Introduction

To develop spintronic devices and integrated circuits, such as magnetic random access memories, it is necessary to use current to generate an effective magnetic field for the manipulation of the individual magnetization in each element. To date, many investigations have given us clear evidence showing that electrical current can modulate the magnetization direction in magnetic tunnel junctions through spin transfer torque1,2, spin–orbit torque3, and the spin Hall effect in heavy 5d metal wires4,5, which realizes magnetic random access memories with low energy consumption. However, magnetization manipulation still requires a large current density (> 105 A/cm2). This is probably because typical ferromagnetic materials consist of 3d transition metals, in which intra- and interatomic exchange interactions of spins are too strong to interplay with electrical current.

The rearrangement of two-dimensional (2D) layered crystals is very important because novel properties and functions emerge that the bulk form of the corresponding material does not have. For example, bilayer graphene shows superconductivity6 and Hofstadter’s butterfly7 by twisting the orientation of the upper layer; a 2D single-layer ferromagnet changes into an antiferromagnet by stacking one more layer8; and transition metal dichalcogenide MoS2 shows memristive behaviour by connecting misoriented sheets that form grain boundaries (GBs)9. Moreover, MoS2 is a not magnetic material in pure single-crystal form, but it has been found to show ferromagnetism in polycrystalline structures, edge-rich nanowires, and defective structures10,11,12,13,14,15,16,17,18,19. Additionally, theoretical analysis indicates that imperfections in MoS2 crystals, such as point defects and topological defects, induce spin polarization in the 4d electrons of Mo atoms20,21. Since both conduction electrons and localized spins consist of mainly Mo 4d electrons, they would easily interact with each other because of the same orbital and relatively weaker intra- and interatomic exchange interactions in 4d spins compared to those of 3d ferromagnets. Thus, it can be estimated that magnetization will be easily modulated using electrical current in polycrystalline ferromagnetic MoS2. In this study, we demonstrate the current-induced modulation of ferromagnetism in a polycrystalline MoS2 film with several nanometre grains22,23 deposited by sputtering method, which produces a high density of GBs inducing ferromagnetism that we previously reported11. We measure the magnetic field H dependence of the magnetoresistance (MR) by applying a widely ranging current (1 nA–0.562 mA), by which we find that the MR curves show a variety of changes depending on the current intensity. Positive MR is mainly observed because of the spin-split band structure, and thus, we can estimate the magnetization properties, such as the coercive force, the magnetic field for magnetization saturation and the spin-split band structure inducing ferromagnetism. Additionally, linear MR is observed, which depends on the direction of the applied magnetic field.

Figure 1 shows a schematic representing the localized spin states in the Hz (out of plane) measurement. When the current is small, the spin density is not high enough to form magnetization in the whole film, so a magnetic field is needed to align the localized spins (Fig. 1a). As the current increases, current electrons start to be trapped at the GBs, which leads to an increase in the spin density and results in the spontaneous formation of film magnetization (Fig. 1b). As the current increases further, a current-induced magnetic field is effectively applied to the localized spins because of the spin-dependent scattering at the GBs, which results in the alignment of the localized spins along the Hy (in-plane) direction (Fig. 1c). With a further increase in current, the magnetization aligns along the Hz direction again because of a further increase in the localized spins in the GBs (Fig. 1d). The current density is estimated to be approximately 7 × 10–3 A/cm2–4 × 103 A/cm2 by dividing 1 nA–0.562 mA by the area defined by a 1.8 mm width and 7.5 nm depth. Considering the critical current of magnetization switching in magnetic tunnel junctions (> 105 A/cm2)2,24,25,26,27,28, our MR modulation is successfully achieved at ultralow current densities (< 103 A/cm2), even though the spin–orbit interaction in 4d electrons is weaker than that in 5d electrons, which provides evidence that current electrons easily interact with the localized 4d spins in the GBs in a polycrystalline MoS2 film. Our results place focus on the future investigation of 4d ferromagnets29, polycrystalline ferromagnetic semiconductors, and recently discovered 2D ferromagnets8,30,31,32,33,34, by controlling and manipulating ferromagnetism via basic electronics with low power consumption35,36,37,38,39.

Figure 1
figure 1

Schematic of the localized spin states in our magnetoresistance measurements. (a) In the small current applied, broad MR curves with dips A & A′ are observed in the Hz measurement because of the low spin density with disorder. (b) As the current increases, dip B with a large MR ratio is observed because of the high spin density along the Hz direction. (c) With a greater increase in current, the positive MR disappears, and flat or linear MR is observed because of the current-induced spin–orbit effective magnetic field along the Hy direction. (d) With a further increase in current, dip C is observed because of the high spin density, in which magnetization is along the Hz direction.

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Results and discussion

In our previous study, out-of-plane 2θ–θ X-ray diffraction was measured40, in which MoS2 (002) peak was observed at 2θ  = 13.5°. Using Bragg’s law, we can estimate the layer distance of MoS2 c = n × λ/2sinθ = 6.56 Å. Here, we use n = 1 and λ = 1.5418 Å (wavelength of CuKα). It is confirmed that this value is near the layer distance of bulk MoS2 (c = 6.15 Å)41. The observed MoS2 (002) peak is broad because our sample is polycrystal with imperfection of periodicity and incomplete flatness of van deer Waals surface.

Also, in our previous study, height distribution of MoS2 surface fabricated by sputter in the similar condition was measured using atomic force microscopy, in which root mean square (RMS) was 0.515 nm42. Compared to monolayer MoS2 by the chemical vaper deposition, this value is not bad because it is less than two layers distance 0.656 nm. Thus, our polycrystal MoS2 keeps van der Waals horizontal structure.

In addition, cross sectional lattice structure in polycrystal MoS2 was observed using the transmission electron microscopy (TEM) in our previous study11, from which we guess that the grain size is 5 nm. Based on this value, we can estimate the ratio of Mo atoms along GBs as follows. We assume x cm × y cm polycrystal monolayer MoS2, in which grains are regular squares with 5 nm edge length and are arranged like the grid of a checkerboard. The length of GBs is x cm/5 nm × y cm × 2 = 4xy × 106 cm, while the Mo density in GBs is 1/3.16 Å = 1/3.16 × 108 cm−1, in which we assume that Mo-Mo distance in GBs is 3.16 Å. Thus, the number of Mo atoms along GBs is 1/3.16 × 108 cm-1 × 4xy × 106 cm = xy × 1.27 × 1014 atoms. In single crystal monolayer MoS2 with a = 3.16 Å41, the Mo density is 1.16 × 1015 cm−2, and thus, the number of Mo atoms in the bulk area of xy cm2 is xy × 1.16 × 1015 atoms. Therefore, the ratio of Mo atoms along GBs and in bulk is (xy × 1.27 × 1014)/(xy × 1.16 × 1015) = 11%. This result agrees with the density of magnetic Mo atoms 0.61–16% estimated from the saturation magnetization 1–26 emu/cm3 reported in our previous study (see “Calculation for the density of magnetic Mo atoms” in “Methods” section)11.

Moreover, TEM image in Ref.11 provides us information about surface morphology: The most surface layer is incontiguous and interrupts by several nm. This surface morphology agrees with RMS value 0.515 nm from the AFM measurement42. See Supplementary Fig. 1 for the Raman measurement, the temperature dependence of resistance and the voltage-current characteristic.

We analyse the details of the MR data measured in the two terminal device shown in Fig. 2. The MR-H curves measured at various currents are shown as multiple-curve plots in Fig. 3, where these curves are summarized according to the directions of H and the current. These curves are transformed into the colour-coded maps shown in Fig. 4. The MR-H curves mainly show positive MR curves, and a linear MR feature is observed in the Hy measurement. The positive MR curves are divided into three types: dips A and A′ with a large offset of H, dip B with a wide shape and dip C with a sharp shape. These observations indicate that the ferromagnetism in polycrystalline MoS2 is modulated by the applied current.

Figure 2
figure 2

Schematic sample structure examined in our magnetoresistance measurement. Current is applied along the Ix direction between the two Ag contacts formed at the surface. The in-plane (out-of-plane) magnetic field is applied along the Hy (Hz) direction.

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Figure 3
figure 3

Magnetoresistance measured with various current intensities at 4 K. The current increases in steps of 1.78 times. (a,b) Magnetic field is applied along the out-of-plane direction (Hz). (c–f) Magnetic field is applied along the in-plane direction crossing the current (Hy). The current directions are + Ix (a–d) and − Ix (e,f). The magnetic field is swept from positive to negative (+ scan) in (a,c,e) and from negative to positive (− scan) in (b,d,f). (a/b,c/d,e/f) are superimposed together with + scan and − scan curves. The tick on the left axis indicates 0 in each curve. The tick space indicates 2%.

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Figure 4
figure 4

Colour-coded map of magnetoresistance measured with various currents at 4 K. (a,b) Magnetoresistance as functions of current and magnetic field applied along the out-of-plane direction (Hz). (c–f) Magnetoresistance as functions of current and magnetic field applied along the in-plane direction crossing the current (Hy). The current directions are + Ix (a–d) and − Ix (e,f). The magnetic field is swept from positive to negative (+ scan) (a,c,d) and from negative to positive (− scan) (b,d,f).

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From the measurement data, we extract the physical values: the dip gap between + scan and -scan for dips B and C, MRmax − MRmin, the c and d values of dips B and C obtained by fitting to the Khosla–Fischer equation43, and the slope of the odd function as a function of current, as shown in Fig. 5 (see “Methods” section for detail). The Khosla–Fischer equation represents positive MR based on up- and down-spin band model43, in which the parameters c and d are described by mobility and conductivity of up- and down-spin bands44,45,46,47. According to Takiguchi et al., conductivity can be described by the band energy, and thus, the spin split energy can be obtained from the d value by using this semi-empirical model (see “Calculation for spin split energy” in “Methods” section)48. Also, magnetic field for the saturation magnetization Hs can be evaluated numerically, so we can analyze it as a function of the current intensity.

Figure 5
figure 5

Dip gap, MR ratio, c value, d value and odd function slope obtained from our magnetoresistance measurements. (a–e) Data obtained in Hz + Ix measurement. (f–j) Data obtained in Hy + Ix measurement. (k–o) Data obtained in Hy − Ix measurement. Blue circles and orange squares in (b–d,g–i,l–o) correspond to + scan and − scan, respectively.

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As shown in Fig. 5a,f,k, the dip gap between + scan and − scan, which corresponds to coercive force Hc, decreases 1/30 times as the current increases. A similar behaviour is seen in Ga1−xMnxAs, where the coercive force significantly decreases as the magnetic impurity x increases49. Based on this analogy, we can suppose that the density of spin magnetic moments increases as the current increases in polycrystalline MoS2.

As shown in Fig. 5d,i,n, the d value, which corresponds to the dip width and correlates to Hs, is 20 times larger for dip C than for dip B. This behaviour is also seen in the Ga1−xMnxAs case reported in Ref.49, where Hs decreases as x increases. The dip gap and d value data indicate that the ferromagnetic properties are changed only by increasing the current without changing the magnetic doping required in typical ferromagnetic semiconductors.

The magnetic properties Hc and Hs are influenced by the density of magnetic atoms or distance between neighboring spins. Thus, similar density is one of the reasons of comparable behaviour of Hc and Hs in these two materials. The density of magnetic atoms of GaMnAs in Ref.49 is 0.5% and 7.4%. Meanwhile, the density of the magnetic atoms in our polycrystal MoS2 is estimated to be 0.61–16% using saturation magnetization 1–26 emu/cm3 measured on polycrystal MoS2 fabricated in the similar condition in our previous study (see “Calculation for the density of magnetic Mo atoms” in “Methods” section)11. Additionally, the similar mechanism of ferromagnetism in these two materials supports the comparison of the descriptions of Hc and Hs. The mechanism of ferromagnetism in GaMnAs is carrier mediated exchange interaction between 3d localized spins, while the presumed mechanism of ferromagnetism in polycrystal MoS2 is carrier assisted exchange interaction between 4d localized spins in GBs. It is noted that Hc decreases has been observed in InMnAs as the increase in MnAs fraction50.

Additionally, we can estimate the spin-split energy of the 4d band from the d values44,48, which are 2.5 meV and 100 meV for dips B and C, respectively (see “Calculation for spin split energy” in “Methods” section for details). Although this estimation includes many assumptions, the derived values are worth considering for the band structure of polycrystalline MoS2 because the order of these values is near that of the theoretical calculation20,21.

The ferromagnetism enhancement by current probably occurs because the charges are trapped at the spin-dependent 4d sites in the Mo atoms in the GBs or because the itinerant carrier density increases in the long channel.

Linear MR starts to be observed at 3.9 A/cm2 (0.56 μA) (see in Fig. 3c/d,e/f to check which curves are linear MR). If the efficiency of the equivalent field because of the spin–orbit torque is the same as GaMnAs [99 Oe/(1 MA/cm2)]3, the effective magnetic field at 3.9 A/cm2 is 0.39 mOe. This value is quite small to change magnetic behaviour in the sample, and thus, the mechanism of MR change is thought to be different from the spin–orbit torque observed in 3d metal ferromagnets and ferromagnetic semiconductors. Conceivable mechanism of linear MR is the change of occupancy in 4d orbitals of Mo atoms in GBs because of spin-dependent scattering and the change of electron density in the long channel. The change of occupancy results in the change of the exchange interaction between localized 4d spins and results in the change of magnetic anisotropy because of spin–orbit interaction between spins and 4d orbitals with the magnetic quantum number.

In Ref.51, linear MR was observed in SmCo5 when the magnetization was independent of the magnetic field. This is described by Equation j = A(M·H)E with steady M when H is swept, where j, A, M and E are the current vector, coefficient, magnetization vector and electric field vector, respectively. As far as this theory is concerned, our observation of linear MR in the Hy measurement indicates that M is fixed to in-plane directions because of the spin–orbit effective magnetic field and the change of the exchange interaction induced by the current (Fig. 1c). This hypothesis is confirmed by the three pieces of experimental evidence below. One: When flipping the current direction, the odd function shows the opposite sign of slope (see Fig. 5j,o and “Calculation for linear MR” in “Methods” section). This is thought to occur because flipping the current leads to flipping the direction of the spin–orbit effective magnetic field, and thus, the sign of M flips. Two: There is no hysteresis. A similar shape of MR is observed between + scan and − scan. From this, we can guess that the localized spins are not ordered by the external magnetic field, but their directions are determined by spin–orbit effective magnetic field through the current. Three: In the Hz measurement, flat MR is observed when Hz is small (from − 0.3 to + 0.3 T) in the current region where linear MR is observed in the Hy measurement (Fig. 5e,j,o). This is because M is oriented in the in-plane direction, but H is out of plane; thus, M·H = 0. Moreover, when a large magnetic field is applied, M is released from the domination by current and is oriented to Hz, and thus, the MR curve shows a kink (see MR data at 10 μA in Supplementary Fig. 2).

For the Hy measurements, linear MR starts to be observed when the positive MR starts to weaken (indicated by arrows in Fig. 5h–j,m–o). This indicates that the current-induced spin–orbit effective magnetic field changes the exchange interaction between the localized spins.

Double dips are seen for low current denoted by dips A and A′ (Fig. 3a,b). The reason for this is speculated to be that the magnetic domain is not single-domain but is multidomain, or likely because the magnetization direction is variously changed.

The disappearance of MR above 0.1 mA is probably because the localized 4d levels are fully occupied or because spin-dependent scattering does not occur because of the high current intensity.

Our results are related to recent progress of 2D ferromagnets, recommend 4d transition metal compounds as materials for spintronics, and indicate that the arrangement of polycrystalline structures unveils hidden characteristics and phenomena related to the interactions between localized spins and itinerant electrons.

Methods

Fabrication

We deposited a polycrystalline MoS2 film (7.5 nm) on a SiO2 (400 nm)/Si (0.7 mm) substrate using radio-frequency (RF) magnetron sputtering (EIKO ENGINEERING, LTD.) with a 4 N-purity MoS2 target (Matsurf Technologies Inc.). The sputtering conditions were as follows: the substrate temperature was 450 °C, Ar pressure was 0.35 Pa with 7 sccm flow, the substrate-target distance was 180 mm, and the RF power was 40 W. After deposition, we deposited an Al2O3 layer (2 nm) on the sample using atomic layer deposition (Fiji Inc.) at 300 °C with (CH3)3Al (trimethylaluminium; TMA) and H2O as precursors. Next, we deposited Ag pads (50 nm thickness) as electrical contacts using a current-heating vacuum evaporation tool with a shadow mask placed in front of the sample. The Ag pad pattern was a 1.8 mm × 1.8 mm square array with a 1.2 mm space. Finally, we cut the sample into small specimens, including 2 Ag pads, and bonded Au wires on them to connect to the electrodes in a sample holder.

Magnetoresistance measurement

We performed magnetoresistance measurements using our custom-made 4 K cryostat equipment and Keithley 2400 as a source measure unit. The magnetic field was first applied at + 0.8 T and swept towards − 0.8 T at a 20 mT step (+ scan). After that, the field was swept from − 0.8 to + 0.8 T (− scan). Each magnetoresistance curve was normalized by dividing by the average value of the curve (R − Rave)/Rave × 100.

Data analysis

To extract physical values from MR curves, we used the following equation for positive MR:

$$\frac{R-{R}_{AVE}}{{R}_{AVE}}\left(\%\right)=\sum_{i}\frac{{c}_{i}^{2}{\left(H-{H}_{0}^{i}\right)}^{2}}{1+{d}_{i}^{2}{\left(H-{H}_{0}^{i}\right)}^{2}},$$
(1)

where H0 is the centre position of positive MR. The summation of multiple curves was performed because the curve structure was not simple, but we discussed only the parameters for dips B and C. The fitting results and each component of the curves are shown in Supplementary Figs. 2–7.

Calculation for spin split energy

We estimated the spin-split energy of the 4d band from the d values by using equation44,48,

$${d}^{2}=\frac{{\left({\sigma }_{1}{\mu }_{2}-{\sigma }_{2}{\mu }_{1}\right)}^{2}}{{({\sigma }_{1}+{\sigma }_{2})}^{2}},$$

in which subscripts 1 and 2 represent up and down spins, respectively. In 2D system, the band energy is described by electron density,

$${E}_{i}=\frac{2\pi {\hslash }^{2}}{{m}^{*}}{n}_{i} \left(i=1, 2\right),$$

where μ, n, ћ, m* correspond to the mobility, two-dimensional electron density, plank constant, and effective mass of electron, respectively. The relation between conductivity and electron density is

$${\sigma }_{i}=q{n}_{i}{\mu }_{i}, \left(i=1, 2\right).$$

Thus, d value can be modified using above equations,

$$d=\frac{1}{\frac{{n}_{1}}{{\mu }_{2}}+\frac{{n}_{2}}{{\mu }_{1}}}\left({n}_{1}-{n}_{2}\right)=\frac{1}{\frac{{n}_{1}}{{\mu }_{2}}+\frac{{n}_{2}}{{\mu }_{1}}}\frac{{m}^{*}}{{2\pi \hslash }^{2}}\Delta E\approx \frac{\mu }{n}\frac{{m}^{*}}{{2\pi \hslash }^{2}}\Delta E,$$
(2)

where ΔE represents spin split energy of the 4d band. With the assumption of μ = 0.01 cm2/V/s, n = 1011/cm2 for dip B, n = 2 × 1011/cm2 for dip C and m* = m0 (electron mass), ΔE is estimated to be 2.5 meV and 100 meV for dips B (d/μ0 = 4 m2/V/s) and C (d/μ0 = 80 m2/V/s), respectively. Here, μ0 is the vacuum permeability.

Calculation for linear MR

To clearly observe linear MR, we examined odd functions by using [MR+(H) − MR−(-H)]/2, where MR+ and MR- correspond to the MR observed in the + scan and − scan measurements, respectively. The extracted odd function data are shown in Supplementary Figs. 8–10. The slope of odd function was numerically obtained by fitting the odd functions to a linear equation y = ax + b. The obtained values are shown in Fig. 5e,j,o.

Calculation for the density of magnetic Mo atoms

Since there are 1 + 6/3 = 3 Mo atoms in a regular hexagon with one side length a = 3.16 Å, we calculated the number of Mo atoms in a square centimeter in monolayer MoS2:

$$\frac{3}{\frac{3\sqrt{3}}{2}{a}^{2}}=1.156 \times {10}^{15} \,{\text{cm}}^{-{2}}.$$

Similarly, the number of Mo atoms in a centimeter along out-of-plane direction was calculated:

$$\frac{1}{6.55\, {\text{{\AA}}} }=1.527 \times {10}^{7}\,{\text{cm}}^{-{1}}.$$

Thus, the density of Mo atoms in multilayer MoS2 was calculated:

$$1.156 \times {10}^{15}\,{\text{cm}}^{-{2}}\times 1.527\times {10}^{7}\,{\text{cm}}^{-{1}}=1.765\times {{10}^{22}\, \text{Mo/cm}}^{3}.$$
(3)

The saturation magnetization in Ref.11 was described using Bohr magneton μB:

$$1\, \text{emu/}{\text{cm}}^{3} =1.078\times {10}^{20}\, {\mu }_{B}/{\text{cm}}^{3}.$$
(4)

This means the number of spin 1/2 in a cubic centimeter. The density of magnetic Mo atoms was calculated by dividing Eq. (4) with Eq. (3):

$$\frac{1.078\times {10}^{20}\, {\mu }_{B}/{\text{cm}}^{3}}{1.765\times {{10}^{22} \,{\text{Mo}}/{\text{cm}}}^{3}}=0.611\times {10}^{-2}\, {\mu }_{B}/\text{Mo.}$$

This means that 0.61% of Mo atoms have one spin 1/2.