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PRL 104, 246804 (2010) PHYSICAL REVIEW LETTERS 18 JUNE 2010
Ferromagnetic Proximity Effect in a Ferromagnet–Quantum-Dot–Superconductor Device
L. Hofstetter,1 A. Geresdi,2 M. Aagesen,3 J. Nygard,3 C. Schonenberger,1 and S. Csonka1,2,*
˚ ¨
1
Department of Physics, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland
2
Department of Physics, Budapest University of Technology and Economics, Budafoki ut 6, 1111 Budapest, Hungary
3
Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen, Denmark
(Received 16 October 2009; published 18 June 2010)
The ferromagnetic proximity effect is studied in InAs nanowire based quantum dots strongly coupled to
a ferromagnetic (F) and a superconducting (S) lead. The influence of the F lead is detected through the
splitting of the spin-1=2 Kondo resonance. We show that the F lead induces a local exchange field on the
quantum dot, which has varying amplitude and sign depending on the charge states. The interplay of the F
and S correlations generates an exchange field related subgap feature.
DOI: 10.1103/PhysRevLett.104.246804 PACS numbers: 85.35.Gv, 72.15.Qm, 72.25.Àb, 74.45.+c
Superconductor-ferromagnet (S=F) heterostructures (NWs). NWs are dissolved in 2-propanol and deposited
have been investigated extensively in the past and they on doped Si substrates with 400 nm insulating SiO2 .
have a potential impact on the field of spintronics and Afterwards, Ohmic contacts at spacings of 300–500 nm
quantum computation. Because of the different spin order- are fabricated. The F contacts consist of a Ni=Co=Pd
ing of an s-wave superconductor and a ferromagnet, a large trilayer (15 nm=80 nm=10 nm), whereas the S ones con-
variety of interesting phenomena can be studied at a S=F sist of a Ti=Al bilayer (10 nm=110 nm). Prior to metal
interface: probing the spin polarization by Andreev reflec- evaporation, argon gun sputtering is used to remove the
tion [1], -junction behavior [2,3], ferromagnetically in- native oxide layer from the nanowires. In agreement with
duced triplet superconductivity [4], or ferromagnetically our previous measurements, QDs form between these con-
assisted Cooper pair splitting [5]. tacts, which can be tuned by the voltage applied on the
Here we focus on a novel S=F hybrid device where a back gate, VBG [17,18]. Measurements are performed at a
quantum dot (QD) is incorporated between a S and a F temperature of 25 mK. A B field is applied parallel to the
lead. Recently, the modification of the Andreev reflection easy axis of the F contact which is defined by shape
of such hybrid systems has been calculated [6,7]. Also anisotropy [see Fig. 1(a)]. The B field allows us to switch
configurations, where a QD is strongly coupled to two F the orientation of the F stripe and to control the size of the
leads (F-QDot-F) attracted increasing theoretical [8–11] superconducting gap. To magnetize the F lead the external
and experimental [12–15] attention. It has been verified field is ramped to B ¼ þ300 mT and then back to B ¼
[13–15] that in this situation the spin- " and # energy levels 0 mT before measuring.
of the QD can split by an exchange energy, Eex due to the In Fig. 1(b) the energy diagram of our devices is shown
hybridization between the QD states and the F lead. This schematically. The F lead induces an asymmetry of the
proximity ferromagnetism has the same effect on the QD tunnel coupling (À) of spin- " and spin- # electrons to
as the presence of an external magnetic field, B. Thus, the the QD, described by the tunneling spin polarization
exchange splitting is often characterized by the so-called
local magnetic exchange field (Bex ) in the literature, where E εd ~ 0
a) b) c)
Eex ¼ gB Bex . As has been proposed by Martinek et al.
U
↓
U +∆
[16], Bex can be gate dependent and even change sign.
↑
Hence, electric controlled reversal of the spin occupation EF
Eex
εd ~ -U
B −∆
of the QD can be achieved. This has very recently been
shown in carbon nanotubes with two F contacts [15]. F S U
In this Letter, we show the influence of F and S corre-
lations on the transport properties of F-QD-S devices. We
demonstrate that already a single F lead introduces a local FIG. 1 (color online). (a) A scanning electron microscopy
exchange field which strongly varies for different QD picture of a device. The right lead is a Ti=Al bilayer supercon-
ductor, while the left longer one is a Ni=Co=Pd trilayer ferro-
levels. Furthermore, it even can change its sign within
magnet. The B field is applied parallel to easy axis of the F lead.
the same charge state. On the other hand, the presence of (b) Schematic view of the F-QDot-S system. The spin degener-
the S contact serves as a spectroscopic tool. Concentrating acy on the QD is lifted by an exchange splitting induced by the
on the subgap transport, a novel minigap feature is ob- ferromagnetic proximity effect. (c) Because of the spin polarized
served, which is related to Bex . charge fluctuations, the spin ground state of the QD is opposite
A typical device is shown in Fig. 1(a). We use high- when the occupation of the highest orbital level fluctuates
quality molecular beam-epitaxy grown InAs nanowires between 1 and 0 (d % 0) or 1 and 2 (d % ÀU).
0031-9007=10=104(24)=246804(4) 246804-1 Ó 2010 The American Physical Society
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PRL 104, 246804 (2010) PHYSICAL REVIEW LETTERS 18 JUNE 2010
P ¼ ðÀ" À À# Þ=ðÀ# þ À" Þ. This asymmetry is caused by the In Fig. 2(a) the differential conductance as a function of
difference of the spin- " and spin- # electron density of the VBG and source drain voltage Vsd , GðVBG ; Vsd Þ, of several
F lead at the Fermi energy and by the tunneling matrix charge states of a studied F-QD-S device is presented.
elements of these electrons. E.g., in Ni two bands contrib- Measurements were performed with a standard lock-in
ute at EF with opposite spin imbalance and very different technique with an ac excitation of 4 eV. In accordance
tunneling matrix elements to the QD [19]. By hybridiza- with the spin-1=2 Kondo effect, pronounced conductance
tion, the spin dependent tunnel coupling generates a spin is seen around (Vsd ¼ 0 V) in every odd charge state.
imbalance on the QD, described as an exchange field. The However, in these states (labeled with numbers 1, 3, 5, 7)
S lead is represented by the BCS density of states with its the Kondo resonance shows different signatures due to
energy gap, Á. correlations induced by the F lead. State 7 demonstrates
In order to investigate the ferromagnetic proximity ef- a spin-1=2 Kondo situation with a single resonance line at
fect, the QD is operated in the strongly coupled regime, Vsd ¼ 0 V. As it is shown in Fig. 2(b) this zero bias Kondo
which allows the study of the cotunneling induced many resonance splits up linearly with B. In contrast, state 3
body spin-1=2 Kondo resonance [20] at odd occupation exhibits a clear signature of F correlations; i.e., the Kondo
number of the QD. Kondo resonances split into a doublet in resonance has a finite and roughly constant splitting at B ¼
a B field according to the Zeeman energy E#=" ¼ 0 mT (see black cross section). Figure 2(c) shows that this
Ç1=2gB B, thus being also a sensitive tool to visualize splitting is compensated by B % 64 mT and split again at
Bex . Probing the exchange splitting by the Kondo effect has higher B fields. Thus Bex has an opposite sign as the B field.
been demonstrated in C60 molecule [13] and carbon nano- Another type of B dependence of the Kondo ridge is
tube based QDs [15]. InAs NW QDs have the advantage presented in Fig. 2(d) (measured at VBG ¼ 2:31 V), where
that the g factor can be comparable to the bulk value of the zero field splitting of the resonance is further increased
jgj % 15 [17], making them particularly sensitive for by an applied B field. It means that Bex is parallel to B for
studying the level splitting created by Bex . Much smaller this state. The three markedly different B field behaviors
external fields are needed to access the regime, where the [Figs. 2(b)–2(d)] demonstrate that Bex strongly depends on
exchange energy and the Zeeman splitting are comparable. the QD level. Even in a small back gate range the ampli-
The ferromagnetic proximity effect and the therewith tude and the sign of Bex varies. This observation highlights
connected ground state transition on the QD can be de- the particular importance of the coupling of the QD state to
scribed in a simple model. Using perturbative scaling the F lead for the charge fluctuations induced local ex-
analysis for a flatband band structure with spin dependent
tunneling rates and including finite Stoner splitting of the
a) 0.10 G [G0]
leads, an analytical formula for the energy splitting of the B=0T 0.75
spin- " and the spin- # is found [16]: 0.05
0.57
eVsd ¼ gB B þ Á0 þ ðPÀ=Þ lnðjd j=jU þ d jÞ: (1)
Vsd [mV]
+∆
0.00
0.40
Here P is as defined earlier, À is the coupling to the F lead −∆
(À ¼ À" þ À# ), U the charging energy of the QD, and d -0.05 0.22
the level position of the QD, tunable by VBG . gB B is the
-0.10 1 2 3 4 5 6 7 0.05
Zeeman splitting due to an external magnetic field, and Á0 1.075 1.165 1.255 1.345 1.435 1.525
is a Stoner splitting induced shift. Elaborated numerical VBG [V]
renormalization group method calculations also support
the result of Eq. (1) [16]. Interestingly, based on Eq. (1), b) Bex=0 c) Bex0
Vsd
Vsd
Vsd
the spin ground state of the QD is different for d close to 0
than for d close to ÀU, if Á0 or the Zeeman term are not 0.3 0.25
0.2
too big. This change in the ground state of the QD can be
Vsd [mV]
Vsd [mV]
Vsd [mV]
0.0 0.00
explained by the charge fluctuations between the QD and 0.0
the F lead [see Fig. 1(c)]. Electrons with majority tunnel- -0.2
7 -0.25
-0.3 3
ing spin orientation dominate the charge fluctuations. 0.00 0.10 0.20 0.00 0.20 0.40 0.00 0.125 0.25
Thus, when the QD occupation fluctuates between 1 and B [T] B [T] B [T]
0 (d % 0), the majority tunneling spin occupies the QD
preferably. However, when the occupation fluctuates be- FIG. 2 (color online). (a) Differential conductance as a func-
tion of VBG and Vsd of a F-QD-S device at B ¼ 0 T. Bex
tween 1 and 2 (d % ÀU), the remaining (nonfluctuating)
modifies the Kondo resonances (odd numbered states) differ-
spin on the QD has the minority spin orientation of the ently. The S lead induces peaks in the conductance at Vsd ¼ ÆÁ.
tunneling electrons [15,16]. The transition between these B dependence of different charge states: (b) with no signature of
opposite ground states is described by the sign change of Bex [state 7 in Fig. 2(a)], (c) with Bex 0, which is
nant term, a roughly constant splitting of the Kondo reso- enhanced by B. Panel (d) is measured in a charge state at VBG ¼
nance is expected within a charge state. 2:31 V.
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PRL 104, 246804 (2010) PHYSICAL REVIEW LETTERS 18 JUNE 2010
0.1 0.2 0.3 0.13 0.44 0.75 0.05 0.25 0.45
change field [16]. Note that the different B dependencies a)
1.2
G [G0]
b) G [G0] G [G0]
0.9
0.9
also prove that the observed effect cannot solely be de- 1 2, εd = -U 0.6
B=0.1T
0.6
B=0.2T
scribed by a stray field, since the stray field cannot depend
Vsd [mV]
Vsd [mV]
0.3 0.3
VBG [V]
0.0 0.0
on VBG . 1.1
-0.3 -0.3
The most interesting class among the different exchange 0 1, εd = 0 -0.6
1
-0.6
-0.9 -0.9 1
field manifestations is the one of state 1 [see Fig. 2(a)]. The -0.3 -0.1
B [T]
0.1 0.3 1.06 1.10 1.14
VBG [V]
1.05 1.10 1.15
VBG [V]
Kondo resonance is also split for this state. However, the
c) 400 mT
280 mT
size of the splitting strongly varies with VBG . [The reso- 0.4 200 mT
100 mT
G [G0]
0.05 0.20 0.35
G [G0]
0.13 0.38 0.63
nance lines are highlighted with dashed lines in Fig. 2(a).] 0 mT 0.9
0.6
B=0.28T 0.9
B=0.4T
0.6
Interestingly, the split Kondo resonance lines also cross the 0.2
Vsd [mV]
Vsd [mV]
Vsd [mV]
0.3 0.3
Vsd ¼ 0 mV value inside the charge state. This depen- 0.0
0.0 0.0
-0.3 -0.3
dence suggests that within this charge state Bex first gets -0.6 -0.6
1 1
smaller as VBG is increased. With further increasing VBG it -0.2
0.25 0.5 0.75
-0.9
1.08 1.13 1.18
-0.9
1.08 1.13 1.18
changes its sign and increases further in the opposite −εd /U VBG [V] VBG [V]
direction. This situation corresponds to the electrically
controlled ground state transition on the QD described by FIG. 3 (color online). Measurements on state 1. (a) Differential
conductance as a function of VBG and B measured at Vsd ¼
Eq. (1) and Fig. 1(c).
0 mV. The two horizontal ridges (dotted lines) are the charge
Since Bex in situations like state 1 of Fig. 2(a) is strongly state boundaries. The high conductance ridge is the restored
gate dependent, a measure for the exchange splitting at Kondo resonance, where B ¼ ÀBex ðVBG Þ. This ridge separates
different gate voltages can be obtained by measuring the the regions where spin- " or spin- # is the ground state. The white
compensation field for which the Kondo peak is restored. line is a plot based on Eq. (1) using the parameters obtained from
Thus, if one measures GðVBG ; BÞ at Vsd ¼ 0 mV, at each the fits shown in (c). The white arrow shows the sweeping
VBG signatures of high conductance are expected if B ¼ direction of B. The black arrow points out the position where
ÀBex ðVBG Þ due to the restored Kondo resonance. Such a the magnetization of the F lead changes sign. (b) Color scale
plot is presented in Fig. 3(a). The lower or upper ridge (see plots at different magnetic fields. The dashed line highlights the
dashed lines) defines the resonance positions when the position of the tilted Kondo resonance at B ¼ 0:2 T. (c) The
occupation of the QD level changes between 0 $ 1 and evolution of the Kondo resonance is presented for different B
fields by symbols. The lines are fits using Eq. (1).
1 $ 2. The white arrow indicates the sweep direction of B.
The high conductance lines with finite slope show the
evolution of the Kondo resonance (marked with a white spin orientation on the QD is the majority tunneling spin
line). At each B field the gate position of the restored orientation [see Fig. 1(c)] [15,16]. Since the F lead has
Kondo resonance defines the border between the spin- " been previously polarized into a spin- # state by a positive
and the spin- # ground states. At high external magnetic B field, we can conclude that the polarization of the F lead
fields (i.e., B ! 0:3 T) the Zeeman term dominates [see and the polarization of tunneling electrons are the same.
Eq. (1)]. Therefore, considering that the g factor of InAs is Equation (1) describes the energy difference between
negative, the spin- " is the ground state for all gate values in the spin- " and the spin- # states as a function of VBG . This
high field and the Kondo resonance coincides with the is equivalent to the energy (eVsd ), where the Kondo ridge
border at d ¼ 0. As the B field decreases the restored appears. GðVBG ; Vsd Þ of state 1 is also measured in different
Kondo peak moves towards d ¼ ÀU, opening back gate magnetic fields. As is seen in Fig. 3(b), the position of the
regions where spin- # is the ground state. At B ¼ 0 mT the more pronounced split Kondo line moves to higher source
spin- # state dominates, and spin- " remains only in a small drain voltage values as B is increased. The (VBG , Vsd )
gate region around d ¼ ÀU, the preferable spin orienta- coordinates of this line are read out from the measure-
tion. The gate voltage value as a function of B, where the ments; see, e.g., the dotted line for B ¼ 0:2 T. Figure 3(c)
spin ground state change takes place, can be expressed with summarizes the measured position of the Kondo ridge by
Eq. (1) using the condition of eVsd ¼ 0. The white line in symbols at different B fields. The theory described by
Fig. 3(a) shows such a curve, giving a reasonable agree- Eq. (1) nicely fits the experiment (see lines) with the
ment with the measurement using the parameters of jgj ¼ parameters used for the plot in Fig. 3(a).
12:3, Á0 ¼ À90 mT, and PÀ ¼ 0:22 meV. Since our device has a novel hybrid configuration, i.e., a
As the polarization of the F lead is switched to the QD connected to one F and one S lead, the interplay of S
opposite direction by a B field larger than the coercive and F correlations can be studied. Up to this point, charge
field of the contact, Bex also changes its sign. This appears states with Kondo physics were investigated, where the
as a step in the GðVBG ; BÞ measurement [see Fig. 3(a)] Kondo resonance dominates the low energy behavior also
since the splitting turns from gB ðB þ Bex Þ to gB ðB À for the S state. For such states the S lead induces conduc-
Bex Þ. Because of the high g factor of the InAs QD state, this tance maxima at Vsd ¼ ÆÁ related to the singularities of
is clearly seen in Fig. 3(a) at the position of the black arrow. the S density of states, which diminish with increasing B
Note that in the vicinity of the 0 $ 1 border at B ¼ 0 mT, field. However, in several charge states of different devices,
the ground state is spin- # . At this border the preferable where spin-1=2 Kondo resonances are not present (neither
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PRL 104, 246804 (2010) PHYSICAL REVIEW LETTERS 18 JUNE 2010
0.05 0.18 0.32 0.45
0.18 0.24 0.30 0.36
a) G [G0] b) G [G0] Danish Natural Science Research Council, the OTKA-
0.3 e o e Norwegian Financial Mechanism NNF 78842, OTKA
0.2 0.2
∆ ∆ 72916, and the EU M.C. 41139 projects. S. C. was sup-
0.1
Vsd [mV]
Vsd [mV]
ported by a Bolyai Janos grant.
0.0 0.0
-0.1
−∆ −∆
-0.2
-0.2
-0.3
0.00 0.05 0.10 0.15 11.15 11.20 11.25 11.30
B [T] VBG [V]
*To whom correspondence should be addressed.
csonka@dept.phy.bme.hu
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by the Swiss NSF, the NCCR on Nanoscale Science, the (2010).
246804-4