Evolution of Microscopic Magnetic Domains in Quasi‐2D Cr0.92Te at Room Temperature

2D materials with long‐range ferromagnetic order hold promises for the development of compact spintronic devices with unprecedented multifunctionality and tunability. Among various 2D magnets, self‐intercalated transition metal chalcogenides Cr1+δTe2 exhibit unique features, especially excellent ambient stability and intrinsic ferromagnetic ordering above room temperature, which are critical requirements for real‐life device applications. Despite the many investigations of the magnetic properties of the Cr1+δTe2 family on the averaging macroscopic level, the domain evolution on the microscale, which is vital to nanoscale spintronics, is yet to be fully understood. Here, the evolution of magnetic behaviors of Cr0.92Te crystals is presented on both macro‐ and micro‐scales under magnetic field and thermal excitation. The crystal exhibits a high Curie temperature (Tc ≈ 343 K) among the Cr1+δTe2 family with weak magnetic anisotropy and in‐plane magnetic easy axis. Utilizing magnetic force microscopy, a pristine multidomain state and typical domain‐switching behavior are observed. Moreover, the evolution of domain texture under thermal excitation shows statistical power‐law scaling as approaching Tc. The results provide microscopic insight into the ferromagnetic behavior of a room‐temperature quasi‐2D crystal, which can be useful for further engineering of domain texture in low‐dimensional magnetic materials.


Introduction
[3][4][5][6][7][8] 2D magnetics were considered impossible owing to the Mermin-Wagner theorem, in which spontaneous magnetization cannot exist in the 2D isotropic Heisenberg model at a finite temperature. [9]The situation has been changed upon recognizing the significance of magnetic anisotropy in a 2D system, which is believed to be capable of overcoming thermal fluctuation and enabling stable long-range magnetic order down to the atomic scale. [1,10,11][14] Therefore, the search for 2D magnetic materials beyond the most-studied prototypical compounds expedites, especially for some unprecedented transition-metal dichalcogenides (TMDs). [15]mong synthesized layered VSe 2 , [16] CrSe 2 [17] and CrTe 2 [18]   and non-layered FeTe, [19] Cr 2 S 3 and CrS materials, [20][21][22] a series of binary Cr-based tellurides Cr 1+ Te 2 have been noticed because of their stability in ambient condition and intriguing magnetic behaviors.The structure of Cr 1+ Te 2 can be considered as Cr intercalated into alternative layers of NiAs-type CrTe 2 backbone (Figure 1a). [23]The amount of Cr intercalants () is vital to the interaction of spins.[26][27][28] The rotation from perpendicular magnetic anisotropy to in-plane magnetic anisotropy has been reported when  is above 0.4. [24]Due to their high transition temperature and tunable magnetic behavior, binary Cr-based tellurides are further taken as a platform for exploring nontrivial spin interactions at reduced dimensionality. [18,29]The Cr 1+ Te 2based magnetic tunnel junction shows giant tunneling magnetoresistance up to 14.5% by engineering antiferromagnetic interlayer exchange coupling. [30,31]In addition, electric-field mod-ulation of magnetism in a CrTe/CdTe heterostructure field effect capacitor and the current-driven magnetization switching in ZrTe 2 /CrTe 2 were also reported. [32,33][36] Magnetic force microscopy (MFM) and single-spin quantum magnetometry were utilized in highly uniaxial-magnetic-anisotropic 2D systems such as CrI 3 , [37] CrBr 3 , [38] Cr 2 Ge 2 Te 6 , [39] Fe 3 GeTe 2 , [7,40] Fe 2.5 Co 2.5 GeTe 2 [41,42] to unravel the structure of magnetic domains and their domain walls.However, for tellurides in the Cr 1+ Te 2 family, especially those with high magnetic transition temperature and extensive Cr intercalation, the in situ evolution of their magnetic structure at the microscopic scale is still unknown.Moreover, the spatial distribution of magnetic domains under a magnetic field and thermal excitations could further advance our understanding of the magnetic behaviors of quasi-2D magnetic systems.
Here, we show that Cr 0.92 Te single crystals synthesized by chemical vapor transport (CVT) present clear alternate layers of intercalated Cr atoms along the c-axis and demonstrate a high T c ≈ 343 K with robust domain structure at room temperature.The as-grown crystal has a random magnetic domain distribution that can be switched by an out-of-plane magnetic field at ambient conditions, and we reconstructed a butterfly-like switching pattern by extracting domain fractions under different magnetic fields.Furthermore, by thermal excitation, the magnetic domains shrink continuously from the micrometer to the nanometer scale, which is found to statistically follow the power law scaling behavior.Combining atomic-imaging experiments, macroscopic magnetic measurements, and in situ MFM studies under magnetic field and thermal activations, the interplay between the microscopic domain structure and macroscopic magnetic anisotropy of quasi-2D Cr 0.92 Te is unraveled.

Crystal Structure of Quasi-2D Cr 0.92 Te
A schematic of the Cr 1+ Te 2 crystal structure is shown in Figure 1a.The intercalated Cr atoms are marked as dashed cycles, which are located at the interlayer sites of the CrTe 2 frame.CrTe 2 belongs to the P63/mmc space group with a hexagonal NiAstype structure. [43]The Cr atoms are located at two crystallographically different sites, forming a quasi-layered structure that can be viewed as a Cr self-intercalation compound of layered CrTe 2 .
The Cr 1+ Te 2 crystals used in this work were synthesized by CVT.The synthesis setup is depicted in Figure S1 (Supporting Information).Ultrahigh purity Cr and Te powders were utilized as reactants with Iodine as a transport agent to grow Cr 1+ Te 2 crystals directly (see Experimental Section for details).The optical images of as-grown CrTe crystals are shown in Figure S1b,c (Supporting Information), where hexagonal-shaped crystals were formed.The Cr 1+ Te 2 flakes have an in-plane length scale of millimeters and a thickness of ≈200 m.The composition of the Cr 1+ Te 2 crystals was measured to be Cr:Te = 0.92:1 (therefore  = 0.84) using energy dispersive spectroscopy (EDS).The presence of Cr vacancies is consistent with the reported Cr-Te phase diagram where the hexagonal NiAs-type CrTe phase is stabilized in the Cr deficiency region. [44]The EDS elemental mapping in Figure 1c shows a homogenous distribution of Cr and Te, confirming the absence of elemental segregation during crystal synthesis.
The structure and crystal orientation of Cr 0.92 Te crystals were measured using X-ray diffraction (XRD), which shows diffraction peaks from (002) family plane solely.This observation demonstrates that the [002] crystal axis is perpendicular to the surface plane of Cr 0.92 Te crystals, indicating a quasi-2D growth mode during synthesis.The out-of-plane lattice constant is extracted as 0.62 nm, consistent with literature reports of Cr 0.923 Te. [45] To assess the atomic details of the Cr 0.92 Te crystals, we conducted Cs-corrected scanning transmission electron microscopy (STEM) characterization.Figure 1d shows the high-angle annular dark field (HAADF) image in the viewing direction of [010] and the corresponding Fast Fourier Transform (FFT) pattern.The HAADF image intensity is roughly proportional to Z 2 , where Z represents the average atomic number of the atomic column along the viewing direction.Since the atomic number of Te (Z = 52) is much larger than that of Cr (Z = 24), the bright spots represent the positions of Te columns.The image intensity of Cr columns is much weaker as compared to that of Te columns.The Cr and Te layers are stacked alternately along the vertical direction.A zoom-in HAADF image is displayed in Figure 1e, in which the Cr atomic sites are better visualized.We also transferred the HAADF image to the inverted FFT (iFFT) image to improve the signal-to-noise ratio, as shown in Figure 1f.It is worth noting that the Cr column dots along the vertical direction show some differences, with one of the two adjacent Cr layers displaying a slightly more elongated shape, as marked by the yellow arrows.This elongation behavior of image spots could be attributed to the stronger atomic distortions in the intercalated Cr layers due to an insufficient amount of atoms.

Magnetic Properties of Quasi-2D Cr 0.92 Te
We conducted temperature and field-dependent magnetic measurements of the Cr 0.92 Te crystal (Figure 2).The magnetization profiles of field-cooling (FC, 3 T) with the magnetic field applied parallel and normal to the c-axis of the crystal are shown in Figure 2a.The magnetization with a field normal to the caxis is ≈1  B f.u.−1 at 2 K, which decays gradually with the increase in temperature.The magnetization suddenly drops from 0.11 to 0.01  B f.u.−1 near ≈343 K (i.e., T c ) indicating the ferromagnetic to paramagnetic transition.As regards the situation with the magnetic field applied parallel to the c-axis, the magnetization decays more rapidly as T increases.The T c of Cr 0.92 Te observed in this work is well above room temperature and is much higher than that of other compounds in the chromium telluride family, including CrTe 2 (T c ≈ 167-213 K), [18] Cr 3 Te 4 (T c ≈ 325K), [43] Cr 5 Te 8 (T c ≈ 230 K). [46] It is also comparable with electrically tuned high-T c 2D ferromagnetic materials at room temperature. [47]In Figure S2 (Supporting Information) we plot a diagram comparing the intrinsic T c of various 2D and quasi-2D magnetic materials.The Cr 0.92 Te crystal reported in this work is among the highest in terms of intrinsic T c .
Figure 2b shows the field-dependent magnetization (M-H hysteresis loop) collected at 2 K.It shows that the magnetization can be saturated at a low field (≈1.1 T) with the field vertical to c-axis and at a larger field (≈2.5 T) with the field parallel to c-axis, indicating that the magnetic easy axis should lie in-plane.The M-H loops show a small coercive field H c of 0.015 T and 0.040 T with field vertical and parallel to the c-axis, respectively, which suggests a soft magnetic nature of Cr 0.92 Te.Unlike the magnetic materials with strong anisotropy, the squareness ratio (M r /M s ) of Cr 0.92 Te crystal is as small as 0.126, indicating that the magnetic domains should be randomly oriented in Cr 0.92 Te at zero magnetic field.
The temperature dependent M-H loops are further collected to verify the robustness of ferromagnetic order (Figure 2c).M s shows limited variations at and below 100 K, while it quickly deceases from 3.08  B f.u.−1 at 100 K to 1.91  B f.u.−1 at 300 K in the ferromagnetic hysteresis loops.The saturation magnetization observed in this work is larger than reported values for bulk CrTe (≈2.3  B /Cr at 2 K and ≈1.16  B /Cr at 300 K) which may result from the quantum confinement effect appearing in the quasi-2D Cr 0.92 Te. [18] The ferromagnetic hysteresis loop transforms to a paramagnetic state at ≈350 K.The hysteresis loop does not go linear above the defined T c at 343 K (Figure 2c), which may be due to the uncompensated magnetic moment at Cr 0.92 Te surface or defects, echoing the nonvanishing magnetic moment in the M-T curve at such high temperatures.M r stays at a low value in the whole temperature range both for the field applied parallel and normal to the c-axis (Figure 2d), confirming the small squareness ratio.The H c is below 0.04 T across the entire temperature range with sections of fast slow decay, and slight increase along increasing temperature (Figure 2e).This phenomenon could result from the presence of a wide range of magnetic domain size [48] in Cr 0.92 Te samples.
The effective magnetic anisotropy constants K eff can be calculated by the relation , where  0 is permeability of free space, H A is anisotropy field, and M S is saturation magnetization.The calculated K eff is 13 × 10 5 J m −3 at 2 K, which is comparable to that of hexagonal Co (5 × 10 5 J m −3 ).The K eff decays to 4 × 10 5 J m −3 at 300 K as temperature increases, which is still comparable to that of CoFeB thin film on MgO single crystal (7.17 × 10 5 J m −3 ). [49]As a result, Cr 0.92 Te crystal has robust mag-netization at room temperature, an in-plane easy axis, small H c for both in-plane and out-of-plane magnetization and weak bulk anisotropy.

Magnetic Domain Structure under Magnetic Field
To reveal the microscopic picture underlying the magnetic property of Cr 0.92 Te under an applied field, its magnetic domain structure was studied using MFM.The shift of resonant frequency of the cantilever f is used to reveal the magnetic domain structure.The f results from the interaction between the local stray magnetic field on the sample surface and the magnetic Co/Pt-coated silicon tip.The MFM images of pristine Cr 0.92 Te are shown in Figure 3a.The blue (red) domains with positive (negative) frequency shift represent the repulsive (attractive) interaction between the MFM tip and the local magnetic field.It can be found The scanned position of the crystal was aligned using their topographic images to compensate for drifting.The magnetic field was increased stepwise from 0 to 80 mT and then reduced to 0 mT, after which a magnetic field with opposite direction was applied up to −80 mT.l) The evolution on the profile of the MFM signal (i.e., f) along the marked line in (b) under applied magnetic fields, where changes in both direction and magnitude of domain states are observed.m) The extracted area percentage of magnetic domains parallel to the applied magnetic field.The area of red domains increases with increasing positive magnetic field, while the area of blue domains rises when the polarity of the applied magnetic field is reversed.
that the patterns shown in MFM images have no counterpart in the atomic force microscopy (AFM) image, confirming that the observed contrast is solely attributed to the tip-sample magnetic interaction and the topographic crosstalk is negligible.To improve the signal-to-noise ratio, the noise of raw MFM images was filtered using the procedure described in Figure S3 (Supporting Information) without changing the domain features.A "featherlike" domain pattern can be observed in the MFM image of the as-grown Cr 0.92 Te crystal sample.
Figure 3a-k shows the evolution of domain structure at room temperature with magnetic field applied along the c-axis.The scanned area of MFM images was aligned based on their topographic features to countervail thermal drift.Compared to the pristine state, the structure of magnetic domains shows substantial change upon the applied magnetic field of 10 mT (Figure 3b; Figure S4, Supporting Information), which is consistent with the low coercive field (≈50 Oe) obtained in macroscopic magnetic hysteresis loop at room temperature.Over 80% of the scanned area has reversed the color.With further increasing the magnetic field to 80 mT (Figure 3c-e; Figure S4, Supporting Information), a gradual expansion of red domains and shrinkage of blue domains can be observed, where the propagation of domain boundary is indicated in the local MFM images and the profile across the dotted line in MFM images (Figure 3f).Within the range of the applied magnetic field in situ during MFM measurements (from −80 to 80 mT), a single magnetic domain is hard to achieve under such field strength at room temperature, consistent with the macroscopic M-H loops when H was applied along c-axis (Figure S5, Supporting Information).When the applied magnetic field was reduced to 0 mT from 80 mT (Figure 3f), the domain pattern showed clear changes compared with that of the pristine state (Figure S4, Supporting Information), which can be explained by its weak magnetic anisotropy.
With changing the polarity of the magnetic field, substantial domain switching occurs at −10 mT due to the low coercive field (Figure 3g).Over 90% of the scanned area has reversed the color again (Figure S4, Supporting Information).An expansion of the blue domain appears with increasing magnetic field to −80 mT (Figure 3h-j,l).Finally, when the magnetic field is reduced from −80 to 0 mT (Figure 3k; Figure S4, Supporting Information), the domain structure keeps evolving and demonstrates a similar feature as its initial state (Figure 3a).Such a domain memory behavior upon applied magnetic field may be due to the existence of defects at the sample surface or bulk (e.g., Cr vacancies) which act as pinning centers for the domain boundaries.The domain area percentage is extracted from MFM images and shown in Figure 3m.Similar to its M-H results (Figure 2c), the domain area percentage curve shows a symmetric feature with a change of domain area percentage by ≈4% upon applying the magnetic field.

Evolution of Domain Structure under Thermal Excitation
The evolution of magnetic domains at elevated temperatures was also studied.To minimize the thermal drift, the sample was stabilized at each temperature for ≈5 min before the measurements.As the setting temperature increases from 298 to 333 K, the magnetic domain size of the Cr 0.92 Te crystal gradually decreases (Figure 4a).At 333 K, which is close to their Curie temperature (343 K), the average size of magnetic domains diminishes to ≈400 nm.Such a change in MFM images is due to the thermal excitation but not the sample degradation or drifting since the morphology images of the sample (Figure S6, Supporting Information) remain intact upon heating to 333 K at ambient conditions.Comparing the MFM images obtained at 313 and 323 K, thermal agitation alone is sufficient to cause magnetic domain switching in some areas as pointed out by the black arrows.The profile of f along the dashed line in the MFM images was extracted and compared in Figure 4b.By increasing the temperature, the amplitude of f and its root mean square decreases gradually by ≈50% indicating a reduction of effective magnetic field strength of domains and a continuous nature of the phase transition.At the same time, the number of domains in the scanned area (10 × 10 m 2 ) (Figure 4c) increases from ≈15 to 40 as the temperature increases.It thus provides a detailed microscopic picture of the diminishing magnetization when approaching T c as observed in the M-H curves (Figure 2).Furthermore, the statistical analysis of the domain distribution of MFM images reveals a scaling behavior of domain size.As shown in Figure 4d, magnetic domains with a negative f were selected and separated from all other domains for statistical analysis.The logarithmical plot of domain area distribution is summarized in Figure 4e.A power-law scaling behavior (D∝A − ) spanning more than one decade can be observed.As indicated by the dashed line, the critical exponent  obtained from the fitting is 1.40, 1.57, and 1.49 at 313, 323, and 333 K, respectively.The relationship between the circumference and the area of the domains (Figure 4f) further confirms such a scaling behavior, where most points fall onto a single line at different temperatures.The critical exponent d h /d  fitted using power-law relation (P∝A dh/d ) remained almost unchanged, 0.85, 0.87, and 0.84 for 313, 323, and 333 K, respectively.The critical exponent d h /d  observed here deviates from that of uncorrelated percolation (d h /d  ≈ 0.93), which indicates the important role of magnetic interaction in Cr 0.92 Te on the formation of domain patterns.

Conclusion
We synthesize and systematically investigate the ferromagnetic behaviors of high-T c Cr 0.92 Te crystals.The STEM characterization reveals a visible difference in the adjacent Cr layers along c-axis.The Cr 0.92 Te crystal exhibits a stable ferromagnetic behavior at ambient condition with T c ≈ 343 K.The effective magnetic anisotropy constant was estimated as 4 × 10 5 J m −3 at 300 K with the magnetic easy axis lying in-plane.The weak magnetic anisotropy makes Cr 0.92 Te very sensitive to magnetic and thermal excitation.MFM images of Cr 0.92 Te crystals upon applied magnetic field show a typical domain behavior of a soft ferromagnet.A domain memory behavior is observed, which may stem from the pinning effect.The ferromagnetic domain structure of Cr 0.92 Te shows a substantial change upon thermal excitation, which diminishes both the domain size and the local magnetization.Our work provides useful information combining the macroscopic and microscopic aspects of the evolving magnetic properties of the quasi-2D Cr 0.92 Te flakes, which could shed new light on high-T c 2D materials and van der Waals spintronics.

Experimental Section
Synthesis of Self-Intercalated Cr 1+ Te 2 Crystals: Cr 0.92 Te bulk crystals were synthesized via the chemical vapor transport technique.Ultrahigh purity Cr (99.95%,Aladdin) and Te (99.99%,Aladdin) powders mixed in stoichiometric proportions (Cr : Te = 1:1) with Iodine as a transport agent were all placed in a silica ampoule in a glove box.The ampoules were evacuated to the lowest attainable pressure (10 −5 Torr) and sealed immediately.The ampoules were inserted into a two-zone tube furnace system.The source and growth zones of the furnace were heated up to 1000 and 820 °C, respectively, over 50 min and kept for 130 h.Then, the furnace was cooled down naturally to room temperature.The Cr 0.92 Te crystals were observed to exhibit extraordinary stability under ambient conditions.Subsequent characterizations of the samples, including both macroscopic and microscopic measurements, were performed at ambient conditions in this work.
X-Ray Diffractions: The X-ray diffractions of Cr 0.92 Te samples were carried out using the Bruker D8 Advance diffractometer with Cu K  radiation at ambient conditions.Cr 0.92 Te flakes were stored in a nitrogen-filled glove box holder and loaded quickly on the Si low background specimen before the measurement.
SEM/EDS Analysis: The morphology and composition of Cr 0.92 Te samples were characterized using a scanning electron microscope with energy-dispersive X-ray spectroscopy attachment (Gemini SEM500).
STEM-HAADF Characterizations: The cross-section TEM specimen was prepared by a focused ion beam (FIB) system (Hitachi NX5000) with a Ga ion beam at 30 kV and polished at 5 kV and 2 kV to remove potential damage on the surface of the lamellar.The atomic resolution STEM-HAADF imaging experiment was performed on a Hitachi HF5000 environmental aberration-corrected electron microscope equipped with a probe aberration, operated at 200 kV.
Magnetic Measurements: Magnetic properties of Cr 0.92 Te samples were studied using the Magnetic Property Measurement System (MPMS3) by Quantum Design.
AFM and MFM: Magnetic force microscopy (MFP-3D-Infinity, Oxford instrument, USA) was carried out to observe the evolution of local magnetic domains of Cr 0.92 Te under varying external magnetic fields.Commercial magnetic probes (ASYMFMHC: 30 nm CoPt/FePt coating, nominal H c > 5000 Oe, k ≈2.8 N/m, f ≈75 kHz) were used for MFM measurements so the applied external field (800 Oe in maximum) will not change the magnetization of the probe.The Cooler-Heater accessory for MFP-3D was used to thermally control the sample while at the same time measuring magnetic domain evolution with magnetic probes.The measurement process was configured with a phase-locked loop feedback on the cantilever oscillation.In this configuration, every line of the image was scanned twice: first pass, the normal topography profile was taken in a tapping mode, then, on the second pass (nap mode), the tip was raised an offset distance above the surface, which was 30 nm in this work.The magnetic contrast was then measured by the shift of the frequency f from a reference value.A negative frequency shift indicates an attractive tip-sample interaction (f < 0) while a positive frequency shift indicates a repulsive tipsample interaction (f > 0).There were two distinct contrasts.Red ones as a result of an attractive interaction between the tip and sample surface and blue ones where the tip appears to be repelled.The same modulation of measured frequency shift at the same position was observed for MFM scans using different Δh values, ruling out the influence of other long-range forces, such as the electrostatic force. [50]

Figure 1 .
Figure 1.Structural characterization of single-crystal Cr 0.92 Te flakes.a) Schematic illustration of Cr self-intercalated Cr 1+ Te 2 .The purple and golden spheres indicate the Cr and Te atoms in the 2D structure, respectively.The hollow spheres indicate potential positions for intercalated Cr atoms.b) The measured XRD pattern of the as-grown Cr 0.92 Te crystals.The SEM image of the sample is shown in the inset.c) The EDS mapping of Te and Cr for the Cr 0.92 Te sample.d) The HAADF image of the Cr 0.92 Te sample.The inset shows the corresponding FFT pattern.e) The zoom-in HAADF image and f) the inverse-FFT image of the Cr 0.92 Te sample.The yellow arrows mark the Cr layers with slightly more elongated image spots.

Figure 2 .
Figure 2. The magnetic characterization of the Cr 0.92 Te single crystal.a) The magnetization (M) as a function of temperature (T) for Cr 0.92 Te crystal in the field cooling-zero field heating experiment with the applied magnetic field parallel and normal to the c-axis of the crystal.The static magnetic field of 3 T was applied during the cooling process.The magnetic measurement was conducted upon heating at 5 mT.Curie temperature of ≈343 K is observed.b) The M-H hysteresis loops measured at 2 K with the applied magnetic field parallel and normal to the c-axis of the crystal.c) The M-H loops obtained at various temperatures with the applied magnetic field vertical to the c-axis of the crystal.d) The extracted saturation magnetization M S and remnant magnetization M r as a function of temperature.e) Temperature dependence of the coercive field.f) The calculated effective magnetic anisotropy constant K eff of the Cr 0.92 Te crystal.

Figure 3 .
Figure 3. Microscopic evolution of magnetic domains of Cr 0.92 Te single crystal sample under applied magnetic field at room temperature.a-k) MFM images of the Cr 0.92 Te sample showing multidomain magnetic microstructures.The scanned position of the crystal was aligned using their topographic images to compensate for drifting.The magnetic field was increased stepwise from 0 to 80 mT and then reduced to 0 mT, after which a magnetic field with opposite direction was applied up to −80 mT.l) The evolution on the profile of the MFM signal (i.e., f) along the marked line in (b) under applied magnetic fields, where changes in both direction and magnitude of domain states are observed.m) The extracted area percentage of magnetic domains parallel to the applied magnetic field.The area of red domains increases with increasing positive magnetic field, while the area of blue domains rises when the polarity of the applied magnetic field is reversed.

Figure 4 .
Figure 4. Temperature-dependent magnetic domain structure of Cr 0.92 Te sample.a) MFM images of a Cr 0.92 Te sample observed at 298, 313, 323, and 333 K. b) The profile of MFM signal (i.e., f) along the marked line in (a) at T = 298, 313, 323, and 333 K. c) Temperature dependence of root mean square (rms) and amplitude (amp.) of MFM signals, as well as the number of domains across the marked line in (a).d-f) Statistical analysis of the MFM domain features at 313, 323, and 333 K. d) The magnetic domains with a negative f (yellow color) were selected for statistical analysis in the MFM image (T = 333 K as a representative).e) The logarithmical plot of domain area distribution, shows a power law scaling (D ≈ A − ) spanning more than one decade.f) The logarithmical plot of the circumference as a function of the domain area, shows a power law scaling (P ≈ A dh/d ) spanning over roughly two decades.