Room temperature ferromagnetic ordering from bound magnetic polarons in rare-earth-doped ultrathin MoS₂ nanosheets

Abstract

Dilute magnetic semiconductors (DMSs) endowed with room-temperature ferromagnetic capabilities that arise from bound magnetic polarons (BMPs) have been attractive for spintronics, information storage and magneto-optical applications. In particular, the inclusion of rare-earth lanthanide ions as magnetic dopants in semiconductors presents significant potential owing to their strong free-ion magnetic moments. Herein, we evaluate the influence of various rare-earth dopants (Tb³⁺, Er³⁺, and Eu³⁺) magnetically coupled to vacancy carrier spins in MoS₂ nanosheets. The manifested ferromagnetic magnitudes adopt a trend that differs from that of free ion moments, with 5% Tb-doped MoS₂ exhibiting maximum saturation magnetization. The characteristic dependence of sample magnetization on dopant concentration and stringent annealing conditions (defect concentration) justifies the BMP model in describing the system. The rational creation of these ferromagnetic nanosheets is expected to provide value in low-temperature, solution-based processing of spintronic components into monolithic integrated electronics and multifunctional devices. These findings are also expected to contribute to a comprehensive understanding of the design of rare-earth-doped transition metal dichalcogenides (TMDs) as DMSs for such future spintronic applications.

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1. Introduction

Since the initial predictions of room temperature ferromagnetic properties in dilute magnetic semiconductors (DMSs),^1,2 numerous trials across a range of dopant and host combinations have prompted continual research efforts in this domain. At low doping concentrations, the acquired ferromagnetic magnitudes in these systems have challenged the prevailing notions of magnetism. It is expected that short-range interactions in conventional super-exchange and double-exchange processes are incapable of explaining the long-range magnetic order from such a low-density distribution of magnetic inclusions. Only with the subsequent studies involving bound magnetic polarons (BMP),^3–8 a reasonable model became available to account for the magnetic performance of DMSs involving wide bandgap semiconductor hosts embedded with transition metal (TM)^9–12 and rare-earth dopants.

The subsequent surge in experimental explorations initiated many nano-systems inclusive of Mn-doped CdX (X = S, Se, and Te),^13,14 CaMn₇O₁₂,¹⁵ Ce-doped BaTiO₃,¹⁶ Co-doped Dy₂O₃¹⁷ and M-doped ZnO (M = Yb,¹⁸ Mn,¹⁹ Tb,²⁰ Eu,²¹ Co,^22,23 Cu,²⁴ Ni,²⁵ and Sm²⁶), each with magnetic characteristics befitting the BMP theory. Furthermore, with massive research attention invested in semiconducting 2D transition metal dichalcogenides (TMDs) in recent years, ensuing studies on doped TMDs with various nanostructure morphologies have expanded tremendously. The incorporation of various transition metal dopants such as Zn,²⁷ Mn,^28–31 Fe,^32–34 Co,^35–38 Cu^39,40 and V^41–46 into these TMD nanostructures have successfully induced localized magnetic behaviours that were experimentally verified against theoretical models. More importantly, subsequent theoretical predictions^47,48 supported the thermodynamic substitution of lanthanide ions in MoS₂, prompting targeted modulation of optical and magnetic properties through doping. Amidst the limited literature on lanthanide-doped MoS₂, the majority revolves around Er and Eu dopants studied across a diverse range of optical (NIR-related),^49–54 thermometric⁵⁵ and photoelectric^56,57 applications. Only a handful of studies have evaluated the ferromagnetic performances of MoS₂ nanosheets arising from lanthanide doping, chiefly from Nd-,⁵⁸ Dy-⁵⁹ and Ho-induced^60,61 BMP formation.

On account of the scarce availability of studies assessing the magnetic properties of rare-earth-doped MoS₂ nanosheets, the current work presents a systematic analysis of magnetic influence from representative lanthanide ions (terbium (Tb), europium (Eu) and erbium (Er)) doped into MoS₂ nanosheets. Leveraging on the expected abundance of vacancy defects in the nanosheets, we anticipate different magnetic anisotropies for the respective ions amid the crystal host lattice with varying extents of BMP interactions. Across low doping concentrations (up to 8%), the resultant ferromagnetic ordering was indeed dependent on nanosheet quality, dopant variant and doping concentrations, with exceptional fitting statistics in accordance with the BMP model. The acquired ferromagnetic transitions and Curie temperatures near room temperature further validated the potential of lanthanide-doped nanosheets as DMSs for room-temperature spintronics, in line with preceding theoretical expectations.

Furthermore, with the ever-increasing involvement of 2D materials in the development of advanced micro- and nanoelectronics owing to the diversified electronic properties of these materials,^62–65 the production of solution-based TMD nanosheets has prompted the potential for mass-producing printed electronics via low-temperature processing technologies.^66–69 It is imperative to evaluate the capability for inducing a magnetic response in MoS₂ nanosheets through a convenient and scalable doping process to develop the technology as a magnetic or spintronic component to be integrated into multifunctional devices and monolithic integrated electronics.^70–72 The advantage of functionalized nanosheet inks to produce printed layer stacks without the need for orthogonal considerations, coupled with the ease to alter the nanosheet properties flexibly, will encourage seamless integration of multifunctional and flexible printed electronics.

2. Experimental section

2.1. Chemicals

Ammonium thiomolybdate ((NH₄)₂MoS₄, 99.97%), dimethylformamide (DMF, 99.8%), isopropanol (IPA, 99.5%) and rare-earth lanthanide chloride salts: terbium(III) chloride (TbCl₃·6H₂O, 99.9%), erbium(III) chloride (ErCl₃·6H₂O, 99.9%) and europium(III) chloride (ErCl₃·6H₂O, 99.9%) were purchased from Sigma Aldrich. All chemicals are used without further purification or processing steps.

2.2. Synthesis of lanthanide-doped MoS₂ nanosheets

Dark red crystals of (NH₄)₂MoS₄ (6.67 mg; 0.025 mmol) were sonicated in DMF (12 mL) until a homogeneous red solution was obtained. Aqueous stock solutions of various lanthanide salts (TbCl₃, ErCl₃, EuCl₃) were prepared prior to use (2.5 mM), with the appropriate quantity (depending on the respective atomic doping%, detailed calculations and solution volumes utilized are presented in Table S1, ESI†) withdrawn and added to the red thiomolybdate solution above. The resultant mix was sonicated before transferring into a Teflon-lined stainless-steel autoclave. The resultant suspension was heated in the oven at 200 °C for 15 hours. After the autoclave was allowed to cool naturally to room temperature, the dark precipitate obtained was isolated by centrifugation, followed by repeated procedures of redispersion and centrifugation washes in a DMF (4 mL)/IPA (11 mL) solvent pair. The resultant lanthanide-doped MoS₃ nanosheets were redispersed in IPA (4 mL) and dried overnight in the oven at 80 °C. The subsequent annealing step was conducted in a tube furnace (850–900 °C, 2 hours) under different conditions (inert Ar; Ar with air) to yield crystalline lanthanide-doped MoS₂ nanosheets.

2.3. Physical characterization

Raman spectra were obtained using a Renishaw inVia 2000 Micro-Raman spectrometer equipped with a 532 nm laser. SEM images with corresponding EDX spectra were acquired using a JEOL JSM-6700F field-emission scanning electron microscope (FESEM) operated at 15 kV, under Secondary Electron Imaging (SEI) with a chamber pressure of 9.63 × 10⁻⁵ Pa. The system is coupled with an Oxford Instruments X-Max^N 150 EDX detector. HRTEM and TEM measurements were acquired from a JEOL-JEM 3010 field emission transmission electron microscope operating at a 200 kV acceleration voltage under a chamber pressure of 3 × 10⁻⁸ Pa. XPS elemental analyses were conducted using a Thermo Fisher Scientific Theta Probe XPS system. Magnetic measurements were performed using a PPMS tagged to a Lakeshore model 7404 VSM.

3. Results and discussion

3.1. Characterization of lanthanide-doped nanosheets

The lanthanide-doped nanosheets herein were synthesized through a two-step hydrothermal-annealing process involving an intermediate amorphous MoS₃ state. Spiked with small quantities of lanthanide chlorides (LnCl₃; Ln = Tb, Eu, Er), ammonium thiomolybdate was broken down to yield Ln-doped MoS₃ nanosheets, prior to a subsequent high temperature annealing to form crystalline MoS₂. Fig. 1(a)–(c) presents the Raman signals of the as-produced MoS₂ nanosheets characterized by the distinct E_2g and A_1g vibrational modes,^73,74 in contrast with the relatively featureless profile of the pre-annealed amorphous MoS₃ forms⁷⁵ (Fig. 1(a)–(c) insets). This confirms the successful conversion under optimal annealing conditions with no alternate magnetic phase (1T-MoS₂)⁷⁶ or oxidized (MoO₃ or MoO_xS_y) side products. With SEM-EDX, the nanosheet morphology of the MoS₂ samples (Fig. 1(d)–(f) insets) was ascertained, with the successful incorporation of these selected f-block dopants (Tb³⁺, Er³⁺, Eu³⁺) verified via the presence of the corresponding elemental signals (Fig. 1(d)–(f)).

Fig. 1 Raman and SEM-EDX characterization of Ln-doped MoS₂ nanosheets. (a)–(c) Raman spectra of the respective Ln-doped MoS₂ nanosheets acquired under 532 nm excitation: (a) Tb-doped MoS₂, (b) Eu-doped MoS₂ and (c) Er-doped MoS₂. Inset: Corresponding Raman spectra of pre-formed Ln-doped MoS₃ nanosheets prior to annealing: Tb-doped MoS₃, Eu-doped MoS₃ and Er-doped MoS₃. (d)–(f) EDX elemental profile of Ln-doped MoS₂ (Ln = (d) Tb, (e) Eu, (f) Er) at 5% atomic doping. Inset: Respective SEM images of the annealed nanosheets (scale bars = 10 μm).

Upon analyzing the HRTEM images (Fig. 2(a)–(c)), the nanosheet cluster was found to comprise multilayer stacks with an expected interlayer spacing of 0.7 nm, an observation coherent with the wide Raman inter-peak separation (E_2g, A_1g) typical of multilayer samples (Fig. 1(a)–(c)). Similar nanostructure morphologies and interlayer spacings were observed across various samples (Fig. S1, ESI†), ensuring the consistency and reproducibility of the nanosheet synthesis process, along with the absence of obvious clustering of the rare-earth ions. Complementary to EDX, the indication of successful lanthanide doping was corroborated by detailed XPS analysis. As shown in Fig. 2(d) and (e), the Mo 3d and S 2p elemental signals displayed clean spectra with prominent Mo 3d_5/2–Mo 3d_3/2 and S 2p_3/2–S 2p_1/2 doublet pairs. The absence of MoS₃-related peaks (S₂²⁻ and bridging S peaks for S 2p; MoS₃ peaks for Mo 3d; Fig. S2, ESI†) affirmed a complete conversion after the annealing step, while the lack of any impurity-related signals assures the nanosheet quality. The absence of signals associated with any magnetically active Mo⁵⁺ species (spin 1/2, B.E. 234 eV) ensures no ferromagnetic interference from any Mo⁵⁺ components.⁷⁷ Comparatively, the similar peak distributions and intensity ratios for the Mo 3d and S 2p spectra across all three samples (Ln = Tb, Eu, Er) affirm high sample consistency (Fig. S3, ESI†).

Fig. 2 TEM characterization and XPS analyses of Ln-doped MoS₂ nanosheets. (a) Representative low-magnification TEM image of Ln-doped MoS₂ nanosheet clusters. (b) Representative HRTEM of Ln-doped MoS₂ nanosheets detailing the 0.7 nm interlayer stacking. (c) Corresponding SAED pattern. (d) and (e) Representative XPS spectra of (d) Mo 3d and (e) S 2p composition in the Ln-doped nanosheets. (f)–(i) Elemental signals for (f) Tb 3d, (g) Tb 4d, (h) Eu 3d and (i) Er 4d for the respective variants of Ln-doped nanosheets.

Meanwhile, the discernible lanthanide signals confirmed the presence of dopants (Tb³⁺, Eu³⁺, Er³⁺) within different chemical environments in the samples. Interestingly, terbium ions doped into the nanosheets adopt dual oxidation states, comprising Tb³⁺ and Tb⁴⁺. The XPS peaks were mapped in a similar correspondence to the mixed oxidation states in Tb₄O₇ (Tb³⁺ and Tb⁴⁺)^78–80 and Tb₂O₃/TbO₂ (Tb³⁺ and Tb⁴⁺)^81–83 analogues (Fig. 2(f) and (g)). While it may be intuitively understandable that a redox conversion from Tb³⁺ ion to the Tb⁴⁺ state should allow greater thermodynamic stability for substitution at the Mo⁴⁺ site, discussions relating to such possibilities have not been typically addressed in preceding computational investigations and may warrant further studies. On the contrary, without the option of a stable +4 oxidation state, the erbium and europium dopants were unsurprisingly found to be prominent in the trivalent states (Fig. 2(h) and (i)), with the respective distinct signals of Eu 3d_5/2 and Er 4d at 1136.0 eV and 168.5 eV. Furthermore, an additional peak for erbium at 172.6 eV can be assigned to the Er satellite signal (Fig. 2(i)). Coherently, the results of EDX and XPS measurements ascertained the identity of the nanosheets formed, along with the presence of the respective dopants, effectively substantiating the successful formation of the proposed nanosheet formulations.

3.2. Magnetic performance of lanthanide-doped nanosheets

The magnetic properties of MoS₂ nanosheets doped with various lanthanide ions were evaluated by vibrating sample magnetometry (VSM). Standardized across 5% doping concentrations, the nanosheets doped with Tb³⁺, Eu³⁺ and Er³⁺ demonstrated differing magnetization dependence in response to the external magnetic field (Fig. 3(a)). The ferromagnetic signals exhibited a trend of increasing magnetization values, with the sample doped with Tb³⁺ having the strongest magnetization, followed by Eu³⁺, then Er³⁺. In contrast, pristine MoS₂ (Fig. 3(a) inset) crafted via the same synthetic procedure presented a distinct diamagnetic signal. Herein, it is imperative to note that the diamagnetic signature in the pristine MoS₂ nanosheets indicates that inherent defect-related magnetic origins (vacancy clusters, edges,^84,85 and grain boundaries^86,87) are significantly trivial in comparison to the effects brought about by rare-earth doping. Besides, given that most rare-earth oxides, even if present in trace quantities, are paramagnetic and not ferromagnetic at room temperature,^88,89 the observed ferromagnetic ordering should signal the importance of dopants in altering the magnetic properties of the host. After brief omission of the ion paramagnetic contributions through linear extrapolation, the room temperature saturation magnetization at 10 kOe yielded an impressive 0.1963 emu g⁻¹ for 5% Tb³⁺ doping, while that for 5% Eu and 5% Er attained 0.0400 and 0.0078 emu g⁻¹, respectively.

Fig. 3 Magnetic characterization of dopant variable Ln-doped MoS₂ (Ln = Tb, Eu, and Er) nanosheets. (a) M–H plot of Ln-doped MoS₂ nanosheets with different dopant ions (Ln = Tb, Eu, and Er) at 5% atomic doping measured at room temperature after the correction of background paramagnetic contributions. Inset: Diamagnetic dominant signal from pristine MoS₂ nanosheet reference. (b) Comparative M–H plot of Ln-doped MoS₂ nanosheets (Ln = Tb³⁺, Eu³⁺, and Er³⁺) produced under more stringent annealing conditions after correction against background paramagnetic signals. Comparison reveals a reproducible trend of the influence of dopant species and magnitude changes stemming from the stringency of annealing conditions. (c) Corresponding susceptibility (χ–H) plot at room temperature (300 K). (d) Enlarged low field region of the M–H plot within ±300 Oe, demonstrating a minimal loop hysteresis in the measurements. (e)–(h) Proposed 4f electron distributions under crystal field (CF) splitting from a trigonal prismatic (D_3h symmetry) arrangement of surrounding sulphur atoms for (e) Eu-doped MoS₂, (f) Tb-doped MoS₂ and (g) Er-doped MoS₂ nanosheets comprising Ln substitutional doping at Mo atomic sites. (h) Proposed trend of effective magnetic moment (μ_eff) across 14 lanthanide ions, derived from spin–orbit interactions, under the crystal field influence proposed in (e)–(g).

Beyond dopant dependence, the magnetic capabilities of the samples were also assessed in relation to the quality of the nanosheets. In a parallel study, a separate batch of nanosheets produced under identical experimental conditions, except with greater stringency in the inert annealing process, yielded magnetic performance of uniformly reduced magnitudes (Fig. 3(b)). Under highly inert annealing conditions, the improved sample quality displayed inferior magnetic performance, indicating the critical role of potential defects, such as sulphur vacancies (V_S), in contributing to the overall magnetic performance. Here, it is notable that despite the overall decrease in magnetization, the trend of dopant influence remains in the order of Tb³⁺ > Eu³⁺ > Er³⁺, ensuring the reliability of the results acquired. Unsurprisingly, the derived susceptibility (χ–H) affiliation displays an identical trend of sample magnetizability in the order of Tb³⁺ > Eu³⁺ > Er³⁺ (Fig. 3(c); derived from Fig. 3(a)), while a magnified examination of the M–H curves under low-field (−300 Oe to 300 Oe) conditions unveils lower coercivity, asserting a soft ferromagnetic character to the nanosheets (Fig. 3(d); magnified from Fig. 3(a)).

Through a preliminary correlation of the magnetization dependence upon dopant variation and sample quality, it is possible to ascribe the ferromagnetic origin to the formation of bound magnetic polarons (BMPs). The BMPs are typically evaluated in various DMS systems,^37,42,61 where polaron domains are created through ferromagnetic exchange between defect-localized carrier spins and vicinal magnetic ions. Since electron-bound V_S defects have been known to be typically abundant in TMD nanostructures, the inclusion of lanthanide dopants is expected to produce BMPs from close radial proximity alignment of the lanthanide unpaired spins with the localized defect state. The hybridization of the dopant energy levels with the vacancy defect states effectively drives the ferromagnetic interactions between the Ln³⁺ dopant ions located within the polaron radius.⁷ Therefore, the overall magnetization is expected to be directly proportional to the density of defects, as well as the magnetic moment of the dopant. Since lanthanide ion substitution at the Mo⁴⁺ sites was previously determined to be the most thermodynamically favorable,⁴⁸ a proposed distribution of the f-electrons under the context of a D_3h trigonal prismatic crystal field^90,91 of S atoms was applied for each of the dopant ions (Tb³⁺, Eu³⁺, Er³⁺) in Fig. 3(e)–(g). With a reasonable assignment of the crystal field splitting, the overall effective magnetic moment was determined, taking into account spin–orbit coupling from the spin and unquenched orbital momentum contributions.^92–94 The resultant theoretical trend across the family of lanthanides (Fig. 3(h)) was coherent with the experimental results, yielding magnetization values in the order of MoS₂:Tb³⁺ > MoS₂:Eu³⁺ > MoS₂:Er³⁺. Herein, it is notable that the magnetic moments determined from Fig. 3(h) should only adopt a qualitative relation to the actual moments measured; the theoretical derivation for magnetic moments (in μ_B/magnetic ion) should be less effective in quantifying non-conventional diluted magnetic systems involving coupling interactions between magnetic ions and localized defect states.

Owing to the strong ferromagnetic response of Tb-doped MoS₂ nanosheets, the correlation between dopant concentration and magnetic performance was investigated based on the Tb doping concentration (at%). Across two separate batches of Tb-doped samples, similar trends were observed, with an increasing magnetic response up to an optimum at 5% Tb-doping, followed by a subsequent decline. The respective batches of nanosheets displayed magnetization trends in the order 5% > 2% > 8% (Fig. 4(a)) and 5% > 7% > 3% (Fig. 4(b)). Plotted together across a normalized scale, the comparative magnetization between the samples showed a reasonable correlation similar to doped magnetic systems—an increasing trend at low concentrations, followed by a tapering decline beyond the optimal doping concentration (Fig. 4(c)). Similar trends (with maximum magnetic performance at 5% doping) were also observed for Er- and Eu-doped samples when examined across 3%, 5% and 8% doping concentrations (Fig. S4, ESI†). Naturally, with doping concentrations exceeding the optimum, the decreased inter-ionic distance between these embedded foreign ions, and/or dopant clustering beyond the solid solubility limit, promoted antiferromagnetic coupling between adjacent dopants over the BMP ferromagnetic mechanism. The ferromagnetic performance is gradually compromised by the thermodynamically favored antiferromagnetic coupling, resulting in the progressive weakening of the ferromagnetic signal. Nonetheless, with consistent assignment of elemental signals for the Tb content under XPS analyses (Fig. 4(d)–(f); full XPS data set under Fig. S5, ESI†), the lack of any new chemical states or clustering signals assures doping below the host solubility limit; the decreased magnetic ordering therefore stems merely from antiferromagnetic coupling at reduced Tb–Tb inter-ionic distances.

Fig. 4 Magnetic characterization of Tb–MoS₂ nanosheets under variable atomic doping concentrations. (a) M–H plot for single batch Tb-doped MoS₂ nanosheets with 2%, 5% and 8% atomic doping concentrations after correction of background paramagnetic contributions. (b) M–H plot for single batch Tb-doped MoS₂ nanosheets with 3%, 5% and 7% atomic doping concentrations after the correction of background paramagnetic contributions. (c) Normalized comparison of saturation magnetization across samples of various doping concentrations, demonstrating a parabolic relation optimal at 5% Tb doping. Values standardized at H = 10 kOe, black and red plot points refer to sample batches presented in (a) and (b), respectively, normalized against the strongest magnetization in 5% Tb samples. (d)–(f) XPS characterization of Tb 3d signals from (d) 5% Tb-doped MoS₂, (e) 7% Tb-doped MoS₂, and (f) 8% Tb-doped MoS₂ nanosheets.

In relation to temperature, the ferromagnetic feature of the 5% Tb-doped MoS₂ sample was found to persist beyond room temperature. The unconventional shape of the M–T plot reveals a rich complex interplay of multiple magnetic processes that can be deconvoluted in the subsequent analysis of individual M–H plots at different temperature points (Fig. 5(a)). The processed plot of 1/χ against T revealed magnetic transitions with extrapolated x-intercepts yielding positive values (Fig. 5(b)), confirming the ferromagnetic nature of these processes. The derivative spectrum of dM/dT against T further details a Curie transition temperature (T_C) at 308 K (Fig. 5(c)), reaffirming the capability of these doped nanosheets as room temperature DMSs. Through a series of M–H spectra acquired at different temperature points, systematic changes in magnetic features can provide a holistic understanding of the magnetic transitions across the temperature scale. At higher temperatures (T > T_C) (Fig. 5(d)), a mixed strength of paramagnetic and ferromagnetic signals exists, which increases marginally with decreasing temperature. Below T_C, the system transitions into a ferromagnetic order, presenting a competitive ferromagnetic–antiferromagnetic interaction through a cusp feature between 250 K and 300 K, before stabilizing into a ferromagnetic state over a large temperature range down to 50 K (Fig. 5(a) and (e)). At 10 K, the spike in overall magnetization of the system is characterized by a paramagnetic or antiferromagnetic contribution in addition to the ferromagnetic feature, resulting in an unconventional upward curvature under both field-cooled (FC) and zero field-cooled (ZFC) conditions, with reduced bifurcation at low magnetization. Such a feature is expected to arise from an inherent low-temperature response stemming from the Tb dopants or the MoS₂ host.^77,85 Subtracting the background linear contribution through extrapolation, the resultant ferromagnetic signal was compared against the next acquired data point at 100 K, revealing minimal changes in the ferromagnetic feature with certainty that the overall increased magnetization stems purely from the additional linear magnetic component (Fig. 5(f)).

Fig. 5 Temperature-dependent magnetic characterization of 5% Tb-doped MoS₂ nanosheets. (a) M–T relation for 5% Tb-doped MoS₂ nanosheets under FC-warming, FC-cooling, FC-high field (1T) and ZFC measurement conditions. (b) 1/χ against T plot demonstrating the ferromagnetic characteristics of the sample through positive x-intercepts. (c) Derivative dM/dT against T relation in the determination of transition Curie temperature (T_C) at approximately 308 K. (d) M–H characteristics at high temperature domains of 325 K, 350 K and 390 K. (e) M–H characteristics across the low-intermediate temperature range from 10 K to 325 K. (f) M–H characteristics at low temperatures (10 K, 100 K) with processed plot (10 K) upon paramagnetic subtraction.

In comparison, the M–T curves for the 2% and 7% Tb-doped samples were found to feature similar plot morphologies (Fig. 6(a), (b); red and black), with the 2% Tb-doped sample featuring a T_C at approximately 319 K, while the 7% Tb-doped sample has a T_C value of 300 K, along with a separate ferromagnetic transition at the onset of 259 K. (Fig. 6(a) and (b); blue). Once again, the consistent positive x-intercepts in the 1/χ plots reiterate the ferromagnetic transitions involved (Fig. 6(c) and (d)). Plotted upon a standard scale, the relation between the ascribed T_C and Tb-dopant concentration presented a linear plot of inverse relation (Fig. S6, ESI†).

Fig. 6 Temperature-dependent magnetic characterization of 2% and 7% Tb-doped MoS₂ nanosheets. (a) and (b) Respective M–T curves (red and black) for 2% and 7% Tb-doped MoS₂ nanosheets under FC-ZFC measurement conditions, overlaid with the derivative dM/dT against T (blue) to determine the transition Curie temperatures (T_C) for the respective samples: 319 K for 2% Tb-doped sample (with side transition at 310 K); 300 K for the 7% Tb-doped sample (with side transition at 259 K). (c) and (d) Corresponding plots of 1/χ vs. T, demonstrating magnetic transition characteristics of the samples through x-intercepts.

3.3. Bound magnetic polaron modelling

In further evaluation of the BMP model in describing the observed ferromagnetic trends, the initial onsets of the M–H plots were fitted in accordance with the following relation.

M = M₀L(x) + χ_mH

Here, the first term models magnetic contributions from the BMPs, while the second term relates to paramagnetic contributions from the host matrix. The overall magnetization, M₀ = Nm_s/ρ, where m_s is the moment per BMP, N refers to the number of BMPs per unit volume and ρ is the density of the host matrix (ρ(MoS₂) = 5.06 g cm⁻³). L(x) = coth(x) − 1/x is the Langevin function with x = Hm_eff/k_BT, where m_eff is the effective moment per BMP. Ignoring the interactions between the BMPs, an approximation for m_s = m_eff allows for the determination of variables M₀, m_eff and χ_m from the equation fit. As displayed in Fig. 7 and Fig. S7; ESI,† the appropriate fits detailed by quality modelling statistics (Fig. S8 and S9; ESI† reduced χ² at 10⁻⁶ to 10⁻⁸) were obtained for the M–H plots under the respective variations in dopant concentrations and temperature. The parameters derived from the various plots are summarized in Table 1.

Fig. 7 BMP model fitting of the initial M–H relation for the Tb-doped MoS₂ sample at different atomic doping concentrations. (a) 2% Tb doping, (b) 5% Tb doping, (c) 7% Tb doping and (d) 8% Tb doping.

Table 1 Magnetization parameters (M₀, m_eff, χ_m, N) derived from the BMP model fitting for Tb-doped samples under varied dopant concentrations (2%, 5%, 7%, and 8%) and the 5% Tb-doped sample under temperature variation

Dopant conc. (%Tb^3+)	M 0 (emu g^−1)	m eff (emu)	χ m (emu g^−1 Oe^−1)	N (cm^−3)
2	0.056	1.0 × 10^−16	3.8 × 10^−6	2.8 × 10^15
5	0.219	1.2 × 10^−16	3.9 × 10^−6	9.6 × 10^15
7	0.013	2.0 × 10^−16	6.4 × 10^−6	3.3 × 10^14
8	0.014	1.3 × 10^−16	4.3 × 10^−7	5.3 × 10^14

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Temperature (K)	M 0 (emu g^−1)	m eff (emu)	χ m (emu g^−1 Oe^−1)	N (cm^−3)
10	0.352	2.5 × 10^−18	2.7 × 10^−5	7.2 × 10^17
100	0.277	2.8 × 10^−17	1.4 × 10^−6	5.0 × 10^16
200	0.255	6.7 × 10^−17	3.3 × 10^−7	1.9 × 10^16
275	0.268	1.2 × 10^−16	1.6 × 10^−6	1.1 × 10^16
300	0.195	1.4 × 10^−16	4.1 × 10^−7	6.9 × 10^15
325	0.065	1.0 × 10^−16	2.7 × 10^−6	3.3 × 10^15
350	0.047	1.5 × 10^−16	8.7 × 10^−7	1.6 × 10^15
390	0.020	9.8 × 10^−17	5.4 × 10^−7	1.0 × 10^15

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The extracted values for effective BMP moments were in the order of 10⁻¹⁶ emu, adopting a general trend of marginal increment with increasing dopant content. Precluding any counteracting antiferromagnetic contributions, the above-mentioned correlation is expected to present a reasonable trend, in which the increased dopant count homogeneously elevates the density of the magnetic dopant within the BMP radius, enhancing the magnetic moment of individual BMPs. Considering the batch samples, the relation of 2%, 5% and 8% doping demonstrated a linear trend against m_eff (Fig. 8(a)). In contrast, the sample densities of BMPs were found to be in the order 10¹⁴–10¹⁵ BMPs per cm³, with an inverse relation to the increasing dopant concentrations. The resultant trend exhibits the same curvature as the overall sample magnetization (Fig. 8(b)), with an optimal value at 5% doping, followed by a subsequent decline with higher concentrations. The matrix paramagnetic susceptibilities revealed low influence from the host material, yielding non-trending values of the order of 10⁻⁶ emu g⁻¹ Oe.

Fig. 8 Relation of the BMP model-derived parameters to Tb doping concentrations and temperature influence. (a) Dependence of effective magnetic moment per BMP (m_eff) on Tb doping concentrations, together with associated model fitting details. (b) BMP density (N) relation to Tb doping concentrations. (c) Variation in density of BMPs (N) within the sample in relation to temperature changes, together with associated model fitting details. (d) Variation in effective magnetic moment per BMP (m_eff) depending on the temperature measurement conditions, together with associated model fitting details.

With temperature variation, the samples accommodated a higher density of BMPs at lower temperatures, ranging from 1.0 × 10¹⁵ BMPs cm⁻³ at 390 K up to 7.2 × 10¹⁷ BMPs cm⁻³ at 10 K through a trend approximated by a (1 + x)^−1.3 relation (Fig. 8(c)). It may be reasonable to accord the reduced BMP count towards greater instability when faced with increased thermal disruptions at higher temperatures. The polarons were ascribed with effective magnetic moments that generally increase with temperature for values below T_C, ranging from 2.5 × 10⁻¹⁸ emu at 10 K and 1.4 × 10⁻¹⁶ emu at 300 K. The trend within this temperature range could be approximated by a cubic function (Fig. 8(d), trending statistics in Fig. S10, ESI†). Beyond T_C, the values do not follow a proper trend due to the interplay of additional magnetic (paramagnetic, antiferromagnetic) contributions.

4. Conclusions

Using different lanthanide dopants (Ln = Tb, Eu, Er), doped MoS₂ nanosheets were synthesized to assess their various magnetic properties. The effective trend across consistently doped (5%) samples yielded magnetization in the order of Tb³⁺ > Eu³⁺ > Er³⁺, which is justified by the consolidation of possible mechanistic contributions stemming from crystal field influence and BMPs. Based on the Tb-doped MoS₂ systems, the dependence of sample magnetic response on dopant concentration was evaluated, presenting an increasing trend at low concentration levels, followed by a subsequent decline beyond the optimal doping threshold. Such an observation could be attributed to a competing interplay between ferromagnetic and antiferromagnetic processes, resulting in acquired modulation of sample magnetization through doping proportions. The dependency of magnetization on doping ratios and annealing conditions, along with appropriate modelling of M–H relations in the BMP model, served to strengthen the notion that BMP production contributes to room-temperature ferromagnetic properties. These findings are expected to provide further insights into the limited experimental studies on rare-earth-doped MoS₂ systems, highlighting the potential of lanthanide-doped nanosheets for spintronic and magnetic applications.

Author contributions

Eng Tuan Poh – conceptualization, investigation, formal analysis, methodology, validation, data curation, visualization, writing – original draft; Rajasree Das – investigation, formal analysis, Manikandan Marimuthu – investigation, formal analysis; Zheng Zhang – investigation, formal analysis; Ramanathan Mahediran – funding acquisition, project administration, supervision, writing – review & editing; Chorng Haur Sow – funding acquisition, project administration, supervision, writing – review & editing.

Conflicts of interest

The authors declare no conflict of interest.

Data availability

The data supporting the article “Room Temperature Ferromagnetic Ordering from Bound Magnetic Polarons in Rare Earth Doped Ultrathin MoS₂ Nanosheets” have been included as part of the ESI.†

Acknowledgements

Our gratitude to Dr Chen Yun and Dr Zhao Fangfang from Bruker, along with Dr Wang Xinyun, for advice on magnetic force microscopy (MFM) as applied in this project.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d5tc01225b

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