Electric field enhancement of the superconducting spin-valve effect via strain-transfer across a ferromagnetic/ferroelectric interface

In a ferromagnet/superconductor/ferromagnet (F/S/F) superconducting spin-valve (SSV), a change of the magnetization alignment of the two F layers modulates the critical temperature (Tc) of the S layer. The Tc-switching (the SSV effect) is based on the interplay between superconductivity and magnetism. Fast and large resistive switching associated with the Tc-switching is suitable for nonvolatile cryogenic memory applications. However, external magnetic field-based operation of SSVs is hindering their miniaturization, and therefore, electric field control of the SSV effect is desired. Here, we report epitaxial growth of a La0.67Ca0.33MnO3/YBa2Cu3O7/La0.67Ca0.33MnO3 SSV on a piezo-electric [Pb(Mg0.33Nb0.67)O3]0.7-[PbTiO3]0.3 (001) substrate and demonstrate electric field control of the SSV effect. Electric field-induced strain-transfer from the piezo-electric substrate increases the magnetization and Tc of the SSV, and leads to an enhancement of the magnitude of Tc-switching. The results are promising for the development of magnetic-field-free superconducting spintronic devices, in which the S/F interaction is not only sensitive to the magnetization alignment but also to an applied electric field.


I. INTRODUCTION
The field of spintronics has emerged and rapidly developed following the discovery of the giant magnetoresistance (GMR) effect in a multilayer of a ferromagnet (F) and a nonmagnetic metal (N) 1,2 .Resistive switching of a spinvalve (i.e., a F/N/F trilayer) 3,4 is a basis of the modern spintronic technology and is based on the GMR effect: the electrical resistance increases at the antiparallel (AP) magnetization alignment of the two F layers compared to the parallel (P) alignment due to spin-dependent scattering of spin-polarized electrons.Numerous efforts have been undertaken to decrease the size and energy consumption of spin-valve-based logic and memory devices, and electric field control of ferromagnetism 5,6 and magnetic anisotropy [7][8][9] , which does not require an external magnetic field or electric currents for the resistive switching of spin-valves, is emerging as a promising technology.
Inserting a superconductor (S) instead of N in a spin-valve facilitates a F/S/F superconducting spin-valve (SSV).
A SSV is compatible with cryogenic electronics in which self-heating that changes the properties of superconducting circuits and consumes a limited cooling power of a refrigerator needs to be suppressed.In addition to the normal state resistance of S, the critical temperature (Tc) of S is controlled by the magnetization alignment in a SSV [10][11][12] .Although the mechanism of Tc-switching in SSVs depends on material combinations and is complicated, it is broadly categorized into three effects: the magnetic exchange field effect [13][14][15] , the spin scattering effect 16,17 and the stray field effect 18,19 .For a SSV with an s-wave S, Tc-switching is observed when the S layer thickness (ds) is either comparable to or thinner than the superconducting coherence length (ξ) [13][14][15] .However, in a SSV with a d-wave S, Tc-switching is observed up to the length scale of ds ≈ 100 ξ 20 , which may be due to the nodal superconducting gap with an effectively long ξ, enabling Tc-switching of a relatively thick d-wave S with Tc close to the bulk value.Tc-switching of a SSV (the SSV effect) can be used for cryogenic memory devices, which are compatible with energy-efficient superconducting digital circuits and quantum computing circuits [21][22][23][24] .However, similar to conventional spin-valves, a technological breakthrough is necessary to realize small devices that do not require external magnetic fields or electric currents.

II. EXPERIMEMTS
A LCMO(100 nm)/YBCO(15 nm)/LCMO(50 nm) SSV was epitaxially grown on a commercially available [001]oriented PMN-PT substrate by pulsed laser deposition (the fourth harmonic of a Q-switched Nd:YAG laser; wavelength λ = 266 nm).SSVs with LCMO show a large and clear Tc-switching with a magnitude up to about 2 K 25- 27 and are therefore suitable to investigate an electric field modulation of Tc-switching via strain-transfer from PMN-PT with a large piezo-electric constant 28 .Prior to the deposition of the SSV, the PMN-PT substrate was annealed at 633°C for 1 hour and a 20-nm-thick SrTiO3 (STO) buffer layer was grown at the same temperature to prevent the reaction between the substrate and the SSV.The SSV was subsequently grown at 780 °C in 300 mTorr of flowing oxygen.The laser fluence is 0.25 J cm −2 for YBCO and 0.5 J cm −2 for LCMO and the laser frequency is 10 Hz.After the growth, the SSV was post-annealed at 500°C for 1 h in 600 Torr of oxygen.In-plane electrical resistance (R) measurements using a current (I) of 100-1000 μA were performed in a Gifford-McMahon cryogen-free system using a four-terminal electrical setup with Au (30 nm)/Ti (5 nm) contacts on the SSVs.A Au/Ti contact was also deposited at the bottom of the substrate to apply an electric field.R was measured as a function of the in-plane magnetic field (H), temperature (T), and electric field (E).H was applied parallel to I, and E = 4 kV/cm was applied along the [001] direction of PMN-PT at room temperature prior to low temperature measurements.Care was taken to ensure that the leakage current (typically less than 10 nA for a 4.5×4.5 mm 2 device area) has no effect on Tc and the resistive switching.We note that E = 4 kV/cm is high enough to switch the polarization of PMN-PT 29 but low enough to keep the leakage current below 10 nA.The magnetization (M) was measured using a Quantum Design Magnetic Property Measurement System.

III. RESULTS AND DISCUSSION
We first discuss a magneto-elastic coupling between LCMO and PMN-PT.Figure 1 The diffraction peaks shift to a higher angle by applying E = 4 kV/cm, suggesting that an in-plane compressive strain is transferred from the PMN-PT substrate.The lattice spacing of the (110) planes and the (11 0) planes is calculated to be 2.743 and 2.744 Å, respectively at E = 0, and 2.738 and 2.743 Å, respectively at E = 4 kV/cm.We, therefore, estimate the average in-plane lattice constant to be 3.880 Å at E = 0 and 3.875 Å at E = 4 kV/cm.Figure 1(d) shows out-of-plane x-ray diffraction data from which we estimate the c-axis lattice constant of the LCMO layer to be 3.845 Å at E = 0, which is smaller than the in-plane lattice constant, indicating the presence of a lattice mismatch-induced tensile strain along the in-plane.By applying E = 4 kV/cm, the c-axis lattice constant of LCMO increases to 3.848 Å, suggesting that the tensile strain along the in-plane is partially relaxed by strain transfer from PMN-PT.The electric field-induced change in the lattice constants (0.11% along the in-plane and 0.072% along the c-axis) of the LCMO layer is of the order of that reported for PMN-PT at 4 kV/cm (about 0.05% 29 ), implying that the electric field-induced compressive strain along the in-plane is coherently transferred from the PMN-PT substrate to the LCMO layer.for E = 0 and 4 kV/cm.The magnetization of LCMO is increased by 10 emu/cm 3 (5.0%) at E = 4 kV/cm compared to E = 0. Similar electric field modulations of the magnetization have been reported for manganite/ferroelectric heterostructures, and several mechanisms have been proposed (e.g., strain-transfer [29][30][31] , carrier doping 29,32 , and oxygen migration 33 ).We note that an enhancement of the magnetization is observed also at E = ─ 4 kV/cm in our sample.The symmetric change in the magnetization with respect to the polarity of E rules out the carrier doping effect and the oxygen migration effect, and therefore, the strain-transfer is the most likely origin of the electric field enhancement of the magnetization.Since the hopping integral of eg electrons responsible for the double exchange interaction in Mn 3+ -O-Mn 4+ chains is proportional to cos 2 φ/l 3.5 , where φ is the Mn-O-Mn angle and l is the Mn-O bond length 34 , a stronger double exchange interaction is expected under the compressive strain which decreases l without a change in φ.This is consistent with the electric field enhancement of the magnetization.
We next discuss a LCMO(100 nm)/YBCO(15 nm)/LCMO(50 nm) SSV grown on a PMN-PT (001) substrate.In Fig. 3(a), we plot R(T) of the SSV near the superconducting transition at E = 0 and 4 kV/cm, which shows a parallel shift of the R(T) curve indicating an electric field enhancement of Tc down to R/RN ≈ 10 ─6 , where RN is the normal state resistance at the onset temperature of the superconducting transition.An enhancement of Tc via straintransfer from a (001)-oriented PMN-PT substrate has been reported for YBCO thin films 35 .The Tc enhancement induced by a compressive strain along the in-plane is consistent with a Tc enhancement in YBCO single crystals under uniaxial pressure along the b-axis 36 .Figure 3(b) shows R(H) curves at 36 K (≈ Tc) for E = 0 and 4 kV/cm, where R is normalized at the minimum value.The sharp peaks at H ≈ ± 200 Oe indicate a decrease in Tc near the antiparallel magnetization alignment of the two LCMO layers.Since the sign of the resistive switching is opposite to that of the magnetic exchange field effect 16,17 and the stray field effect is negligibly small [see Fig. S3(b) within the Supplemental Material], the switching is likely due to the spin-scattering effect reported for the similar SSVs consisting of YBCO and LCMO [25][26][27] .The magnitude of the peaks of the normalized R is enhanced by 33% by applying E = 4 kV/cm.
To estimate the effective change in Tc resulting from the change in the magnetization alignment (ΔTc), we compare the magnitude of the resistance peak (ΔR) from the R(H) curve with the slope of the superconducting transition from the R(T) curve [i.e., ΔTc is estimated from the relation ΔR = αΔTc, where α is the slope of the R(T) curve at the temperature of the R(H) measurement].Figure 3(c) shows the temperature dependence of ΔTc at E = 0 and 4 kV/cm.The ΔTc(T) curves show a peak at 31 K for E = 0 and 32 K for 4 kV/cm, meaning that the magnitude of the SSV effect is temperature-dependent.The opening of the superconducting gap with decreasing temperature decreases the density of quasiparticles responsible for the spin-scattering while the density of Cooper pairs decreases with increasing temperature.Hence, the quasiparticle-mediated pair breaking effect is maximized at a certain temperature, and this results in the peak feature of the ΔTc(T) curves.The electric field-induced shift of the ΔTc(T) curve by about 1 K is due to the shift of Tc [shown in Fig. 3(a)].The maximum ΔTc at E = 4 kV/cm (700 mK) is higher than that at E = 0 (660 mK), meaning that the SSV effect is enhanced by 6% by applying an electric field.
Regardless of the origin of the SSV effect, ΔTc can be enhanced by either increasing the magnetization or increasing the maximum magnetization misalignment angle of the two F layers.We note that the coercive fields of the two LCMO layers in our SSVs are comparable.Therefore, the magnetization misalignment angle at H corresponding to the R peak in R(H) is less than 180° and the misalignment angle can be increased if the electric field-induced strain increases the difference of the coercive fields of the two LCMO layers.However, a broadening of the resistive switching in R(H) is not observed at E = 4 kV/cm, suggesting that the coercivities are not sensitive to the electric field.Therefore, the likely origin of the enhancement of ΔTc is the enhanced magnetization of the two LCMO layers.
If this is the case, a similar enhancement of the SSV effect should be observed also in SSVs with other Tc-switching mechanisms (e.g., the magnetic exchange effect [13][14][15]20,37 and the stray field effect 18,19 ) and the enhancement can be amplified with decreasing thickness of the S layer, which could be subjects of future investigation.

IV. CONCLUSION
In conclusion, we have prepared a LCMO/YBCO/LCMO epitaxial SSV on a piezoelectric PMN-PT substrate and demonstrated an electric field enhancement of the SSV effect.Upon application of an electric field, a compressive strain along the in-plane is induced in the SSV and the magnetization of LCMO and Tc of YBCO is enhanced accordingly.These led to an enhanced magnitude of the Tc-switching.The electric field control of the S/F interaction demonstrated in this work is a new concept in the field of superconducting spintronics and the results can be potentially applied to various S/F multilayers including magnetic Josephson junctions and are promising for the development of size-scalable superconducting spintronic devices.

SUPPLEMENTARY MATERIALS
See supplementary materials for the effect of the electric field polarity on the magnetization enhancement of LCMO on PMN-PT(001), and the structural and superconducting properties of YBCO/LCMO on PMN-PT(001).

ACKNOWLEDGMENTS
The authors acknowledge the funding from JST CREST Grant (No. JPMJCR18J), JSPS KAKENHI Grant (a) shows a schematic illustration of the polarization directions and strain of PMN-PT with E along the [001] direction.The polarization along the [111], [11 1], [1 11], and [1 1 1] directions induced by E leads to a decrease in the a-and b-axis lattice constants and an increase in the c-axis lattice constant.Since the polarization is symmetric with respect to the polarity of E, a similar change in the lattice constants is induced for E along the [001 ] direction.Figures 1(b) and 1(c) show in-plane x-ray 2θχ-φ scan profiles of a LCMO(50 nm)/STO(20 nm)/PMN-PT control sample measured with a grazing-incidence angle of 0.3° around the pseudocubic LCMO (110) and (11 0) diffraction peaks, respectively.

Figure 1 (
Figure 1(e) shows M(T) curves of the LCMO/STO/PMN-PT sample at H = 5000 Oe (close to the saturation field)

Figure 2 (
Figure 2(a) shows out-of-plane x-ray diffraction data, which confirm the c-axis oriented growth of the SSV and the absence of impurity phases.The c-axis lattice constants of LCMO and YBCO are determined to be 3.869Å and 11.55Å, respectively.Rocking curves around the diffraction peaks of the LCMO (002) [Fig.2(b)] and the YBCO (005) [Fig.2(c)] show narrow full width at half maximum values of 0.216° and 0.241°, respectively, confirming that the SSV is highly oriented along the [001]-axis of the PMN-PT substrate.