Highly efficient heat-dissipation power driven by ferromagnetic resonance in MFe2O4 (M = Fe, Mn, Ni) ferrite nanoparticles

We experimentally demonstrated that heat-dissipation power driven by ferromagnetic resonance (FMR) in superparamagnetic nanoparticles of ferrimagnetic MFe2O4 (M = Fe, Mn, Ni) gives rise to highly localized incrementation of targeted temperatures. The power generated thereby is extremely high: two orders of magnitude higher than that of the conventional Néel-Brownian model. From micromagnetic simulation and analytical derivation, we found robust correlations between the temperature increment and the intrinsic material parameters of the damping constant as well as the saturation magnetizations of the nanoparticles’ constituent materials. Furthermore, the magnetization–dissipation-driven temperature increments were reliably manipulated by extremely low strengths of applied AC magnetic fields under resonance field conditions. Our experimental results and theoretical formulations provide for a better understanding of the effect of FMR on the efficiency of heat generation as well as straightforward guidance for the design of advanced materials for control of highly localized incrementation of targeted temperatures using magnetic particles in, for example, magnetic hyperthermia bio-applications.

The microscopic origin of damping has been intensively studied [22][23][24] in the research area of magnetization dynamics; however, direct experimental measurements of FMR-driven heat generation have been reported only in several studies on thermoelectric detection 25,26 , the bolometric effect 18,27 , and mechanical detection via the magnetostriction effect 14 . In our earlier theoretical and numerical calculation work in Ref. 28 , we proposed an idea on how to obtain ultra-high heating power by deriving explicit forms of the energy-dissipation rate (heating power) in Permalloy nanospheres under specific resonance conditions. In Ref. 20 , we also experimentally demonstrated that high-efficiency heat generation can be achieved through resonant spin-excitation and dissipation mechanism.
In the present study, by the combination of analytical derivation, micromagnetic simulation, and experimental verification, we explored temperature incrementation through local heating under FMR in superparamagnetic nanoparticles of three different ferrimagnetic materials, namely Fe 3 O 4 , MnFe 2 O 4 , and NiFe 2 O 4 . The measured temperature increments were associated directly with FMR-driven heat-dissipation power that is two orders of magnitude greater than that driven by Néel-Brown relaxation mechanisms 29 . We further correlated the temperature increments with the saturation-magnetization and damping-constant parameters of three different constituent materials, as well as the parameters of the strengths of AC and DC fields and of AC field frequency. No experimental correlations between FMR driven heat-dissipation power and temperature increment have yet been reported in terms of material parameters or low strengths of AC field under resonance field conditions, except for our earlier theoretical study 28 . This work offers necessary guidance for design of advanced materials that can be utilized for generation of efficient heat dissipation and control of the increment of targeted temperature in a highly local area.

Results and discussion
Energy-dissipation rate Q. In order to numerically estimate heat-dissipation power (the energy-dissipation rate) during magnetization excitation and relaxation processes in magnetic particles, we first conducted a micromagnetic simulation of a model sphere of 12 nm diameter (see left of Fig. 2a) and composed of ferrimagnetic MnFe 2 O 4 (for details, see Supplementary Material S1). The model includes magnetizations oriented in the direction of an applied DC field in the initial state. Then, to excite the magnetizations with a low field strength, we choose a counter clock-wise (CCW) rotating field H rot = H AC cos(2πf AC t)x + H AC sin(2πf AC t)ŷ on the xy plane, as illustrated in the right of Fig. 2a, because this field is the resonant eigen-basis of the CCW precession motion of M. We should note that CW rotating fields lead to no precession motion of M. Upon application of Oe), as shown in Fig. 2b. At the given field strength of H AC , the m x and m y oscillatory amplitudes reach the steady state with a certain polar angle of ~ 2° and then precess sustainably at that angle until the rotating field is sustained. According to the inherent and irreversible nature of the magnetization dynamic process, the field energy injected into the sphere model is transformed into heat through magnetization dissipation. In order to quantify the amount of heat-dissipation power during the continuous precession/relaxation dynamics in the model sphere, we numerically calculated the magnetic energy-dissipation rate (power loss) Q from the simulation data shown in Fig. 2b on the basis of energy conservation and fundamental Maxwell equations. The time-varying external magnetic forces constitutes dual power, which contributes the time variation of Gibbs free energy as well as energy dissipation rate 30 . Therefore, the resultant power loss can be given as the sum of Gibbs free energy density P Gibbs = −[1/(ρV )] V (dε Gibbs /dt)dV and the dual power density where ε Gibbs is the Gibbs free energy density, and V and ρ are the volume and the density of magnetic material, respectively. Figure 2c compares the resultant calculations of P Gibbs , P dual , and Q (= P Gibbs + P dual ) for MnFe 2 O 4 under the resonance field condition (f AC = f res = 3.0 GHz at H DC = 1010 Oe) with H AC = 3.0 Oe. P dual (red) gradually increases and then reaches a certain constant value, while P Gibbs (blue) decreases in the beginning and then converges to zero in the steady state. Thus Q turns out to be equal to P dual at the steady state. Accordingly, the steadystate Q values at resonance (noted as Q res ) could be obtained using P dual = −[1/(ρV )] V (M · dH ext /dt)dV from the simulation data, as illustrated in Fig. 2c. Figure 2d compares Q res for the three different materials Fe 3 O 4 , MnFe 2 O 4 , and NiFe 2 O 4 , and we finally obtained the steady-state Q res values, Q res = 6.2, 11.5, and 5.8 kW/g, respectively. Surprisingly, these estimated values are one or two orders of magnitude greater than the typical values (0.1-1 kW/g) of specific loss power (SLP) obtained from Fe 3 O 4 31,32 , Fe 2 O 3 33 , etc., by conventional means, which represents the initial rate of release of heat from a unit weight of magnetic material during exposure to an oscillating magnetic field according to the conventional Néel-Brown relaxation mechanism 29 . Such large energy dissipation rates are very promising with respect to the efforts to achieve efficient, fast heat generation using magnetic nanoparticles.

Measurements of temperature increments in MFe 2 O 4 (M = Fe, Mn, Ni) nanoparticles. Based
on the above calculation of heat-dissipation power in nanoparticles, we set up the apparatus schematically illustrated in Fig. 3a in order to experimentally verify the temperature increments by heat dissipation from nanoparticles without any environmental aqueous solutions. The apparatus is composed mainly of two separate parts: a microwave power pumping system to allow for magnetization excitations, and a temperature probing system to detect thermal radiation from the particles (for details, see Supplementary Materials S2-S5). Temperature increments were measured directly from the magnetic nanoparticles covered with silica shells of 12 nm thickness to avoid their agglomeration, as shown in the inset of Fig. 3a. The purpose of the silica-shell coating around each magnetic particle is to suppress inter-dipolar and inter-exchange interactions between the individual particles, thus allowing for reliable measurements of heat-dissipation power from ensemble-averaged isolated particles (see Supplementary Materials S3 and S4 for further information). To compare the quantitative values of the temperature increments from the nanoparticles of the three different materials Fe 3 O 4 , MnFe 2 O 4 , and NiFe 2 O 4 , in Fig. 3b we plotted the ∆T spectra as measured by increasing DC field strength in the range of H DC = 0 ~ 2 kOe (at a rate of 7 Oe/s) for each of the different frequencies of f AC = 1.5, 2.0, 2.5, and 3.0 GHz with a single constant value of H AC = 3.0 Oe. The ∆T-vs-H DC spectra resemble characteristic FMR spectra with single peaks maximized at certain H DC values according to f res = (γ /2π )(H DC + H int ) with H int internal fields including a magnetocrystalline anisotropy field and intra-dipolar interaction inside each magnetic particle. Note that, since the DC field strength (~ 1 kOe) is sufficiently higher than the internal field (~ 0.15 kOe) owing to the randomly oriented anisotropy axes of individual particles, the precession frequency and its related heating power are affected dominantly by the applied DC field strength. The height and position of the maximum peak in each spectrum are remarkably varied with f AC . On the other hand, the peak position does not much change with the constituent material, while the peak height rather varies with the material. Comparison of energy-dissipation rate Q and temperature increments ΔT. According to the differential equation of Newton's law of heating (cooling), the quantity of the energy-dissipation rate Q can be associated with ΔT, which temperature increment, as driven by FMR, converges to a saturation value within just a few seconds 20 . Therefore, in order to understand such temperature-incremental behaviors and their underlying mechanism as well as the material dependence of ΔT max , we accordingly compared the numerical calculations confirming that the temperature increments originate specifically from the heat (energy) dissipation driven by the FMR excitation/relaxation processes. Since the quantity of Q can be readily manipulated by tuning H DC as well as the AC field frequency, targeting temperatures also can be manipulated by those field parameters. Furthermore, the steady-state energy-dissipation rate Q was found to have its maximum peak value at resonance. This maximum value, denoted as Q res , can be analytically expressed for H rot basis as 28  Fig. 4). To verify the relation of Q res to ΔT max , we plotted analytical calculations (solid lines) of Q res and corresponding simulation data (cross symbols). For illustrative simplicity, the micromagnetic simulation data represent only the case of f AC = f res = 3.0 GHz and H AC = 3.0 Oe. The overall data on ΔT max and Q res , shown in Fig. 4, are in agreement in terms of H 2 AC dependence. For MnFe 2 O 4 (middle panel), ΔT max and Q res agree quite well except for f AC = 1.5 GHz. This slight difference between the experimental data on ΔT max and the analytical and simulation data on Q res was due to the fact that the DC field strength was not sufficient to saturate magnetizations in the real samples under the resonance condition of f AC = 1.5 GHz. On the other hand, for Fe 3 O 4 and NiFe 2 O 4 , relatively large differences between ΔT max and Q res are likely that we could not include the exactly same value of the internal field of each sample, being caused by the magnetocrystalline anisotropy field and intra-dipolar field arising from disorders of the surface and volume of each particle. The above results clearly indicate that a highly efficient energy-dissipation rate driven by FMR directly leads to temperature increments from nanoparticles, depending on the given intrinsic material parameters. Also, the temperature increments are reliably controllable by adjusting the parameters of the DC and AC field strengths and the AC field frequency. (1)

Summary
We demonstrated a considerable magneto-thermal effect driven by resonant magnetization precession/relaxation in superparamagnetic nanoparticles of ferrimagnetic oxides. The extra-ordinarily high energy-dissipation rate (power loss) during resonance magnetization dynamics was evidenced by experimental measurements of temperature increments in the nanoparticles, with the help of analytical calculation as well as micromagnetic simulations. In comparison with other mechanisms related to power loss, such as the Néel-Brownian model, the amount of heat dissipation can be significantly enhanced, via resonant spin-excitation and relaxation, by about two orders of magnitude larger than by other means. We experimentally explored robust correlations between the temperature increment and the intrinsic material parameters: i.e., the damping constant as well as the saturation magnetizations of three different constituent materials, MFe 2 O 4 (M = Fe, Mn, Ni). It revealed that the heat-dissipation power is proportional to the saturation magnetization and inversely proportional to the damping parameter of a constituent material. In order to further maximize the power loss, such critical magnetic parameters can be tailored optimally through the existing novel engineering techniques: saturation magnetization can be increased by substitution of transition metal ions in iron-oxides 34 , synthesis of bimagnetic core-shell materials 35 , or the thermolysis process 36 . Also, Gilbert damping constants can be reduced by the annealing process 37 , the optimal stoichiometric composition 38,39 , the strain-engineered process 40 , or other means. The measured temperature increments were also well controllable with low-magnetic-field-strength parameters. The present work quantitatively clarifies the fundamentals of heat generation associated with FMR in nanomaterials; additionally, it not only opens up a new opportunity for the application of FMR to magnonics or magnetic hyperthermia, but also provides guidance for the design of advanced materials that enable highly localized heating with extra-high-energy power by choosing nanoparticles' constituent materials of given saturation magnetization and damping parameters.

Methods
Micromagnetic simulation. We conducted finite-element micromagnetic (FEM) simulations at zero temperature on a single sphere of MFe 2 O 4 (M = Fe, Mn, Ni) and 2R = 12 nm diameter using the FEMME code (version 5.0.9) 41 , which incorporates the Landau-Lifshitz-Gilbert (LLG) equation. The integration of LLG ordinary differential equation (ODE) is achieved using the fourth-order Runge-Kutta methods as the predictorcorrect solver. The curved surface of the model sphere was discretized into triangles of approximately equal area using Hierarchical Triangular Mesh 42 (see Fig. 2a). The material parameters used in the simulations were as follows: magnetization at H DC = 1 kOe, M 1kOe = 85.5 emu/g, Gilbert damping parameter α = 0.180, magnetocrystalline anisotropy K 1 = − 1. Temperature measurements. Using a drop-casting method , nanocrystalline particles were placed on the surface of a 400-μm-length Cu line in a microstrip. To excite magnetization dynamics in the particles, AC currents of different GHz frequencies using a signal generator (E8257D, Agilent) were applied to the microstrip and were amplified to several watts by a radio-frequency (RF) power amplifier (5170FT, Ophir) to generate sufficient strengths of AC magnetic fields (H AC ) around the signal line. The magnetic field strength generated by AC currents flowing along the microstrip was calculated to be H AC ~ 1.0 Oe with input power of 1 W 20 . By sweeping H DC from 0 to 2.1 kOe at a rate of 7 Oe/s for each of f AC = 1.5, 2.0. 2.5, and 3.0 GHz, we measured temperature increments using an infrared camera (T650sc, FLIR) to an accuracy of about ± 1 K at a maximum temporal resolution of 30 Hz. Temperature calibration was made by measuring boiling water (99.2 ± 2.1 °C) and melting ice (− 1.2 ± 0.2 °C) temperatures from the infrared emissivity of 0.98 and 0.97, respectively. Particle temperature was estimated by averaging the temperatures within a local 200 μm × 200 μm area at the center position of the signal trace.