## Abstract

Increasingly impressive demonstrations of voltage-controlled magnetism have been achieved recently, highlighting potential for low-power data processing and storage. Magnetoionic approaches appear particularly promising, electrolytes and ionic conductors being capable of on/off control of ferromagnetism and tuning of magnetic anisotropy. A clear limitation, however, is that these devices either electrically tune a known ferromagnet or electrically induce ferromagnetism from another magnetic state, e.g., antiferromagnetic. Here, we demonstrate that ferromagnetism can be voltage-induced even from a diamagnetic (zero-spin) state suggesting that useful magnetic phases could be electrically induced in “nonmagnetic” materials. We use ionic liquid–gated diamagnetic FeS_{2} as a model system, showing that as little as 1 V induces a reversible insulator-metal transition by electrostatic surface inversion. Anomalous Hall measurements then reveal electrically tunable surface ferromagnetism at up to 25 K. Density functional theory–based modeling explains this in terms of Stoner ferromagnetism induced via filling of a narrow *e*_{g} band.

## INTRODUCTION

Magnetic materials have been linchpins of high technology for decades. Contemporary examples include hard disk drives and magnetic random access memories, although ongoing advances in spintronics have created myriad additional possibilities, in sensing, data storage, and processing (*1*). One such advance is the capability to control ferromagnetic magnetization with electrical currents, in addition to magnetic fields, via spin-transfer (*2*) and spin-orbit torques (*3*, *4*). Field- and current-based manipulation of ferromagnetism intrinsically involves power consumption, however, which is a critical limiting factor in data storage and processing (*1*, *5*). This situation has focused great attention on voltage-based (i.e., electric field–based) control of magnetism, with potential for much lower power consumption (*1*, *5*–*7*).

While multiple approaches to voltage-controlled magnetism exist, magnetoionics, where electric field–induced ion motion is used to manipulate magnetism, appears particularly promising (*6*–*8*). The electric double-layer transistor (EDLT; Fig. 1A) is foundational to this effort, as it has proven highly effective in voltage control of insulator-metal and superconducting transitions and is now being used in magnetoionics (*6*–*9*). An EDLT is formed by replacing the dielectric in a field-effect transistor with an electrolyte, often an ionic liquid (IL). When a gate voltage (*V*_{g}) is applied between the magnetic material and a metallic gate, IL cations or anions (depending on the *V*_{g} polarity) drift to the surface of the magnet, where they accumulate (Fig. 1A, right). The electric field created is then screened by induction of a two-dimensional (2D) sheet of electrons/holes in the magnetic material, forming an electric double layer (EDL). This EDL is essentially a nanoscale capacitor, resulting in tens of microfarad per square centimeter capacitances and electron/hole densities up to 10^{15} cm^{−2} at just a few volts (*8*–*10*). This is sufficient to induce and control electronic phase transitions and order, including magnetism (*8*–*10*).

EDLT-based voltage control of ferromagnetism is advancing rapidly. Control of the Curie temperature (*T*_{C}) of ferromagnets, for example, has progressed from *V*_{g}-induced shifts of ~30 K in IL-gated perovskite manganites (*11*) to 110 K in ultrathin Co (*12*) to >150 to 200 K in perovskite cobaltites (*13*–*16*). The reversible voltage induction of ferromagnetism from nonferromagnetic states, such as antiferromagnetic LaMnO_{3} (*17*) or SrCoO_{2.5} (*14*), has also been demonstrated. The gating mechanisms in these EDLTs are often not simply electrostatic, as in Fig. 1A, but involve electrochemistry (*8*). Oxide ionic gating effects based on creation and annihilation of oxygen vacancies (*13*–*15*, *18*–*20*) and insertion and extraction of hydrogen (*14*, *21*, *22*) are now known, for example. This has spawned expansion from IL-based EDLTs to devices based on ion gels, solid electrolytes, ionic conductors, etc. (*6*–*8*, *10*), applied beyond insulators and semiconductors to thin film ferromagnetic metals, for example (*12*, *23*–*29*). Notable achievements include sizable voltage-based modulation of *T*_{C}, magnetization, coercivity, and magnetic anisotropy (*6*–*8*, *11*–*17*, *23*–*29*), in addition to encouraging progress with reversibility and speed (*27*, *30*).

While impressive, these advances are subject to a clear limitation. Specifically, they involve either voltage control of a known ferromagnet (*11*, *12*, *23*–*29*) or voltage-induced ferromagnetism from some other magnetic state (*13*, *14*, *16*, *17*, *31*), be it ordered (e.g., antiferromagnetic) or disordered (paramagnetic). This raises a simple question with deep implications: Can ferromagnetism be voltage-induced from a “nonmagnetic” state, i.e., a diamagnet, with a zero-spin electronic configuration? We address this here using IL-gated single crystals of diamagnetic FeS_{2}, i.e., Fool’s Gold. This is a pyrite structure 0.95-eV gap semiconductor with *t*_{2g}^{6}*e*_{g}^{0} electronic configuration and well-established zero-spin diamagnetism (*32*–*34*). What makes FeS_{2} ideal for such studies is that alloying with ferromagnetic CoS_{2} (electronic configuration, *t*_{2g}^{6}*e*_{g}^{1}) to produce Fe_{1−x}Co* _{x}*S

_{2}induces ferromagnetism at as little as 1% Co (

*35*,

*36*), eventually reaching a state with

*T*

_{C}≈ 150 K in Fe

_{0.2}Co

_{0.8}S

_{2}(

*37*–

*39*). Interfacial charge transfer in pyrite-containing heterostructures has also been predicted to induce ferromagnetism in FeS

_{2}(

*40*). While likely not unique, diamagnetic FeS

_{2}thus exists in unusual proximity to a ferromagnetic instability, rendering it ideal for investigation of the plausibility of voltage-induced ferromagnetism in a diamagnetic system.

## RESULTS AND DISCUSSION

As described in Materials and Methods, EDLTs based on pyrite FeS_{2} single crystals (see fig. S1 and table S1 for structural and chemical characterization details) were fabricated using a metallized cylinder as both the gate electrode and IL container (Fig. 1A). Figure 1B shows the resulting temperature (*T*) dependence of the sheet resistance (*R*_{s}) of a representative EDLT (sample 1) at *V*_{g} values between 0 and +3 V (i.e., in electron accumulation mode). At *V*_{g} = 0, typical single-crystal FeS_{2} behavior is observed, semiconducting transport (*dR*_{s}/*dT* < 0) occurring down to ~150 K, where *R*_{s}(*T*) flattens before increasing at low *T*. This arises due to the surface conduction that is now established in FeS_{2} crystals, where the semiconducting interior, which is lightly n-doped (e.g., 10^{16} cm^{−3} at 300 K) by S vacancies, is shunted at low *T* by a heavily doped (e.g., 10^{20} cm^{−3} to 10^{21} cm^{−3}) p-type surface layer (see fig. S2 for further details) (*41*–*44*). The surface Fermi level pinning and band bending required for this likely arise from surface states, with important implications for pyrite photovoltaics (*41*, *42*, *44*). More important in the current context, application of *V*_{g} up to +3 V is seen in Fig. 1B to result in marked decreases of the low *T* resistance (by ~10^{4}-fold at 30 K, extrapolating to much more at lower *T*). *R*_{s} falls beneath *h*/*e*^{2} ≈ 26 kilohm, *R*_{s}(*T*) becoming flat by +3 V, aside from a weak low *T* upturn. As discussed below, detailed *R*_{s}(*T*, *H*) data and analyses (where *H* is the applied magnetic field) establish that this occurs due to a transition from Efros-Shklovskii variable-range hopping (*45*) to weak localization (*46*) at ≥1.2 V. Note that the 300 K (bulk) resistance in Fig. 1B is barely affected by *V*_{g}, meaning that this strongly localized to essentially metallic transition occurs on the FeS_{2} surface. This occurs at positive *V*_{g}, implying inversion of the initially p-type surface (*44*) to an n-type metal, as confirmed below.

The reversibility of the observed *V*_{g}-induced surface insulator-metal transition is explored in Fig. 1C using a second sample (sample 2). This sample has lower bulk n-doping (see Materials and Methods), resulting in higher *R*_{s} (300 K) and thus a higher bulk-to-surface crossover temperature (>300 K). The solid black and red lines in Fig. 1C depict the 0- and +3 V behavior during the initial *V*_{g} cycle, where the 30 K resistance drops by a factor of ~10^{5}. Returning *V*_{g} to zero (dashed black line, cycle 2) then results in *R*_{s}(*T*) essentially identical to the initial state, reapplication of +3 V (dashed red line, cycle 2) inducing very similar *R*_{s}(*T*) to initial gating. This extraordinary level of reversibility, in a system where even minor surface structural or chemical modifications result in large changes in surface conduction (*41*, *42*), provides strong evidence of a reversible, predominantly electrostatic gating mechanism (Fig. 1A), as opposed to the electrochemical mechanisms frequently encountered (*8*).

The data of Fig. 1B replotted to permit Zabrodskii analysis are shown in Fig. 2A. In this approach, ln*W* is plotted versus ln*T*, where *W*, the reduced activation energy, is defined as *W* = −*d*ln*R*_{s}/*d*ln*T*. This linearizes *R*_{s} = *R*_{0}exp(*T*_{0}/*T*)* ^{m}*, where

*T*

_{0}is a characteristic temperature,

*R*

_{0}is

*R*

_{s}(

*T*→ ∞), and the exponent

*m*provides insight into conduction mechanisms. The rapid decrease in ln

*W*on initial cooling in Fig. 2A reflects the bulk to surface conduction crossover, which is followed by a clear progression with

*V*

_{g}in the low

*T*limit. At

*V*

_{g}= 0 and +1 V, positive ln

*W*values that increase linearly with decreasing ln

*T*are seen in Fig. 2A, with a slope

*m*≈ 0.5 (blue solid line). As in prior work on ungated FeS

_{2}crystals (

*42*,

*47*), this indicates Efros-Shklovskii variable-range hopping (

*45*), i.e.,

*R*

_{s}=

*R*

_{0}exp(

*T*

_{0}/

*T*)

*, on the insulating side of the insulator-metal transition. As*

^{1/2}*V*

_{g}is increased above 1.1 V, however, ln

*W*becomes negative and

*T*independent, indicating a crossover to nonactivated transport, i.e., effectively metallic behavior. Figure 2B further emphasizes this by plotting (

*R*

_{s}−

*R*

_{s,100K}) versus ln

*T*(where

*R*

_{s,100K}is the value of

*R*

_{s}at 100 K) at each

*V*

_{g}. The rapid increase in

*R*

_{s}on cooling at low

*V*

_{g}is seen to give way to a weak, approximately ln

*T*dependence at high

*V*

_{g}. This behavior is expected for weakly localized transport in a 2D surface layer (

*46*), which we show below to be the case in these EDLTs.

Further support for these conclusions is provided by magnetoresistance (MR) measurements (with *H* perpendicular to the crystal surface), as in Fig. 2C at 30 K. At *V*_{g} = 0, parabolic positive MR occurs, consistent with the Efros-Shklovskii variable-range hopping (*45*) deduced from Fig. 2A. As *V*_{g} is increased, the MR switches to negative, taking on a form characteristic of weak localization, again consistent with Fig. 2 (A and B). Figure 2D then illustrates MR(*T*) at fixed *V*_{g} = 3 V, which is also qualitatively consistent with our analysis of *R*_{s}(*T*). Specifically, positive parabolic MR at high *T* (due to the ordinary MR effect when bulk semiconducting conduction dominates) crosses over to negative MR at low *T* (when weakly localized surface conduction dominates). Figure 2 thus evidences a positive-*V*_{g}–induced transition in the low *T* surface-dominated conduction from strongly localized variable-range hopping to effectively metallic/weakly localized transport at *V*_{g} ≥ 1.2 V.

The magnetic behavior in the *V*_{g}-induced effectively metallic FeS_{2} surface state is explored in Fig. 3 via anomalous Hall effect measurements. The 30 K *V*_{g} dependence of the transverse (i.e., Hall) conductance versus perpendicular magnetic field (*H*) is shown in Fig. 3A. This is defined as *G*_{xy} = *R*_{xy}/*R*_{s, 0}^{2}, where *R*_{xy} is the transverse resistance and *R*_{s,0} is the zero field sheet resistance. The data in Fig. 3A were acquired on sample 1 at the same *V*_{g} values as in Figs. 1B and 2, the inset showing a low *H* view. *G*_{xy} is negligible at *V*_{g} = 0, as the Hall effect in this sample is suppressed at low *T* by hopping conduction (fig. S2) (*42*, *47*). Increasing *V*_{g} to +1.6 V induces a clear Hall effect, however, with both negative slope and distinct curvature (Fig. 3A, inset). The negative slope is important, as it suggests that at this *V*_{g} (which is effectively metallic from Figs. 1B and 2), inversion of the p-type surface to n-type has occurred. Further increasing *V*_{g} to +1.8, +2, and +3 V (Fig. 3A, main panel) then leads to the emergence of a very different state with a much larger, positive slope, nonlinear Hall effect. *G*_{xy}(*H*) is sigmoidal, immediately suggestive of the anomalous Hall effect, the positive slope being consistent with the anomalous Hall coefficient in ferromagnetic Fe_{1−x}Co* _{x}*S

_{2}(

*36*).

To probe for possible hysteresis, Fig. 3B shows *V*_{g}-dependent (from +1.1 to +3 V) *G*_{xy}(*H*) in the same sample at 1.8 K, with the low-field behavior highlighted in the inset. Clear coercivity (*H*_{c} = 700 Oe) and remanence occur at the highest *V*_{g} (see inset). The data of Figs. 1 to 3 thus establish gate induction of an effectively metallic FeS_{2} surface state with a strong, sigmoidal *G*_{xy}(*H*), a sign consistent with the anomalous Hall coefficient of Fe_{1−x}Co* _{x}*S

_{2}and both coercivity and remanence. We take these observations as strong evidence for electric field–induced ferromagnetism in this diamagnet. The data of Fig. 3C establish repeatability, demonstrating finite low temperature

*H*

_{c}at high

*V*

_{g}in anomalous Hall data on three samples (samples 1, 2, and 3). Note that the cutoff

*H*

_{c}value in Fig. 3C (which has a log

_{10}scale) is 7 Oe, the minimum value detectable in our superconducting magnet-based measurements. We thus take the point where

*H*

_{c}falls to ≤7 Oe as a good estimate of

*T*

_{C}. At a high

*V*

_{g}of +3 V, the

*H*

_{c}(1.8 K) and

*T*

_{C}values vary somewhat from sample to sample (from 400 to 2300 Oe and 10 to 24 K), although both increase monotonically with

*V*

_{g}in a single sample: Fig. 3C shows sample 3 at +2, +3, and +4 V, for example, where

*T*

_{C}is 10, 12, and 15 K, respectively. The crystal-to-crystal variations in the gate-induced surface ferromagnetic parameters may be related to variations in surface conduction in FeS

_{2}single crystals, which are highly sensitive to the surface structure and chemistry (

*42*); this is a topic worthy of further study. The highest

*T*

_{C}achieved was 24 K in sample 2 at 3 V, where

*H*

_{c}(1.8 K) reached 2300 Oe.

To further explore the temperature evolution of the high *V*_{g} ferromagnetism, Fig. 3D plots *R*_{xy}(*H*) in sample 1 from 1.8 (blue open circles) to 300 K (red open circles). The large positive slope anomalous Hall effect at low *T* is seen to eventually give way to a linear negative slope ordinary Hall effect at 300 K. However, two effects are convoluted here: the loss of surface magnetism and the crossover to conduction dominated by the n-type interior. What is remarkable in Fig. 3D is that, while *T*_{C} = 16 K, the anomalous Hall effect remains dominant to 200 K and is detectable (on the ordinary Hall background) at 280 K. While *H*_{c} vanishes at 16 K, clear contributions to anomalous Hall thus exist at up to 280 K (i.e., 20 times *T*_{C}), suggesting that ferromagnetic correlations persist to unusually high *T*. This is highlighted in Fig. 4 (A and B), which shows the *T* dependence of |*dR*_{xy}/*dH*|_{H → 0} and *R*_{xy}^{F}. The first of these quantities is simply the low-field Hall slope, while the second is the *R*_{xy} obtained by linearly extrapolating high *H* data (>70 kOe) to *H* = 0; both thus probe the nonlinear magnetic contribution to *R*_{xy}(*H*). Both quantities fall rapidly at *T*_{C} (see the dashed vertical line in Fig. 4, A and B) but exhibit long, near-linear high *T* tails, reaching zero only at 300 K, where bulk conduction dominates. This *T* dependence is in stark contrast to standard Curie-Weiss behavior in an interacting paramagnet, as illustrated by the solid line in Fig. 4A of the form *C*/(*T* − 16 K) (where *C* is a constant).

One possible interpretation of Fig. 4 (A and B) is that the induced FeS_{2} surface ferromagnetism occurs close to the 2D limit, thus suppressing *T*_{C} despite strong ferromagnetic correlations. While the cubic magnetocrystalline anisotropy of Fe_{1−x}Co* _{x}*S

_{2}is unknown at low

*x*, at

*x*= 1 (i.e., CoS

_{2}), it is parameterized by low

*T*anisotropy constants

*K*

_{1}and

*K*

_{2}of only −2.5 × 10

^{4}erg cm

^{−3}and ~0 erg cm

^{−3}. (

*48*) This is an order of magnitude lower than even face-centered cubic Ni. (

*49*) The ferromagnetism electrically induced in FeS

_{2}could thus be expected to be weakly anisotropic, i.e., of Heisenberg type (

*50*). Mermin-Wagner physics (

*51*) would then apply, limiting the 2D

*T*

_{C}despite strong ferromagnetic interactions. In this context, we note that electrostatic calculations (fig. S3) indicate that 90% of the induced electrons in these EDLTs are confined within (at most) ~2 nm (i.e., four unit cells) of the surface. In terms of direct extraction of information on magnetic anisotropy from our data, some weak perpendicular magnetic anisotropy apparently occurs based on the finite

*H*

_{C}and remanence in Fig. 3B. Simple estimates using

*H*

_{C}≈ 1 kOe (Fig. 3C) and saturation magnetization ~0.2 μ

_{B}per Fe (see below, Fig. 5) yield low effective uniaxial anisotropy values, ~10

^{4}erg cm

^{−3}. Further work will be needed to fully characterize magnetic anisotropy in the voltage-induced ferromagnetic state, including understanding the origin of the perpendicular magnetic anisotropy. We note, in this context, that the high-field curvature in Fig. 3B may indicate an additional paramagnetic contribution, rather than ferromagnetic anisotropy.

An alternative interpretation of the temperature dependence in Fig. 3D involves superparamagnetism. The zero-coercivity sigmoidal-shaped curves seen above 16 K in Fig. 3D can be well fit to *R*_{xy} = *k*_{1}*L*(μ_{c}μ_{0}*H*/*k*_{B}*T*) + *k*_{2}μ_{0}*H*, where *L* is the Langevin function, μ_{c} is a cluster magnetic moment, μ_{0} is the vacuum permeability, and *k*_{B} is Boltzmann’s constant. This describes the *H* and *T* dependence of the magnetization with a Langevin function (as expected in a simple superparamagnet above its blocking temperature), *k*_{1} being related to the anomalous Hall coefficient and *k*_{2} capturing a paramagnetic background and the ordinary Hall effect. As shown by the solid lines in Fig. 3D, good fits can be obtained, indicating that *R*_{xy}(*H*) at any *T* > 16 K can be described as a Langevin superparamagnet. Figure 4C further illustrates that the extracted *k*_{2}(*T*) behaves rationally, crossing from positive at low *T* (likely a paramagnetic background) to negative at high *T* (due to the bulk negative ordinary Hall coefficient). The extracted μ_{c} values (Fig. 4D) of ~200 to 1000 μ_{B} are also plausible. Using again an approximate magnetization of 0.2 μ_{B} per Fe (see below, Fig. 5) and an accumulation layer thickness of 2 nm, we deduce superparamagnetic volumes corresponding to disk-shaped clusters of diameter ~4 to 12 nm (Fig. 4D, right axis). Inhomogeneities in the EDL or at the FeS_{2} crystal surface could be responsible for this nanoscopic magnetic inhomogeneity, rendering the 16 K scale a superparamagnetic blocking temperature. However, there are at least two issues with this picture. First, as shown in Fig. 4D, the deduced μ_{c}(*T*) has non-negligible *T* dependence, meaning that the expected *H*/*T* scaling of a Langevin function is not exactly obeyed. Second, in this interpretation, the true *T*_{C} would be as high as ~280 K, around double the maximum *T*_{C} of bulk Fe_{1−x}Co* _{x}*S

_{2}, which is also only reached at high

*x*. We thus view it as unclear whether the high

*T*behavior in Fig. 3D is best viewed as a paramagnet with strong ferromagnetic correlations persisting to high

*T*or as a superparamagnet. Vitally, however, regardless of interpretation of Figs. 3 and 4 in terms of a ferromagnetic to paramagnetic transition or a ferromagnetic (blocked) to superparamagnetic (unblocked) transition, voltage-induced ferromagnetism in diamagnetic FeS

_{2}remains clear.

In terms of rationalization of the *V*_{g}-induced ferromagnetism in FeS_{2} EDLTs, we first note that quantitative comparison to Fe_{1−x}Co* _{x}*S

_{2}supports feasibility of induction of a ferromagnetic state. Prior work on Fe

_{1−x}Co

*S*

_{x}_{2}crystals found ferromagnetism to emerge with

*T*

_{C}≈ 1 to 2 K at a doped electron density of ~1 × 10

^{20}cm

^{−3}(

*35*). This is equivalent to a 2D surface density of ~2 × 10

^{13}cm

^{−2}, assuming a four unit cell accumulation layer (see fig. S3). These 2D densities are easily achievable in EDLTs (

*8*–

*10*), although quantitative comparison is frustrated by the fact that the anomalous Hall effect overwhelms the ordinary Hall effect at high

*V*

_{g}(consider Fig. 3, A, B, and D where there is no indication of a negative high

*H*slope at low

*T*), precluding quantification of induced electron densities.

Further insight is provided by first-principles electronic structure calculations, which have been previously applied to Fe_{1−x}Co* _{x}*S

_{2}(

*52*). Hubbard

*U*–corrected density functional theory (DFT +

*U*) using approaches described in Materials and Methods (

*53*,

*54*) was used to first reproduce the known crystal and electronic structures of FeS

_{2}. Electrostatic gating was then simulated by artificially adding electrons to the FeS

_{2}unit cell to the 3D and projected 2D densities shown in Fig. 5 (top and bottom axes, respectively). The magnetization (

*M*) was then extracted versus electron density, resulting in the colored points in the main panel. Ferromagnetic magnetization is found to emerge above ~3 × 10

^{14}cm

^{−2}, which, critically, is again within realistic capabilities of IL gating (

*8*–

*10*). Note that the magnetization eventually reaches 1 μ

_{B}per Fe, consistent with the half-metallicity, or at least high spin polarization, in Co

_{1−x}Fe

*S*

_{x}_{2}(

*37*–

*39*,

*52*). Additional understanding of the origin of the induced ferromagnetism was obtained from Wannier function–based (

*55*) tight-binding parameterization of the DFT-calculated FeS

_{2}conduction band structure, followed by calculation of the filling-dependent susceptibility χ(

*k*) (see Materials and Methods). The resulting χ(

*k*) is shown in the inset in Fig. 5, color-coded to the electron densities in the main panel. As the density is increased, a single peak in χ(

*k*) emerges at the Γ point (

*k*= 0), demonstrating instability toward long-range ferromagnetism, apparently of Stoner type. The threshold filling for the onset of ferromagnetism corresponds to the point at which the Fermi level moves from sulfur

*p*states in the lower region of the conduction band to Fe

*e*

_{g}states. These calculations thus confirm the feasibility of ferromagnetism in FeS

_{2}induced solely by filling of a narrow

*e*

_{g}band, strongly supporting the experimental findings. More detailed calculations will be reported elsewhere, clarifying the different mechanisms and doping thresholds for ferromagnetism in Co-doped and electrostatically doped FeS

_{2}(

*56*).

Additional insight into the *V*_{g}-induced insulator-metal and diamagnet-ferromagnet transition is provided by *V*_{g} sweep data (Fig. 6). The resistance (*R*) during a 5 mV s^{−1} ± 4 V cycle at 240 K is shown in Fig. 6A; this temperature was chosen to be as low as possible (to maximize the *R* modulation) while maintaining tolerable ion mobility in the IL (see Materials and Methods). Unlike the data in Figs. 1 to 4, which were acquired after a 30 min saturating *V*_{g} application (see Materials and Methods), these data reveal gating dynamics. Substantial hysteresis is apparent in Fig. 6A, with a consequent sweep rate dependence (fig. S4). Given the evidence of predominantly electrostatic gating, this hysteresis is ascribed not to electrochemistry at the FeS_{2} surface but rather to limited ion mobility in the IL, as expected in a macroscopic side-gate device at this *T* (*10*, *57*). Beginning at *V*_{g} = 0, *R* is seen to rapidly increase with increasing *V*_{g}, reaching a peak at 1.5 V, at about twice the initial *R*. Further increasing *V*_{g} then induces a precipitous drop to ~1.5 kilohm, which is maintained as *V*_{g} is decreased back to 0 V. *R* is thus bistable at *V*_{g} = 0 due to hysteresis associated with IL dynamics. Negative *V*_{g} then increases *R* to a small, broad peak at −2 V and ~24 kilohm, *R* remaining relatively constant out to −4 V and back to −1 V. Simply, we interpret the peak at small positive *V*_{g} as a characteristic signature of the previously deduced surface inversion. Specifically, *R* first increases with positive *V*_{g} due to depletion of the initially p-type surface, reaching a peak at the compensation point, limited only by bulk conduction. Further increasing *V*_{g} then accumulates electrons, rapidly decreasing *R*. Under the slow gating in Fig. 1B (see Materials and Methods), this inversion is already complete in the +1 V *R*_{s}(*T*), highlighting the complementary information in Fig. 6A. As shown in fig. S5, resistance anisotropy also peaks at the +1 V compensation point in Fig. 6A, likely due to gating inhomogeneity at the highly sensitive compensation point; these factors will also play a role in the more subtle inversion from n- to p-type on reversing *V*_{g} in Fig. 6A.

Further supporting the above, Hall data at the indicated *V*_{g} are shown in Fig. 6 (C to J) (color coded to the points in Fig. 6A), taken by pausing loops such as Fig. 6A and then rapidly cooling to 180 K. This cooling freezes the IL, thus achieving sufficiently stable resistances to permit Hall measurements. At *V*_{g} = 0 (Fig. 6C), *R*_{xy}(*H*) is near linear with a negative slope due to the small (hopping-suppressed) surface contribution but finite n-type bulk contribution. The situation is similar at +1 V (Fig. 6D), although the increased surface resistance (Fig. 6A) now drives additional bulk current, increasing the magnitude of the Hall slope. However, marked changes occur at +2 V (Fig. 6E), where *R*_{xy}(*H*) transforms to a nonlinear sigmoidal shape with positive slope. As already discussed, this occurs due to a positive anomalous Hall coefficient, the anomalous Hall effect arising from ferromagnetic correlations that extend far above *T*_{C} at high positive *V*_{g}. Figure 6E is thus consistent with Fig. 6A, where *R* is falling precipitously at +2 V, indicating transformation to the n-type ferromagnetic metallic state. Also consistent with Fig. 6A, the positive slope sigmoidal *R*_{xy}(*H*) is maintained at +4, +2, and 0 V (Fig. 6, F to H) due to persistence of the magnetic state. This is then lost on going from 0 to −4 V (compare Fig. 6, H and I), panels (I) and (J) in Fig. 6 being similar to panels (C) and (D) in Fig. 6. Last, we note that the corresponding gate current (*I*_{g}) sweep in Fig. 6B is also consistent with the above. The overall form is typical of electrostatically functioning EDLTs, ascending and descending *V*_{g} sweeps inducing positive and negative *I*_{g}, respectively, due to charging and discharging. These currents are small for such a macroscopic device (<0.5 μA), except at ∣*V*_{g}∣ > 3 V, which we attribute to the electrochemical stability window of the IL. The only additional features are small peaks on the ascending *V*_{g} sweep at −1 and 2 V, which (see the vertical dashed lines) correspond to the onset and completion of surface inversion.

## CONCLUSIONS

Detailed experimental evidence has been presented establishing that semiconducting diamagnetic FeS_{2} with a zero-spin electronic configuration can be electrolyte-gated into a ferromagnetic metallic state in single-crystal EDLTs. A predominantly electrostatic gating mechanism is concluded, driving inversion of the initially p-type FeS_{2} surface to an n-type ferromagnetic metal with voltage-tunable *T*_{C} up to 25 K. Computational and analytical theory support this, demonstrating feasibility of inducing ferromagnetism by band filling alone. State-of-the-art electrolyte gating is thus capable of inducing surface ferromagnetism in even nonmagnetic materials, with deep implications. Future work could focus on theoretical identification and experimental verification of other diamagnets in which ferromagnetism can be induced, extension to thin films, further exploration of the nature of the voltage-induced ferromagnetism (including the ferromagnetic anisotropy and the issue of paramagnetism versus superparamagnetism), enhancement of the induced *T*_{C}, and demonstration of important device function. The latter could include generation of voltage-controlled highly spin-polarized surface currents for spin injection into diamagnetic interiors or overlying heterostructures, representing a small fraction of the possibilities opened up by this work.

## MATERIALS AND METHODS

### Crystal and device preparation

Pyrite FeS_{2} single crystals were grown using chemical vapor transport, as described earlier (*42*, *43*, *47*). Precursor FeS_{2} powder was first synthesized by reacting Fe (99.998% purity; Alfa Aesar) and S (99.9995% purity; Alfa Aesar) powders in evacuated quartz ampoules at 500°C for 6 days, followed by repeated grinding and reaction until phase-pure pyrite FeS_{2} was obtained by powder x-ray diffraction. Quartz ampoules were then loaded with 2.2 g of this precursor FeS_{2}, 100 mg of FeBr_{2} transport agent (99.999% purity; Sigma-Aldrich), and additional S powder (0.06 g for sample 1 and 0.34 g for samples 2 and 3), followed by evacuation to ~10^{−6} torr and flame sealing. The ampoule was then placed in a two-zone furnace for a 17-day growth with the source and growth zones at 670° and 590°C, respectively [after a 3-day inversion period (*42*, *43*, *47*)]. Detailed characterization was presented earlier (*42*, *43*, *47*), indicating phase purity, total metals-basis impurity concentrations of <40 parts per million, and unit cell–level surface roughness. Select structural and chemical characterization data are provided in fig. S1 and table S1. As described in prior work (*43*), lower S loading (as for sample 1) leads to increased S vacancy density and n-type doping and thus lower bulk resistivity.

Crystals were prepared for transport by polishing from the opposite side of a large facet (with SiC grinding paper and diamond slurries down to 3 μm) to thicknesses of ~200 μm, followed by sequential ultrasonication in acetone, methanol, and isopropanol. Au contacts (~50 nm thick) were then sputtered on the pristine (i.e., unpolished) facet. Crystals were then placed on an Al_{2}O_{3} wafer with an Au-coated quartz cylinder, which served as both a high-area gate electrode and liquid container. Two ILs were used: 1-ethyl-3-methylimidazolium bis(trifluoro-methylsulfonyl) imide (EMI/TFSI) and diethylmethyl(2-methoxyethyl)ammonium TFSI (DEME/TFSI).

### Electronic transport measurements

Four-terminal van der Pauw resistance measurements [as well as gate voltage (*V*_{g}) application and gate current measurement] were achieved with Keithley 2400 source-measure units in a commercial cryostat from 1.4 to 300 K in perpendicular magnetic fields to 9 T. In Figs. 1 to 4, *V*_{g} was applied at 300 K for ~30 min, followed by cooling to the base temperature or the temperature shown before warming or sweeping field. EMI/TFSI was the IL for these measurements. In contrast, the *V*_{g} sweep in Fig. 6 (A and B) was collected by cooling to 240 K at *V*_{g} = 0, followed by sweeping *V*_{g} from 0 to 4 V to −4 to 0 V at 5 mV s^{−1} using DEME/TFSI as the IL. This IL was selected in this case as its lower melting point than EMI/TFSI-enabled *V*_{g} sweeps at lower temperature, where surface conduction is more dominant, and the dynamic range in sample resistance is thus higher. The 0 to 4 V to −4 to 0 V voltage sequence was repeated until no qualitative features of the hysteresis loop changed in subsequent loops (the loop in Fig. 6 was the third taken). A subsequent and final *V*_{g} loop was then performed to collect the Hall data in Fig. 6 (C to J). At each *V*_{g} shown in Fig. 6 (C to J), the 240 K *V*_{g} sweep was paused, the sample was cooled to 180 K at ~10 K min^{−1}, Hall data were collected, the sample was returned to 240 K, and the *V*_{g} sweep was continued. The cooling to 180 K (below the melting point of DEME/TFSI) was done to minimize drift during the Hall sweep.

### Theoretical methods

First principles calculations were performed with DFT with a Hubbard *U* correction (i.e., DFT + *U*) using the Vienna ab-initio simulation package implementation of the projector-augmented-wave (PAW) approach (*53*, *54*). The PBEsol-generalized gradient approximation was used to approximate the exchange-correlation functional. A Γ-centered 8 × 8 × 8 *k*-point grid and a plane wave cutoff of 500 eV were used. As discussed elsewhere (*56*), *U* = 5 eV was used for these calculations, achieving agreement with FeS_{2} lattice constants and S─S bond lengths to within <1 and <2.5%, respectively. Electrostatic gating was then simulated by varying the total number of electrons per unit cell, with the highest level considered being 0.5 added electrons per Fe ion (see Fig. 5). The ion positions and lattice vectors were allowed to relax at each electron concentration. The magnetization per Fe ion was then calculated by integrating the magnetization density over the whole cell and dividing by the number of Fe ions. Following this, a Wannier function–based (*55*), tight-binding model was built using nonspin-polarized DFT calculations as an input, and the electronic susceptibility was then calculated using the Lindhard function. More detailed theoretical results will be reported elsewhere (*56*).

## SUPPLEMENTARY MATERIALS

Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/6/31/eabb7721/DC1

This is an open-access article distributed under the terms of the Creative Commons Attribution-NonCommercial license, which permits use, distribution, and reproduction in any medium, so long as the resultant use is **not** for commercial advantage and provided the original work is properly cited.

## REFERENCES AND NOTES

**Acknowledgments:**We gratefully acknowledge E. S. Aydil for his role in shaping our understanding of electronic transport in FeS

_{2}crystals, forming a foundation for this work.

**Funding:**This work was primarily supported by the NSF through the University of Minnesota (UMN) MRSEC under DMR-1420013. Parts of the work were carried out in the Characterization Facility, UMN, which receives partial support from NSF through the MRSEC program. Portions of this work were also conducted in the Minnesota Nano Center, which is supported by the NSF through the National Nano Coordinated Infrastructure Network under NNCI-1542202. The Minnesota Supercomputing Institute is acknowledged for providing resources that contributed to the research results reported.

**Author contributions:**C.L. and J.W. conceived the study. J.W. and B.V. performed the measurements, assisted by K.H., on single crystals grown and characterized by B.V. and J.W. Supervision of all aspects of the experimental work was provided by C.L. Calculations were performed by E.D.-R. and supervised by T.B. and R.M.F. The paper was written by J.W. and C.L. with input from all authors.

**Competing interests:**The authors declare that they have no competing interests.

**Data and materials availability:**All data needed to evaluate the conclusions in the paper are present in the paper and/or the Supplementary Materials. Additional data related to this paper may be requested from the authors.

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