compensation and E. Reinwald
be expected for a magnetic nanoparticle with a signifi- for performing a detailed AFM study on our samples.
cant uniaxial magnetic anisotropy. The large dispersion We also thank H. Pothier, A. Buzdin, E. Goldowin, J.
in shifts can be related to an intrinsic limit of the device Lesueur for stimulating discussions; S. Collin for tech-
itselfsincethesamedispersionisobservedwhenmeasur- nical assistance and H. Bernas for a critical reading of
ingdeviceswithuniform0−couplingferromagneticjunc- the manuscript. This work has been partially founded
tion,wherethemeanshiftvalueis0. At2K,thethermal by ESF through the ”π−shift” program.
activation energy (K T ≃ 0.2meV) is negligible with re-
b
specttothe Josephsonenergy(E = Icφ0 ≃105−106eV
J 2π
for J ∼ 104 −105A/cm2 and a junction area, D ×w,
c
of 0.48mm2) and hence no hopping between the two po-
∗
Electronic address: [email protected]
tential walls can occur. Fig.3(b) shows the temperature
[1] A.O. Caldeira and A.J. Leggett, Ann.Phys. 149, 347,
dependenceoftheshiftmeasuredforthejunctionswhose
(1983).
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duringcoolingdownthroughT (Field-Cool(FC)).This
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+φ /4 (red and black circles) or −φ /4 (open circles).
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0
1373, (1999).
positetothespontaneousflux,thescreeningcurrentand
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the spontaneous ones add up, inducing a net flux equal
Phys. Rev.B 68, 054531, (2003).
to half a quantum in the direction opposite to the spon-
[20] M. Aprili et al., Proceeding of NATO Adwanced Re-
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