Modern logic and memory devices work through electrical control of n- or p-type charge carriers in semiconductor transistors. However, their further miniaturization has reached a bottleneck due to the quantum tunneling effect and also due to energy-consumption issues. Making use of another property of electrons (i.e., the spin property) to develop semiconductor spintronic devices is key to overcome these barriers^[1] because electrically manipulating spin is more both energy-efficient and faster than controlling charge. To this end, many theoretical and experimental studies have been conducted in the last two decades to attempt to discover room-temperature (RT) ferromagnetic semiconductors^[2], as producing long-range spin ordering (ferromagnetism) in semiconductors is the first step to constructing spintronic devices. Because natural ferromagnetic semiconductors are rare, RT ferromagnetic semiconductors are initially created by artificially doping nonmagnetic wide band-gap metal oxides or nitrides (e.g., ZnO, TiO₂, SnO₂, CeO₂, and GaN) with magnetic 3d transition metal (TM) atoms (e.g., Mn, Fe, Co, or Cu)^[3-7]. Soon after, it was found that many semiconductors, including the above-mentioned ones, could show RT ferromagnetism, even without any magnetic dopants. This phenomenon was termed d⁰ ferromagnetism, to underline the absence of partially-filled d or f orbitals in the semiconductors^{[8, 9]}. Experimental evidence has suggested that d⁰ ferromagnetism is strongly correlated to vacancy defects in crystals^[10-13]. Theoretical studies have revealed that both cation and anion vacancy defects can produce local spin moments by breaking the symmetry of spin structures, and the exchange coupling between the vacancy spins gives rise to the d⁰ ferromagnetism^[14−17]. Given the inevitability of growth-related vacancy defects in real crystals, vacancy-induced d⁰ ferromagnetism may have congenital advantages for designing semiconductor spintronic devices.

However, there is an increasing number of studies which have reported that the vacancy defects that are responsible for the d⁰ ferromagnetism; for example, the oxygen vacancy in ZnO, TiO₂, and SnO₂, the zinc and titanium vacancies in ZnO and TiO₂, and the gallium vacancy in GaN are deep in energy levels^[18-21]. It is known that deep-level defects typically act as carrier recombination centers, and therefore they should be eliminated to avoid degradation in semiconductor performance. This conflicts with the theory of vacancy-induced d⁰ ferromagnetism, which requires a considerable number of vacancies to develop long-range exchange coupling, and thus hampers d⁰ ferromagnetism in future applications. From this point of view, it is highly desirable to produce d⁰ ferromagnetism in a semiconductor host that is tolerant of defects.

Recently, a class of lead halide perovskite (LHP) semiconductors with the chemical formula ABX₃ (A = Cs⁺, CH₃NH₃⁺et al., B = Pb²⁺, and X = Cl⁻, Br⁻, or I⁻) has attracted extensive studies in the fields of photovoltaics and optoelectronics^[22]. These materials are commonly synthesized via solution processing methods, and thus often contain an ultrahigh thermal vacancy equilibrium concentration, typically at percent level^[23]. Nevertheless, LHPs show impressive performances, such as ultralong carrier diffusion lengths^[24], near-unit photoluminescence quantum yields^[25], and efficiencies above 20% in solar cells and light-emitting devices^[26-28]. These attributes indicate that the electrical and optical properties of LHPs have a high defect tolerance. Theoretical studies have suggested that these outstanding performances are helped by a special property that the predominating lattice defects in LHPs (i.e., the halide vacancy) is in shallow energy levels^{[29, 30]}. Furthermore, LHPs have large spin-orbit coupling, due to them containing Pb, which is a heavy element. A number of spin-orbit related phenomena, such as large Rashba spin splitting, field-induced spin polarization, and spin-to-charge current conversion, have been recently demonstrated in LHPs^[31-34]. These phenomena suggest that LHPs have potential for spintronic applications. Therefore, it is highly interesting to explore whether the shallow-level halide vacancies in LHPs can produce ferromagnetism, which is critical for future spintronic applications. This question is yet to be studied, either from an experimental or a theoretical viewpoint.

Here, we demonstrate, through both theoretical and experimental approaches, that even without partially-filled d or f orbitals, defective LHPs can show ferromagnetic states, due to their lifted spin degeneracy by halogen vacancy. The vacancy-induced d⁰ ferromagnetism is robust at RT, and can be improved by incorporating a tiny fraction of 3d ions into Pb sites. Our results may boost LHPs with excellent optical properties for applications in novel spintronic devices, such as spin light-emitting diodes and spin field-effect transistors.

PbBr₂ (99.99%), CsBr (99.5%), PbCl₂ (99.99%), PbI₂ (99.9%), CsCl (99.99%), CsI (99.9%), manganese(II) acetylacetonate [Mn(acac)₂, 97%], Fe(acac)₂ (98%), Co(acac)₂ (99%), Ni(acac)₂ (96%), Cu(acac)₂ (99%), Zn(acac)₂ (98%), hydrobromic acid (HBr, 40%), hydroiodic acid (HI, 47%), hydrochloric acid (HCl, 36.5%), 1-octadecene (ODE, 90%), and diethyl ether were purchased from Macklin. Cs₂CO₃ (99.99%), oleylamine (OAm, 90%), oleic acid (OA, 85%), dimethylsulfoxide (DMSO, 99.8%), methanol (MeOH, 99.9%), ethyl acetate (99%), and dimethylformamide (DMF, 99.9%) were purchased from Aladdin. Toluene (99.5%) was purchased from Sinopharm Chemical Reagent Corp., China. Methylammonium bromide (MABr, 99.5%) was purchased from Xi'an Polymer Light Technology Corp., China. All materials were used without further purification.

We take OAmBr as an example to show how OAmBr (Cl or I) was made. OAmBr was synthesized by reaction of the OAm with HBr. 20 mmol OAm in absolute ethanol was stirred and cooled in ice-bath, and then 20 mmol HBr was added drop by drop. The reaction solution was stirred for 12 h until all OAm was reacted. Then rotary evaporation was applied to obtain OAmBr pulp at 70 °C. After three times washing with diethyl ether, white powder was obtained and dried under vacuum at 40 °C overnight for future use. Similarly, OAmCl and OAmI were synthesized by reaction of the OAm with HCl and HI, respectively.

We take CsPbBr₃ as an example to show how LHPs were made. Firstly, a mixture of PbBr₂ (1.2 mmol), CsBr (1.0 mmol), and Ni(acac)₂ at a designated Ni/Pb molar ratio from 0 to 20 mol% were dissolved in dimethylsulfoxide (DMSO, 10 mL). The insoluble residues were removed by using a filter with 22 μm pore size, and then the precursor solution was obtained. Next, oleylammonium (OAm, 20 μL), oleic acid (OA, 20 μL), and the precursor solution (0.2 mL) were then loaded into a 20 mL vial. Then, toluene (15 mL) was quickly added into the vial under vigorous stirring. After 5 min, the solution was centrifuged by 8000 rpm and then CsPbBr₃ nanocrystals were obtained. Finally, the obtained nanocrystals were washed by 8 mL toluene twice. After washing, the nanocrystals were redispersed in 4 mL toluene for further use. OAmBr (0.025 mg/mL) was added into the toluene-dispersed nanocrystals to situ passivate the nanocrystal surfaces. The whole synthetic process was carried out at room temperature.

Cs₂CO₃ (0.36 g), OA (1.5 mL) and ODE (15 mL) were added to a 100 mL three-neck round-bottom flask and degassed under an Ar flow at room temperature for 15 min, and then heated at 120 °C under an Ar flow with constant stirring for 15 min to remove the moisture from the raw materials. Thereafter, the mixture was heated to 150 °C for 15 min under an Ar flow with constant stirring and lowered to 110 °C until further use.

We take CsPbBr₃ as an example to show how hot-injection LHPs were made. A mixture of 0.54 mmol of PbBr₂, Ni(acac)₂ at a designated Ni/Pb mole ratio from 0 to 20 mol% and 15 mL of ODE, 1.5 mL of OA, 1.5 mL of OAm was first added to a 100 mL three-neck flask, dried under vacuum for 1 h at 120 °C with constant stirring to remove the moisture from the raw materials, and then heated at 120 °C under a Ar flow. After 5 min, the mixture was heated to 170 °C, the Cs-oleate precursor (1.5 mL) were subsequently quickly injected. After reacting for 5 s, the reaction mixture was cooled to 20 °C rapidly by using an ice-water bath. The obtained quantum dots were inject 40 mL ethyl acetate collected by centrifugation at 10 000 rpm for 1 min.

2 mmol CsBr and 3 mmol PbBr₂ were dissolved by 5 mL DMSO with continuous stirring for 1 h at room temperature. Then, the solution was filtered using 45 μm-sized filter to remove the precipitate, and clear solution was obtained. After that, MeOH was titrated into the clear solution until the orange precipitates no longer dissolved. Finally, the orange precipitates were filtered and the clear precursor was collected for further crystal growth.

CsPbBr₃ single crystals were grown by the antisolvent vapor-assisted crystallization method. About 10 mL clear precursors obtained above were put in a 20 mL container, and 15 mL MeOH was then added into an outer petri dish before sealing. MeOH was volatilized from the outer container to the inner one, forming saffron yellow CsPbBr₃ crystals. This growing process took 2 days. Finally, the obtained CsPbBr₃ crystals were washed with 110 °C DMF solution to remove the precursors attached to the crystal surfaces.

The real molar ratios of TM ions relative to Pb in TM-doped CsPbBr₃ were determined by using an inductively coupled plasma mass spectrometry (iCAP TQ, Thermo Scientific). The crystalline structures were characterized by powder X-ray diffraction (Bruker-AXS D8 Advance). The microstructure was characterized by using a Tecnai G20 transmission electron microscopy with operation voltage of 200 kV. The samples used for magnetic properties measurements were dried in a vacuum drying oven at vacuum of 2 × 10⁻² Pa and at temperature of 40 °C. Then, the obtained powders were loaded into a capsule, and the magnetic properties were measured using a physical property measurement system (Quantum Design). The elemental valence states were investigated using an X-ray photoelectron spectrometer (Thermo Scientific ESCALAB 250Xi). Before recording the spectra, the surface contaminants of samples were removed by Ar ion etching with etching time of 60 s. To eliminate the charge effect, all binding energies were calibrated by the C 1s line at 284.6 eV. The electron spin resonance was carried out on a JEOL FA-200 instrument at X-band. The photoluminescence spectra were detected on Varian Cary Eclipse instrument.

The theoretical derivation was carried out using first-principle density functional theory implemented in the Vienna Ab-initio Simulation Package (VASP)^[35]. Geometry optimization and electronic structure calculations were carried out under the PBESOL exchange-correlation functional^[36]. A kinetic energy cutoff of 500 eV was set on a grid of 5 × 5 × 5 k-points for cubic CsPbBr₃ unit cell. The maximum force, maximum stress and maximum displacement are set to 0.01 eV/Å, 0.02 GPa and 5.0 × 10⁻⁴ Å, respectively. The lattice constant for a perfect cubic-phase CsPbBr₃ unit cell was optimized to be 5.80 Å. A single positively charged Br vacancy was introduced by removing one Br atom, and overall charge neutrality was achieved via a compensating background charge. Spin-orbit coupling was not considered here.

Before showing the magnetic results, we would like to present some structural and optical characterizations of Ni-doped CsPbBr₃ as a representative. The samples are named as CsPb_1–xNi_xBr₃, where x is the real molar ratio of Ni relative to Pb, as determined from inductively coupled plasma mass spectrometry (Table S1, Supporting Information), and x = 0 represents pure CsPbBr₃. The samples were synthesized at RT through solution processing (see Experimental section). Figs. 1(a) and 1(b) display high-resolution transmission electron microscopy (TEM) images of CsPb_1–xNi_xBr₃ with x = 0 and 0.31%, respectively. Clear lattice fringes can be observed, indicating that our samples are well crystalized. The fringe spacing determined by using fast Fourier transform patterns was found to be 0.5765 nm for both samples, which we attribute to the (100) plane. The low-resolution TEM images shown in insets reveal that both samples have typical square nanocrystal morphology, with an average size of ~ 55.2 nm. Fig. 1(c) shows X-ray diffraction (XRD) patters of CsPb_1–xNi_xBr₃ with different x values. All samples can be indexed as CsPbBr₃ with cubic-phase structure. Close examination of the XRD patterns near 2θ = 21.5º reveals that the Bragg angle θ shifted slightly but systematically to higher positions as x increased, suggesting that the lattice shrank. Fig. 1(d) shows the X-ray photoelectron spectrum of the Ni 2p level in CsPb_1–xNi_xBr₃ with x = 0.31%. The peak located at around 855.42 eV is assigned to the Ni²⁺ 2p_3/2 level. As the ion radius of Ni²⁺ (~0.83 Å for an octahedral site) is smaller than that of Pb²⁺ (~0.1 Å for an octahedral site), the lattice shrink confirms that the Ni²⁺ dopants were incorporated into the Pb²⁺ sites. Fig. 1(e) shows normalized photoluminescence spectra of CsPb_1–xNi_xBr₃ nanocrystals with different x values measured at RT. The optical gap (i.e., the energy value at the photoluminescence peak) was 2.4 eV for x = 0, which exhibits a slight red-shift with increasing x.

We adopted electron spin resonance (ESR, also known as electron paramagnetic resonance) to determine the type of defects that is predominant in our samples, as ESR is a defect-sensitive technique that is widely used to study defect physics. Fig. 1(f) shows the ESR first derivative signals as a function of the external magnetic field (H_ext), obtained from CsPb_1–xNi_xBr₃ nanocrystals with x = 0 and 0.31% at RT. The two samples had the same weight (10.2 mg) for these ESR measurements. We can see that, although they are weak, clear resonance signals can be observed. Both samples exhibit the same resonance peak, same line shape, and same line width, indicating that the signals share the same origin. Using the formula g = hγ/μ_BH_ext, where h is the Planck’s constant, γ is the microwave frequency (9.85 GHz), and μ_B is the Bohr magnetron, the g factor was calculated to be 2.0033 for both samples, which can be assigned to the Br vacancy (V_Br) donor defect^[37]. The value of the calculated g factor is very close to that of the free electron (2.0023), indicating that the donor electron is loosely bound to V_Br. This means that V_Br is in a shallow energy level, consistent with previous theoretical calculations^{[29, 30]}. Given the relatively low formation energy among all possible type defect in LHPs (i.e., vacancy defect, interstitial defect, and antisite defect)^{[23, 29, 30]}, we conclude that shallow-level V_Br was the predominant defect in our samples. Note that the peak intensity of the signals was almost the same for the two samples, indicating that the V_Br concentration varies not much in the undoped and doped CsPbBr₃.

We next elucidated the defect-induced magnetic states in CsPbBr₃ through first-principle density functional theory (DFT) calculations. Based on the above ESR results, we focused only on V_Br and its effects on the electronic structures of CsPbBr₃. Fig. 2(a) shows the perfect 3 × 3 × 3 cubic-phase CsPbBr₃ supercells (left-hand column) used in the DFT calculations. As for defective CsPbBr₃ (right-hand column), a Br atom (indicated by the blue arrow) was removed from the perfect supercell to create a V_Br, and the lattice was then fully relaxed to a stable state for study; see Experimental section for calculation details. Fig. 2(b) displays the slice of deformation charge density (DCD) of the Pb−Br layer from the CsPbBr₃ (200) plane, without and with V_Br. This permits us to study the effects of V_Br on charge transfer after forming chemical bonds. The Pb−Br bonds showed ionic character, where the Br atoms gained electrons and the Pb atoms contributed electrons. The charge density distribution in perfect CsPbBr₃ was highly symmetric. When V_Br was introduced, it became asymmetric, particularly in the vicinity of V_Br. The V_Br site exhibited a charge-accumulation environment, indicating that there was strong bonding between the Pb atoms around V_Br.

To study whether or not the charge distribution asymmetry could induce magnetic states, calculations on spin-resolved density of states (DOSs) were carried out; the results are shown in Fig. 2(c). As expected, the total DOSs of the perfect CsPbBr₃ showed high spin-degeneracy, that is, the distribution of the spin-up and spin-down electrons was completely symmetrical, indicating the nonmagnetic nature of perfect CsPbBr₃. The total DOSs of the perfect CsPbBr₃ were discrete and sharp, revealing that the electronic states were rather localized. No states were present inside the bandgap of perfect CsPbBr₃. Regarding defective CsPbBr₃, clear spin splitting can be seen from its total DOSs (i.e., the spin degeneracy has lifted). The magnitude of the spin splitting near the valence band maximum was ~ 38 meV. The net magnetic moment of the defective supercell was calculated to be 6μ_B. Moreover, the defective CsPbBr₃ exhibited extended DOSs, indicating that the electronic states in defective CsPbBr₃ were much more delocalized than those in perfect CsPbBr₃. Particularly, some impurity states were present inside the bandgap of defective CsPbBr₃. Analysis of the partial DOSs of the defective CsPbBr₃ revealed that: (1) the conduction band consisted of Pb 6p orbitals (predominant) and Br 4s and 4p orbitals; (2) the valence bands were formed by Br 4p orbitals (predominant) and Pb 6s and 6p orbitals; (3) Pb 6s and 6p orbitals exhibited strong hybridization with Br 4s and 4p orbitals; and (4) the impurity states were mainly composed of Pb 6p orbitals, whereas the Br 4p orbital also contributed a small part of the impurity states, due to its hybridization with the Pb 6p orbital. The exchange interaction between vacancies was studied by calculating the total energy of a 3 × 3 × 3 CsPbBr₃ supercell containing two V_Br and comparing the energy for the ferromagnetic (E_FM) and antiferromagnetic (E_AFM) states. It was found that E_FM was lower than E_AFM, with an energy of 3.73 meV, suggesting that the bivacancy system had a ferromagnetic ground state.

In experiment, we measured the magnetic properties of a number of LHPs including pure CsPbCl₃, CsPbBr₃, CsPbI₃, and CH₃NH₃PbBr₃, using a vibrating sample magnetometer (see Experimental section). Fig. 3(a) displays the magnetization versus H_ex curves of RT-synthesized CsPbBr₃ nanocrystals at measuring temperatures of 4, 100, 200, 300, and 400 K. The linear diamagnetic backgrounds have already been subtracted. All curves show a clear ferromagnetic behavior with S-shape signals. That is, the magnetization increased with H_ex before then becoming saturated at a certain H_ex value. The curves show little or no hysteresis (inset of Fig. 3(a)), and the saturation magnetization (M_s) does not change much with temperature (Fig. 3(b)), features of d⁰ ferromagnetism^{[38, 39]}. The ferromagnetic behaviors observed at low temperatures persisted as the temperature rose to 400 K, suggesting that the Curie temperature of the CsPbBr₃ nanocrystals is above 400 K.

Moreover, as shown in Fig. 3(c), the ferromagnetism of the CsPbBr₃ nanocrystal could be tuned by treating the nanocrystal surfaces with oleylammonium bromide (OAmBr): the M_s decreased from 0.99 memu/g before the treatment to 0.57 memu/g after the treatment. We also studied the magnetic properties of CsPbBr₃ quantum dots synthesized by hot injection at 170 ºC and CsPbBr₃ single crystals (see Experimental section for synthesis details). We found that both samples only showed diamagnetic background signals at 300 K (Fig. S1, Supporting Information), which indicates that they were nonmagnetic at 300 K. Surface treatment with OAmBr can passivate the V_Br and thus decrease V_Br concentration near the surfaces. Hot-injection synthesized and single-crystal CsPbBr₃ also have reduced V_Br, as indicated by our ESR measurements (Fig. S2, Supporting Information). Together with the first-principle calculation results, the magnetic results of the surface-passivation and high-quality CsPbBr₃ samples confirmed the V_Br origin of the ferromagnetism observed in the RT-synthesized CsPbBr₃ nanocrystals.

Figs. 3(d)–3(f) present the magnetic properties of RT-synthesized tetragonal-phase CsPbCl₃, orthorhombic-phase CsPbI₃, and cubic-phase CH₃NH₃PbBr₃ (structure and optical characterizations are shown in Fig. S3, Supporting Information), respectively. They all exhibited clear d⁰ ferromagnetism at 300 K, and surface passivation suppressed it. Moreover, similar to the case of CsPbBr₃, no ferromagnetism was observed in the hot-injection synthetized CsPbCl₃, CsPbI₃, and CH₃NH₃PbBr₃ at a measuring temperature of 300 K (Fig. S4, Supporting Information). Accordingly, we conclude that vacancy-induced d⁰ ferromagnetism should be universal in LHP materials.

For practical device applications, the ferromagnetism should be as strong as possible, to stabilize the spins against external thermal fluctuations. As it has a defect-origin nature, d⁰ ferromagnetism can in principle be enhanced by increasing the defect concentration. However, having too many vacancies in LHPs is potentially hazardous to their structural stability, due to the vacancy-mediated ionic migration effect^[40], a tough issue that remains to be solved. Recently, doping LHPs with TM ions has been shown to improve both the optical properties and structural stability of LHPs^[41]. Therefore, we attempted to dope the RT-synthesized CsPbBr₃ nanocrystals with 3d TM ions, and studied whether this could enhance the d⁰ ferromagnetism.

Fig. 4(a) presents the magnetization versus H_ex curves of RT-synthesized CsPbBr₃ nanocrystals doped with Mn, Fe, Co, Ni, Cu, and Zn, measured at 300 K (The XRD study confirmed the successful incorporation of these 3d dopants into the Pb site; see Fig. S5, Supporting Information). Even a tiny fraction (< 1%) of 3d dopants led to a significant modulation of the ferromagnetism of the CsPbBr₃ nanocrystals. Compared with pure CsPbBr₃, as shown in Fig. 4(b), doping with 0.54% Fe, 0.87% Co, and 0.31% Ni enhanced the M_s by a factor of three, two, and four, respectively, while doping with 0.35% Cu and 0.86% Zn impaired the M_s. The remarkable variation of the M_s indicates that the exchange coupling is sensitive to 3d ions doped, which have variable electron configuration in the 3d orbitals. As a representative, Fig. 4(c) shows the Ni²⁺ dopant concentration dependence of magnetic properties in CsPb_1–xNi_xBr₃ (see Fig. 1 for structural characterizations). The M_s roughly increased as increased from 0 to 0.46% (inset of Fig. 4(c)). Due to solubility limitation, we were unable to investigate the effects of higher x on the M_s. Fig. 4(d) displays the magnetization curves of CsPb_1–xNi_xBr₃ with x = 0.31% at measuring temperatures of 4, 100, 200, 300, and 400 K. In contrast to pure CsPbBr₃, where the M_s did not vary significantly with temperature (Figs. 3(a) and 3(b)), the M_s of Ni-doped CsPbBr₃ exhibited strong temperature dependence behavior: it decreased by approximately 42% as the temperature increased from 4 to 400 K. Nevertheless, all of the magnetization curves presented in Figs. 4(c) and 4(d) showed little or no hysteresis, indicating that the ferromagnetism of Ni-doped CsPbBr₃ should also originate from V_Br – the same as for pure CsPbBr₃. The dramatic temperature dependence of the M_s reflects that there was strong coupling between the V_Br and Ni²⁺ dopants. Only paramagnetism was found in the hot-injection-synthesized Ni-doped CsPbBr₃ quantum dots (Fig. S6, Supporting Information), further confirming the V_Br origin of the ferromagnetism.

Here we discuss V_Br-induced ferromagnetism and its enhancement with 3d dopants in an exchange coupling mechanism based on a magnetic polaron model^{[42, 43]}, which is depicted in Fig. 5. A magnetic polaron is a phonon cloud carrying net spin moments, and it usually appears with the formation of a vacancy defect^[41]. As mentioned above, V_Br in CsPbBr₃ is a shallow donor defect. This means that the magnetic polaron associated with a particular V_Br is confined in a hydrogenic orbital with a diameter D = 2ε(m/m*)a₀, where ε is the high-frequency dielectric constant, m is the electron mass, m* is the effective mass of the donor electron, and a₀ is the Bohr radius (~0.053 nm). Using ε = 4.3 and m/m* = 6.71^[44], the D value of a magnetic polaron in CsPbBr₃ was calculated to be 3.06 nm, which can extend to a distance corresponding to 5.2 unit cells of cubic-phase CsPbBr₃. By virtue of this large size, magnetic polarons in CsPbBr₃ are prone to overlap with each other, and the exchange coupling between them aligns the spin moments of V_Br^{[42, 43]}, leading to the long-range ferromagnetic ordering observed in the defective CsPbBr₃ nanocrystals. When Ni²⁺ ions are introduced and fall into the magnetic polarons, they can interact with V_Br via exchange coupling, because the Ni²⁺ ion has an open 3d⁸ subshell where the e_g level is partially filled. As the 3d orbital has a stronger exchange coupling constant than the s and p orbitals, the exchange coupling strength between the magnetic polarons can be enhanced through Ni²⁺-mediated interactions, leading to the enhancement of ferromagnetism in doped CsPbBr₃ nanocrystals. Obviously, ferromagnetism will increase with increasing dopant concentration, as observed in Fig. 4(c). As for Zn dopants, the Zn²⁺ ion has a fully-filled 3d¹⁰ subshell, which has no exchange coupling with the magnetic polaron, and thus did not enhance ferromagnetism (Fig. 4(b)). Regarding the cases of the surface passivation, the hot-injection prepared LHP quantum dots and the single crystals, decreases in V_Br concentration will increase the distance between the spins of V_Br, and thus weaken the exchange coupling strength between the magnetic polarons, explaining the lack of ferromagnetism in them.

It is worthy to point out that, because of the large magnetic polarons, even a very low doping level of Ni²⁺ ions (up to 0.46%) can lead to the significant enhancement of the RT ferromagnetism in CsPbBr₃. In contrast, previously widely studied oxide semiconductors had much smaller magnetic polaron than CsPbBr₃; the D values for ZnO, TiO₂, and SnO₂ were 1.52, 0.96, and 1.72 nm, respectively^[43]. As a result, a much higher doping level of 3d ions (usually above 3%) was required to modulate the ferromagnetism. High-level doping may cause segregation of 3d ions, which puzzled the origin of ferromagnetism in previous dilute ferromagnetic oxide semiconductors^[45]. The ability of the modulation of the ferromagnetism at low-level doping indicates that the LHP materials should be an idea platform for further theoretical and experimental studies aiming at clarifying the relationship between ferromagnetism, lattice defects, and exotic dopants.

In summary, we have reported a universal observation of vacancy-induced ferromagnetism in nominally nonmagnetic LHP semiconductors, including CsPbCl₃, CsPbBr₃, CsPbI₃, and CH₃NH₃PbBr₃. We have documented that this phenomenon is stable at temperatures well above 300 K, and that it is enhanced by doping LHPs with 3d ions. Our first-principle calculations suggest that the vacancy-induced ferromagnetism arises from spin-splitting states produced by halide vacancy. Our results are expounded within an exchange-coupled magnetic polaron model, and provide new physical insights for comprehensive understanding of defect physics in LHPs. Given that growth-related vacancies in LHP materials are unavoidable, making use of the vacancy-induced ferromagnetic properties will extend the functionalities of LHP-based devices, for example, for spintronic applications in spin light-emitting diodes and spin transistors. It would also be interesting to study more dopants, such as 4d TM ions and 4f rare-earth metal ions, and investigate whether they can lead to an even stronger ferromagnetism in LHPs, which would be crucial for practical applications.

Z. Sun and B. Cai contributed equally to this work. This work was financially supported by NSFC (61725402) and the Natural Science Foundation of Jiangsu Province (BK20190475).