By measuring the current–voltage characteristics and the switching current distributions as a function of temperature, we have investigated the phase dynamics of Al tunnel ferromagnetic Josephson junctions (JJs), designed to fall in the typical range of parameters of state-of-the-art transmons, providing evidence of phase diffusion processes. The comparison with the experimental outcomes on non-magnetic JJs with nominally the same electrodynamical parameters demonstrates that the introduction of ferromagnetic barriers does not cause any sizeable detrimental effect and supports the notion of including tunnel ferromagnetic JJs in qubit architectures.

1.
V. V.
Ryazanov
,
V. A.
Oboznov
,
A. Y.
Rusanov
,
A. V.
Veretennikov
,
A. A.
Golubov
, and
J.
Aarts
, “
Coupling of two superconductors through a ferromagnet: Evidence for a π junction
,”
Phys. Rev. Lett.
86
,
2427
2430
(
2001
).
2.
A. A.
Golubov
,
M. Y.
Kupriyanov
, and
E.
Il'ichev
, “
The current-phase relation in Josephson junctions
,”
Rev. Mod. Phys.
76
,
411
469
(
2004
).
3.
A. I.
Buzdin
, “
Proximity effects in superconductor-ferromagnet heterostructures
,”
Rev. Mod. Phys.
77
,
935
976
(
2005
).
4.
F. S.
Bergeret
,
A. F.
Volkov
, and
K. B.
Efetov
, “
Odd triplet superconductivity and related phenomena in superconductor-ferromagnet structures
,”
Rev. Mod. Phys.
77
,
1321
1373
(
2005
).
5.
M.
Weides
,
M.
Kemmler
,
E.
Goldobin
,
D.
Koelle
,
R.
Kleiner
,
H.
Kohlstedt
, and
A.
Buzdin
, “
High quality ferromagnetic 0 and π Josephson tunnel junctions
,”
Appl. Phys. Lett.
89
,
122511
(
2006
).
6.
M.
Eschrig
and
T.
Löfwander
, “
Triplet supercurrents in clean and disordered half-metallic ferromagnets
,”
Nat. Phys.
4
,
138
143
(
2008
).
7.
J. W. A.
Robinson
,
J. D. S.
Witt
, and
M. G.
Blamire
, “
Controlled injection of spin-triplet supercurrents into a strong ferromagnet
,”
Science
329
,
59
61
(
2010
).
8.
H.
Sickinger
,
A.
Lipman
,
M.
Weides
,
R. G.
Mints
,
H.
Kohlstedt
,
D.
Koelle
,
R.
Kleiner
, and
E.
Goldobin
, “
Experimental evidence of a φ Josephson junction
,”
Phys. Rev. Lett.
109
,
107002
(
2012
).
9.
B.
Baek
,
W. H.
Rippard
,
S. P.
Benz
,
S. E.
Russek
, and
P. D.
Dresselhaus
, “
Hybrid superconducting-magnetic memory device using competing order parameters
,”
Nat. Commun.
5
,
3888
(
2014
).
10.
A.
Singh
,
S.
Voltan
,
K.
Lahabi
, and
J.
Aarts
, “
Colossal proximity effect in a superconducting triplet spin valve based on the half-metallic ferromagnet CrO 2
,”
Phys. Rev. X
5
,
021019
(
2015
).
11.
J.
Linder
and
J. W. A.
Robinson
, “
Superconducting spintronics
,”
Nat. Phys.
11
,
307
315
(
2015
).
12.
E. C.
Gingrich
,
B. M.
Niedzielski
,
J. A.
Glick
,
Y.
Wang
,
D. L.
Miller
,
R.
Loloee
,
W. P.
Pratt
, Jr.
, and
N. O.
Birge
, “
Controllable 0– π Josephson junctions containing a ferromagnetic spin valve
,”
Nat. Phys.
12
,
564
567
(
2016
).
13.
S. M.
Dahir
,
A. F.
Volkov
, and
I. M.
Eremin
, “
Phase-dependent spin polarization of cooper pairs in magnetic Josephson junctions
,”
Phys. Rev. B
100
,
134513
(
2019
).
14.
A. K.
Feofanov
,
V. A.
Oboznov
,
V. V.
Bol'ginov
,
J.
Lisenfeld
,
S.
Poletto
,
V. V.
Ryazanov
,
A. N.
Rossolenko
,
M.
Khabipov
,
D.
Balashov
,
A. B.
Zorin
,
P. N.
Dmitriev
,
V. P.
Koshelets
, and
A. V.
Ustinov
, “
Implementation of superconductor/ferromagnet/superconductor π-shifters in superconducting digital and quantum circuits
,”
Nat. Phys.
6
,
593
597
(
2010
).
15.
T. I.
Larkin
,
V. V.
Bol'ginov
,
V. S.
Stolyarov
,
V. V.
Ryazanov
,
I. V.
Vernik
,
S. K.
Tolpygo
, and
O. A.
Mukhanov
, “
Ferromagnetic Josephson switching device with high characteristic voltage
,”
Appl. Phys. Lett.
100
,
222601
(
2012
).
16.
N.
Satchell
,
P.
Shepley
,
M.
Algarni
,
M.
Vaughan
,
E.
Darwin
,
M.
Ali
,
M. C.
Rosamond
,
L.
Chen
,
E. H.
Linfield
,
B.
Hickey
et al, “
Spin-valve Josephson junctions with perpendicular magnetic anisotropy for cryogenic memory
,”
Appl. Phys. Lett.
116
,
022601
(
2020
).
17.
R.
Satariano
,
L.
Parlato
,
A.
Vettoliere
,
R.
Caruso
,
H. G.
Ahmad
,
A.
Miano
,
L. D.
Palma
,
D.
Salvoni
,
D.
Montemurro
,
C.
Granata
,
G.
Lamura
,
F.
Tafuri
,
G. P.
Pepe
,
D.
Massarotti
, and
G.
Ausanio
, “
Inverse magnetic hysteresis of the Josephson supercurrent: Study of the magnetic properties of thin niobium/permalloy ( Fe 20 Ni 80) interfaces
,”
Phys. Rev. B
103
,
224521
(
2021
).
18.
H. G.
Ahmad
,
M.
Minutillo
,
R.
Capecelatro
,
A.
Pal
,
R.
Caruso
,
G.
Passarelli
,
M. G.
Blamire
,
F.
Tafuri
,
P.
Lucignano
, and
D.
Massarotti
, “
Coexistence and tuning of spin-singlet and triplet transport in spin-filter Josephson junctions
,”
Commun. Phys.
5
,
2
(
2022
).
19.
L.
Parlato
,
R.
Caruso
,
A.
Vettoliere
,
R.
Satariano
,
H. G.
Ahmad
,
A.
Miano
,
D.
Montemurro
,
D.
Salvoni
,
G.
Ausanio
,
F.
Tafuri
,
G. P.
Pepe
,
D.
Massarotti
, and
C.
Granata
, “
Characterization of scalable Josephson memory element containing a strong ferromagnet
,”
J. Appl. Phys.
127
,
193901
(
2020
).
20.
L. N.
Karelina
,
R. A.
Hovhannisyan
,
I. A.
Golovchanskiy
,
V. I.
Chichkov
,
A.
Ben Hamida
,
V. S.
Stolyarov
,
L. S.
Uspenskaya
,
S. A.
Erkenov
,
V. V.
Bolginov
, and
V. V.
Ryazanov
, “
Scalable memory elements based on rectangular SIsFS junctions
,”
J. Appl. Phys.
130
,
173901
(
2021
).
21.
H. G.
Ahmad
,
V.
Brosco
,
A.
Miano
,
L.
Di Palma
,
M.
Arzeo
,
D.
Montemurro
,
P.
Lucignano
,
G. P.
Pepe
,
F.
Tafuri
,
R.
Fazio
, and
D.
Massarotti
, “
Hybrid ferromagnetic transmon qubit: Circuit design, feasibility, and detection protocols for magnetic fluctuations
,”
Phys. Rev. B
105
,
214522
(
2022
).
22.
P.
Krantz
,
M.
Kjaergaard
,
F.
Yan
,
T. P.
Orlando
,
S.
Gustavsson
, and
W. D.
Oliver
, “
A quantum engineer's guide to superconducting qubits
,”
Appl. Phys. Rev.
6
,
021318
(
2019
).
23.
J.
Clarke
and
A. I.
Braginski
,
The SQUID Handbook: Applications of SQUIDs and SQUID Systems
(
John Wiley & Sons
,
2006
).
24.
C.
Granata
and
A.
Vettoliere
, “
Nano superconducting quantum interference device: A powerful tool for nanoscale investigations
,”
Phys. Rep.
614
,
1
69
(
2016
).
25.
H. G.
Ahmad
,
V.
Brosco
,
A.
Miano
,
L.
Di Palma
,
M.
Arzeo
,
R.
Satariano
,
R.
Ferraiuolo
,
P.
Lucignano
,
A.
Vettoliere
,
C.
Granata
,
L.
Parlato
,
G.
Ausanio
,
D.
Montemurro
,
G. P.
Pepe
,
R.
Fazio
,
F.
Tafuri
, and
D.
Massarotti
, “
Competition of quasiparticles and magnetization noise in hybrid ferromagnetic transmon qubits
,”
IEEE Trans. Appl. Supercond.
33
,
1700306
(
2023
).
26.
A.
Leggett
, “
Macroscopic quantum tunneling and related effects in Josephson systems
,” in
Percolation, Localization, and Superconductivity
(
Springer
,
1984
), pp.
1
41
.
27.
M. H.
Devoret
,
J. M.
Martinis
, and
J.
Clarke
, “
Measurements of macroscopic quantum tunneling out of the zero-voltage state of a current-biased Josephson junction
,”
Phys. Rev. Lett.
55
,
1908
1911
(
1985
).
28.
J. M.
Martinis
,
M. H.
Devoret
, and
J.
Clarke
, “
Energy-level quantization in the zero-voltage state of a current-biased Josephson junction
,”
Phys. Rev. Lett.
55
,
1543
1546
(
1985
).
29.
J. M.
Martinis
,
M. H.
Devoret
, and
J.
Clarke
, “
Experimental tests for the quantum behavior of a macroscopic degree of freedom: The phase difference across a Josephson junction
,”
Phys. Rev. B
35
,
4682
4698
(
1987
).
30.
J. M.
Martinis
, “
Superconducting phase qubits
,”
Quantum Inf. Process.
8
,
81
103
(
2009
).
31.
J.
Clarke
,
A. N.
Cleland
,
M. H.
Devoret
,
D.
Esteve
, and
J. M.
Martinis
, “
Quantum mechanics of a macroscopic variable: The phase difference of a Josephson junction
,”
Science
239
,
992
997
(
1988
).
32.
D.
Vion
,
M.
Götz
,
P.
Joyez
,
D.
Esteve
, and
M. H.
Devoret
, “
Thermal activation above a dissipation barrier: Switching of a small Josephson junction
,”
Phys. Rev. Lett.
77
,
3435
3438
(
1996
).
33.
J.
Kivioja
,
T. E.
Nieminen
,
J.
Claudon
,
O.
Buisson
,
F.
Hekking
, and
J. P.
Pekola
, “
Observation of transition from escape dynamics to underdamped phase diffusion in a Josephson junction
,”
Phys. Rev. Lett.
94
,
247002
(
2005
).
34.
T.
Bauch
,
F.
Lombardi
,
F.
Tafuri
,
A.
Barone
,
G.
Rotoli
,
P.
Delsing
, and
T.
Claeson
, “
Macroscopic quantum tunneling in d-wave YBa 2 Cu 3 O 7 δ Josephson junctions
,”
Phys. Rev. Lett.
94
,
087003
(
2005
).
35.
J.
Männik
,
S.
Li
,
W.
Qiu
,
W.
Chen
,
V.
Patel
,
S.
Han
, and
J. E.
Lukens
, “
Crossover from Kramers to phase-diffusion switching in moderately damped Josephson junctions
,”
Phys. Rev. B
71
,
220509
(
2005
).
36.
V. M.
Krasnov
,
T.
Golod
,
T.
Bauch
, and
P.
Delsing
, “
Anticorrelation between temperature and fluctuations of the switching current in moderately damped Josephson junctions
,”
Phys. Rev. B
76
,
224517
(
2007
).
37.
L.
Longobardi
,
D.
Massarotti
,
G.
Rotoli
,
D.
Stornaiuolo
,
G.
Papari
,
A.
Kawakami
,
G. P.
Pepe
,
A.
Barone
, and
F.
Tafuri
, “
Thermal hopping and retrapping of a Brownian particle in the tilted periodic potential of a NbN/MgO/NbN Josephson junction
,”
Phys. Rev. B
84
,
184504
(
2011
).
38.
L.
Longobardi
,
D.
Massarotti
,
D.
Stornaiuolo
,
L.
Galletti
,
G.
Rotoli
,
F.
Lombardi
, and
F.
Tafuri
, “
Direct transition from quantum escape to a phase diffusion regime in YBaCuO biepitaxial Josephson junctions
,”
Phys. Rev. Lett.
109
,
050601
(
2012
).
39.
D.
Stornaiuolo
,
G.
Rotoli
,
D.
Massarotti
,
F.
Carillo
,
L.
Longobardi
,
F.
Beltram
, and
F.
Tafuri
, “
Resolving the effects of frequency-dependent damping and quantum phase diffusion in YBa2Cu3O7−x Josephson junctions
,”
Phys. Rev. B
87
,
134517
(
2013
).
40.
D.
Massarotti
,
A.
Pal
,
G.
Rotoli
,
L.
Longobardi
,
M.
Blamire
, and
F.
Tafuri
, “
Macroscopic quantum tunnelling in spin filter ferromagnetic Josephson junctions
,”
Nat. Commun.
6
,
7376
(
2015
).
41.
D.
Massarotti
,
N.
Banerjee
,
R.
Caruso
,
G.
Rotoli
,
M.
Blamire
, and
F.
Tafuri
, “
Electrodynamics of Josephson junctions containing strong ferromagnets
,”
Phys. Rev. B
98
,
144516
(
2018
).
42.
V. E.
Manucharyan
,
N. A.
Masluk
,
A.
Kamal
,
J.
Koch
,
L. I.
Glazman
, and
M. H.
Devoret
, “
Evidence for coherent quantum phase slips across a Josephson junction array
,”
Phys. Rev. B
85
,
024521
(
2012
).
43.
D. Z.
Haxell
,
E.
Cheah
,
F.
Křížek
,
R.
Schott
,
M. F.
Ritter
,
M.
Hinderling
,
W.
Belzig
,
C.
Bruder
,
W.
Wegscheider
,
H.
Riel
et al, “
Measurements of phase dynamics in planar Josephson junctions and SQUIDs
,”
Phys. Rev. Lett.
130
,
087002
(
2023
).
44.
J. M.
Martinis
,
S.
Nam
,
J.
Aumentado
, and
C.
Urbina
, “
Rabi oscillations in a large Josephson-junction qubit
,”
Phys. Rev. Lett.
89
,
117901
(
2002
).
45.
D.
Massarotti
and
F.
Tafuri
, “
Phase dynamics and macroscopic quantum tunneling
,” in
Fundamentals and Frontiers of the Josephson Effect
, edited by
F.
Tafuri
(
Springer International Publishing
,
Cham
,
2019
), pp.
455
512
.
46.
E.
Gümüş
,
D.
Majidi
,
D.
Nikolić
,
P.
Raif
,
B.
Karimi
,
J. T.
Peltonen
,
E.
Scheer
,
J. P.
Pekola
,
H.
Courtois
,
W.
Belzig
et al, “
Calorimetry of a phase slip in a Josephson junction
,”
Nat. Phys.
19
,
196
200
(
2023
).
47.
W.-S.
Lu
,
K.
Kalashnikov
,
P.
Kamenov
,
T. J.
DiNapoli
, and
M. E.
Gershenson
, “
Phase diffusion in low- E J Josephson junctions at milli-kelvin temperatures
,”
Electronics
12
,
416
(
2023
).
48.
A. O.
Caldeira
and
A. J.
Leggett
, “
Influence of dissipation on quantum tunneling in macroscopic systems
,”
Phys. Rev. Lett.
46
,
211
214
(
1981
).
49.
R. L.
Kautz
and
J. M.
Martinis
, “
Noise-affected I-V curves in small hysteretic Josephson junctions
,”
Phys. Rev. B
42
,
9903
9937
(
1990
).
50.
T. A.
Fulton
and
L. N.
Dunkleberger
, “
Lifetime of the zero-voltage state in Josephson tunnel junctions
,”
Phys. Rev. B
9
,
4760
4768
(
1974
).
51.
Y. M.
Ivanchenko
and
L. A.
Zil'berman
, “
Destruction of Josephson current by fluctuations
,”
JETP Lett.
8
,
113
115
(
1968
).
52.
M.
Büttiker
,
E.
Harris
, and
R.
Landauer
, “
Thermal activation in extremely underdamped Josephson-junction circuits
,”
Phys. Rev. B
28
,
1268
(
1983
).
53.
A.
Garg
, “
Escape-field distribution for escape from a metastable potential well subject to a steadily increasing bias field
,”
Phys. Rev. B
51
,
15592
15595
(
1995
).
54.
J. C.
Fenton
and
P. A.
Warburton
, “
Monte Carlo simulations of thermal fluctuations in moderately damped Josephson junctions: Multiple escape and retrapping, switching- and return-current distributions, and hysteresis
,”
Phys. Rev. B
78
,
054526
(
2008
).
55.
M.
Iansiti
,
A. T.
Johnson
,
W. F.
Smith
,
H.
Rogalla
,
C. J.
Lobb
, and
M.
Tinkham
, “
Charging energy and phase delocalization in single very small Josephson tunnel junctions
,”
Phys. Rev. Lett.
59
,
489
492
(
1987
).
56.
V. M.
Krasnov
,
T.
Bauch
,
S.
Intiso
,
E.
Hürfeld
,
T.
Akazaki
,
H.
Takayanagi
, and
P.
Delsing
, “
Collapse of thermal activation in moderately damped Josephson junctions
,”
Phys. Rev. Lett.
95
,
157002
(
2005
).
57.
A.
Vettoliere
,
R.
Satariano
,
R.
Ferraiuolo
,
L.
Di Palma
,
H. G.
Ahmad
,
G.
Ausanio
,
G. P.
Pepe
,
F.
Tafuri
,
D.
Massarotti
,
D.
Montemurro
et al, “
High-quality ferromagnetic Josephson junctions based on aluminum electrodes
,”
Nanomaterials
12
,
4155
(
2022
).
58.
A.
Vettoliere
,
R.
Satariano
,
R.
Ferraiuolo
,
L.
Di Palma
,
H. G.
Ahmad
,
G.
Ausanio
,
G. P.
Pepe
,
F.
Tafuri
,
D.
Montemurro
,
C.
Granata
,
L.
Parlato
, and
D.
Massarotti
, “
Aluminum-ferromagnetic Josephson tunnel junctions for high quality magnetic switching devices
,”
Appl. Phys. Lett.
120
,
262601
(
2022
).
59.
J.
Majer
,
J. M.
Chow
,
J. M.
Gambetta
,
J.
Koch
,
B. R.
Johnson
,
J. A.
Schreier
,
L.
Frunzio
,
D. I.
Schuster
,
A. A.
Houck
,
A.
Wallraff
,
A.
Blais
,
M. H.
Devoret
,
S. M.
Girvin
, and
R. J.
Schoelkopf
, “
Coupling superconducting qubits via a cavity bus
,”
Nature
449
,
443
447
(
2007
).
60.
L.
DiCarlo
,
J. M.
Chow
,
J. M.
Gambetta
,
L. S.
Bishop
,
B. R.
Johnson
,
D. I.
Schuster
,
J.
Majer
,
A.
Blais
,
L.
Frunzio
,
S. M.
Girvin
, and
R. J.
Schoelkopf
, “
Demonstration of two-qubit algorithms with a superconducting quantum processor
,”
Nature
460
,
240
244
(
2009
).
61.
W. D.
Oliver
and
P. B.
Welander
, “
Materials in superconducting quantum bits
,”
MRS Bull.
38
,
816
825
(
2013
).
62.
H.
Ahmad
,
R.
Caruso
,
A.
Pal
,
G.
Rotoli
,
G.
Pepe
,
M.
Blamire
,
F.
Tafuri
, and
D.
Massarotti
, “
Electrodynamics of highly spin-polarized tunnel Josephson junctions
,”
Phys. Rev. Appl.
13
,
014017
(
2020
).
63.
J.
Koch
,
T. M.
Yu
,
J.
Gambetta
,
A. A.
Houck
,
D. I.
Schuster
,
J.
Majer
,
A.
Blais
,
M. H.
Devoret
,
S. M.
Girvin
, and
R. J.
Schoelkopf
, “
Charge-insensitive qubit design derived from the Cooper pair box
,”
Phys. Rev. A
76
,
042319
(
2007
).
64.
D.
Massarotti
,
D.
Stornaiuolo
,
P.
Lucignano
,
L.
Galletti
,
D.
Born
,
G.
Rotoli
,
F.
Lombardi
,
L.
Longobardi
,
A.
Tagliacozzo
, and
F.
Tafuri
, “
Breakdown of the escape dynamics in Josephson junctions
,”
Phys. Rev. B
92
,
054501
(
2015
).
65.
H. F.
Yu
,
X. B.
Zhu
,
Z. H.
Peng
,
Y.
Tian
,
D. J.
Cui
,
G. H.
Chen
,
D. N.
Zheng
,
X. N.
Jing
,
L.
Lu
,
S. P.
Zhao
, and
S.
Han
, “
Quantum phase diffusion in a small underdamped Josephson junction
,”
Phys. Rev. Lett.
107
,
067004
(
2011
).
66.
Y.
Yoon
,
S.
Gasparinetti
,
M.
Möttönen
, and
J. P.
Pekola
, “
Capacitively enhanced thermal escape in underdamped Josephson junctions
,”
J. Low Temp. Phys.
163
,
164
169
(
2011
).
67.
X.
Hao
,
J. S.
Moodera
, and
R.
Meservey
, “
Spin-filter effect of ferromagnetic europium sulfide tunnel barriers
,”
Phys. Rev. B
42
,
8235
8243
(
1990
).
68.
G.-X.
Miao
,
J.
Chang
,
B. A.
Assaf
,
D.
Heiman
, and
J. S.
Moodera
, “
Spin regulation in composite spin-filter barrier devices
,”
Nat. Commun.
5
,
3682
(
2014
).

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