M. G. Christiansen , A. W. Senko , R. Chen , G. Romero , and P. Anikeeva
Citation: Applied Physics Letters 104, 213103 (2014); doi: 10.1063/1.4879842
View online: http://dx.doi.org/10.1063/1.4879842
View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/104/21?ver=pdfcov
Published by the AIP Publishing
Articles you may be interested in
Recording-media-related morphology and magnetic properties of crystalline CoPt3 and CoPt3-Au core-shell nanoparticles synthesized via reverse microemulsion
J. Appl. Phys. 116, 093907 (2014); 10.1063/1.4894154
Ferromagnetism, hysteresis and enhanced heat dissipation in assemblies of superparamagnetic nanoparticles
J. Appl. Phys. 112, 114912 (2012); 10.1063/1.4768904
Magnetic properties of Sm0.1Ca0.9MnO3 nanoparticles
J. Appl. Phys. 112, 063921 (2012); 10.1063/1.4754310
Publisher’s Note: “Simple models for dynamic hysteresis loop calculations of magnetic single-domain nanoparticles: Application to magnetic hyperthermia optimization” [J. Appl. Phys. 109, 083921 (2011)]
J. Appl. Phys. 110, 039902 (2011); 10.1063/1.3617122
Magnetic hyperthermia in single-domain monodisperse FeCo nanoparticles: Evidences for Stoner–Wohlfarth behavior and large losses
J. Appl. Phys. 105, 023911 (2009); 10.1063/1.3068195
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 18.7.29.240
On: Sun, 21 Sep 2014 20:04:48

APPLIED PHYSICS LETTERS 104 , 213103 (2014)
M. G. Christiansen, A. W. Senko, R. Chen, G. Romero, and P. Anikeeva
a)
Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge,
Massachusetts 02139, USA
(Received 21 February 2014; accepted 13 May 2014; published online 28 May 2014)
Selective hysteretic heating of multiple collocated types of single domain magnetic nanoparticles
(SDMNPs) by alternating magnetic fields (AMFs) may offer a useful tool for biomedical applications. The possibility of “magnetothermal multiplexing” has not yet been realized, in part due to prevalent use of linear response theory to model SDMNP heating in AMFs. Dynamic hysteresis modeling suggests that specific driving conditions play an underappreciated role in determining optimal material selection strategies for high heat dissipation. Motivated by this observation, magnetothermal multiplexing is theoretically predicted and empirically demonstrated by selecting SDMNPs with properties that suggest optimal hysteretic heat dissipation at dissimilar
AMF driving conditions. This form of multiplexing could effectively offer multiple channels for minimally invasive biological signaling applications.
V
2014 AIP Publishing LLC .
[ http://dx.doi.org/10.1063/1.4879842
]
Alternating magnetic fields (AMFs) offer a convenient form of noninvasive stimulus that can reach deep into the body due to the weak magnetic properties and low electrical conductivity of tissue. In the presence of an AMF, single domain magnetic nanoparticles (SDMNPs) may act as transducers of heat for biomedical purposes.
1
cell death,
2 sitive drug release.
5
spatial proximity.
ence has long been studied,
6 , 7 amplitude.
8
Although decades of research have focused primarily on magnetic hyperthermia, in which bulk heating of tumor tissue results in targeted emerging applications make use of heating localized at the scale of nanoparticles. These include magnetic actuation of single biochemical pathways
3 , 4
and thermosen-
The capability to selectively heat
SDMNPs with differing magnetic properties by varying the driving conditions of the AMF, hereafter referred to as
“magnetothermal multiplexing,” has the potential to enhance the functionality of these techniques. For instance, magnetothermal multiplexing would allow for independent and remote control of multiple pathways or cell types in close
The feasibility of magnetothermal multiplexing relies on accounting for the effect of the applied AMF on the timescale of stochastic magnetization reversal. Though such dependit is frequently neglected in the context of SDMNP heat dissipation due to prevalent use of linear response theory (LRT), in which the assumed
“relaxation time” often has no explicit dependence on AMF
A growing body of experimental evidence indicates that LRT’s domain of validity is more restricted than the range of conditions in which it is typically applied.
9
–
11
In this Letter, we explain how a more general model, dynamic
hysteresis (DH),
12
,
13
motivates feasible strategies for multiplexing. We then experimentally evaluate the applicability of a DH model to our ferrite SDMNPs, with particular emphasis on AMF amplitude dependence of specific loss power (SLP) as especially relevant to the feasibility of multiplexing. For a proof of concept, multiplexing with respect to SLPs is demonstrated by selectively heating two types of ferrite SDMNPs with AMFs of differing amplitude and frequency.
There are several approaches to develop a more generalized theory of heat dissipation in ensembles of noninteracting SDMNPs in AMFs. One is to model coherent precession and reversal with the Landau–Lifshitz–Gilbert equation, incorporating a fictitious stochastically varying thermal field in addition to the effective field.
14 , 15
DH models offer a simpler alternative, treating the coherent reversal of SDMNP moments as kinetically limited by thermal activation over a time-varying energy barrier determined by both the SDMNP anisotropy and the Zeeman energy of its moment in the field
(See Fig.
1(a)
).
12 , 13
The essential physics of DH is contained in the relative magnitudes of these energetic contributions normalized to the ambient thermal energy, which defines unitless parameters r and
n
12
r
KV k
B
T n l
0
H
0
M s
V
: k
B
T
(1)
Here, K is the effective anisotropy energy of the
SDMNP, V the volume, H
0 the AMF amplitude, M s the saturation magnetization, and l
0 the permeability of free space.
These definitions of r and n assume idealized spherical single crystal SDMNPs with uniform magnetization and effective anisotropy that scales with volume regardless of contributions from surface, shape, or magnetostrictive effects. While these assumptions do not fully describe the complexity of real
SDMNPs,
16
identifying the physical origins of r is not conceptually essential for multiplexing.
Our DH model follows previous work,
12
though with several mathematical and interpretational differences: (1)
Easy alignment of the SDMNPs is assumed so that the results that can be interpreted as a predicted upper bound. (2)
Thermal spreading of the moments about the easy axes is estimated by a Boltzmann distribution for a second order
Taylor expansion of the local energy minima, labeled A and
B. The magnetization M normalized to M s is given by a)
Author to whom correspondence should be addressed. Electronic mail: anikeeva@mit.edu.
0003-6951/2014/104(21)/213103/5/$30.00
104 , 213103-1 2014 AIP Publishing LLC
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 18.7.29.240
On: Sun, 21 Sep 2014 20:04:48

213103-2 Christiansen et al.
Appl. Phys. Lett.
104 , 213103 (2014)
M
M s
¼ C
A
P
A
þ C
B
P
B
; (2) where P
A and P
B are the probabilities of SDMNP moments occupying the minima at h ¼ 0 and h ¼ p , respectively.
C
A and C
B are terms that account for the projection of these moments along the easy axis while taking into account thermal spreading
C
A
¼
ð p
2 sin h cos h exp
0
ð p
2 sin h exp
0
ð n þ
2
2 r
ð n þ 2 r Þ h
2
2
Þ h
2
þ
þ n n d h d h
; (3)
C
B
¼
ð p p
2 sin h cos h exp
ð p p
2 sin h exp
ð n 2 r Þ
2
ð h p Þ
ð n 2 r Þ
ð h p Þ
2
2
2 n n d h d h
: (4)
This affects calculated power dissipation rates by less than a few percent for most r and n combinations, but avoids the hyperbolic tangent-like saturation for superparamagnetic
SDMNPs that is predicted by constraining the moments to
the easy axes.
12
(3) For applications that rely on local heating, individual particle loss power (IPLP) is a more relevant metric than the SLP of an ensemble. To calculate IPLPs, we consider M = M s vs.
n hysteresis loops, with an area equal to the individual particle loss energy per cycle of the AMF normalized to the ambient thermal energy. The results can be extended to SLPs by making assumptions about SDMNP volume V and mass density q . The maximal area of these
hysteresis loops is predicted by Stoner-Wohlfarth theory
17
and is equal to 8 r .
The area of these M = M s vs.
n hysteresis loops, proportional to IPLPs, can be plotted in a r n space for a given
AMF frequency (Fig.
1(b)
). Defining the anisotropy field H k as the applied field at which the barrier to reversal vanishes, the ratio n = ð 2 r Þ can be rewritten as H
0
= H k
, describing a linear path through the origin of r n space with a slope determined by the magnitude of the AMF amplitude (Figs.
1(b)
and
H
0
1(c)
H k
). In the limit of low AMF amplitudes (i.e.,
), a critical r time of stochastic magnetization reversal in the absence of an AMF is equal to the timescale of measurement set by its
frequency.
12 , 14
to the maximum SLP predicted by LRT. Moments on either side of this maximum either escape more rapidly or more slowly than the timescale set by the AMF frequency, which divides the superparamagnetic and ferromagnetic regimes,
respectively.
12
crit value occurs where the mean life-
For low AMF amplitudes, r crit corresponds
DH simulations predict markedly different dependence of IPLP on AMF amplitude for the two regimes.
(See Figs.
1(d)
–
1(f)
for plots of the hysteresis loops.)
With this graphical representation, the strategy for efficiently producing maximal IPLPs with the constraint of a given H
0 f product seems clear (Fig.
1(c) ). Large SDMNPs
driven by AMFs with H
0 approaching or exceeding H k at high frequencies will produce hysteresis loops approaching the theoretical limit set by the material, provided that the
fastest available relaxation process is coherent reversal
9
and
FIG. 1. (a) A schematic of the SDMNP in the AMF and energy as a function of h (angle between the magnetic moment and the easy axis of the SDMNP).
(b) Contour plot of hysteresis loop area as a function of r and n for uniaxial anisotropy at 500 kHz, superimposed with paths representing AMF amplitudes of different magnitude relative to H k
. (c) Hysteresis loop area as a function of r plotted along the paths in (b). The dashed line represents 8 r , the theoretical maximum predicted by Stoner-Wohlfarth theory at T ¼ 0K.
(d)–(f) Simulated hysteresis loops for points in r n space for representative r values from the superparamagnetic regime (d), ferromagnetic regime (f), and the r crit dividing them (e), which varies with frequency.
the detailed dynamical picture of damped precession can be
neglected.
14
This strategy was borne out experimentally in the highest heating rates reported, where a high H
0 f product is used and “tuning” of materials parameters has little to do with attaining r crit and instead involves finding the largest
SDMNPs in which coherent reversal still dominates.
18
Therapeutic limitations on the allowable H
0 f
product
19 , 20
make it more pragmatic to reframe the problem of optimization as one of adjusting material parameters to make best use of a set of available driving conditions. This suggests the possibility of multiplexed heating by selecting materials with properties that lead to dramatically different optimal driving conditions with a similar H
0 f product.
DH modeling in Fig.
2
illustrates an example of magnetothermal multiplexing employing three materials with H k values differing by orders of magnitude: 100 H k ; 1
¼ 10 H k ; 2
¼ H k ; 3
. Here H k ; 1
, H k ; 2
, and H k ; 3 are the anisotropy fields of idealized low, medium, and high coercivity materials, respectively. Figs.
2(a) – 2(c)
display IPLPs of these materials at three
AMF amplitude and frequency conditions selected to maintain a constant H
0 f product. From the IPLP vs r plots, particular r values can be chosen that dissipate significant power at only one of the three driving conditions. The hysteresis loops corresponding to these selected r values are shown in Figs.
2(d) – 2(f)
.
The ability to experimentally infer r and n values facilitates the application of DH modeling to power dissipation by
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 18.7.29.240
On: Sun, 21 Sep 2014 20:04:48

213103-3 Christiansen et al.
real SDMNPs.
n can be determined by observing M = M s vs field B using vibrating sample magnetometry (VSM) (Fig.
3(a) ). For randomly oriented ensembles of anisotropic
SDMNPs, the susceptibility converges on the Langevin function as B !
0.
21
This allows linear fits of M = Ms vs.
B to be related to n and the magnetic moment m
" # m ¼ 3 k
B
T dM = M s dB
B !
0
; n ¼ H
0
3 l
0 dM = M s dB
B !
0
:
(5)
In turn, the magnetic moment can be translated to magnetic diameter d m
, a proxy that assumes bulk M s and spherical shape d m
6 m
M s p
1
3
: (6)
Figure
3(a)
demonstrates this characterization method on a set of previously reported Fe
3
O
4 cal diameter.
22
SDMNPs of varying physi-
In estimating r according to Eq.
(1)
, we assume
SDMNPs to be normally distributed in diameter and uniaxial with an estimated K
U 1
j K
1 j , where K
U 1 and K
1 are coefficients for first order terms of bulk uniaxial and cubic anisotropy, respectively. The frequency response of samples at
AMF with H
0
¼ 0 : 5 kA = m was characterized with a home-
built AC magnetometer
10
and is shown in Figs.
3(b)
and
3(c)
for two superparamagnetic (13.1 nm Fe
3
O
4
, and stoichiometric Mn
0.04
Fe
2.96
O
4 as measured by inductively coupled
Appl. Phys. Lett.
104 , 213103 (2014) plasma atomic emission spectroscopy (ICP-AES) with d m
¼ 13 : 6nm) and one ferromagnetic sample (22.9 nm
Fe
3
O
4
). The crossover of the imaginary component of the volumetric magnetic susceptibility Im ð v Þ in the vicinity of
200 kHz (Fig.
3(b)
) suggests that the superparamagnetic
SDMNPs will dissipate more heat when driven by an AMF with high frequency and low amplitude.
In addition to exhibiting a larger Im v value at 100 kHz and 0.5 kA/m, the suitability of the ferromagnetic sample for multiplexing at this frequency relies upon the dependence of its SLP and IPLP on AMF amplitude. Calorimetry measurements at various AMF amplitudes and frequencies were performed on the samples shown in Fig.
3(a)
to determine SLP values. Several homemade AMF coils were used, driven by a
200 W amplifier (Electronics & Innovation, Inc.). The two coils used to produce AMFs with amplitudes exceeding
5 kA/m at 100 kHz and 500 kHz consisted of a ferrite toroid
(Ferroxcube, 3F3) machined to include a gap and wrapped with litz wire. Calorimetric measurements at lower AMF amplitudes were conducted using simple solenoid coils without soft ferromagnetic components, allowing for operation at higher frequencies. AMF amplitudes were measured with homemade inductive field probes. Thermal effects of resistive power losses in all coils were offset by ice water cooling, and the samples were insulated to approach adiabatic conditions. SLP values were calculated from linear fits to temperature vs time plots measured by a fiber optic thermometer (Omega Engineering), with small background heating rates measured for water samples subtracted as controls.
Figures
3(d)
and
3(e)
show power law fits of specific loss energy (SLP/frequency) for the 22.9 nm Fe
3
O
4
SDMNPs,
FIG. 2. (a) Simulated IPLP for SDMNPs driven by an AMF at 1 MHz and amplitude H
0 solid lines correspond to low ( H k ; 1
), medium ( H k ; 2
¼ H k ; 1
¼ 0 : 1 H k ; 2
¼ 0 : 01 H k ; 3
. Dashed-dotted-dashed, dashed, and
), and high ( H k ; 3
) coercivity materials, respectively. Markers represent r values of SDMNPs selected from each set for multiplexing. The long black dashed line represents 8 r , the theoretical maximum. (b) Analogous plot for an AMF of amplitude H
0
100 kHz. (c) Analogous plot for an AMF of amplitude H
0
¼ H k ; 3
¼ H k ; 2 at at 10 kHz. (d)–(f) Simulated hysteresis loops for the SDMNPs selected for multiplexing at the AMF conditions corresponding to the plots in (a)–(c), respectively. Numerical area of the M = M s vs.
n loops is equal to individual particle loss energy per cycle normalized to ambient thermal energy. The axes are rescaled such that the graphical area is proportional to IPLP.
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 18.7.29.240
On: Sun, 21 Sep 2014 20:04:48

213103-4 Christiansen et al.
Appl. Phys. Lett.
104 , 213103 (2014)
FIG. 3. (a) Normalized magnetization vs applied B field is shown at room temperature for Fe
3
O
4
SDMNP samples with physical diameters: 11 6 0.4 nm
( d m
¼ 9 : 1nm), 16 6 0.5 nm ( d m
¼ 13 : 1nm), 18 6 1.2 nm ( d m mission electron microscopy (TEM).
22
¼ 16 : 6nm), 22 6 1.3 nm ( d m
¼ 18 : 8nm), and 25 6 1.6 nm ( d m
¼ 22 : 9nm), as measured by trans-
The inset displays linear fits of this data in the low field limit used to determine magnetic diameter, a proxy for magnetic moment. (b) The imaginary component of the volumetric magnetic susceptibility Im ð v Þ in SI units is shown for two superparamagnetic samples and one ferromagnetic SDMNP sample. Note the cross-over point in the vicinity of 200 kHz. (c) The real component of the volumetric magnetic susceptibility Re ð v Þ in
SI units is plotted for the same samples. A driving AMF of amplitude energy per cycle as a function of AMF amplitude H
0 markers,
䊉
100 kHz,
䊏
500 kHz) are shown for the d m
H
0
¼ 0 : 5kA = m was used at all frequencies. (d) Power law fits (lines) of specific loss for simulated data (open markers,
䊊
100 kHz,
ⵧ
500 kHz) and (e) experimental calorimetry (solid
¼ 22 : 9 6 1 : 6nm Fe
3
O
4
SDMNPs. The exponents extracted from identical fits on SDMNP samples of various diameters are shown inset for (d) simulated and (e) experimental data as a function of d m
.
predicted by DH (Fig.
3(d) ) and corroborated experimentally
by calorimetry (Fig.
3(e)
). The insets of Figs.
3(d)
and
3(e)
show the results of similar fits performed on the rest of the
Fe
3
O
4 set of varying diameter. At 100 kHz, SLP vs H
0 for the ferromagnetic 22.9 nm sample is fitted with a power law exponent of 2.1, whereas the fit for superparamagnetic
13.1 nm sample yields an exponent of only 0.68. DH qualitatively predicts the saturation behavior of SLP vs H
0
, as well as trends in power law rate of increase with increasing r , observed in Fig.
3(e) . This saturation behavior stems from
constraining the coercive field H c to not exceed H k
, connecting the limiting behavior at high AMF amplitudes to the pre-
dictions of Stoner-Wohlfarth theory.
12
In contrast, even versions of LRT that use a “chord approximation” to constrain M from exceeding M s in their elliptical hysteresis loops still predict SLPs that grow linearly without bound as
H
0
! 1 because they do not constrain H c
.
As indicated by Fig.
2 , one strategy for multiplexing
with IPLPs is to use SDMNPs with differing H k
, however multiplexing with SLPs can be accomplished using
SDMNPs with the same H k and different r values. It should be emphasized that multiplexing with either IPLPs or SLPs relies upon the same dependences of heat dissipation on
AMF amplitude and frequency (Fig.
3
). A proof of concept for SLP multiplexing in a single material system is to use
Fe
3
O
4
SDMNPs of different diameters, establishing a low frequency, high amplitude AMF mode (e.g., 100 kHz,
35 kA/m) and a high frequency, low amplitude AMF mode
(e.g., 2.5 MHz, 5 kA/m) (Fig.
4
).
The higher amplitude mode favors heat dissipation by
22.9 nm SDMNPs in the ferromagnetic regime (Fig.
4
). The lower amplitude mode dramatically reduces the heating of the larger SDMNPs, a fact anticipated from the power law dependence of their SLP on AMF amplitude (Fig.
3(e) ).
Increasing the frequency of the lower amplitude mode increases the Im ð v Þ of the superparamagnetic samples as compared to ferromagnetic samples, allowing them to heat more efficiently (Figs.
4
and
3(b)
).
In the low frequency, high AMF amplitude mode, the
22.9 nm SDMNPs exhibit an SLP 6.7 times higher than the
13.1 nm sample. The high frequency, low AMF amplitude mode reverses the situation, with the superparamagnetic
SDMNPs exhibiting an SLP 5.0 times higher than the ferromagnetic sample. Introducing a superparamagnetic sample
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 18.7.29.240
On: Sun, 21 Sep 2014 20:04:48

213103-5 Christiansen et al.
Appl. Phys. Lett.
104 , 213103 (2014) supported by the National Science Foundation (NSF) under
Award No. DMR-0819762. This research was conducted with Government support and awarded by DoD, Air Force
Office of Scientific Research, National Defense Science and
Engineering Graduate (NDSEG) Fellowship, 32 CFR 168a, which funds M.G.C. and A.W.S. R.C. is supported by the
NSF Graduate Fellowship Program. We extend our gratitude to D. Bono for electronics advice and C.A. Ross for insightful comments on our manuscript.
FIG. 4. SLP is shown for two superparamagnetic samples consisting of
Fe
3
O
4 with d
SDMNPs with d m m sample consisting of Fe
3
O
4
SDMNPs with d
䊉 for AMF
2
¼ 13 : 1 nm (
䊏 for 2.55 MHz and 5 kA/m, “AMF and
ⵧ for 100 kHz and 35 kA/m, “AMF
2
¼ 13 : 6nm (
䉱 for AMF
1
”) and Mn and
䉭 for AMF
2 m
0.04
Fe
2.96
1
,”
), and for a ferromagnetic
¼ 22 : 9nm (
䊊 for AMF
1
). The solid line is a LRT simulation for Fe
3
O
4
O
4
SDMNPs and
SDMNPs of varying diameter driven by AMF
1 including Brownian relaxation. The dashed lines correspond to DH simulations for the same SDMNPs driven by
AMF
1
(long dash) and AMF
Scale bars are 20 nm.
2
(short dash). TEMs of the samples are shown.
13.6 nm Mn
0.04
Fe
2.96
O
4 brings these ratios to 14.9 and 8.9, respectively. Based on the bulk properties of MnFe
2
O
4
, this slight Mn doping is expected to lower SDMNPs coercivity, leading to improved performance for multiplexing. Similar strategies based on controlling composition could be applied to classes of materials with a broad range of coercivities, such as A x
Fe
3-x
O
4
(A ¼ Mn, Fe, Co, Zn, Ni). Other approaches for tailoring r and n values for multiplexing may include designing SDMNPs that depend on shape or surface effects
18
or exchange coupled architectures incorporating
multiple materials.
23
r n space provides a graphical representation onto which these approaches could be equivalently mapped and understood.
This work was funded in part by the Sanofi Biomedical
Innovation Award and the Defense Advanced Research
Project Agency (DARPA) Young Faculty Award (No.
D13AP00045) to P.A. The content of this letter does not necessarily reflect the position or the policy of the Government, and no official endorsement should be inferred. This work made use of the MRSEC Shared Experimental Facilities
1
Q. A. Pankhurst, N. T. K. Thanh, S. K. Jones, and J. Dobson, J. Phys. D
42 (22), 224001 (2009).
2
R. Hergt, S. Dutz, R. M uller, and M. Zeisberger, J. Phys: Condens. Matter
3
18 (38), S2919–2934 (2006).
H. Huang, S. Delikanli, H. Zeng, D. M. Ferkey, and A. Pralle, Nat.
Nanotechnol.
5 (8), 602–606 (2010).
4
S. A. Stanley, J. E. Gagner, S. Damanpour, M. Yoshida, J. S. Dordick, and
5
J. M. Friedman, Science 336 (6081), 604–608 (2012).
A. Riedinger, P. Guardia, A. Curcio, M. A. Garcia, R. Cingolani, L.
Manna, and T. Pellegrino, Nano Lett.
13 (6), 2399–2406 (2013).
6
L. Ne el, Ann. Geophys.
5 (2), 99–136 (1949).
7
M. P. Sharrock, IEEE Trans. Magn.
26 (1), 193–197 (1990).
8
R. E. Rosensweig, J. Magn. Magn. Mater.
252 , 370–374 (2002).
9
B. Mehdaoui, A. Meffre, J. Carrey, S. Lachaize, L.-M. Lacroix, M.
Gougeon, B. Chaudret, and M. Respaud, Adv. Funct. Mater.
21 (23),
10
4573–4581 (2011).
E. Garaio, J. M. Collantes, J. A. Garcia, F. Plazaola, S. Mornet, F.
Couillaud, and O. Sandre, “A wide-frequency range AC magnetometer to measure the specific absorption rate in nanoparticles for magnetic hyper-
11 thermia,” J. Magn. Magn. Mater (in press).
R. Hergt, S. Dutz, and M. Zeisberger, Nanotechnology 21 (1), 015706
(2010).
12
J. Carrey, B. Mehdaoui, and M. Respaud, J. Appl. Phys.
109 (8), 083921
13
(2011).
H. Mamiya and B. Jeyadevan, Sci. Rep.
1 , 157 (2011).
14
N. A. Usov, J. Appl. Phys.
107 (12), 123909 (2010).
15
G. T. Landi and A. D. Santos, J. Appl. Phys.
111 (7), 07D121 (2012).
16
N. A. Usov and J. M. Barandiar an, J. Appl. Phys.
112 (5), 053915 (2012).
17
E. C. Stoner and E. P. Wohlfarth, Philos. Trans. R. Soc. London, Ser. A
240 (826), 599–642 (1948).
18
S. H. Noh, W. Na, J. T. Jang, J. H. Lee, E. J. Lee, S. H. Moon, Y. Lim, J.
19
S. Shin, and J. Cheon, Nano Lett.
12 (7), 3716–3721 (2012).
R. Hergt and S. Dutz, J. Magn. Magn. Mater.
311 (1), 187–192 (2007).
20
W. J. Atkinson, I. A. Brezovich, and D. P. Chakraborty, IEEE Trans.
21
Biomed. Eng.
BME-31 (1), 70–75 (1984).
P. E. J € ıa-Palacios, Phys. Rev. B 64 (17), 174416
(2001).
22
R. Chen, M. G. Christiansen, and P. Anikeeva, ACS Nano 7 (10),
23
8990–9000 (2013).
J.-H. Lee, J.-T. Jang, J.-S. Choi, S. H. Moon, S.-H. Noh, J.-W. Kim, J.-G.
Kim, I.-S. Kim, K. I. Park, and J. Cheon, Nat. Nanotechnol.
6 (7), 418–422
(2011).
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 18.7.29.240
On: Sun, 21 Sep 2014 20:04:48