Magnetic properties of ErN films

Article abstract of DOI:10.1016/j.jmmm.2010.01.016

We report a magnetization study of stoichiometric ErN nanocrystalline films grown on Si and protected by a GaN passivating layer. According to the temperature dependence of the resistivity the films are heavily doped semiconductors. Above 100 K the magnetization data fit well to a Curie-Weiss behavior with a moment expected within the free-ion Er^{3 +}J = frac(15, 2) multiplet. Below 50 K the Curie-Weiss plot steepens to an effective moment corresponding to that in the crystal-field determined quartet ground state, and develops a clear paramagnetic Curie-Weiss temperature of about 4.5 K. Zero-field- and field-cooled magnetization curves and the AC susceptibility firmly establish a ferromagnetic ground state within that multiplet below a Curie temperature of 6.3 ± 0.7 K. Due to the (1 1 1) texture of the film the comparison between the magnetization behavior, when the field is applied parallel and perpendicular to the film plane, gives new information about the magnetic structure. An arrangement of the moments according to the model derived from neutron diffraction for bulk HoN is strongly suggested.

Full text of DOI:10.1016/j.jmmm.2010.01.016

ARTICLE IN PRESS
Journal of Magnetism and Magnetic Materials 322 (2010) 1973–1978
Contents lists available at ScienceDirect
Journal of Magnetism and Magnetic Materials
journal homepage: www.elsevier.com/locate/jmmm
Magnetic properties of ErN films
Ã
C. Meyer a,b, , B.J. Ruck a, A.R.H. Preston a, S. Granville a, G.V.M. Williams c, H.J. Trodahl a
a The MacDiarmid Institute for Advanced Materials and Nanotechnology, School of Chemical and Physical Sciences, Victoria University, PO Box 600, Wellington 6140, New Zealand
b Institut Ne´el (CNRS and UJF), 25 rue des Martyrs, BP 166, F-38042 Grenoble, France
c The MacDiarmid Institute for Advanced Materials and Nanotechnology, Industrial Research Ltd., PO Box 31310, Lower Hutt 5040, New Zealand
a r t i c l e i n f o
a b s t r a c t
Article history:
We report a magnetization study of stoichiometric ErN nanocrystalline films grown on Si and protected
by a GaN passivating layer. According to the temperature dependence of the resistivity the films are
heavily doped semiconductors. Above 100 K the magnetization data fit well to a Curie–Weiss behavior
Received 3 September 2009
Available online 18 January 2010
with a moment expected within the free-ion Er3þ J ¼ multiplet. Below 50 K the Curie–Weiss plot
15
Keywords:
2
Thin film
steepens to an effective moment corresponding to that in the crystal-field determined quartet ground
Nitride
state, and develops a clear paramagnetic Curie–Weiss temperature of about 4.5 K. Zero-field- and field-
cooled magnetization curves and the AC susceptibility firmly establish a ferromagnetic ground state
within that multiplet below a Curie temperature of 6:370:7 K. Due to the (1 1 1) texture of the film the
comparison between the magnetization behavior, when the field is applied parallel and perpendicular
to the film plane, gives new information about the magnetic structure. An arrangement of the moments
according to the model derived from neutron diffraction for bulk HoN is strongly suggested.
& 2010 Elsevier B.V. All rights reserved.
Evaporation
Ultra high vacuum
Erbium
ErN
Resistivity
Magnetic structure
Magnetic anisotropy
Crystal field
Nanocrystalline
1. Introduction
magnetic properties of ErN films. The results are discussed in the
light of recent theoretical predictions of the band structure [7].
Er has eleven 4f electrons leading for Er3þ to a well-isolated
Although examined in the 1960s, the magnetic properties of
the rare earth mononitrides (RN) have since been largely ignored,
with the exception of GdN, until a recent resurgence of interest
[1]. Perhaps the strongest driving factor for the revival is that
improvements in the band calculations for strongly correlated
electrons have permitted their electronic structure to be better
described. Within the series there are now predictions of
ferromagnetic semiconductors and half metals [2], both of which
might be of interest for spintronics applications. However, there
are experimental challenges to a study of these nitrides, which are
difficult to prepare oxygen-free and stoichiometric, and until
recent advances there remained uncertainty about whether their
ground states are metallic or semiconducting. Using a parallel
development of experimental and theoretical work, we have
recently shown that GdN is a small gap semiconductor with
potentially spin polarized carriers [3,4]. Subsequently, we have
found that DyN and SmN are also ferromagnetic semiconductors
in their ground states [5,6]. In the present paper we describe the
15
ground state J ¼
and
a
free ion magnetic moment
2
´
m0 ¼ gJJmB ¼ 9mB (with the Lande factor gJ ¼ 6=5). Earlier magnetic
data on bulk ErN are collected in the reviews of RE pnictides
[1,8,9]. Those data all agree that ErN is ferromagnetic, but with
Curie temperatures that vary between 3.4 and 6 K. There is a
rough agreement about the paramagnetic state: in the high
temperature range ðT r750 KÞ where the crystal field splitting is
smaller than kBT, the susceptibility follows a Curie–Weiss law
with a magnetic moment of 9:4mBð70:1Þ close to the free ion Er3þ
pffiffiffiffiffiffiffiffiffiffiffiffiffiffi
value, meff ðFIÞ ¼ gJ JðJþ1ÞmB ¼ 9:59
mB. The paramagnetic Curie
temperature yP varies from þ4 K [10,11] to þ14 K [12]. The
spontaneous moment of 5:5mB in the ferromagnetic state is lower
than m0, which has been attributed to an exchange interaction
that is smaller in comparison to the crystal field splitting. Thus,
saturation is not yet achieved under an applied field of 13 T
ð7:9mBÞ [10,11]. Neutron diffraction experiments also reported a
ferromagnetic ordering, characterized for HoN and ErN by a
complicated non-collinear magnetic structure with successive
ferromagnetic sheets perpendicular to ½1 1 1ꢀ [13]. For ErN a
magnetic moment of 6mB=ion was reported and the reduction with
Ã
Corresponding author at: Institut Ne´el (CNRS and UJF), 25 rue des Martyrs, BP
respect to the free ion moment attributed to the crystal field
effect. A more detailed analysis of HoN suggested a retarded spiral
structure with the moments along the /1 0 0S directions giving
166, F-38042 Grenoble, France.
E-mail addresses: claire.meyer@grenoble.cnrs.fr (C. Meyer),
ben.ruck@vuw.ac.nz (B.J. Ruck).
0304-8853/$ - see front matter & 2010 Elsevier B.V. All rights reserved.
doi:10.1016/j.jmmm.2010.01.016

ARTICLE IN PRESS
1974
C. Meyer et al. / Journal of Magnetism and Magnetic Materials 322 (2010) 1973–1978
rise to a net ferromagnetic moment along ½1 1 1ꢀ. As pointed out
by Vogt and Mattenberger [9,14], such a spin arrangement in a
modern view would be rather described as a multi-Q structure,
with
a coexistence of antiferro- and ferromagnetic ordered
components of the spins.
In contrast to the magnetism, authors have shown no
consistent view of the electronic properties of ErN samples. The
first experimental data obtained on ErN evidenced the complexity
of the problem due to a lack of stoichiometry. Early reports [15]
suggest an optical gap near 2 eV, together with a resistivity of the
order of 100 mOcm at room temperature, which shows a metallic
behavior with a large concentration of electron carriers, attributed
to nitrogen vacancies. This behavior was in fact found for most of
the RN in those early studies.
There is no consensus about the computed band structure of
ErN. According to successive band calculations in a local-spin-
density approximation (LSDA), ErN was first found to be metallic
through a LSD plus self-interaction corrections (SIC) method [2],
and then semiconducting within the LSDAþU approach, for which
a small 0.2 eV indirect gap is predicted [7]. However, another
LSDAþU calculation found [1] a half-metallic zero-gap in ErN.
A half metallic ground state has also been obtained in a spin
polarized charge-self-consistent density functional based tight
binding (DFTB) approach [16]. Both the electronic structure and
magnetic ordering have been investigated theoretically in ErAs
and ErN [17]. An antiferromagnetic ordering was predicted for
both compounds in agreement with the experiment for ErAs but
not for ErN. The authors suggested the dipolar interaction might
take part in the magnetic ordering and also explain the magnetic
anisotropy. As a matter of fact, according to Trammell [18], the
minimum in the dipolar energy occurs when the moments are
perpendicular to the [1 1 1] direction. Note that magneto-trans-
port studies suggest that the dipole–dipole interactions are the
dominant exchange mechanism in ErAs [19].
Fig. 1. X-ray diffraction diagram of the ErN film ðlCuÞ.
Fig. 2. Temperature dependence of the resistivity. Inset: derivative of the
resistivity showing an upturn below 6 K.
It is interesting that ErN was also recently reinvestigated for its
huge magneto-caloric effect, which makes it a potential material
for magnetic refrigeration at helium temperature [20]. Arrott
plots of the magnetization curves provide a Curie temperature
the expected 1:1 stoichiometry for ErN (within a 1% error). Not
more than 1–2% oxygen was found in the film.
Fig. 1 shows the X-ray diffraction pattern obtained for the film
TC ¼ 872 K. The specific heat exhibits a
l
- type anomaly peak at
with the Cu Ka radiation. A strong (1 1 1) texture develops during
4.4 K.
growth onto the amorphous SiOx surface layer. The line
broadening reflects a coherence length of the crystallites of
20 nm in the direction perpendicular to the film. Compared to the
characteristic length scale of magnetism, this size is larger than
the exchange length ð ꢂ 6 nmÞ or the Bloch domain wall width
ð ꢂ 15 nmÞ so that bulk-like magnetic behavior is expected,
together with the 2D shape effect associated with the thin film
geometry. A random in-plane orientation of the crystallites is
assumed with respect to their [1 1 1] axis. The lattice parameter of
the NaCl face-centered-cubic structure was derived to be
The aim of the present work is to re-examine the properties of
ErN using films that have been shown to display high
a
stoichiometry compared to the aforementioned bulk samples.
We find that ErN is a highly doped ferromagnetic semiconductor
and we show that the magnetic behavior in the ordered state is
well explained assuming an exchange field much smaller than the
crystal field splitting derived from a simple point charge model.
˚
˚
4.83670.005A, comparable to the literature bulk data of 4.83 A.
As oxygen inclusions in RN have been demonstrated to decrease
the lattice parameter [21,22], we believe that the ErN film is
highly stoichiometric and that potential residual oxygen is
confined at the interface.
2. Film preparation and characterization
The films were grown by thermal evaporation in an ultra-high
vacuum chamber as described previously [3]. Er metal was
evaporated in the presence of 10ꢁ4 mbar of ultra-high purity N2
The DC electrical resistivity was measured ex situ as a function
of the temperature between 300 and 5.2 K, shown in Fig. 2. The
relatively small negative temperature coefficient and the room
gas and deposited on
a Si(1 1 1) substrate held at room
temperature. The native oxide upon the Si surface was not
removed so that ErN grows on an amorphous oxide layer.
A capping layer of GaN was deposited to protect against oxidation
in the outer atmosphere. The resistance was measured in situ and
monitored as the system was vented to determine that the
capping layer was effective. The thickness and composition were
measured by Rutherford backscattering spectroscopy (RBS) and
nuclear reaction analysis (NRA). The configuration of the ErN thin
temperature resistivity of 0:04
Ocm are both characteristic of a
heavily doped semiconductor, similar to our results on previously
grown RN films [3,5,23]. Recalling that the stoichiometry
determination is accurate to 1% at best, we believe that N
vacancies dope the film, as has been demonstrated to be the case
in GdN films grown by the same process [3]. A clear upturn occurs
at the Curie temperature (see next section) when the derivative of
the resistivity is plotted, as can be seen in the inset of Fig. 2. This
phenomena is observed in other RN films [5].
film investigated in the present work is Sið400
mmÞ=
ErNð215 nmÞ=GaNð90 nmÞ. The composition of the film showed

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1975
3. Magnetic measurements
Magnetization measurements were performed with a SQUID
magnetometer with a maximum field of 6 T applied mainly
parallel to the film plane. Some complementary experiments were
carried out in the perpendicular geometry. The diamagnetic
contribution from the Si substrate is small in comparison to the
magnetic signal of the RN but cannot be neglected. Measurements
of a bare substrate show a susceptibility of ꢁ3:3 ꢃ 10ꢁ6 710%,
close to the theoretical Si susceptibility
300 K.
w
ðSiÞ ¼ ꢁ3:4 ꢃ 10ꢁ6 at
Magnetization isotherms were measured at 16 temperatures
between 2 and 300 K, and a selection are represented in Fig. 3. The
isotherms are linear with the applied field for temperatures down
to 50 K, compatible with a Curie–Weiss behavior. Below 50 K the
magnetization is curved according to a Brillouin evolution at high
field and the probable influence of the crystal field. The
susceptibility at zero-field increases sharply below 10 K and a
close look at low field shows the presence of a hysteresis loop in
the temperature range 2–5 K, as reproduced for 2 K in Fig. 4.
The critical field is about 0.2 T with a coercive field of 20 mT and
Fig. 4. Detail of the hysteresis loop observed at T ¼ 2 K.
there is a very small remanent magnetization of 0:2m
B=Er3þ . The
occurrence of a ferromagnetic ordering is accompanied by a non-
saturation of the magnetization at high field, as has been reported
previously [10,11]. At 2 K, the magnetization in 6 T is only
B=Er3þ
5m . The linear behavior found in the magnetically
ordered region is attributed to the rotation of the magnetic
moments from their easy direction towards the applied field
direction, as a large magnetocrystalline anisotropy is expected for
Er3 þ compounds. Moreover, a non-collinear arrangement of the
moments has been suggested by neutron experiments as
discussed above. This magnetic structure would also explain the
small remanence. Extrapolation to the origin of the high field
pseudo-linear contribution provides an order of magnitude of the
Fig. 5. Magnetization isotherms with the magnetic field applied perpendicular to
the film plane.
spontaneous magnetic moment mextr ¼ 3:8570:05
mB at 2 K. In fact
demagnetizing field effect. An extrapolation of the high field
if we refer to the magnetic structure proposed for HoN [13], this
value rather corresponds to the virtual arrangement of the
moments parallel to the randomly distributed /1 0 0S
directions along two half-cones of axis [1 1 1] and angle 54:733.
part of the 2 K curve crosses the M axis at Mperp ¼ 3:5370:06
mB. In
that case we assume that the magnetization lies randomly
oriented on the full cone of angle 54:733 centered on the
applied field direction [1 1 1]. The virtual residual magnetization
The average of the spontaneous magnetization is therefore
pffiffiffi
pffiffiffi
is ð1= 3ÞMs and thus Ms ¼ 6:170:1mB, which is again consistent
p=ð2 6ÞMs, leading to Ms ¼ 670:1mB, in perfect agreement with
with the parallel value.
neutron diffraction.
The review paper of Vogt and Mattenberger [9] has proposed
an easy moment direction perpendicular to [1 1 1], in direct
disagreement with the HoN-like spiral magnetic structure invol-
ving a [0 0 1] easy-axis within which we have interpreted our
data. However, the question is still open, for there are no data in
the literature that directly support the [1 1 1]-perpendicular easy
axis direction. We now demonstrate that our data cannot be
interpreted within that model. In that picture the present film
magnetization should lie in-plane parallel to a high symmetry
axis like /1 1 0S, with no perpendicular component of the
magnetization. The spontaneous magnetization in-plane should
To improve our knowledge of the magnetic structure and of
the anisotropy energy, we have performed magnetization mea-
surements in the perpendicular geometry i.e. with the magnetic
field applied perpendicular to the film plane and parallel to
the [1 1 1] axis. Some curves are shown in Fig. 5. They exhibit the
same ferromagnetic behavior below 10 K, apart from the
be 0:5Ms giving rise to Ms ¼ 7:770:1mB
. The spontaneous
magnetization perpendicular to the plane should correspond to
the magnetic moments randomly distributed along the /1 1 0S
directions defining a cone of axis [1 1 1] and angle 35:263,
therefore 0:81Ms giving rise to Ms ¼ 4:370:1
mB. In that case
there is no agreement between the two geometries.
In Fig. 6 the magnetization curves at 2 K along the two
directions are compared. The area between the curves is
proportional to the anisotropy energy difference mainly due the
demagnetizing field energy at low field. The contribution of
the erbium magnetocrystalline energy is an order of magnitude
higher if we refer to the anisotropy constant in rare earth metals
ð107 J=m3Þ. There is a small aperture in the perpendicular loop,
Fig. 3. In-plane magnetization isotherms.

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Fig. 6. (Color online) First magnetization at 2 K with the magnetic field applied
parallel (circles) and perpendicular (squares) to the film plane (1 1 1). Inset:
hysteresis loop in the two configurations.
Fig. 8. Magnetization in the maximum field of 6 T applied in-plane. Inset: plot of
H/M in 6 T. The solid line is a Curie–Weiss fit in the 100–300 K temperature range.
T ¼ 5:571 K provides another estimate of the onset of the
magnetic transition. Note that the anomaly in the thermal
variation of the resistivity also takes place at this temperature.
Consequently, we infer the average Curie point of ErN to be
TC ¼ 6:370:7 K.
The temperature dependence of the in-plane magnetization
under the maximum field of 6 T is plotted in Fig. 8. The
magnetization shows
temperature as expected in
quantitatively the temperature
a
tendency to saturation at low
ferromagnet. To analyze
dependence of the
a
magnetization in the paramagnetic state, we have focused on
the temperature range where the moment is linear as a function
of the applied field ðT ¼ 1002300 KÞ and set
wðTÞ ¼ MðTÞ=H (see
Fig. 3). The reciprocal susceptibility wꢁ1ðTÞ is plotted in the inset of
Fig. 8.
Fig. 7. (Color online) Magnetization versus T in an in-plane applied field of 25 mT
The curve is linear above T ¼ 50 K. A Curie–Weiss fit of
wꢁ1 ¼ ðTꢁyPÞ=C, within the range 100–300 K, provides
meff ¼ 9:1170:07mB and yP ¼ ꢁ372:5 K. However, the quantita-
tive analysis of the susceptibility at high temperature depends
on the correction arising from the Si substrate. For example
if we use the theoretical Si susceptibility, we rather find:
meff ¼ 8:7470:07mB and yP ¼ þ3:872:5 K. On average, we end
up with meff ¼ 9:070:3mB and yP ¼ 074 K. These uncertainties
arise from the limited fitting range in the high temperature
region, which we cannot extend above room temperature as in
previous studies. Nevertheless we obtain the magnitude of the
in the low temperature region where
a hysteresis takes place in a ZFC-FC
measurement process. The inset shows the AC-susceptibility measured at two
different frequencies in zero applied DC-field.
shown in the inset of the figure. This irreversibility suggests the
existence of domains not strictly parallel to the film plane, which
is expected if the arrangement of the moments is non collinear.
The zero-field susceptibility should give nearly the demagnetizing
field slope. The anisotropy field is determined as the crossing
point with the saturation magnetization: m0Han ¼ 2:1 T. The
theoretical demagnetizing field calculated for Ms ¼ 6mB is
m0Hdem ¼ 2:48 T. Even if the difference is not very large, it is
probably real. This would mean that the energy necessary to
overcome the film shape effect is less than the magnetostatic
energy and this is consistent with a non-zero component of the
magnetization perpendicular to the film plane, once again in
agreement with the non-collinear magnetic structure described
from neutron diffraction in HoN.
The temperature dependence of the in-plane magnetization at
low field (25 mT) shows a clear upturn at low temperature and
the magnetization becomes irreversible below about 6.5 K, as
indicated by the zero field cooled/field cooled (ZFC/FC) data
shown in Fig. 7. Thus, below 6 K the applied field used for these
measurements is smaller than the coercive field, as already seen
in the hysteresis loops. A field of 25 mT is not sufficient to induce
the reversal of the inverse domains in the demagnetized sample.
The maximum of the derivative of the FC curve occurs at T ¼ 7 K,
providing the first estimate of the Curie point in this film.
We have also measured the AC-susceptibility in zero applied
field at low temperature and two frequencies, 33 and 800 Hz, for
the 0.2 mT AC-field (inset of Fig. 7). A maximum of the curves at
effective moment close to the free ion value of 9:59mB, in
agreement with the earlier data.
We can get more detailed information by focusing on low-
temperature data. The very low magnetic ordering temperature
implies that the exchange field interaction is much smaller than
the crystal field splitting, which is generally of the order of several
100 K in the RN [8]. Therefore, the magnetic ordering does not
involve the full multiplet as excited at temperatures above
T ¼ 50 K, but takes place in the low-lying crystal field sublevel.
To investigate the susceptibility at lower temperature it is
necessary to investigate only the low-field data, which are
unaffected by saturation associated with the Brillouin function.
We thus plot in Fig. 9 the inverse of the initial slope of the
magnetization isotherms as a function of temperature. Note that
these data have been corrected assuming the measured value of
the substrate susceptibility, though at this low field that
correction is very small and Fig. 9 is entirely unaffected by
using instead the alternative value discussed above. The points
above T ¼ 50 K are superimposed on the 6 T (H/M) curve as
expected, but there is a strong deviation at lower temperature.
Below T ¼ 50 K the low-field curve falls below the 6 T data, and at

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C. Meyer et al. / Journal of Magnetism and Magnetic Materials 322 (2010) 1973–1978
1977
we limit the calculation to the first order perturbation Zeeman
term linear in H.
ꢀ
ꢁ
2
X
¼
~
~
m
C
0N
j/mjmzjmSj
w
¼
expðꢁEn=kBTÞ
ð1Þ
kBT
n;m
P
with
C
nexpðꢁEn=kBTÞ, and where N is the atom density, En is
B. As
E½Gð82ÞꢁG8ð1Þꢀ ꢂ 90 K, we neglect the contribution of the upper Gð82Þ
quartet and all upper levels and calculate the summation in the
ground state. In the approach of a Curie–Weiss variation, that is,
at low applied field and temperatures higher than TC,
the energy of the crystal field level Gn and mz ¼ gJJz
m
w
¼ C=ðTꢁyPÞ, we therefore obtain inside the Gð81Þ quartet:
ꢀ
ꢁ
X
m
0Ng2J m2B
1
4
2
~
~
C ¼
j/mjJzjmSj
:
ð2Þ
kB
G8
Fig. 9. Plot of the inverse of the initial slope of the parallel isotherms (open circles)
as a function of T. The black circles are (H/M) in an applied field of 6 T. The Curie–
Weiss fit in the high temperature regime is represented as a dotted curve and the
full line curve is the fit in the low temperature regime of the linear part of the
initial slope.
Finally the calculated effective moment within this approach is:
B, in agreement with the measured low temperature
meff ¼ 7:95
m
effective moment meff ¼ 7:5670:1mB
.
4. Conclusion
T ¼ 20 K it shows a change in slope, followed by saturation below
the Curie temperature of 6 K. A fit of the linear portion below the
inflection point (approximately between T=7 and 15 K) gives
meff ¼ 7:5670:1mB and yP ¼ 4:370:4 K. These data thus imply a
ferromagnetic exchange interaction, with a reduced moment on
the Er ions when in the ground state of the crystal field split
multiplet.
Highly stoichiometric ErN nanocrystalline films have been
grown on a silicon substrate, passivated with a GaN capping layer
and found to be semiconductors. These films are ferromagnetic
below a Curie temperature of 6 K. The magnetic ordering takes
place inside
a crystal field quartet ground state. The low
temperature susceptibility agrees with the theoretical value
calculated within a simple point charge model. Furthermore, the
extrapolated spontaneous magnetization at 2K can be quite well
explained in the magnetic structure model proposed for HoN by
neutron diffraction [13] with the moments along /0 0 1S
directions, arranged in successive ferromagnetic ð1 1 1Þ planes.
Such a structure shows a better agreement than the up-to-now
accepted assumption of easy axes perpendicular to ½1 1 1ꢀ.
The crystal field splitting level scheme is unknown for ErN, so
any calculation has to make use of an approximate set of most
probable data. In the review by Hulliger [8] the crystal field
calculation performed by the authors in the approximation of a
point charge model gives a quartet ground state level G8ð1Þ
,
separated from the excited levels Gð82Þ and G7 by about 70 K in
the purely ionic assumption, while the full crystal field splitting is
E=kB ¼ 340 K. To get some more information, we can refer to the
crystal field level configuration experimentally derived for ErAs in
an ErAs/GaAs epitaxial film, from infrared spectroscopy [24].
The ground state Gð81Þ quartet is separated from the first excited
states, Gð82Þ and G7 by an energy of 27:2 cmꢁ1 (39 K). This
experimental result is in reasonable agreement with the point
charge model approximation, in which this difference of energy is
Acknowledgments
The authors are grateful to J. Kennedy for the RBS/NRA
measurements. The MacDiarmid Institute is supported by the
New Zealand Centres of Research Excellence Fund and the
research reported here by a grant from the New Zealand New
Economy Research Fund. C.M. is grateful to the staff of the School
of Chemical and Physical Sciences for their hospitality, and
acknowledges the financial support of the MacDiarmid Institute
and of the Royal Society of New Zealand.
calculated as
around Er3þ . For ErN within the same point charge model
approximation
E ¼ 23:8Z K, [8] and assuming the same Z, we
derive
E ¼ 91 K. However, in the RN, the effective parameter Z is
found to be larger than in the other rare earth pnictides [8].
Therefore, this value of
E might be even larger. If we take Z ¼ 3,
in the purely ionic model, we get
E ¼ 71 K. So it is reasonable to
assume
DE ¼ 10:5Z K, where Z is the effective ligand charge
D
D
D
References
D
D
E ¼ 90720 K. This is large compared to the ordering
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temperature of 6 K and therefore we can assume that the
magnetic ordering only takes place within the Gð81Þ quartet.
~
The wave functions jmS of this quartet are linear combina-
tions of the jmZS and are given by Lea et al. [25]. The coefficients
are functions of the crystal field parameter x. We take x ¼ 0:8 close
to the value calculated within the approximation of the point
charge model, x ¼ 0:836 [8].
The susceptibility
w is anisotropic in such a quartet, depending
on the direction of the applied field with respect to the crystal
lattice. As the magnetic field is perpendicular to the ½1 1 1ꢀ axis
and is randomly oriented inside the crystallite ð1 1 1Þ plane, the
~
w is isotropic in this plane and on average
susceptibility tensor
w
¼ wzz.
In the limit of low applied fields, the Zeeman effect can be
considered as a perturbation of the crystal field energy level and

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