Spin-Triplet SQUID: Magnetic Phase Control

• Spin-triplet SQUIDs are phase-sensitive interferometers that use magnetic control to switch the Josephson junction state between 0 and π.
• They employ multilayer superconductor/ferromagnet structures with noncollinear magnetizations to generate and detect long-range triplet supercurrents.
• Experiments reveal half-period shifts in SQUID oscillations and reproducible switching, highlighting potential for superconducting memory and logic applications.

Searching arXiv for the specified papers and closely related spin-triplet SQUID work. Spin-triplet superconducting quantum interference devices (SQUIDs) are phase-sensitive interferometric devices in which the Josephson coupling is governed by superconducting states with nontrivial spin structure, most directly by spin-triplet supercurrent in superconductor/ferromagnet hybrids, and more broadly by platforms proposed to host unconventional $p$-wave-like or ferromagnetic triplet order. In the experimentally established junction-based realization, the defining property is controllable switching of a Josephson junction ground-state phase between $0$ and $\pi$ by reversing one magnetic layer inside a multilayer ferromagnetic junction, with the phase change detected as a half-period shift of the SQUID oscillation (Glick et al., 2018). Other works have clarified adjacent concepts: topological-insulator SQUIDs as phase-sensitive probes of mixed $s$- and $p$-type proximity superconductivity without direct triplet confirmation (Maier et al., 2015), atomic-scale spin-active Josephson interferometers in which a single magnetic impurity produces $0$- to $\pi$-junction behavior in analogy to a SQUID (Karan et al., 2021), and a theoretical junctionless “spin-triplet SQUID” based on a ferromagnetic triplet-superconducting ring whose flux response is governed by coupled charge-winding and spin-texture dynamics in an SO(3) order parameter manifold (Dao et al., 9 Aug 2025). Taken together, these results define the term across three levels: demonstrated spin-triplet phase control in Josephson SQUIDs, phase-sensitive searches for unconventional pairing, and theoretical extensions in which the internal spin degrees of freedom of the condensate themselves supply the interferometric variable.

1. Definition and scope

A spin-triplet SQUID, in the strongest experimental sense, is a SQUID incorporating Josephson junctions that carry spin-triplet supercurrent and whose phase state can be controlled through magnetic configuration. The clearest realization is a dc SQUID containing two Josephson junctions fabricated from multilayer S/F/S heterostructures, with one junction magnetically switchable and the other fixed, so that a change in the junction’s intrinsic phase appears as a shift of the SQUID interference pattern (Glick et al., 2018). In this setting, phase-sensitive detection establishes not only the presence of supercurrent through ferromagnets but also the equilibrium phase of the triplet-carrying junction.

The broader literature uses closely related but not identical device concepts. A SQUID fabricated on the surface of strained HgTe was designed as a phase-sensitive probe of unconventional proximity-induced superconductivity expected from helical Dirac surface states, but the measured response was conventional, $2\pi$-periodic, and showed no measurable orientation-dependent phase shift, so it did not establish spin-triplet superconductivity (Maier et al., 2015). An STM-based atomic interferometer demonstrated that a single magnetic impurity in a superconducting tunnel junction can reverse the sign of the Josephson coupling, with phase sensitivity supplied by a second transport channel “in analogy to a SQUID,” but the electrodes remained conventional spin-singlet BCS superconductors (Karan et al., 2021). A later theoretical proposal defined a “spin-triplet SQUID” as a continuous ring of a ferromagnetic spin-triplet superconductor with no Josephson weak link, where flux response arises from SO(3) topology and nonsingular $4\pi$ phase slips mediated by spin texture (Dao et al., 9 Aug 2025).

This suggests that the phrase “spin-triplet SQUID” can denote either a junction-based interferometer that directly measures the phase of spin-triplet supercurrent or a more general flux-sensitive device whose operation depends on the internal spin structure of a triplet condensate. The former has been experimentally demonstrated (Glick et al., 2018); the latter remains theoretical (Dao et al., 9 Aug 2025).

2. Junction-based spin-triplet SQUIDs in superconductor/ferromagnet hybrids

The experimentally established architecture uses Josephson junctions containing three magnetic layers, following the prediction that a junction with three ferromagnetic layers with coplanar magnetizations should exhibit a ground-state phase shift of either zero or pi depending on the relative orientations of those magnetizations (Glick et al., 2018). The relevant multilayer is of the form

$\text{S/N/F'/N/F/N/F''/N/S},$

implemented as

$0$0

with a top electrode

$0$1

all thicknesses in nm (Glick et al., 2018).

In this stack, the bottom and top Nb electrodes are conventional spin-singlet superconducting reservoirs. The Py layer is a soft free layer, the Ni layer is a hard in-plane ferromagnet, and the $0$2 section is a synthetic antiferromagnet with perpendicular magnetic anisotropy. The design ensures that adjacent magnetizations are noncollinear, preferably orthogonal, which maximizes triplet generation, while allowing one magnetic layer to reverse by $0$3 without disturbing the others (Glick et al., 2018).

The SQUID contains two junctions fabricated simultaneously from the same multilayer, but with different lateral shapes: one elliptical with aspect ratio $0$4, the other an elongated hexagon with aspect ratio $0$5, each of area $0$6 (Glick et al., 2018). The shape anisotropy causes the Py layer in one junction to switch at low field while the corresponding layer in the other remains fixed. The paper concludes that the elliptical junction is the one that switches (Glick et al., 2018).

The core claim of the experiment is phase-sensitive control. Long-range supercurrent through ferromagnets had already been taken as evidence for triplet pairing, but that was an amplitude-only signature. Embedding the junction in a SQUID allowed direct detection of the junction ground-state phase. The observed half-period shift of the SQUID oscillation when one magnetic layer reverses is the direct signature that the junction changes from a $0$7 state to a $0$8 state, or vice versa (Glick et al., 2018).

3. Physical mechanism of $0$9-$\pi$0 phase control

The theoretical basis is singlet-to-triplet conversion in superconducting/ferromagnetic hybrids. A spin-singlet pair entering a ferromagnet acquires a relative phase between its $\pi$1 and $\pi$2 components due to exchange splitting, generating the $\pi$3 triplet component; when the pair encounters a region where the magnetization axis rotates, that $\pi$4 component is transformed into $\pi$5 triplets in the rotated basis (Glick et al., 2018). These equal-spin triplet pairs can propagate much farther in strong ferromagnets because both electrons occupy the same spin band (Glick et al., 2018).

For three magnetic layers $\pi$6, $\pi$7, and $\pi$8, triplet generation is strongest when adjacent ferromagnetic layers are noncollinear, ideally perpendicular (Glick et al., 2018). A specific theoretical prediction, verified experimentally in the SQUID geometry, is that if the three magnetizations are coplanar, the resulting spin-triplet junction can have a ground-state phase of either $\pi$9 or $s$0 depending on the magnetic configuration (Glick et al., 2018).

The effective sign reversal of the Josephson coupling is expressed through the Josephson relation

$s$1

A sign reversal of $s$2 is equivalent to a $s$3 shift: $s$4 Thus the state change can be described either as switching the sign of the critical current or as changing the intrinsic phase offset of the junction by $s$5 (Glick et al., 2018).

In the structures used experimentally, reversing the Py layer by $s$6 changes the relation between the two outer in-plane ferromagnets from parallel to antiparallel relative to the fixed Ni layer, and theory predicts that this changes the sign of the spin-triplet Josephson coupling (Glick et al., 2018). The authors emphasize that this mechanism arises from spin rotations rather than simple phase accumulation, unlike earlier two-ferromagnet spin-valve $s$7-$s$8 junctions that relied on careful thickness tuning to make the total exchange-induced phase near an even or odd multiple of $s$9 (Glick et al., 2018).

A plausible implication is that the triplet SQUID architecture is intrinsically suited for programmable phase control: the interferometric phase shift is not imposed externally by flux alone, but encoded in the magnetic state of the junction.

4. SQUID interferometry and phase-sensitive readout

The phase-sensitive readout uses standard dc SQUID flux quantization. If the two junction phase differences are $p$0 and $p$1, then

$p$2

where $p$3 is the loop flux and $p$4 (Glick et al., 2018). If one junction acquires an intrinsic extra phase of $p$5, then the SQUID interference pattern shifts by half a flux quantum,

$p$6

which is the direct signature sought in the experiment (Glick et al., 2018).

In the low-inductance limit, the SQUID critical current is written as

$p$7

with $p$8 for a $p$9-$0$0 SQUID and $0$1 if one junction switches to a $0$2 state (Glick et al., 2018). Changing $0$3 from $0$4 to $0$5 shifts the oscillation by $0$6 (Glick et al., 2018).

The device is measured using a nearby superconducting flux line carrying a current $0$7, rather than by applying a large perpendicular field directly. The SQUID critical current oscillates with period about $0$8 in $0$9, corresponding to one $\pi$0 through the loop (Glick et al., 2018). The arm inductances were fixed to $\pi$1, so the total inductance was $\pi$2, and the SQUID was in the low-inductance limit $\pi$3 (Glick et al., 2018).

The most important observation is that the shift is horizontal rather than merely a change in oscillation amplitude. For sample 2A-4, the average critical current

$\pi$4

shows SQUID oscillations that remain phase-stationary until the set field reaches $\pi$5, where the whole pattern shifts sideways by almost exactly half a period; on sweeping negative, it shifts back at $\pi$6 (Glick et al., 2018). The paper explicitly distinguishes this from a mere change in the magnitude of one junction critical current, which would distort the oscillation amplitude or asymmetry but would not translate the oscillation extrema by $\pi$7 (Glick et al., 2018).

The raw I–V curves are rounded because the junctions are overdamped and noisy. Critical currents are extracted using Ivanchenko-Zil'berman theory, and also using the simpler form

$\pi$8

for rapid analysis (Glick et al., 2018). Fits to standard SQUID theory yield phase changes extremely close to $\pi$9 in units of $2\pi$0, that is, very close to a $2\pi$1 shift, for essentially all functioning devices (Glick et al., 2018).

5. Quantitative performance and reproducibility

The principal quantitative results of the demonstrated spin-triplet SQUID are summarized below.

Quantity	Reported value	Context
Junction area	$2\pi$2	Each junction (Glick et al., 2018)
SQUID period in $2\pi$3	$2\pi$4	One $2\pi$5 (Glick et al., 2018)
Initialization field	$2\pi$6	Sets Ni and Py magnetizations (Glick et al., 2018)
Switching field, sample 2A-4	$2\pi$7	Py reversal in one junction (Glick et al., 2018)
Reverse switching field	$2\pi$8	Switch back (Glick et al., 2018)
Number of measured SQUIDs	$2\pi$9	$4\pi$0 with $4\pi$1, $4\pi$2 with $4\pi$3 (Glick et al., 2018)
Successful devices	$4\pi$4 of $4\pi$5	Similar behavior to main data (Glick et al., 2018)
Repeated switching	$4\pi$6 times	Device 2A-4 (Glick et al., 2018)

Representative fit values from Table 1 include, for device 2A-4, state 1: $4\pi$7 and state 2: $4\pi$8 with fitted phase change

$4\pi$9

(Glick et al., 2018). Other devices yielded phase changes

$\text{S/N/F'/N/F/N/F''/N/S},$0

in units of $\text{S/N/F'/N/F/N/F''/N/S},$1, all close to $\text{S/N/F'/N/F/N/F''/N/S},$2, with one outlier somewhat larger but still clearly near $\text{S/N/F'/N/F/N/F''/N/S},$3 (Glick et al., 2018).

The reproducibility is notable. Seven of eight measured SQUIDs showed behavior similar to the main data, and device 2A-4 was switched $\text{S/N/F'/N/F/N/F''/N/S},$4 times between the two states with two narrow, well-separated critical-current distributions (Glick et al., 2018). Measurements down to about $\text{S/N/F'/N/F/N/F''/N/S},$5 with filtered lines gave similar $\text{S/N/F'/N/F/N/F''/N/S},$6 values and similar rounding, supporting the claim that external interference did not strongly suppress the reported critical currents (Glick et al., 2018).

The authors also identify limitations. The devices have very small $\text{S/N/F'/N/F/N/F''/N/S},$7, which complicates analysis because the I–V curves are strongly rounded by noise and thermal or environmental fluctuations (Glick et al., 2018). The magnitudes of the critical currents in the two states are not generally equal, although theory predicts equality if the free layer reverses by exactly $\text{S/N/F'/N/F/N/F''/N/S},$8; the likely explanation is a shift of the switching junction’s Fraunhofer pattern due to magnetic flux from the Py/Ni configuration (Glick et al., 2018). Small deviations from exactly $\text{S/N/F'/N/F/N/F''/N/S},$9 are attributed mainly to extra flux coupled into the SQUID by the magnetization of the switching Py layer (Glick et al., 2018).

6. Related platforms and boundaries of the concept

Not every phase-sensitive SQUID on a spin-active platform is a demonstrated spin-triplet SQUID. A central boundary case is the HgTe topological-insulator SQUID. In that device, strained HgTe layers $0$00 thick on CdTe substrates serve as a 3D topological insulator with negligible bulk conductance when the Fermi level lies in the band gap, and superconducting Nb electrodes form lateral Nb/HgTe/Nb Josephson weak links (Maier et al., 2015). Because helical spin polarization of the surface states is expected to generate unconventional proximity-induced $0$01-wave superconductivity, the devices were designed as phase-sensitive tests of anisotropic order-parameter signatures (Maier et al., 2015).

Two SQUID geometries were compared: a $0$02-SQUID with two straight junctions and a $0$03-SQUID with one straight junction and one corner junction (Maier et al., 2015). The point of the orientation test was that in anisotropic superconductors such as $0$04-wave or $0$05-wave systems, the Josephson phase can depend on junction orientation relative to the order-parameter symmetry (Maier et al., 2015). However, the measured critical-current modulation followed a conventional SQUID relation very well, with fit values $0$06 for the $0$07-SQUID and $0$08 for the $0$09-SQUID; the oscillation periods were $0$10 and $0$11, respectively (Maier et al., 2015). No measurable phase shift was found between the two geometries, and no $0$12-periodic modulation was observed (Maier et al., 2015). The authors conclude that the results rule out pure $0$13-wave or pure $0$14-wave symmetry, while remaining consistent with a mixed isotropic $0$15 proximity state (Maier et al., 2015). Thus the platform is relevant to spin-triplet-SQUID discussions, but it does not demonstrate triplet pairing.

A second boundary case is atomic-scale SQUID-like interference in STM. In a superconducting STM junction made of a vanadium tip and a V(100) substrate at $0$16, a single magnetic impurity at the tip apex produces a Yu-Shiba-Rusinov state, and the Josephson response is the coherent sum of a dominant YSR channel and a weaker reference BCS channel (Karan et al., 2021). Across a mechanically tuned quantum phase transition, the YSR channel changes sign, so the total current switches from constructive to destructive interference with the reference channel (Karan et al., 2021). The energy-phase relations add coherently,

$0$17

and in the tunnel regime

$0$18

with the YSR contribution explicitly changing sign at the transition (Karan et al., 2021). The measured observable in the dynamical Coulomb blockade regime scales as

$0$19

so the sign reversal is inferred from a step-like reduction in the Josephson response rather than a direct current reversal (Karan et al., 2021). This work is not about spin-triplet superconductivity; the electrodes are conventional spin-singlet BCS superconductors. Its relevance lies in showing that spin-controlled Josephson phase shifts, $0$20-junction behavior, and channel interference can be engineered and read out at the atomic scale (Karan et al., 2021).

These two cases clarify a common misconception: phase-sensitive superconducting interference on a spin-active or topological platform is not by itself evidence for spin-triplet superconductivity. The decisive criterion is whether the experiment directly establishes triplet supercurrent or triplet-order-dependent interferometric behavior, as in the multilayer ferromagnetic SQUID (Glick et al., 2018).

7. Junctionless triplet-SQUID proposals and future directions

A later theoretical proposal introduced a distinct device concept: a closed ring of a ferromagnetic spin-triplet superconductor that functions as a spin-triplet SQUID without a Josephson weak link (Dao et al., 9 Aug 2025). The order parameter is written as

$0$21

where $0$22 is a local orthonormal triad and $0$23 is the spin-orientation field (Dao et al., 9 Aug 2025). The orientational order parameter space is effectively SO(3), with

$0$24

so the natural nonsingular phase slip changes winding by $0$25, not $0$26 (Dao et al., 9 Aug 2025).

The free-energy functional is

$0$27

with gauge-independent supercurrent

$0$28

(Dao et al., 9 Aug 2025). The central topological relation is

$0$29

which links the circulation of supercurrent to the bulk magnetic skyrmion density (Dao et al., 9 Aug 2025). For a ring of length $0$30 threaded by external flux $0$31, the current becomes

$0$32

where $0$33 is the enclosed fictitious skyrmion charge and $0$34 labels the $0$35 sector (Dao et al., 9 Aug 2025).

The device can relax circulating current through smooth, nonsingular $0$36 phase slips mediated by spin texture rather than by suppressing the order-parameter amplitude. This $0$37 periodicity is explicitly distinguished from the $0$38 Josephson effect of Majorana systems: here it arises from SO(3) topology and skyrmion-mediated hydrodynamics, not from fermion-parity protection across a weak link (Dao et al., 9 Aug 2025).

The proposed readout is inductive coupling to a tank circuit, with nonlinear supercurrent response probed via Oersted-field measurements (Dao et al., 9 Aug 2025). The strongest predicted experimental signatures are nonlinear flux response in a continuous ring without Josephson weak links, threshold switching associated with spin-texture evolution, enlarged flux periodicity relative to ordinary singular $0$39 slips, and correlated charge and spin current oscillations (Dao et al., 9 Aug 2025).

This proposal substantially broadens the meaning of “spin-triplet SQUID.” In the demonstrated ferromagnetic-junction devices, triplet pairing modifies the phase state of a Josephson weak link inside an otherwise standard SQUID geometry (Glick et al., 2018). In the theoretical ring, the triplet order parameter itself supplies the relevant interferometric degree of freedom, so the device is SQUID-like in flux sensitivity and nonlinear inductance but not junction-based in the usual dc or rf SQUID sense (Dao et al., 9 Aug 2025).

A plausible implication is that future work may split into two distinct lines. One line extends magnetically switchable $0$40-$0$41 junctions toward superconducting memory, single-flux-quantum logic, and quantum circuits with engineered phase elements (Glick et al., 2018). The other seeks direct signatures of ferromagnetic spin-triplet order through junctionless flux devices, where observation of enlarged periodicity and nonsingular $0$42 phase slips would indicate the coupled charge-spin hydrodynamics unique to a triplet condensate (Dao et al., 9 Aug 2025). Both directions preserve the defining feature of the spin-triplet SQUID: superconducting interference whose phase structure is controlled by spin degrees of freedom rather than by conventional singlet Josephson physics alone.