# Magnetic Properties of a Ni Nanonet Grown in Superfluid Helium under Laser Irradiation

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Results

_{s}equals the stray field of a point dipole positioned in its center. The lift value h and the proportionality coefficient c

^{−1}(h) were measured to calculate the phase shift Δφ of the vibrating cantilever [24] as follows:

_{s}·π·d

^{3}/6·c(h)

^{2}was obtained from the dependences of phase shift Δφ on diameter d of nanoballs (Supplementary Materials, Figure S3). Thus, the corresponding magnetic moment of a single nanoball of a 75-nanometer diameter is μ = 4.5 × 10

^{−19}A·m

^{2}, which coincides well with the theoretically estimated value μ = M

_{s}πd

^{3}/6 = 4.2 × 10

^{−19}A·m

^{2}calculated for a single domain nanoball of a 75-nanometer diameter. In addition, we have measured the field dependence of the magnetic moment (Supplementary Materials, Figure S4). Though the approximation of the m(H) dependence and saturation magnetization M

_{s}= 510 emu/cm

^{3}are more or less convenient, the moments of the nanowires or nanoballs cannot be determined separately from the integrated magnetic moment, including contributions of objects of both types.

## 3. Discussion

_{s}also increases, while the coercive field H

_{C}decreases (Figure 5). We decomposed the recorded hysteresis loops into two contributions from nanowires and from nanoballs in accordance with the following expression [25]:

_{s}is the magnetic moment at saturation; H is the external magnetic field; and ${H}_{C}^{i}$ are the respective coercive fields of nanowires and nanoballs. The adjustment of coefficients p

^{i}to reach a true hysteresis loop shape (Figure 5) allowed us to determine the parameters characterizing the rectangularity of the hysteresis loops, p

^{1}= 0.95 for nanowires and p

^{2}= 0.45 for nanoballs. One can see the following two components: a rectangular component belonging to the nanowires and a sloped component corresponding to the nanoballs. We took into account the demagnetizing factors (2/3 for ball and 2π for cylinder) and calculated the relative volume shares of the Ni nanowires and nanoballs at different stages of ablation. In the insets to each hysteresis loop (Figure 5), one can find a circle diagram indicating the relative volume fractions of the nanowires and nanoballs. Simple regularity follows from the comparison of the hysteresis shapes and volume fraction of the nanoballs. The rectangularity of the hysteresis loop decreases as the number of nanoballs grows.

_{S}of the sample for the entire amount of nickel on the ablation time (curve one). Since the saturation magnetization of nickel M

_{s}= 58.6 emu/g (522 emu/cm

^{3}) is well known [27], and there is no reason to think that the magnetic moment in saturation can change due to variations in m

_{s}, the increase in the Ni amount on the substrate is the only reason for the increasing m. It is impossible to determine the mass of nickel deposited on the substrate in another way since it is very small as compared to the mass of the substrate. We can estimate the order of value of Ni yield using an increase in the absolute value of the magnetic moment of the Si substrate Δm ~ 10

^{−6}–10

^{−5}emu caused by network formation. Using the known in advance saturation magnetization M

_{s}= 58.6 emu/g of Ni, we can determine the network mass Δm/M

_{s}~ 10

^{−8}–10

^{−7}g.

^{n}, n = 1.36 > 1. If one assumes that the nickel mass increases linearly with the ablation time, the power law corresponds to a situation when the magnetic properties of the system depend on its size. In our experiments, the gradually changing ratio of the number of nanowires to that of nanoballs as well as the formation of a network are possible reasons for a superlinear m(t) dependence.

_{bulk}= −5.12 × 10

^{4}erg/cm

^{3}[23,28], and its value diminishes due to spin disorder in the surface layer of a 1–2-nanometer depth. Since shape anisotropy is one order of magnitude higher than crystalline anisotropy constant K

_{sh}= 7.4 × 10

^{4}J m

^{−3}= 7.4 × 10

^{5}erg/cm

^{−3}and has the opposite sign, an effective anisotropy field is only due to the shape anisotropy in the nickel nanowire. Neglecting crystalline anisotropy, one can obtain an effective anisotropy field of a single segment of nanowire as H

_{eff}= 2πM

_{s}= 243 kA m

^{−1}= 3042 Oe. This value is quite high in comparison with H

_{c}= 500 Oe obtained in pure nanowires at the early ablation stage (Figure 5a). A similar value of coercive field H

_{C}can be obtained from the Neel–Brawn formula allowing one to calculate the coercive field of a single domain particle H

_{C}= 2K

_{sh}/M

_{s}= 2874 Oe.

_{w}= 2(A/K

_{sh})

^{1/2}= 30 nm, where A is the exchange stiffness of Ni and thereby the multidomain structure within a single wire is likely to form if the nanowire diameter exceeds 30 nm. In fact, single domain nanowires are usually obtained in wire with a diameter narrowing or of the same order as l

_{w}~30 nm and showing coercivity of about 1000 Oe [25,26]. We have obtained coercivity 500 Oe for samples at the early ablation stage, where nanowires 1–2 nm in diameter are presented in the absence of nanoballs. Thus, one should conclude that domain motion should be excluded to explain the decreased H

_{c}value of 500 Oe in the frames of the independent nanowires model. The diminished value of an experimentally determined switching field in the system under study may differ from that predicted theoretically for independent nanowires because non-coherent switching modes, such as curling and fanning, can contribute to magnetization reversal. We should take into account that the wires are connected to each other in our samples. This affects both the demagnetization field and shape factor, and the estimation of the single domain limit. The presence of junctions of nanowires can facilitate propagation of the domain walls or nucleation of the magnetic reversal phase at 500 Oe, i.e., properties of the magnetic network are different from properties of single nanowires.

_{B}in a SQUID magnetometer [29], which is as follows:

_{eff}·V = 25·k

_{B}·T

_{B}

_{B}by substituting effective anisotropy constant K

_{eff}and particle volume V into Equation (3). If we substitute the shape anisotropy of nanoballs that decreased due to form factor K

_{A}= 2/3πM

_{s}= 0.74 · 10

^{5}erg/cm

^{3}instead of K

_{eff}, and V

_{ball}≈ 4.2 · 10

^{−18}nm

^{3}corresponding to the average diameter of the balls of 5 nm at the later stage of ablation (see histogram in Figure 3f) into Equation (3), we can obtain T

_{B}= 548 K. This value coincides well with that found by the extrapolation of the FC and ZFC dependences to their intersection (Figure 6). According to the Neel–Brown theory, in the system of non-interacting separated nanoparticles, the temperature corresponding to the maximum of the M(T) curve is exactly equal to the blocking temperature T

_{b}[30]. The crossing point of the FC and ZFC curves is very close to the blocking temperature, and we assume an approximate equality of these temperatures T

_{c}≈ T

_{b}neglecting the interparticle interaction.

## 4. Materials and Methods

^{3}size, which was covered by TEM grid and placed at the bottom of the cryostat (Figure 1d).

## 5. Conclusions

- (a)
- The laser ablation of Ni in He II supplies Ni to vortexes, where amorphous or nanocrystalline nanowires grow. Crossing nanowires form a continuous ferromagnetic net. In addition to nanowires, the net consists of polycrystalline Ni nanoballs incorporated into the net. The increased ablation time provides an increase in the corresponding Ni concentration in superfluid He and in the resulting number and diameter of nanoballs. Nanowires wrapped around a nanoball have been observed. A possible origin of the nanoball growth with an increase in ablation time is the nucleation of invisible small Ni nuclei and a following increase in their diameters due to the adsorption of Ni nanowires and adatoms from superfluid He.
- (b)
- Analysis of the time dependence of hysteresis shape and comparison with the morphology of the network at each ablation stage allows the contributions of nanowires and nanoballs to the magnetic moment of the network to be distinguished. The nanowire gives perfect rectangular hysteresis, while the hysteresis loop of the nanoballs has a sloped gradual shape at 300 K. The nanowires and nanoballs have different blocking temperatures equal to 235 and 545 K, respectively.
- (c)
- The magneto-crystalline anisotropies of Ni in the nanowires and nanoballs, both, are close to the magnetic anisotropy of the bulk magnetic Ni known in the literature. We have observed a diminished value of coercive field in the nanonet in comparison with a theoretically predicted value for the system of isolated non interacting microwires at the early stage of ablation when nanowires are mainly present. A possible explanation of this deviation is the facilitated nucleation of the magnetic reversal phase at junctions of nanowires.

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**(

**a**) Cryostat equipped with laser focusing system, quartz window, Ni target, permanent magnet and Si substrate covered with TEM grid; (

**b**) Laser induced evaporation of the Ni accompanied by creation of quantum vortices in He II; (

**c**) Ni atoms and clusters captured by vortices; (

**d**) Elongated nanowire segments cross and result in net, containing nanoballs. All products attracted by permanent magnet are deposited on the Si substrate.

**Figure 2.**(

**a**) EDX spectrum of a separated nanoball. SEM image is shown in the right inset; (

**b**) morphology of the large ball formed by microwires.

**Figure 3.**(

**a**) TEM image of Ni nanowires at early stage of ablation (free segments of nanowires are shown by arrows); (

**b**) SEM image of the net consisting of nanowires and balls at later stage of ablation. Nanoball diameters are marked by arrows; (

**c**) electron diffraction patterns of the sample at early stage of ablation; (

**d**) electron diffraction patterns of the net at later stage of ablation; (

**e**) distribution of lengths of free nanowire segments normalized to their total number at later stage of ablation; (

**f**) distribution of ball diameters normalized to the total number of balls in sample. Solid lines are approximations by lognormal functions.

**Figure 4.**TEM images of the network at different stages of ablation: (

**a**,

**b**) Early stage (10 min), (

**c**,

**d**) intermediate stage (30 min), (

**e**,

**f**) later stage (60 min).

**Figure 5.**Magnetic hysteresis at 300 K: (

**a**) in the sample with low Ni concentration (after short (10 min) laser exposure), (

**b**) lower-intermediate Ni concentration (after 20 min laser exposure); (

**c**) upper-intermediate concentration (30 min laser exposure); (

**d**) high Ni concentration after laser ablation for 1 h. Symbols are experimental data, and solid lines are approximation by the two-hysteresis model described in the text. Separate magnetic contributions of the nanowires and nanoballs are shown by thin red solid lines. Relative volume concentrations of the nanowires (yellow) and nanoballs (grey) are shown in the circle diagrams in the bottom insets to the correspondent hysteresis.

**Figure 6.**Temperature dependences of magnetic moment m of the sample cooled in zero magnetic field (ZFC mode is shown by empty symbols) and in magnetic field of 1 T (FC mode is shown by full symbols). Measurement field was 300 Oe in FC and ZFC modes, both. Possible blocking temperatures, which are 245 K for nanowires and 545 K for nanoballs, are shown by vertical dashed lines.

**Figure 7.**Dependence of saturation magnetic moment m

_{s}of sample on ablation duration (1), dependence of magnetic moment of nanoballs on ablation duration (2), dependence of magnetic moment of nanowires on ablation duration (3).

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**MDPI and ACS Style**

Koplak, O.; Dvoretskaya, E.; Stepanov, M.; Karabulin, A.; Matyushenko, V.; Morgunov, R.
Magnetic Properties of a Ni Nanonet Grown in Superfluid Helium under Laser Irradiation. *Magnetochemistry* **2021**, *7*, 139.
https://doi.org/10.3390/magnetochemistry7100139

**AMA Style**

Koplak O, Dvoretskaya E, Stepanov M, Karabulin A, Matyushenko V, Morgunov R.
Magnetic Properties of a Ni Nanonet Grown in Superfluid Helium under Laser Irradiation. *Magnetochemistry*. 2021; 7(10):139.
https://doi.org/10.3390/magnetochemistry7100139

**Chicago/Turabian Style**

Koplak, Oksana, Elizaveta Dvoretskaya, Maxim Stepanov, Alexander Karabulin, Vladimir Matyushenko, and Roman Morgunov.
2021. "Magnetic Properties of a Ni Nanonet Grown in Superfluid Helium under Laser Irradiation" *Magnetochemistry* 7, no. 10: 139.
https://doi.org/10.3390/magnetochemistry7100139