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Appl. Phys. Lett. 117, 122410 (2020);
https://doi.org/10.1063/5.0023466 117, 122410
© 2020 Author(s).
Magnetic characterization of rare-earth oxidenanoparticlesCite
as: Appl. Phys. Lett. 117, 122410 (2020);
https://doi.org/10.1063/5.0023466Submitted: 29 July 2020 .
Accepted: 10 September 2020 . Published Online: 23 September
2020
Kai Trepka , and Ye Tao
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Magnetic characterization of rare-earth oxidenanoparticles
Cite as: Appl. Phys. Lett. 117, 122410 (2020); doi:
10.1063/5.0023466Submitted: 29 July 2020 . Accepted: 10 September
2020 .Published Online: 23 September 2020
Kai Trepka1,2 and Ye Tao1,a)
AFFILIATIONS1Rowland Institute at Harvard, 100 Edwin H Land
Blvd, Cambridge, Massachusetts 02142, USA2Department of Chemistry
and Chemical Biology, Harvard University, 12 Oxford St, Cambridge,
Massachusetts 02138, USA
a)Author to whom correspondence should be addressed:
[email protected]
ABSTRACT
High saturation magnetization and hysteresis-less magnetic
responses are desirable for nanoparticles in scientific and
technological applica-tions. Rare-earth oxides are potentially
promising materials because of their paramagnetism and high
magnetic susceptibility in the bulk, butthe magnetic properties of
their nanoparticles remain incompletely characterized. Here, we
present full M–H loops for commercial RE2O3nanoparticles (RE ¼ Er,
Gd, Dy, Ho) with radii from 10–25 nm at room temperature and 4K.
The magnetic responses are consistent withtwo distinct populations
of atoms, one displaying the ideal Re3þ magnetic moment and the
other displaying a sub-ideal magnetic moment. Ifall sub-ideal ions
are taken to be on the surface, the data are consistent with � 2�
10 nm surface layers of reduced magnetization. The mag-netization
of the rare-earth oxide nanoparticles at low temperatures (1.3–1.9
T) exceeds that of the best iron-based nanoparticles,
makingrare-earth oxides candidates for use in next-generation
cryogenic magnetic devices that demand a combination of
hysteresis-less responseand high magnetization.
VC 2020 Author(s). All article content, except where otherwise
noted, is licensed under a Creative Commons Attribution (CC BY)
license (http://creativecommons.org/licenses/by/4.0/).
https://doi.org/10.1063/5.0023466
Paramagnetic nanoparticles (NPs) have revolutionized technol-ogy
and everyday life, from targeted drug delivery to geological
engi-neering.1–7 For micro- and nanoscale manipulation, particles
withhigher magnetization can exert comparatively larger forces
necessaryfor sorting of cells and parasites.1–4 In imaging
applications such asmagnetic force microscopy and magnetic
resonance imaging, highermagnetization enables a higher
signal-to-noise ratio and a reducedimaging time.8–10 Rare-earth
oxides (RE2O3) have high susceptibility,v, and RE3þ magnetic
moment, l,11,12 resulting in high saturationmagnetization, Ms, in
the bulk
13 (Table I). However, due to finite-sizeand surface effects,
nanoparticles often have altered magneticresponse, including lower
Ms compared to bulk materials, makingempirical measurements of
rare-earth oxide nanoparticles necessary todetermine their magnetic
properties.14–17
In this study, we experimentally investigate the magnetic
proper-ties of several RE2O3 nanoparticles to elucidate associated
nanoscaleeffects. Magnetic rare-earth oxide nanoparticles—Dy2O3 NP
(SSNano,99.9%, 50 nm), Gd2O3 NP (SSNano, 99.9%,
-
v ¼ CT � h ; (1)
where v is the magnetic susceptibility, C is the Curie constant,
T is thetemperature, and h is the Curie temperature. The
susceptibilities of thenanoparticles follow Eq. (1) [Fig. 2(a)],
with negative Curie tempera-tures h indicative of the emergence of
low-temperature antiferromag-netic phases at N�eel temperature TN ¼
�h.18,19 Because of themagnetic transition at TN, the magnetic
responses of the materialswere analyzed independently above and
below TN. The response of anideal, homogeneous paramagnet to the
applied external field is givenby a Langevin function,
M ¼ MsLll0HkBT
� �¼ NlL ll0H
kBT
� �; (2)
whereM represents the sample magnetization,Ms the saturation
mag-netization, l the magnetic moment per ion, l0 the vacuum
permeabil-ity constant, H the applied field, kB Boltzmann’s
constant, T thetemperature, N the density of magnetically active
ions, andLðxÞ ¼ cothðxÞ � 1=x.20 We assessed the data against Eq.
(2) andfound the model to be insufficient for describing the data.
We attributethe difference to various types of heterogeneity that
can exist at thenanoscale. Because the nanoparticle size is on the
order of a few hun-dred atoms across, nanoparticle properties are
often heterogeneous.21
Substantial fractions of each individual particle can belong to
distinctsubpopulations, with local heterogeneity in the chemical
composition,surface sites, anisotropy, or strain influencing global
particle proper-ties.22–25 As a result, we model the nanoparticles
as composed of twopopulations of active species, sub-ideal (s), and
ideal (i) ions, with thefull response given by a
population-weighted sum,
M ¼ N slsLlsl0HkBT
� �þ ð1� sÞliL
lil0HkBT
� �� �; (3)
where s represents the fraction that are sub-ideal ions, ls the
averagemoment of sub-ideal ions, and li the moment of each ideal
ion, whichwe assume to have the value for the moment of the ideal,
bulk RE3þ
ions, i.e., li ¼ lRE3þ . Temperature and field-dependent data
collectedabove TN and up to 7T were fitted to this two-component
model,resulting in excellent agreement [Figs. 2(b) and 2(c)].
Temperatureand field-dependent data collected below TN and up to 7T
were alsofitted to this two-component model [Fig. 2(d)]. Model
parameters forboth temperature regimes, including the fraction of
sub-ideal/idealions and the magnetic moment of the sub-ideal ions,
are reported inTable I. Overall, the nanoparticles display a
paramagnetic response,with distinct magnetic populations. The
measured remanence of TN regimeMs (T) 1:860:1 1:560:1 2:360:1
2:160:1ls (lB) 2:060:1 0:860:1 5:360:4 0:860:1Sub-ideal fraction s
0:5360:01 0:3760:01 0:6160:04 0:3060:01Thickness t (nm) 1161 461
662 261
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of slow-onset, low-temperature antiferromagnetic contributions
inRE2O3 nanoparticles.
26–29
The magnetic properties of a nanoparticle are often dominatedby
surface chemistry,30 with a typically magnetically weaker
surface
layer.14,15,31,32 As a result, for T > TN , one possible
interpretation isthat the non-ideal ions are ions in the surface
layer. Assuming that theglobular nanoparticles (Dy2O3, Ho2O3, and
Er2O3) have sphericalmorphology, that the columnar nanoparticles
(Gd2O3) have cylindri-cal morphology with length� radius, that all
radii are distributed asin Fig. 1(e), and that all non-ideal ions
are in the surface layer, thethickness of the surface layer can be
computed by numerically solving
1� s ¼Pðri � tÞ3PðR ¼ riÞP
r3i PðR ¼ riÞ; (4)
for the globular nanoparticles and
1� s ¼Pðri � tÞ2PðR ¼ riÞP
r2i PðR ¼ riÞ; (5)
for the columnar nanoparticles, where s is the fraction of atoms
in thesurface layer, t is the thickness of the surface layer, ri is
the radius of aparticle, and R is the random variable describing
the distribution ofparticle radii. Assuming that non-ideal ions are
all found in the surfacelayer, the resulting surface layer
thicknesses are found and reported(Table I), with values (t ¼ 2� 11
nm) consistent with observations ofmagnetic dead layers in other
metal oxide nanostructures (t � 1� 15nm).31,33–35 A future
experiment to help determine whether thesub-ideal ions are on the
surface or distributed evenly throughout theparticle would sort the
particles by size via centrifugation prior tomeasurements to
determine whether the surface-area-to-volume ratiocorrelates with
s.36
The RE2O3 nanoparticles have high magnetic figures of
merit.Linearity of magnetic energy density, Elin, is the energy
density that canbe quadratically stored into a material under the
drive of an externalfield and captures the sensitivity and
linearity of a magnetic material,13
and achievable magnetization is the magnetization at l0H ¼ 7.
Idealmagnetic materials for quantitative metrology require both a
strongmagnetic response and a long, predictable dynamic range
(captured byElin) in order to maximize the signal, minimize the
imaging time, andensure undistorted, quantitative results. A review
of common and state-of-the-art nanoparticles, thin films, and bulk
magnets was per-formed13,37–52 [Fig. 3(a)]. As temperature is
decreased, susceptibilityincreases, but the linear range decreases.
As a result, optimal particleperformance (maximal Elin) is achieved
at cryogenic but non-zero tem-peratures [Fig. 3(b)].13 The
rare-earth oxide NPs have high linearities ofmagnetic energy
density while exceeding the achievable magnetizationof
state-of-the-art iron-based superparamagnetic nanoparticles. As
aresult, rare-earth oxide nanoparticles are promising candidates
for high-spatial resolution cryogenic magnetic sensing and
manipulation.1,4,8–10
In particular, high-Elin, high-magnetization particles may be
used inmagnet-on-cantilever tips for cryogenic magnetic force
microscopy ormagnetic resonance force microscopy.53–55 Even at room
temperature,the particles retain relatively high magnetization and
Elin, allowing con-jugation with biologics for use in cell sorting,
subcellular characteriza-tion, in vivomagnetic resonance imaging,
and drug delivery.56–59
In conclusion, the magnetic properties of rare-earth oxide
nano-particles were investigated, with magnetic responses
consistent withtwo distinct paramagnetic populations of ions, one
with magneticmoment equal to the ideal Re3þ moment and the other
with a sub-ideal magnetic moment. If all the sub-ideal ions are
taken to be on thesurface of the nanoparticles, the data are
consistent with 2–11 nm
FIG. 2. Nanoparticle magnetism. (a) Susceptibility-temperature
relationship. The blackline represents a linear fit on the T � 16 K
data. (b) Temperature curve of the mag-netic response at l0H ¼ 7 T.
(c) M-H loops taken at room temperature. (d) M–H loopstaken at 4 K.
In (b)–(d), black lines represent the two-component Langevin
fit.
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surface layers of reduced magnetization. The particles display
superiorlinearity of magnetic energy density and low-temperature
magnetiza-tion exceeding that of state-of-the-art iron-based
paramagnetic nano-particles. Looking ahead, the combination of high
Ms with a lack ofhysteresis (paramagnetism) suggests that
rare-earth oxide nanopar-ticles are likely to advance devices in
fields from imaging to magneticmanipulation.
This work was supported by a Rowland Fellowship to Y.T.K.T.
acknowledges support from the Rowland Institute and theHarvard
Office of Undergraduate Research and Fellowships. Theauthors would
like to thank Shaw Huang for assistance withSQUID and all group
members for helpful discussions. SEM samplecharacterization studies
were carried out at the Center forNanoscale Systems (CNS) at
Harvard University.
DATA AVAILABILITY
The data and code that support the findings of this study,
includ-ing all SEM data used in the determination of particle
morphology for
Fig. 1(e) and the algorithmic outlines for selected particles
from Fig. 1,are openly available in GitHub at
https://github.com/trepkakai/rare-earth-magnetism, Ref. 60.
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