Hybrid supercapacitors for reversible control of magnetism

Electric field tuning of magnetism is one of the most intensely pursued research topics of recent times aiming at the development of new-generation low-power spintronics and microelectronics. However, a reversible magnetoelectric effect with an on/off ratio suitable for easy and precise device operation is yet to be achieved. Here we propose a novel route to robustly tune magnetism via the charging/discharging processes of hybrid supercapacitors, which involve electrostatic (electric-double-layer capacitance) and electrochemical (pseudocapacitance) doping. We use both charging mechanisms—occurring at the La0.74Sr0.26MnO3/ionic liquid interface to control the balance between ferromagnetic and non-ferromagnetic phases of La1−xSrxMnO3 to an unprecedented extent. A magnetic modulation of up to ≈33% is reached above room temperature when applying an external potential of only about 2.0 V. Our case study intends to draw attention to new, reversible physico-chemical phenomena in the rather unexplored area of magnetoelectric supercapacitors.

During the in situ tuning experiment carried out in the 220-330 K temperature range with a constant surface charge modulation ∆Q ≈ 4 µC cm −2 , the current density-voltage characteristics (see Supplementary Figure 2) displayed nearly symmetric and rectangular shapes of the charging and discharging processes as well as high reversibility upon cycling. The behavior of the magnetic response as a function of temperature is shown in Supplementary Figure 3. The slope of the curves, used to calculate the magnetoelectric (ME) coupling coefficients, revealed positive or negative values of α respectively above or below T cross ≈ 258 K.
Interestingly, high and positive values of α ≈ +6.4 µ B /h + , which exceed the magnetic moment carried by a Mn atom, were found in proximity of the para-ferromagnetic phase transition. The behavior might be ascribed to the enhanced penetration depth λ of the local electric field on insulating domains, which according to phase separation models 7,8 are present in larger amounts comparing to metallic domains around T C . This interpretation is corroborated by the fact that upon decreasing the temperature also the magnitude of α systematically decreases, which is consistent with the expected increased number of conductive domains and consequent reduction of λ (on average on the whole LSMO surface).
At temperatures below T cross , starting from ≈ 235 K down to 220 K, α reaches a nearly constant value of ≈ −3 µ B /h + , in agreement with the fact that the LSMO magnetization approaches saturation (and so also its magnetoelectronic configuration does not remarkably change).
In Supplementary Table 1 (see below) the values of potential window, measured charge, calculated capacitance and ME coupling coefficient obtained from the in situ temperature dependence survey are summarized.

SUPPLEMENTARY NOTE 3. ADDITIONAL INSIGHTS INTO THE QUALITATIVE EXPLANATION OF THE INTERFACIAL ME PHENOMENA
As already stated in the main paper, a phenomenological model based on the LSMO bulk phase diagram can be used to qualitatively describe the La 0.74 Sr 0.26 MnO 3 magnetic response upon surface charge doping. The competition between the change in magnetic transition temperature and ground state magnetization upon charge carrier doping has already been used 9−12 to explain the existence of a crossover point T cross . Naively this can be illustrated by a shift of T C to higher temperatures and, concurrently, to a reduced saturation magnetization when the system is upon hole doping, and viceversa upon electron doping (see Supplementary Figure 4).
To our knowledge, for the first time the results of the isothermal-charge dependence study at 220 K (see Fig. 4) prove that it is possible to control at a fixed temperature the sign of the magnetic modulation by simply adjusting the external voltage analogously to the behavior observed below or above T cross in the temperature dependence study (see Fig. 3).
The phenomenological picture, notwithstanding its limitations, is still helpful to qualitatively interpret the results at 220 K upon progressive increasing ∆Q. Using as a starting point the profile of the bulk, untuned M (T ) curve (black curve in Supplementary Figure 4), progressive electron doping can be described with a gradual shift of T C towards higher temperatures simultaneously accompanied by a decrease in ground state magnetization (red curves in Supplementary Figure 4). The opposite trend is expected upon hole doping (blue curves in Supplementary Figure 4).
The insets in Supplementary Figure 4 represent the behavior expected below and above T cross , labeled with the arbitrarily-chosen temperatures of 220 K and 270 K, respectively.
Considering the inset below T cross in Supplementary Figure 4, on the one hand an initial increase in magnetization up to a maximum and afterwards a decrease in its value are expected upon progressive electron doping (see the red symbols at 220 K). On the other hand, upon hole doping, the consequent increase in T C , which is not playing the major role at the low temperature of 220 K, and decrease in the ground state magnetization, bring to a systematic decrease in magnetization (blue symbols at 220 K). These behaviors are consistent with the trend of the isothermal charge-dependence study performed at 220 K (see Fig. 4).
Similar considerations are also valid to describe the inset above T cross . However, in this case a reversed effect is expected upon charge doping: an initial increase and afterwards a decrease in magnetization upon increased hole concentration (red symbols at 270 K), while a systematic decrease in magnetization upon electron doping (blue symbols at 270 K). In this sense, contrary to the results obtained at 220 K, a splitting of the M (Q) curve at temperatures above T cross should be manifested upon progressive hole accumulation. This prediction, despite based on a relatively simple and qualitative model, is confirmed by the results of an isothermal charge-dependence study performed at 270 K (see Supplementary Note 4).
Furthermore, it should be stressed that this qualitative scenario, based on the shift of the bulk, untuned M (T ) curve, can be used only as a first rough approximation. Additional parameters, such as magnetoelectronic phase separation with possible variations in the electric field penetration depth and the quantitative values of α, should be considered to build a more realistic model.
A last speculative remark pertains to the nearly symmetric shape of plot e in Fig. 4, characterized by positive or negative slopes (i.e. α) at the fixed temperature of 220 K. It is known from the temperature dependence study that T cross is ≈ 258 K and it separates the regions with positive or negative α. Thus, one could argue that with respect to the two opposite extremes of the hole accumulation/depletion branches (see plot e in Fig. 4), the LSMO surface magnetic configuration shifts ∼160 K in total. Analogously, the splitting in the M (t) curve at 323 K upon hole doping (see Fig. 6a), suggests a total shift of ∼65 K. The authors underline that these hypotheses require to be verified by independent experiments and an adequate theoretical model.

SUPPLEMENTARY NOTE 4. ISOTHERMAL CHARGE-DEPENDENCE STUDY AT 270 K
In analogy to the isothermal charge-dependence experiment at 220 K, the LSMO magnetic response was analyzed upon progressive expansion of the potential window at a fixed temperature of 270 K, i.e., above T cross .
For potential windows below ∼0.8 V, the magnetic signal was in-phase with respect to the surface charge modulation (a in Supplementary Figure 5a), in agreement with the temperature-dependence study (see Fig. 3). Beyond this threshold voltage, the M (t) curve manifested a splitting on the hole accumulation side (b in Supplementary Figure 5a) with the distinctive anti-phase characteristic with respect to Q(t), as observed below T cross . As the potential window was further increased (c,d in Supplementary Figure 5a), this behavior became more and more pronounced. Upon application of a positive bias V b ≈ +0.9 V, the magnetic signal turned out to be directly anti-phase with the interface charge modulation (e in Supplementary Figure 5a). It should be noticed the similarity with the results obtained at 220 K, keeping in mind the reversed role of the hole/electron doping in controlling the magnetic response, which supports the considerations discussed in Supplementary Note 3.
The trend of Supplementary Figure 5b, featuring positive or negative values of α respectively along the hole depletion or accumulation branches, suggests once again that upon increasing ∆Q the system behaves as being toggled back and forth with respect to T cross .
The shape and reversibility of the J (V ) characteristics (see Supplementary Figure 5c) and the values of calculated capacitance confirm that upon expansion of ∆V , the charging/discharging processes in the LSMO/ionic liquid system are due to a combination of electric-double-layer capacitance and surface pseudocapacitance. The values of potential window, surface charge, capacitance and ME coupling coefficient are summarized in Supplementary Table 3. The curves are constructed by averaging several consecutive cycles (40 for the measurements at 323 and 220 K and 10 for the plot at 258 K). The three plots belong to the same set of data already shown in Fig. 3d-f, respectively. Where not visible, the statistical errors are smaller than the symbols size. The slope of the curves provides the magnetoelectric coupling coefficient α (see Supplementary Table 1). Each curve consists of at least 10 consecutive CV cycles. Above (white area) or below (gray area) T cross ≈ 258 K the tuning coefficient is positive or negative, respectively. The curves at 323 K, 258 K and 220 K belong to the same set of data already shown in Fig. 3d-f, respectively. In a,b,c the white and gray areas qualitatively separate the data with the LSMO magnetic modulation responding as above or below T cross , respectively.  Figure 5. The data of plot "e" refer to an experiment performed with a starting bias voltage V b ≈ +0.8 V. Unless specified, the errors on the reported data are within a 5% accuracy.