Ambipolar ferromagnetism by electrostatic doping of a manganite

Complex-oxide materials exhibit physical properties that involve the interplay of charge and spin degrees of freedom. However, an ambipolar oxide that is able to exhibit both electron-doped and hole-doped ferromagnetism in the same material has proved elusive. Here we report ambipolar ferromagnetism in LaMnO3, with electron–hole asymmetry of the ferromagnetic order. Starting from an undoped atomically thin LaMnO3 film, we electrostatically dope the material with electrons or holes according to the polarity of a voltage applied across an ionic liquid gate. Magnetotransport characterization reveals that an increase of either electron-doping or hole-doping induced ferromagnetic order in this antiferromagnetic compound, and leads to an insulator-to-metal transition with colossal magnetoresistance showing electron–hole asymmetry. These findings are supported by density functional theory calculations, showing that strengthening of the inter-plane ferromagnetic exchange interaction is the origin of the ambipolar ferromagnetism. The result raises the prospect of exploiting ambipolar magnetic functionality in strongly correlated electron systems.


Supplementary Note 1. Ionic liquid gating
In our study, the gate voltage, VG, was applied at room temperature, and the voltage remains during the low-temperature measurement. Sheet resistance (RS) measurement is performed during the cooling process from 300 to 2 K and the desired gate voltage was maintained throughout the whole process. The same gating procedures are maintained in all measurements.
Before characterizing our samples, a leakage current test was performed for every sample, with purposes of selecting functional devices and reducing leakage current. The leakage current test was always conducted using two sequential processes, namely a cooling process with VG = -1 V applied from 300 to 180 K and a warming process without VG from 180 to 300 K. The leakage current remains in the nA range for good samples. It shall be noted that the leakage current is typically reduced after the two processes, possibly benefited from crystallization of water moisture in the ionic liquid.
We have completed a comprehensive characterization of the device stabilization and relaxation in a vacuum environment of 10 -4 Torr at 300 K. Supplementary Figure 1 shows the temporal changes in the RS when a constant gate voltage is applied at 300 K. With the VG applied, the RS reaches a nearly constant value after 30 min. Subsequently, the gate voltage is settled to zero, the RS gradually returns to the initial value of RS after a few hundred minutes at VG = 0. Finally, RS reaches a stable value that remains approximately constant, demonstrating that the electrostatic gating is the dominant effect. Figure 1. Temporal changes in the sheet resistance (RS) of an ionic liquid/3 unit cell (uc) LaMnO3/SrTiO3 (LMO/STO) device. The RS as a function of time on applying a positive/negative voltage for 30 min and then setting the gate voltage to zero. All measurement were carried out inside a high vacuum chamber at a pressure of 10 -4 Torr.

Supplementary Note 2. Electrical and morphology characterization before and after the gating
We conducted electrical and atomic force microscope measurements on 3 unit cell (uc) LaMnO3 (LMO) samples before and after the gating measurements. Supplementary  Figure 2a shows the RS as a function of the temperature of an as-grown LMO before adding ionic liquid, exhibiting a semiconducting behaviour. Supplementary Figure 2b shows a typical atomic force microscope image of the surface of the as-grown 3 uc LMO. The surfaces of the samples are atomically flat, with a root-mean-square (RMS) surface roughness of ~ 0.16 nm. Subsequently, the temperature-dependent RS of the LMO thin film was measured with positive and negative 3 V VG across ionic liquid at 300 K. Supplementary Figure 2c shows that the -3 V induces a clear metal-to-insulator transition, and the RS recovers original state after removing the gate voltage. Then, a 3 V VG was applied and the device shows consistent transport phenomena. In the case of structural defects, such as cationic defects or oxygen vacancy, the RS will not immediately revert to the original state, due to the extremely low mobility of the defects around or below room temperature and the dramatic impact on RS from the defects.

Supplementary Note 4. Cooling and warming runs for the resistance measurements
In manganites competing phases, namely ferromagnetic conducting phase (FM-C) and charge-ordered insulating phase (CO-I), may coexist at the mesoscopic length scale. Typically, the presence of thermal hysteresis serves as evidence of phase separation in manganites and its absence may suggest a single-phase magnetic state in our samples. In addition, studying phase separation from first-principles would be very valuable. However, the task of taking into account non-uniform doping and local structural distortions in first-principles calculations, which also need to include electron-electron correlation effects, to explore competing phases in strongly correlated oxide materials is enormously complicated. Thus far, there is no clear understanding how even to approach this problem yet. The only attempts are analysis based on model Hamiltonians 4,5 , which were used to map out the spatial distribution and size of the competing phases on the mesoscopic scale. Therefore, more work is needed to understand the possibility of competing phases in our samples, which we cannot completely exclude.

Supplementary Figure 4. Cooling and warming measurement of resistance for both electron-and hole-doped LaMnO3.
The electron-and hole-doping were realized by applying +3 and -3 V VG across the ionic liquid.

Supplementary Note 5. Hall effect measurement
The Hall effect measurement was performed at different temperatures in a magnetic field up to 9 Tesla. The Hall conductivity (σxy) is defined by the expression of ρxy/ρxx 2 , where ρxx and ρxx are transverse and longitudinal resistivity, respectively. The σxy of CMR material can usually be expressed as where and are the ordinary and anomalous Hall conductivity, respectively. At room temperature, 300 K, the slope of ρxy is dominated by the anomalous Hall effect (AHE) contribution. Hence, the sign of the ρxy at 300 K represents reversed type of carriers for both electron-and hole-doping gating cases 6,7 .
It is therefore inappropriate to conclude the sign and density of carrier at room temperature. At low temperature, the ρxy has a measureable and stronger ordinary Hall effect (OHE) contribution at high field. The OHE can be written as RH = 1/n(p)e, where RH is the ordinary Hall coefficient, e is elementary charge, and n(p) is carrier density for electron(hole). In Fig. 2d  which dominant at different regimes of longitudinal conductivity (σxx). As a function of σxx for diverse materials, the three broad regimes are (i) a high conductivity regime [10 6 (Ω cm) -1 < σxx] in which AHE are due to dominant skew scattering and normal Hall effect can be visible; (ii) in intermediate regime [10 4 (Ω cm) -1 < σxx < 10 6 (Ω cm) -1 ] where AHE is independent of σxx due to intrinsic contribution; and (iii) a bad-metal regime [σxx < 10 4 (Ω cm) -1 ] where AHE changes dramatically with changing σxx. In particular, the intrinsic mechanisms occur in magnetic materials with strong spin-orbit coupling, such as oxides and diluted magnetic semiconductors (DMSs). Manganites, including the gated 3 uc LMO, have a σxx between 10 -1 to 10 4 (Ω cm) -1 and are in the bad-metal regime.
Unfortunately, direct measurement of magnetism in LMO is prohibited by two mauor technical challenges, namely (a) the extremely weak signal from the limited volume of our 5 uc-thick, 300 µm-long and 50 µm-wide LMO, and (b) spurious signal from applied current, gold electrode, and contamination in ionic liquid.

Supplementary Figure 5. xy of (a) hole-and (b) electron-doped LMO under
various gate voltages at 2 K.

Supplementary Note 6. First-principles calculations
Theoretical modelling of the orthorhombic Pbnm LMO was performed using density functional theory, the prouected augmented wave method, and PBEsol pseudopotentials 8 , as implemented in the Vienna ab initio simulation package 9 .
Correlation effects beyond generalized gradient approximation (GGA) were treated at a semi-empirical GGA+U level within a rotationally invariant formalism with U = 5 eV on Mn 3d-orbitals 10  where 1 and 2 are the first and the second nearest-neighbor intra-plane exchange interactions and 1 and 2 are the first and the second nearest-neighbor inter-plane exchange interactions. Taking into account of a reference energy, this system of five linear equations contains five unknowns and can be uniquely solved with respect to the exchange constants. In a layered system, it is convenient to express the exchange in terms of total intra-plane exchange Jab and total inter-plane exchange . Considering the number of the first and the second nearest neighbors, the total intra-plane exchange coupling is given by = 4 1 + 2 2 . Similarly, the total inter-plane exchange is Supplementary Figure 6h shows the calculated nearest-neighbor exchange parameters 1 , 2 , 1 and 2 , as a function of doping. As seen in the figure, 1 , 1 and 1 are positive (ferromagnetic), while 2 is negative (antiferromagnetic). With doping, 1 and 1 increases, 2 remains nearly constant, while 2 decreases. The overall intra-plane exchange in the first nearest neighbors involves twice more than that in the second nearest neighbors, which leads to a FM ordering in the plane The orbital ordering of biaxially strained LMO was found to be similar to that known for bulk LMO. Supplementary Figure 6f shows the charge density contour of LMO in the a-b plane, which reveals a checker-board-type orbital ordering in that plane, similar to that found previously for bulk LMO 12 . This ordering is maintained when the system is homogeneously doped.

Supplementary Note 7. Structural characterization
First, we imaged 3 uc LMO deposited on STO substrate. Supplementary Figure 7a shows a high-angle annular dark field (HAADF) image of the sample along the [010] zone axis. Supplementary Figure 7b shows the EELS of the uncapped 3 uc LMO. In the ADF image, the contrast of the outermost unit cell of LMO becomes gradually blurry. But, the EELS signal from the outermost unit cells of LMO is still visible. This indicates that the outermost unit cell of LMO becomes partially amorphous possibly due to the damage by the focused ion beam during the STEM sample preparation.
Therefore, in order to correctly characterize the 3 uc LMO and avoid the damage during the STEM sample preparation, we added a STO capping layer to protect the surface of LMO and performed STEM-EELS using the same conditions (see Fig. 1 of Main Text).