An efficient magnetothermal actuation setup for fast heating/cooling cycles or long-term induction heating of different magnetic nanoparticle classes

Alternating magnetic fields (AMFs) in the ∼100 kHz frequency regime cause magnetic nanoparticles (MNPs) to dissipate heat to their nanoscale environment. This mechanism is beneficial for a variety of applications in biomedicine and nanotechnology, such as localized heating of cancer tissue, actuation of drug release, or inducing conformational changes of molecules. However, engineering electromagnetic resonant circuits which generate fields to efficiently heat MNPs over long time scales, remains a challenge. In addition, many applications require fast heating/cooling cycles over ΔT= 5 °C–10 °C to switch the sample between different states. Here, we present a home-built magnetothermal actuation setup maximized in its efficiency to deliver stable AMFs as well as to enable fast heating/cooling cycles of MNP samples. The setup satisfies various demands, such as an elaborate cooling system to control heating of the circuit components as well as of the sample due to inductive losses. Fast cycles of remote sample heating/cooling (up to ±15 °C min−1) as well as long-term induction heating were monitored via contact-free thermal image recording at sub-mm resolution. Next to characterizing the improved hyperthermia setup, we demonstrate its applicability to heat different types of MNPs: ‘nanoflower’-shaped multicore iron oxide nanoparticles, core shell magnetite MNPs, as well as magnetosomes from magnetotactic bacteria (Magnetospirillum gryphiswaldense). MNPs are directly compared in their structure, surface charge, magnetic properties as well as heating response. Our work provides practical guidelines for AMF engineering and the monitoring of MNP heating for biomedical or nano-/biotechnological applications.


Introduction
Magnetic nanoparticles (MNPs) have been utilized in a variety of approaches to control material properties or biological functions in a defined manner [1][2][3][4][5][6].Of particular interest is their remote, inductive heating by the application of alternating magnetic fields (AMFs).Thus, a contact-free generation of nanoscale hotspots with high temperature control is realized.Hitherto, this approach has been employed across a range of biomaterial applications including cancer hyperthermia [7][8][9][10], spatially controlled drug release [11][12][13][14][15], the control of cell functions [16][17][18], as well as the creation of heat responsive material [17,19,20].However, the MNP heating response highly depends on the AMF generating setup and a thorough description of it exists only in few cases [21][22][23].Moreover, to maximize the heating performance and range of applications, further optimization with regard to its implementation is needed [24].For example, (i) to expand AMF applications to heterogeneous MNP distributions and to monitor their local effect requires recording of spatially resolved temperature data.(ii) For nanotechnological or cell biological applications, the generation of higher and stable magnetic field amplitudes (⩾40 mT) over long time scales is important.Here, small MNPs (⩽50 nm) need to be used, which naturally exhibit a lower magnetic response.(iii) Precise temperature variations, e.g. in the form of oscillations, are very useful to change the state of heat-sensitive matter.E.g. biomolecules can be switched between their active and inactive state and biological membranes can change from a phase separated to a homogenously mixed state.Towards realizing these applications in addition to characterizing the classical homogeneous MNP samples, this work presents solutions to advance the hyperthermia setup.
The generation of heat at the MNP site requires sufficient magnetization of the MNP by magnetic field amplitudes of typically H ≈ 10 kA m −1 [16,18].The magnetic moment then couples to the AMF and follows the orientation of the external field (in phase or with a certain phase lag), the latter exhibiting frequencies of typically 100 kHz-1 MHz.The relative orientation of the magnetic moment and the external field give rise to an effective hysteresis loop [25], whose area is proportional to the heat produced by the MNPs.The dissipated power P H in form of heat is calculated according to where f is the AMF frequency, H the external magnetic field amplitude and B the magnetic flux density generated by the MNP.In case of superparamagnetic particles, which lack an apparent hysteresis loop and hence resemble 'paramagnetic' particles within a certain temperature range, the generated heat can be calculated from the linear-response theory [26] where χ ′ ′ is the imaginary part of the AC magnetic susceptibility, a measure of how much the material becomes magnetized, and P H , f, H as before.Of note, χ ( f ) ′ ′ is a particle inherent property and H ( f ) is defined by the hyperthermia setup, with both depending on the AMF frequency.The lack of an apparent hysteresis loop for superparamagnetic particles is a result of the fact, that the magnetic moment is not blocked but can oscillate due to thermal fluctuations.Here, after an initial magnetization pulse, a relaxation of the orientation of the magnetic moment is observed.Two different processes contribute to this relaxation mechanisms, the Néel and Brownian relaxation.Néel relaxation describes the reorientation of the magnetic moment relative to the particle due to thermal fluctuations, whereas Brownian relaxation occurs due to interactions of the particle with the surrounding medium (figure 1(a)).The in our case faster Néel relaxation then dominates the effective relaxation time of the particle's magnetic moment.The effective relaxation time is directly reflected in the alternating current magnetic susceptibility (AC-susceptibility), χ , and its imaginary part χ ′ ′ has to be maximized, to maximize P H . Overall, the strong dependence of P H on f, H ( f ) and χ ( f ) ′ ′ suggests a critical examination and adjustment of the AMF setup and MNP properties for optimal performance.
To design an efficient hyperthermia setup, one needs to overcome severe constraints, primarily arising from the substantial power dissipated as Joule heating.The resistive losses in the material not only impede the long-time stability of the AMF setup, but also cause substantial side effects, such as immediate heating of the sample and the surrounding.Also, additional input power may be required to reach target magnetic flux densities.
So far, different magnetic hyperthermia setups were constructed, generating magnetic fields of several 10 mT at frequencies around 100 kHz within an electromagnetic gap of few mm in size [21][22][23].These works reported substantial improvements with regard to the choice of the electromagnet core and the generation of higher magnetic flux densities [23], the capability of life cell imaging during magnetic stimulation [18], or the realization of gap sizes up to 11 mm [21].Yet, reconciling these partly countervailing demands in one setup remains a challenge.In particular, setups exhibiting long-time stability of the AMF at high magnetic flux densities as well as efficient, repetitive heating-cooling cycles are lacking.These would be desirable for a variety of applications in material science, such as the switching of thermo-sensitive molecules [12,27,28], or the triggering of biological signaling processes via temperature responsive proteins [16][17][18].Another desirable aspect is the availability of a hyperthermia setup which is effective in terms of costs and technological equipment.
Here, we present a home-built hyperthermia setup addressing the aforementioned needs to demonstrate long-term stability of gap magnetic flux densities in the 45-50 mT regime over 30 min.Our work provides practical guidelines for AMF engineering to sufficiently magnetize MNPs.We demonstrate long-term measurements of MNP heating up to steady state temperatures at 70 • C as well as fast MNP heating/cooling cycles with temperature gradients up to ±15 • C min −1 .With this setup we demonstrate optimized heat generation from three types of (superpara-)MNPs: next to 'nanoflower'like magnetite MNPs (so called Synomag ® ), we probe bionized nanoferrite core shell particles (so called BNF) as well as magnetosomes.Synomag ® and BNF were readily available from micromod (micromod Partikel-technologie, GmbH, Rostock, Germany), whereas Magnetosomes are formed by the magnetotactic bacteria species Magnetospirillum gryphiswaldense through biomineralization and were isolated thereafter (see methods).Figures 1(b)-(e) provide an overview of the setup and measurement procedure with direct temperature mapping at sub-mm resolution.

MNPs
Synomag ® 70 and BNF 100 were purchased from micromod.Magnetosomes were isolated from the bacteria species M. gryphiswaldense.Magnetosomes are single-domain MNP.In bacteria, they are encapsulated by a protein shell that prevents agglomeration and aligns the MNP in chains.Bacteria were cultivated in complex medium (15 mM potassium lactate, 10 mM sodium nitrate, 0.7 mM monopotassium phosphate, 0.6 mM magnesium sulfate, 3 g l −1 peptone, 0.1 g l −1 yeast extract, 0.15 mM iron(III) citrate, 20 mM HEPES (pH 7.0)) for 39 h at 28 • C without shaking and without air exchange.Cultures were fed with supplementary medium (0.75 M potassium lactate, 1 M sodium nitrate, 37 mM monopotassium phosphate, 30 mM magnesium sulfate, 5 mM iron(III) citrate) after 24, 30, 33, 36, and 39 h.Afterwards, bacteria were collected by centrifugation at 4000 g for 7 min and resuspended in HEPES buffer (0.2 M, pH 7.0).Bacteria were lysed with an ultrasonic sonotrode (UP 200S, Hielscher Ultrasonics GmbH, Teltow, Germany) at 30 W for 120 min in an ice bath, to isolate but maintain the magnetosome chains.After lysis, magnetosome chains were collected and washed with a neodymium magnet and resuspended in HEPES buffer (0.2 M, pH 7.0).In some cases, the magnetosome cores were extracted from the chains, wherefore the encapsulating protein shells were denatured at 90 • C for 5 h in a water bath.

MNP sample preparation
For transmission-electron-microscopy (TEM) imaging of Synomag ® and BNF particles the stock solution was diluted to a concentration of 0.125 mg ml −1 in phosphate buffered saline.Afterwards the sample was sonicated in an ultrasonic bath for 10 min and filtered through a syringe filter (Filtropur S, membrane: polyethersulfone, filtration area: 6.2 cm 2 , pore size: 0.2 µm, sarsted AG & Co. KG, Nümbrecht, Germany).7 µl of the prepared samples were dropped onto a formvarni-grid and sedimented for 2 min.The remaining solution was removed using filter paper and the grids were left to dry on air.Images were taken with a Jeol JEM-2100plus (Akishima, Tokyo, Japan) in brightfield mode at 80 kV acceleration voltage.Isolated magnetosomes were diluted 1:20 before transferring a single droplet onto a carbon-cu-grid.The solution was left to sediment for 1 min, then removed using filter paper and the grid was left to dry on air.Images were taken using a Zeiss EM902 (Carl Zeiss Microscopy GmbH, Jena, Germany) at an acceleration voltage of 80 kV.Average particle diameters were determined using FIJI [29].
For dynamic light scattering (DLS) measurements magnetosomes, Synomag ® and BNF particles were diluted with HEPES buffer (0.2 M, pH 7.0) to a concentration of 0.2 mg ml −1 (magnetosomes) or 1 mg ml −1 (Synomag ® and BNF particles).Please note that for Synomag ® and BNF the concentration is given for particles while for magnetosomes the iron concentration is given throughout this work.All solutions were filtered through a 200 nm polytetrafluoroethylene filter (514-0068, VWR, Radnor, USA).The DLS measurements were performed with a Zetasizer Nano ZS (Malvern Panalytical, Malvern, UK).Prior to the measurement, a waiting time of 100 s served to balance the temperature (25 • C).For each sample 5 runs with 15 sub-runs (10 s) were recorded.A break of 100 s was taken between runs.Hydrodynamic diameters of particles were calculated from the mean size of the number distribution and averaged over 5 runs.The error is the standard deviation.
For ζ-potential measurement the sample was identically prepared as for DLS measurements.Since the particles were kept in buffer the 'monomodal mode' was used.Five runs with 15 sub-runs (10 s) were used per sample.Between the runs the lag time was 50 s.The ζ-potential was averaged over all runs and mean and standard deviation values are reported.
For hyperthermia measurements, MNPs dissolved in water or buffer at the indicated concentration were used.

Thermography measurements
Thermography measurements were performed using a VarioCam HD (Infratec GmbH, Dresden, Germany) with an IR 1,0/30 JENOPTIK objective (Supplied by Infratec GmbH, Dresden, Germany).A distance of 40 cm was kept from the magnet to prevent damaging the camera resulting in a ∼300 pixel measurement area of 5 × 10 µm 2 for the sample.Over this area, the sample temperature was averaged.The typical pixel size was ∼300 × 300 µm 2 .A measurement cycle consisted of 1 image before applying the field, 90 images of heating period and 90 images of cooling period taken at a framerate of 0.1 Hz.For each sample the measurement was repeated ⩾3 times.

Data analysis and evaluation
Images were evaluated using the IRBIS3 plus software (Infratec GmbH, Dresden, Germany).The temporal behavior of the sample temperature was extracted accounting for the sample emission coefficient of 0.95 in comparison to a blackbody, which was calibrated beforehand from the emission of a sample with known temperature.The reflected temperature was identified with the room temperature.The room temperature exhibited only slight fluctuations by ±0.3 • C during the measurement and was considered to have negligible influence on the sample temperature.The heating and cooling kinetics were fitted with self-written routines in Matlab (The Mathworks Inc., Natick, MA, USA, Version: R2020b) using the least squares method lsqcurvefit.The mean fit parameters and respective error were calculated from each sample.

General setup and resistive losses
The electric circuit is based on a series resonance circuit which enables the reuse of energy stored in the magnetic field that otherwise would need to be provided by the power supply.The general circuit design was reported before [23], where the setup consists of a function generator, an amplifier, a shunt resistor, a transformer, and an RLC series resonance circuit (figure 2(a)).To operate efficiently, the driving frequency is set to the circuit's resonant frequency where the impedance is at its minimum.
The main cause of energy dissipation in the resonance circuit are resistive losses resulting in heating of the electrical components, even when highly optimized material is used.This heat radiation causes elevated, gradually changing temperatures in the sample environment, thus preventing any measurement of small temperature changes.In order to prevent such effects and to limit the magnet temperature to ∼1 • C above room temperature, specialized circuit components minimizing eddy currents or proximity effects together with an elaborate cooling system need to be used.

Optimized circuit components and characterization
The central component of the AMF setup is the electromagnet which consists of a ferrite core and a wire coil around it (N = 22 turns).As core material MnZn-based SIFERRIT N87 (Tokyo denkikagaku kogyo (TDK), Tokyo, Japan) is chosen, a soft ferrimagnetic ceramic minimizing eddy currents, although losses from hysteresis occur.It exhibits a low power loss (e.g. 120 kW m −3 at 100 mT for 100 kHz frequencies around room temperature [30] compared to other optimized ferrites, such as 3F3 ferroxcube with 170 kW m −3 at identical conditions [31]).A downside of using the ferrite is the comparably low thermal conductivity (e.g.1-5 W m −1 K −1 compared to iron 74 W m −1 K −1 at room temperature [32]).Due to the higher magnetic flux density inside the core in combination with the poor thermal conductivity, active cooling is needed to keep the core and surrounding wires from substantially heating up (see section 3.3).The toroidal magnet exhibits a gap of 10 mm × 20 mm × 10 mm (w ×h ×l), which enables mounting of different in vitro samples (e.g.fitted microscopy slides, vials or microfluidic channels) without direct contact between the sample container and magnet (figure 1(c)).These dimensions were also chosen to keep the flux leakage at minimum.The same ferrite core without gap is used for the transformer, which transmits the source signal to the resonance circuit by inductive coupling.
It is interesting to estimate the conditions at which a particular magnetic flux density at the center of the electromagnet's gap is reached.In case of a toroidal core, which channels the AMF into a small gap (as in this work), it is given by [23] where H g is the amplitude of the magnetic field generated inside the gap, N is the number of turns, I is the peak current, and w is the width of the gap.For an anticipated H g ≈ 36 kA m −1 resulting in a flux density of B = 45 mT with N = 22 turns, this approximation shows that substantial currents of I ≈ 17 A are needed.Of note, since this approximation is invalid for gap sizes ≫ 1 mm, where leakage flux plays a role, even higher currents will be needed to reach the yield H g .In fact, when measuring magnetic flux densities ⩾45 mT at the center of the electromagnet's gap (figure 2(b)), a sinusoidal feed signal of 300 m V PP was applied to the circuit.This signal was generated by a function generator (Agilent 33220A, Agilent Technologies, Santa Clara CA, USA) and amplified by (53.0 ± 1.5) dB using a 1020L radio frequency power amplifier (Electronics and Innovations Ltd, Rochester NY, USA).An input signal of this magnitude at resonance frequency gives rise to a peak-to-peak voltage of (1478 ± 2) V pp at the capacitor array (figure 2(c)) and a calculated current of (44.4 ± 0.2) A.
Next to reaching the desired magnetic flux densities in the gap, an important aspect of a reliable AMF stimulus is the temporal stability of the magnetic field in the center of the gap.For the described setup a magnetic flux density of (48 ± 1) mT was maintained over 20 min and showed less than 10% deviation over the time range of 30 min (figure 2(b)).Such field stability is important, as it enables the recording of heating/cooling kinetics up to the point where a steady-state is reached.
Depending on the input voltage, the capacitor in the resonance circuit can be subject to high voltages in the kV regime (figure 2(c)) and steep voltage rises on the order of 4 •10 8 V s −1 .To account for these demands, high end film capacitors (FKP1 0.1 µF, WIMA, Mannheim, Germany) are used.To distribute the voltage among the capacitors in each branch and to divide the current among the different branches, an array of five parallel branches each containing ten capacitors in series, was implemented.Although similar setups can be realized using mica capacitors, the film capacitors are preferred as they allow for a better distribution of dissipated power and can operate free of any additional cooling.Another benefit is the option to alter the overall capacitance and hence the resonance frequency by selectively removing or adding capacitors.Important is the linear relation between the input voltage and measured magnetic flux density in the gap of the electromagnet (figure 2(c)).This behavior is favorable since it provides scalability of the AMF during experiments.Given these values, it is important to note, that the generation of higher voltages imposes a risk for the experimenter, wherefore additional safety measures as well as shielding and insulation of the setup needs to be installed.In addition, these values show, that the resonance circuit is unmatched in its efficiency to provide a high apparent power of P = U(ω r )•I = 65 kW.
The resonance circuit components (figure 2) were measured with a four-port measurement using an E4990A-030 impedance analyzer (Keysight Technologies, Inc., Santa Rosa, CA, USA).The measured capacitance for the capacitance array amounted to (51.2 ± 0.3) nF, while the measured inductance for the magnet was (55.89 ± 0.09) µH.This led to a calculated resonance frequency of 94.26 kHz.These measurements provide a good estimate of the component properties, although their value in the circuit may differ during operation due to the heating of the setup.To determine the resonance frequency experimentally, a resonance curve was measured.To this end, the capacitor voltage U(ω) at different angular frequencies ω = 2πf was recorded and fitted with the theoretical relation where U in is the input voltage, R is the ohmic resistance, L is the inductance, and C is the capacitance.The resonance frequency derived from the fit function was (93.54 ± 0.01) kHz (figure 2(d)), which is 0.51 kHz lower than the theoretical value.Experimentally, the magnetic field in the electromagnet's gap turned out to be slightly higher at 93.75 kHz, a value in between the initial theoretical and experimental value.For this reason, this latter optimal frequency was used.From the fit function also the quality-factor Q was determined, defined as where f r is the resonance frequency and ∆f is the bandwidth at 1/ √ 2 of the maximum voltage U(ω) amounting to (3.3 ± 0.2) kHz.This resulted in a quality-factor of Q = (29 ± 2).While this high quality-factor signifies an efficient, underdamped operation of the circuit, it limits the accessible bandwidth of the signal amplification at the same time.To still enable flexible adjustments of the frequency range, interchangeable capacitors can be used.
To handle the currents mentioned above, special wires are required.The central wire forming the coil to generate the magnetic field is a special Litz wire (New England Wire Technologies, Lisbon NH, USA).The Litz wire consists of 3 bundles of 54 wire strands of American wire gauge 38, corresponding to a 50.5 µm radius (figure 2(e)).It is designed to minimize the influence of the frequency dependent skin effect, which signifies the current density distribution in a conductor, exponentially decreasing from the edge towards the center.A mitigation of the skin effect is achieved by adapting the size of individually insulated wires to the skin depth δ, the depth below the conductor surface at which the current density has fallen to its 1/e value [33].δ amounts to ∼213 µm at the 93 kHz resonance frequency used in this work.Another aspect of optimization is the proximity effect, where a change in the current density in one conductor arises due to AC-currents in a nearby conductor.The proximity effect is diminished by 'braiding' the wire strands to distribute the position of each individual strand throughout the wire.The Litz wire was used in parts of the secondary circuit of the setup, where high currents develop.A different, stranded wire consisting of 510 copper strands (LIFY 1.00/2.6;supplied by Bürklin GmbH & Co. KG, Oberhaching, Germany) was used in regions of the circuit where lower currents develop, i.e. the primary circuit of the setup and the capacitance array in the secondary circuit.Here, the necessity of using the Litz wire was reduced and combining these wires helps to lower the cost of the whole setup.To compare the performance of both wires, the wire impedance was measured and the corresponding ohmic resistance calculated, the main cause of wire heating.The ohmic resistance over a 50-150 kHz frequency regime showed a continuous resistance increase from 65 to 90 mΩ for the stranded wire, while the resistance of the Litz wire changed only from 48 to 52 mΩ (figure 2(f)).In addition, the coupling factor of the transformer for each wire was determined, using a transformation ratio of 25:5 measured in forward and backward direction (figure 2(g), solid and dashed lines respectively).Both wires exhibited a high coupling of >98% with almost negligible frequency dependence in the 50-150 kHz regime.With 98.8%, the inductive coupling of the Litz wire is marginally higher compared to the stranded wire, with 98.5%.Moreover, to ensure a homogeneous exposure of the sample to AMFs, the flux density value within the gap volume was measured with a hall probe in <1 cm steps (figure 3).

Mitigating heat dissipation by active cooling
To mitigate the heat dissipation by the system, a water-cooling system was developed.To this end, 3D printed housings for the electromagnet and the transformer core were designed with a 3D-computer aided design software and fabricated out of 3D resin (Gray Resin, Formlabs, Somerville, MA, USA).To limit the temperature rise, water of 5 • C temperature was provided by a thermostat and was constantly circulated through the cooling housings.By limiting the magnet temperature around ambient temperatures throughout the measurement, we minimized the influence of the magnet temperature on the sample heating.Moreover, cooling of the electromagnet, the transformer core, and the 0.5 Ω shunt resistor, decreases the strain on these components and increases their temporal stability and lifetimes.An image of the magnet generating 45 mT magnetic flux densities in the gap can be seen in (figure 1(d)).

Characterization of MNP physical properties
To determine the suitability of different MNPs for hyperthermic heating, we first characterized the three MNP classes used in terms of their physical core size, their hydrodynamic size, their charge, as well as their AC susceptibility (figure 4).TEM images revealed a nanoflower shape of Synomag ® MNP, consisting of a quasi-spherical morphology combined with a rough surface due to the nanocrystalline substructure embedded in a dextran matrix.BNF cores exhibited parallelepiped shapes, also encapsulated in a dextran shell.In case of magnetosomes, a cuboctahedral shape surrounded by a bio-membrane layer was found, in line with previous reports [34].Particle size analysis of TEM images revealed a physical diameter of (32 ± 4) nm for Synomag ® .The magnetic cores of BNF comprise several crystallites of magnetic iron oxide having a nominal diameter of 92 ± 19 nm.Both are comparable with previously reported sizes [35,36].Magnetosomes preserved within chains exhibited an average diameter of (39 ± 7) nm, not accounting for the protein rich membrane, which naturally surrounds the magnetosomes regulating the crystal maturation [37].The hydrodynamic size was measured with DLS and the ζ-potential was determined with a Zetasizer.In case of Synomag ® , the hydrodynamic diameter from the number distribution was (46.8 ± 0.6) nm (smaller than the intensity distribution based hydrodynamic size of (64.0 ± 0.4) nm); poly-dispersity-index (PDI) (0.048 ± 0.006) and the ζpotential was slightly negative (−1.8 ± 0.9) mV.In case of BNF, the hydrodynamic size by number distribution was (103 ± 2) nm (smaller than the intensity distribution based hydrodynamic size of (132 ± 2) nm); PDI (0.04 ± 0.01) and the ζ-potential was slightly negative with (−0.8 ± 0.4) mV.The hydrodynamic sizes of Synomag ® and BNF are larger than the size of the MNPs determined by TEM and can be explained by the surrounding dextran shell which is not visible in TEM as well as the layer of solvent molecules surrounding the particle.In case of magnetosomes, DLS measurements of preserved chains indicated a polydisperse sample and could only be performed after filtering the sample with a 200 nm cutoff filter.The hydrodynamic size amounted to (23 ± 9) nm (significantly smaller than the intensity distribution based hydrodynamic size of (202 ± 35) nm; PDI (0.295 ± 0.004).Please note that the PDI is calculated based on the intensity distribution and not the number distribution shown in figure 4).The small number distribution value compared to TEM measurements may arise from the additional filtering step.The ζ-potential was substantially negative with (−31 ± 2) mV (figure 4(c)).The negative surface potential determined for all MNPs is beneficial for their long-term stability as well as for their biocompatibility.For example, a negative ζ-potential was shown to prevent unspecific interactions and MNP mobility inside cells [38,39].
AC susceptibility measurements (figure 4(d)) revealed the MNP dynamic response of the magnetic moment to an AMF.The imaginary part of the AC susceptibility corresponds to the energy 500 of the particle system.An optimal phase lag between the MNP magnetization and the excitation field for energy absorption exists at the frequency where the imaginary part of the AC susceptibility exhibits a maximum, χ ′ ′ max .This primary relaxation frequency also indicates the effective relaxation time τ eff according to which is dominated by the faster of the two, the Néel or the Brownian relaxation time τ N/B .It is important to note, that in contrast to single domain crystals, no simple expression for τ eff exists.Instead τ N/B are determined directly from an AC susceptibility data fit.Since MNPs used in this study did not exhibit single domain crystals, the AC susceptibility data was fitted with the extended multicore model.Here, the Brownian relaxation is given by the Debye model integrated over the particle size distribution, whereas the cole-cole expression is used to model the Néel relaxation part [40]: χ 0B is the directed current (DC) susceptibility for particles that undergo Brownian relaxation, χ 0N the DC susceptibility for particles that undergo Néel relaxation, ω = 2πf is the angular frequency, r H the hydrodynamic radius of the particles and α describes the degree of distribution of the Néel relaxation times (due to size distribution of the single-domains and/or magnetic interactions between the single-domains).The advantage of this model is that the Néel relaxation does not have to be at higher frequencies than the Brownian relaxation as in other models and that both time scales may overlap.
For Synomag ® particles (measured at 5 mg ml −1 ) the imaginary part of the AC susceptibility exhibited a maximum at 3.8 kHz and a shallow plateau around 100 kHz.The real part of the AC susceptibility decayed slowly and exhibited a 0.02 value at 100 kHz.At low frequencies compared to the principal relaxation frequency at 3.8 kHz, the magnetization followed the excitation field.Here, the real part of the susceptibility was at its maximum and the imaginary part close to zero.At high frequencies compared to 3.8 kHz the real and the imaginary part decreased slowly, maintaining a significant phase lag with slow decrease of the magnetization.The rather broad distribution and slow decrease at higher frequencies reflected the multicore nature of Synomag ® and indicated relaxation of internal disordered spins in line with previous reports [41].Moreover, it has been speculated that the phenomenal heating of Synomag ® is primarily a result of an exchange coupling between the cores, which leads to a superferromagnetic magnetization state [42].In case of BNFs, the imaginary part of the AC susceptibility χ ′ ′ exhibited a single maximum at 0.1 kHz, orders of magnitudes lower compared to Synomag ® MNP, together with a steep drop of the real part χ ′ around this frequency.At high frequencies the magnetization vanished quickly.This behavior resembled singledomain crystals, albeit the magnetization lagged the external field already at low frequencies.For magnetosomes the real and imaginary part of the AC-susceptibility decayed in parallel over the whole frequency range with small absolute values on the order of 10 −3 , yet sufficiently above the resolution limit of the volume AC susceptibility of 10 −5 .This data indicates, that magnetosomes get only barely magnetized by the 0.5 mT field of the AC susceptometer.Over the whole frequency range magnetosomes follow the external field only with a substantial phase lag.With increasing frequency, also the magnetosome magnetization gets more and more reduced.This indicates that magnetosomes are in a blocked and not a superparamagnetic state anymore.Due to the small χ (ω) values, a determination of τ N/B was not possible.Table 1 provides an overview of the analysis of the fit according to equation (7).In case of Synomag ® and BNF particles Néel and Brownian relaxation times differed by more than an order of magnitude.Néel relaxation was the faster and dominating process, thus accounting for most of the power dissipation as shown before for maghemite particles [43].Yet, it should be noted, that relaxation times were determined for an excitation field of ≤0.5 mT in the AC susceptometer, which is two orders of magnitude smaller than the excitation field of our home-built magnetothermal actuation setup.While τ N/B are often provided in the zero-field limit, their value and in particular τ N was reported to be dependent on the magnetic field strength [44].
Based on this study, τ N is expected to become even smaller than reported in table 1, when MNPs are placed in higher external fields.Another consequence is, that the apparently small χ values will highly underestimate the actual magnetization and heating response obtained in the home-built AMF setup.

MNP heat response during heating/cooling cycles
To determine MNP heating responses correctly, samples were subjected to the AMF until an equilibrium between the heat generated by the particles and heat dissipated to the surrounding was established.Samples evaluated in this work reached this steady state within <15 min.For this reason, the time intervals of heating or cooling the sample were set to 15 min, except for fast cycle measurements.Absolute temperatures were recorded via thermal imaging at 0.1 Hz.The radiation emitted from the sample surface in the infrared range was recorded and converted into absolute temperatures accounting for the different opacities of the material in the visible and infrared spectrum as well as for the reflection and transmission coefficients of the sample (see methods).Thus, thermal imaging, in comparison to a thermal probe, offers undisturbed non-contact measurements of the sample and recording of spatially resolved data (e.g.detecting heterogeneities or temperature gradients in the sample).Moreover, thermal imaging enabled simultaneous monitoring of the sample environment as well as control over temperature changes of the hyperthermia setup during measurements.The measured temporal behavior of the MNP solutions was analyzed by Newton's law of cooling, which proposes an exponential change of the temperature over time: )] + T env (8) for the heating process and For the cooling process, where T h/c is the sample surface temperature for heating and cooling, respectively.∆T is the maximum temperature change, τ is the heating constant, t 0 is the starting time of the cooling process and T env is the environmental temperature.
The heating kinetics of the three investigated particle classes and its analysis is shown in figure 5. Figure 5(a) shows an example measurement of a magnetosome sample and fits of equations ( 8) and ( 9) together with the temperature change of the magnet side faces as well as the background.As a result of the elaborate cooling system, the temperature of the magnet is kept below room temperature in absence of any AMF application and can be limited to ∼21 • C, which is 1 • C above room temperature, during AMF application.This is important as the magnet temperature and emitted radiation affects the sample temperature.In our case, the near room temperature of the magnet causes no effect on the maximum steady-state temperatures of the sample, while the temperature rise and fall in the first few minutes during and after AMF application is beneficial to accelerate heating/cooling rates of the sample.As a control, the background temperature is depicted.The background temperature remains constant except for a ⩽1 • C variation, which arises from radiation of the magnet which is reflected by the surface in the background.
To test the effect of different active cooling of the magnet, a switch was installed in the cooling setup to enable an immediate exchange of the cooled water for water at ambient temperature (see SI figure 1).The heating kinetics of Synomag ® using (i) constant magnet cooling were compared to the kinetics when (ii) the cooling case around the magnet was flushed with 20 • C water in absence of the AMF and flushing it with 5 • C water during AMF application, as well as with heating kinetics (iii) flushing the cooling system with 20 • C water constantly.This measurement nicely demonstrates the influence of the magnet temperature on the measured sample value, since the sample heating rates became lower and the maximum reachable sample temperature increased due to additional immediate heating by the magnet.This data also confirmed that our MNP data was free from any direct heating influence by the hyperthermia setup.
A comparison of the heating kinetics of the three particle classes is shown in figure 5(b).Intriguingly, the three particle classes measured at identical concentration exhibit distinct heat dissipation kinetics.Magnetosomes reached highest steady-state temperatures of ∼70 • C, whereas Synomag ® and BNF were heated to ∼40 • C and ∼38 • C, respectively.All samples reached the steady-regime during heating or cooling within 15 min and the heating rate was with up to +15 • C min −1 highest for magnetosomes, followed by Synomag ® with up to +6.7 • C min −1 and BNF with up to +5 • C min −1 .Fastest cooling rates were −15 • C min −1 in case of magnetosomes, up to −10 • C min −1 and up to −6.7 • C min −1 in case of Synomag ® and BNF, respectively.Each of the heating/cooling kinetics was fitted with equations ( 8) and ( 9) and the parameters T max = ∆T + T env (figure 5(c)) and characteristic time constant τ h/c of the heating/cooling process (figure 5(d)) extracted.Using the initial slope of the heating curve dT/dt t=0 , we further determined the specific absorption rate (SAR), as a measure of the heating power generated per unit mass where C = 4.19 J(g•K) −1 is the heat capacity of water, m H2O = mass of water in sample, and m MNP = total mass of magnetic material (i.e.all elements contributing to the magnetic cores) in the sample.SAR values for Synomag ® , BNF, and magnetosomes measured in different samples are shown in SI figure 2. On average, Synomag ® exhibited an SAR of (170 ± 13) W g −1 , BNF an SAR of (126 ± 10) W g −1 , and magnetosomes an SAR of (307 ± 21) W g −1 .
The maximum steady-state temperatures increased linearly with sample concentration (figure 5(c)) due to the higher effective heat capacity of the sample.Magnetosomes were measured in three different conditions to probe effects of different extraction steps on their heating response.When living magnetotactic bacteria were exposed to AMFs the maximum reachable temperature was a factor 1.2-1.5 higher compared to magnetosome chains extracted from bacteria or when the chains were disrupted in addition.This behavior is expected as for the free chains a maximum single strand length, and therefore a maximum magnetic moment will be reached.When protein chains were denatured, interactions between magnetosomes led to a reduction of the effective magnetization and hence the maximally reachable steady-state temperature.For Synomag ® and BNF MNPs the maximum reachable temperatures are a factor 1.3-1.7 lower than magnetosomes, but still in a regime suitable for bio-and nanotechnological applications.In addition, Synomag ® and BNF are readily synthesized with identical properties and with the possibility to systematically alter their properties (e.g. by fluorescent labeling, material composition).The characteristic heating/cooling time constant τ h/c exhibited a similar trend as T max : magnetosomes heat/cool fastest (τ h/c ∼ 115-200 s) whereas τ h/c of magnetosomes with denatured chains (τ h/c ∼ 140-230 s), Synomag ® (τ h/c ∼ 150-250 s), and BNF (τ h/c ∼ 200-240 s) were successively longer.Time constants were usually shorter than the water control (τ h/c ∼ 245-270 s).To demonstrate two important measurement settings for biological and nanotechnological applications, on the one hand the long-term, repetitive heating/cooling over 1.5 h was tested (figure 5(e)) and, on the other hand, fast heating/cooling cycles for repetitive switching between states with ∆T = 10 • C was probed (figure 5(f)).For comparison in both cases Synomag ® MNP at 5 mg ml −1 were used.For long-term measurements, MNPs were heated up to steady-state temperatures at 50 • C and cooled to 10 • C starting conditions in three successive cycles.Heating/cooling time constants remained constant over the whole measurement and T max was reduced only by ∆T = 1 • C per cycle (i.e.every 30 min; in line with magnetic flux density measurements in figure 2(b)).
For fast heating/cooling cycles Synomag ® MNP at 5 mg ml −1 were recorded over five cycles over time intervals until a temperature change by ∆T = 10 • C was reached.This is a typical temperature interval needed to switch polymers between distinct conformational states (e.g.thermoresponsive elastin-like peptides between 15 Since the switching behavior also depends on absolute temperatures, we used different settings of the cooling system to shift the average temperature between (I) 39 • C, (II) 36

Conclusion
In this work we present an advanced hyperthermia setup, which outcompetes previously available systems by producing 100 kHz AMFs, which fulfil the partly contradictory demands for (i) sufficient magnetic field amplitudes (48 mT), (ii) high temporal stability (⩾ 20 min), and (iii) sufficiently large working volumes (2 cm 3 ) at the same time.Moreover, the setup is designed to offer spatially resolved heat maps with an instantaneous field of view resolution of 0.8 mrad and enables microscopic observation of MNPs and biological samples for biomedical/nanotechnological studies (see table 2).
We compare the heating response of three structurally different MNPs, namely nanoflower-like and core shell magnetite MNPs, as well as magnetosomes.The latter exhibited highest heating rates and a maximal saturation temperature of 70 • C at 5 mg ml −1 concentration.Yet, considering aspects of particle monodispersity, availability, the possibility of biofunctionalization as well as heating response, nanoflower-like MNPs turn out to be primarily suitable for nanotechnological applications.The realization of long-time (30 min) field stability as well as the option to perform fast reversible heating/cooling cycles (with gradients up to ±15 • C min −1 ), of MNPs with microscopic observation bears high potential of this setup for biomedical assays as well as for biosensor applications in nanotechnology.

Figure 1 .
Figure 1.(a) Scheme of characteristic time scales of the AMF, the magnetization relaxation mechanisms of MNPs (Néel and Brownian relaxation) and the observed heating.(b) Scheme of the magnet setup with color coded components.(c) Sketch of samples for bulk measurements and microscopy measurements.The black wire model indicates the magnetic core around the samples.Typical sample volumes of 200 µl (bulk) and 50 µl (microscopable) are shown in orange.Thermography images show the difference in steady-state temperature of Synomag ® (5 mg ml −1 ) versus water sample for each sample type.Note, that the temperatures of the microscopable sample are underestimated due to the plastic sealing on top of the channel.Scale bar 5 mm.(d) Thermography image of the magnet while running.The core position is indicated in blue, the sample position in red.The inset is a zoomed view of the sample area.Scale bar 5 mm.(e) Fast heating/cooling cycles of Synomag ® (5 mg ml −1 ) and water measured with the setup presented in this work.Errors are shown as shaded areas around the data.

Figure 2 .
Figure 2. (a) Diagram of the resonance circuit with measured inductance and capacitance values for the electromagnet and whole array of 50 capacitors, respectively.Parts where the Litz and stranded wire are used, are marked in red and green, respectively.(b) Temporal evolution of the magnetic flux density measured in the center of the gap.The measured change amounts to less than 10%.(c) Magnetic flux density, B, as function of the peak-to-peak-voltage, x, measured at the capacitor array.The magnetic flux density follows the linear relation B (x) = (33.78± 0.49) mT/V• x + (0.33 ± 0.37) mT (d) measured resonance behavior of the capacitor peak-to-peak-voltage (black).From a Lorentzian function fit (red) the resonance frequency and quality factor are determined.(e) Rendered sketches of wire types used.Stranded wire consisting of 510 individual wire strands (orange) and outer insulation (light gray).Litz wire consisting of 3 bundles of 54 individually insulated wire strands (orange).Outer insulation (pink), insulation of individual wires (dark red).(f) Frequency dependent change of ohmic resistance of the different wires.(g) Frequency dependent coupling factor of a transformer consisting of a N87 core with winding ratios 25:5 (solid lines) and 5:25 (dashed lines).Coupling factors of Litz wire (red) and stranded wire (green) alone in comparison to the combination of stranded and Litz wire (25:5 solid blue line and 5:25 dashed blue line).The latter is used in this work.For all diagrams where applicable the errors are depicted as shaded areas around the data.

Figure 3 .
Figure 3. Magnetic flux density in the electromagnet gap.(a) Scheme of the used coordinate system and color scale of magnetic flux density.(b)-(d) Measured magnetic flux density shown in different planes.In (d) the x-axis is stretched for visibility reasons.

Figure 4 .
Figure 4. Characterization of different MNP classes (from top to bottom): Synomag ® , BNF, and magnetosomes.(a) Sketch of the different MNPs and their composition: Synomag ® -nanoflower multicore; BNF-core shell particles with dextran shell; magnetosomes-magnetic core with bio-membrane layer.Sketches indicate MNP sizes as determined by TEM measurements.(b) TEM images of MNPs at different magnification and inset with size distribution.(c) Dynamic-light-scattering measurement yields the number distribution of MNP sizes.Here, the hydrodynamic size is measured.In addition, the values of ζ-potential measurements are provided.(d) Real and imaginary part of the AC-susceptibility.Note the different y-axes.

Figure 5 .
Figure 5.Comparison of MNP heating/cooling response.(a) Exemplary measurement of heating/cooling kinetics of magnetosome MNP sample, background, and magnet.For long-term induction heating the kinetics were recorded until the steady-state was reached.The fits for heating and cooling (dashed lines) overlay the measured data.(b) Comparison of heating/cooling kinetics of different MNPs at 5 mg ml −1 concentration each.(c) Maximum steady-state temperature of Synomag ® and BNF particles as a function of concentration and using different solvents.Maximum steady-state temperature of magnetosomes as a function of concentration and at different purification stages.Please note that for Synomag ® and BNF the concentration is the particle concentration while for magnetosomes it is the iron concentration.(d) Sample temperature for standard 5 • C cooling, switched cooling for constant magnet temperature and ambient temperature cooling water.(e) Three consecutive heating/cooling cycles of magnetosome MNP measured at 3 mg ml −1 concentration.(f) Fast heating/cooling cycles for characteristic target temperature intervals of Synomag ® MNP at 5 mg ml −1 concentration.(a), (b), (e) Grey shaded areas indicate the time the AMF was applied.Kinetics were recorded until the steady-state was reached.In (f) the indication is not possible since the on-times are slightly different for all samples.For all graphs where applicable the errors are shown as shaded area.

Table 1 .
Iron concentration, number of particles and effective relaxation time for particle concentrations of 1 mg ml −1 .

Table 2 .
Comparison of the herein reported setup with previous works.EM = electromagnet, C = induction coil (as far as the work and values were accessible).Note, that in most cases selected parameters (for different measurements) are reported, but gap size, max.B, and continuous operation time depend on each other.Continuous operation time in this work corresponds to the time where temporal field stability is guaranteed.For other works typical reported operation times are stated.cell measurements were performed, but here the electromagnet is in contact with the medium. *