Helical magnetic structure and hyperfine interactions in FeP studied by 57Fe M?ssbauer spectroscopy and 31P NMR

Article abstract of DOI:10.1016/j.jallcom.2016.03.123

We report results of ⁵⁷Fe M?ssbauer and ³¹P NMR studies of a phosphide FeP powder sample performed in a wide temperature range including the point (T_N ≈ 120 K) of magnetic phase transitions. The ⁵⁷Fe M?ssbauer spectra at low temperatures T < T_N present a very complex Zeeman pattern with line broadenings and sizeable spectral asymmetry. It was shown that the change of the observed spectral shape is consistent with the transition into a space-modulated helicoidal magnetic structure. Analysis of the experimental spectra was carried out assuming an anisotropy of the magnetic hyperfine field H_hf at the ⁵⁷Fe nuclei when the Fe³⁺ magnetic moment rotates with respect to the principal axis of the electric field gradient (EFG) tensor. The obtained large temperature independent anharmonicity parameter m ≈ 0.96 of the helicoidal spin structure results from easy-axis anisotropy in the plane of the iron spin rotation. It was assumed that a very low maximal value of H_hf(11 K) ≈ 36 kOe and its high anisotropy ΔH_anis(11 K) ≈ 30 kOe can be attributed to the stabilization of iron cations in the low-spin state (S_Fe = 1/2). The ³¹P NMR measurements demonstrate an extremely broad linewidth reflecting the spatial distribution of the transferred internal magnetic fields of the Fe³⁺ ions onto P sites in the magnetically ordered state.

Full text of DOI:10.1016/j.jallcom.2016.03.123

Journal of Alloys and Compounds 675 (2016) 277e285
Contents lists available at ScienceDirect
Journal of Alloys and Compounds
journal homepage: http://www.elsevier.com/locate/jalcom
Helical magnetic structure and hyperfine interactions in FeP studied
57
31
€
by Fe Mossbauer spectroscopy and P NMR
,
,
Alexey V. Sobolev a *, Igor A. Presniakov a, Andrey A. Gippius b c, Ivan V. Chernyavskii a,
Martina Schaedler c, Norbert Buettgen c, Sergey A. Ibragimov a, Igor V. Morozov a,
Andrei V. Shevelkov a
a Department of Chemistry, Lomonosov Moscow State University, 119991, Moscow, Russia
b Department of Physics, Lomonosov Moscow State University, 119991, Moscow, Russia
c Experimental Physics V, University of Augsburg, 86159, Augsburg, Germany
a r t i c l e i n f o
a b s t r a c t
We report results of 57Fe Mossbauer and 31P NMR studies of a phosphide FeP powder sample performed
Article history:
€
in a wide temperature range including the point (TN z 120 K) of magnetic phase transitions. The 57Fe
Mossbauer spectra at low temperatures T < TN present a very complex Zeeman pattern with line
Received 14 December 2015
Received in revised form
14 March 2016
Accepted 16 March 2016
Available online 18 March 2016
€
broadenings and sizeable spectral asymmetry. It was shown that the change of the observed spectral
shape is consistent with the transition into a space-modulated helicoidal magnetic structure. Analysis of
the experimental spectra was carried out assuming an anisotropy of the magnetic hyperfine field Hhf at
the 57Fe nuclei when the Fe3þ magnetic moment rotates with respect to the principal axis of the electric
field gradient (EFG) tensor. The obtained large temperature independent anharmonicity parameter
m z 0.96 of the helicoidal spin structure results from easy-axis anisotropy in the plane of the iron spin
rotation. It was assumed that a very low maximal value of Hhf(11 K) z 36 kOe and its high anisotropy
Keywords:
Iron phosphide
Mossbauer spectroscopy
Noncollinear magnetism
NMR
D
Hanis(11 K) z 30 kOe can be attributed to the stabilization of iron cations in the low-spin state (SFe ¼ 1/
2). The 31P NMR measurements demonstrate an extremely broad linewidth reflecting the spatial dis-
tribution of the transferred internal magnetic fields of the Fe3þ ions onto P sites in the magnetically
ordered state.
© 2016 Elsevier B.V. All rights reserved.
1. Introduction
magnetic structure, details and generation mechanisms of which
are still a matter of discussions.
Binary compounds MX (where M is transition metal, X is pnic-
togen) of the MnP structure type are numerous, and many of them
display magnetic properties that attract rapt attention. For
instance, the first-order ferromagnetic phase transition in MnAs
near room temperature gives rise to a pronounced magnetocaloric
effect (MCE), with the change in magnetic entropy exceeding
20 J kgꢀ1 Kꢀ1 at 293 K and 15 kOe, placing MnAs and its substituted
variants among the most studied MCE materials [1,2]. But arguably
the most attractive property is helimagnetism displayed by such
compounds as MnP, FeP, and CrAs [3,4]. The scientific interest into
iron phosphide, which seems rather simple at the first glance, is
largely associated with intrinsic complexity of its unusual helical
This FeP phosphide has an orthorhombic structure with the
Pnma space group at room temperature [1]. The structure consists
of iron ions Fe3þ that occupy equivalent crystal sites with distorted
octahedral phosphorus (P3ꢀ) atoms surrounding them (FeP6), and
bears four formulas units per unit cell (Fig. 1a). According to mag-
netic data for FeP [2], this compound exhibits a magnetic transition
at TN z 120 K to the double antiferromagnetic helix with the iron
moments lying in the (ab) plane. Following the helicoidal structure
proposed in Ref. [5], the magnetic moments are parallel within the
planes 1, 2, 3, 4 normal to the c axis (Fig. 1 b). As the plane changes
1e3 or 4e2, the direction of the spin rotates by ~36ꢁ (the difference
of the angles between the spin directions of two Fe atoms separated
by 0.4 c) with the relative angle 176ꢁ between adjacent planes
separated by 0.1 c (Fig. 1 b). Taking into account that the propaga-
* Corresponding author. Department of Chemistry, Lomonosov Moscow State
University, Leninskie Gory 1-3, 119991, Moscow, Russia.
tion vector, k z (2
with the c axis, such rotation between adjacent moments along the
p
/c) ꢂ 0.20, is only approximately commensurate
E-mail address: alex@radio.chem.msu.ru (A.V. Sobolev).
http://dx.doi.org/10.1016/j.jallcom.2016.03.123
0925-8388/© 2016 Elsevier B.V. All rights reserved.

278
A.V. Sobolev et al. / Journal of Alloys and Compounds 675 (2016) 277e285
Fig. 1. (a) The crystal structure of FeP with the cations octahedrally coordinated by phosphorus anions (not shown). (b) Schematic view of the double helical spin structure and its ab
projections proposed in Ref. [5] from neutron diffraction study. The orange, blue, white and dark colored circles illustrate the iron atoms lying in different (ab) planes (the spins are
parallel within each plane normal to the c axis). (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this article.)
€
€
c axis implies the presence of a quasi-continuum of possible ori-
entations of iron moments mFe lying in the (ab) plane. According to
the results obtained in Ref. [5], the magnetic structure of FeP may
be described assuming two nonequivalent iron positions with
different magnetic moments, m1 ¼ 0.37 mB and m2 ¼ 0.46 mB. At the
same time, in the case of isostructural arsenide FeAs with nearly the
same magnetic structure [6], polarized neutron scattering showed
that magnetic helicoid has elliptic deformation within the (ab)
plane with the longest axis of the ellipse being aligned with the b
axis. It should be noted that the powder neutron diffraction applied
to study the magnetic properties of the iron pnictides FeP and FeAs
cannot distinguish between a simple double spiral model with two
discrete iron positions and a quasi-continuous elliptically polarized
distribution of iron moments, thus suggesting that other tech-
Haggstrom et al. [6]. A reasonable fit was obtained by using a su-
perposition of several Zeeman patterns with different values of
magnetic hyperfine fields on the 57Fe nuclei and partial contribu-
tions. According to [6], each discrete Zeeman pattern arises from
different orientations of the magnetic hyperfine field in the (ab)
plane. It was shown that in order to get a good fit, a bunching of
spins along certain directions in the (ab) plane is necessary. Un-
fortunately, the authors did not discuss the origin of such bunching
in context of the electronic structure of iron ions in FeP. Moreover,
there is no information on the temperature evolution of the hy-
€
perfine Zeeman structure of Mossbauer spectra, in particular, near
the critical point (T z TN) that would be very useful to clarify the
nature of the magnetic phase transition.
€
Recently, a detailed Mossbauer study of isostructural mono-
niques should be employed.
arsenide FeAs was published by Błachowski et al. [10], where the
quasi-continuous variation of the hyperfine magnetic field ampli-
tude with the iron spin orientation varying in the (ab) plane was
taken into account. However, despite good fitting of all experi-
mental spectra measured in a wide temperature range below TN,
this model still leaves some unanswered questions. In particular, it
is assumed the existence of two nonequivalent Fe1 and Fe2 posi-
tions, which disagrees with the high temperature spectra (T > TN)
and structural data for FeAs [11]. Moreover, the authors [11] did not
57
€
Early Fe Mossbauer works performed for FeP [6,7] in the
paramagnetic temperature region (T > TN) showed that all iron
cations occupy unique crystallographic positions, being in accor-
dance with the crystal data [8,9]. However, identification and self-
consistent analysis of the very complex magnetic hyperfine spectra
at T < TN caused serious difficulties [7] and left a number of ques-
€
tions. One of the most comprehensive Mossbauer studies of FeP
single crystals in an external magnetic field was performed by

A.V. Sobolev et al. / Journal of Alloys and Compounds 675 (2016) 277e285
279
explain a rather unusual profile of the spatial anisotropy of Fe1 and
Fe2 magnetic moments that points at a lack of proportionality
between the hyperfine field and the magnetic moments on the iron
atoms. We can not exclude that the above conclusions are the result
of constrains made by the authors in their model fitting of exper-
imental spectra. In particular, one could assume that the angle
defining the relative orientation of the spins for a given propagation
wave vector (k) of helicoid is constant upon moving along the c-
axis. This statement requires independent experimental
confirmation.
the time domain. To avoid skin-depth effects and the reduction of
the resonance circuit quality factor due to high metallic conduc-
tivity the fine powder sample was fixed in paraffin. This also pre-
vents the sample grains from re-orienting in the applied field.
3. Results and discussion
€
3.1. Mossbauer spectrum in paramagnetic state
The Mossbauer spectrum of the 57Fe nucleus (Fig. 2 a) measured
€
In the present work we tried to combine the advantages of the
above the magnetic ordering temperature of FeP (TN z 120 K)
presents a single quadrupole doublet with narrow (W ¼ 0.31(1)
mm/s) and symmetrical lines, thus emphasizing the uniformity of
structural positions of iron atoms in the phosphide [12]. The value
of the isomer shift d300K ¼ 0.31(1) mm/s corresponds to iron atoms
in a formal oxidation state of “þ3” [14]. It is interesting that the
€
€
above two models used by Haggstrom et al. [6] and Błachowski
€
et al. [10] for the analysis of Mossbauer spectra for FeP and FeAs,
respectively. Firstly, we took into account that period of the heli-
coidal magnetic structure of FeP is incommensurate with the
crystal lattice. Therefore, we used the quasi-continuous distribu-
tion of the hyperfine magnetic field amplitude and the angle that
determines its orientation with the spin rotation in the (ab) plane.
Such approach allows us to reproduce from experimental spectra
the profile (polar diagram) of the spatial anisotropy of the hyperfine
magnetic field. Secondly, we took into account the possible
anharmonicity (bunching) of Fe3þ magnetic moments related to
magnetocrystalline anisotropy. High efficiency of this approach was
demonstrated by us in a recent preliminary study [12], the main
result of which is the possibility of a good fitting of the experi-
mental spectra without the involvement of two magnetic iron sites.
In the present work, we show the elliptic contour of the magnetic
anisotropy indicating proportionality between the hyperfine field
and the magnetic moments of iron ions. In addition, we carried out
a detailed analysis of the temperature dependence of hyperfine
parameters and their discussion in light of the peculiarities of the
electronic and magnetic state of the iron cations in FeP. The results
observed
d
value matches typical values of isomer shifts for high-
€
of the Mossbauer study in a wide range of temperatures including
the magnetic transition temperature (TN) supplemented by first
results of 31P NMR spectroscopy in iron phosphide FeP. Analysis of
the experimental spectra was carried out assuming the anisotropy
of the magnetic hyperfine field Hhf at the 57Fe nuclei, when the Fe3þ
magnetic moment rotates with respect to the principal axis of the
EFG tensor.
2. Experimental part
Synthesis was carried out by heating the stoichiometric mixture
of Fe and P (red) powders in an evacuated quartz ampoule. The
mixture was slowly (over 30 h) heated up to 1123 K and annealed at
this temperature for 48 h, after which the furnace was switched off.
Powder X-ray diffraction analysis was performed on a Bruker D8
Advance diffractometer (Cu-Ka1 radiation, Ge-111 monochromator,
reflection geometry) equipped with a LynxEye silicon strip detec-
tor. It revealed the obtained product to be pure FeP phase with the
orthorhombic unit cell: a ¼ 5.203(1) Å, b ¼ 3.108(1) Å and
с ¼ 5.802(1) Å, space group Pnma, which agrees perfectly with the
literature data [5,6]. All operations were carried out in a glovebox
(pH2O, O2) < 1 ppm) to prevent surface oxidation in a moist air.
Mossbauer spectra on the 57Fe nucleus were obtained employ-
€
ing a MS-1104Em spectrometer, operating in a constant accelera-
tion mode. Spectra were processed with SpectrRelax program [13].
57
€
Fig. 2. (a) Fe Mossbauer spectrum of FeP recorded at T ¼ 300 K (T >> TN). The solid
€
All isomer shifts are given relative to the Mossbauer spectra of
at room temperature.
a-Fe
red line is the result of the simulation of the experimental spectra as described in the
57
€
text. (b) Fe Mossbauer spectrum at 11 K (T < TN) fitted (solid red line) using a
The 31P NMR measurements were performed both in the para-
magnetic (at 155 K) and in the magnetically ordered state (at
1.55 K) utilizing a home-built phase coherent pulsed NMR spec-
trometer. NMR spectra were measured by sweeping the magnetic
field at several fixed frequencies in the wide range of 18e120 MHz,
the signal was obtained by integrating the spin-echo envelope in
modulation of the hyperfine interactions as the Fe3þ magnetic moment rotates with
respect to the principal axis of the EFG tensor, and the anisotropy of the magnetic
hyperfine interactions at the Fe3þ sites. The blue shaded area shows the results of the
model fitting assuming the equivalence of crystal and magnetic iron sites (the solid
line in the upper part of the figure corresponds to the resulting error curve). (For
interpretation of the references to color in this figure caption, the reader is referred to
the web version of this article.)

280
A.V. Sobolev et al. / Journal of Alloys and Compounds 675 (2016) 277e285
spin cations Fe3þ(d5), octahedrally surrounded by oxygen [15],
where, in contrast to phosphides, the FeO chemical bonds are
considered to be almost entirely ionic. Apparently, this coincidence
is due to the fact that the Fe)Х transfer of the electron density,
caused by a high degree of covalency in metal-pnictogen bonds
(X ¼ P, As, Sb), induces a simultaneous increase in the 4s- and 3d-
orbital populations, which affects the value of the isomer shift in
the opposite direction [14,15]. Mutual compensation of these two
effects possibly renders the resulting isomer shift “less sensitive” to
specific chemical bonds of iron cations in pnictides, in contrast to
iron oxides, in which the isomer shift value allows estimating the
symmetry of local surrounding and spin state of Fe3þ ions [15].
High quadrupole splitting of the doublet, D300K ¼ 0.57(1) mm/s,
means that a strong electric field gradient (EFG) appears on the 57Fe
nuclei. In the case of high-spin ions Fe3þ(SFe ¼ 5/2) with a spheri-
cally symmetric 3d5 (6S) electron shell, the major contribution to
the EFG must be associated with the distortion of the crystalline
environment of the target nucleus. However, our calculations of the
lat
“lattice” contribution to the EFG tensor {V
}
using the crys-
ij i,j¼x,y,z
tallographic data for FeP [5] showed that it is impossible to reach an
agreement between the experimental and theoretical values under
any physically reasonable values of effective charges of iron (ZFe
)
and phosphorus (ZP) ions. Thus, the symmetry of the crystal envi-
ronment of the iron cations in the FeP crystal structure cannot
cause such high values of the EFG at the 57Fe nuclei. This result
indicates the necessity of considering the electronic contributions
to the EFG that are related to different electronic populations of 3d-
orbitals of iron [15] and the overlapping effects of filled 3р-orbital of
Fe3þ and valence 3(sp) orbitals of phosphorus (overlap distortion)
[17].
According to the Vlat calculations, irrespective of the ZFe and ZP
values, the principal VYY axis for the four crystallographically
equivalent Fei atoms in the orthorhombic unit cell lies along the b
axis (Fig. 3 a). The largest VZZ components for all Fei sites have the
same negative values and are located in the (ac) plane, but the
angles (Qi), which these components make with the a-axis, are
different for the four iron atoms (see Fig. 1 a): Q1 z 78ꢁ,
Q2
¼
p
ꢀ
Q1
,
Q3
¼
p
þ
Q1
,
Q4
¼
p Q1 (Fig. 3 a). Variation of the ZFe
ꢀ
and ZP charges leads only to a slight turn of the principal axes VZZ
and VXX in the plane (ac) of the FeP lattice. This conclusion is in
Fig. 3. (a) Directions of the principal EFG axes for four equivalent Fei sites in the unit
cell of FeP. (b) The local magnetic structure (for one iron site) of FeP. The angle w gives
the orientation of the hyperfine field Hhf in the (ab) plane, varying continuously be-
€
€
disagreement with the data obtained by Haggstrom et al. [6] using
€
tween 0 and 2
in the (ac) plane (when the c axis is normal to the plane of the Hhf(w) ellipse); the polar
) and azimutal (4) angles give orientation of the Hhf field in the coordinate system of
p; the polar angle Q gives the orientation of the principal VZZ component
Mossbauer measurements on the FeP single crystals in an external
magnetic field. It was found that the EFG tensor has a positive VZZ
component parallel to the b-axis and negative VXX one making an
angle of z60ꢁ with the c-axis [6]. Such disagreement with our data
may be related to a very large value of the asymmetry parameter
(
q
the principal axes of the EFG tensor.
principal axes of the EFG tensor [12]:
h
¼ (VYYꢀVXX)/VZZ
(h z 0.7 [6]) and, as a consequence, of the
closeness of the values jVZZj z ꢀjVXXj. This fact leads to considerable
uncertainty in the determination of the true value of the principal
axis for the EFG tensor and its direction in crystal lattice under
investigation.
h
ꢀ
ꢁi
hꢀ
2
2
2
Hm
¼
3IZ ꢀ I2 þ
h
IX ꢀ IY ꢀ gmNHhf IX cos 4
eQVZZ
4Ið2I ꢀ 1Þ
b
b
b
b
b
b
Q
ꢁ
i
b
b
þ IY sin 4 sin
q
þ IZ cos
q
;
€
3.2. Mossbauer spectra for the magnetically ordered state
(1)
b
b
b
Decreasing the temperature down to T z TN did not reveal any
specific features in the monotonic temperature dependence of the
where IX, IY , IZ are the angular momentum operators of the 57Fe
nucleus in its exited state; g is the nuclear g-factor; mN is the nuclear
hyperfineeinteraction parameters (
d
,
D) that is usually observed for
Bohr magneton, and
h
¼ (VYYꢀVXX)/VZZ is the parameter of asym-
the Fe3þ ions. At the same time, a complex Zeeman structure ap-
pears in the spectra upon moving into the low-temperature region
T < TN (Fig. 2b), indicating the hyperfine magnetic fields Hhf induced
at 57Fe nuclei. Since the maximum value of the field Hhf does not
exceed 36 kOe even at the lowest temperature (11 K) and the
quadrupole coupling constant reaches the value of eQVZZ ¼ j1.15(1)j
mm/s (300 K), we used the full Hamiltonian of hyperfine in-
teractions having the simplest form in the coordinate system of the
metry. The eigenvalues Hm depend not only on the hyperfine pa-
rameters of the system (
, 4) that determine the orientation of the hyperfine field Hhf in the
system defined by the principal axes of the EFG tensor (X,Y,Z) (Fig. 3
b). It is important to note that in the case of the FeP lattice there are
four crystallographically equivalent Fei sites with different di-
rections of local principal EFG axes (Fig. 3 a), and, as a consequence,
different qi and 4i values. However, due to the symmetry of the
^
Q
d, eQVZZ, Hhf, h) but also on spherical angles
(q

A.V. Sobolev et al. / Journal of Alloys and Compounds 675 (2016) 277e285
281
complete hyperfine Hamiltonian (1), if the magnetic structure of
FeP were collinear, then for these four values of qi and 4i, angles the
positions and the relative intensities of the nuclear Zeeman pat-
allowed to satisfactorily describe the entire series of experimental
spectra measured in the magnetic ordering temperature range
11 K ꢄ T < TN (Fig. 4).
terns would be the same irrespective of the value of
h [6].
The eigenvalues of such Hamiltonian depend on a number of
3.4. Anisotropy and anharmonicity
parameters (
d, eQVZZ, Hhf,
h
,
q
, 4), many of them are correlated, i.e.,
€
cannot be determined independently from Mossbauer spectra, but
only in certain combinations. However, despite the large number of
variable independent hyperfine parameters we could not
adequately describe the experimental spectra profiles at T < TN
according to this simple model. In Fig. 2b (blue shaded area), we
present an example of the best possible description of the experi-
mental spectrum at T ¼ 11 K, which accounts for the main features,
but can not reconstruct the profile completely.
It is possible to make a number of observations and comments
based on the acquired data. First of all, one should pay attention to
the very small value of the maximal magnetic field
Ha(11 K) ¼ 35.9(1) kOe. It is usually assumed that the Fermi contact
interaction with an s-electron is the dominant hyperfine coupling,
implying that the Fe moment is proportional to the hyperfine field
via the relation Hhf
¼
amFe, where the value of the proportionality
constant
a
is compound specific. In our experiments, the average a
€
value was obtained from Hhf and mFe determined from Mossbauer
and neutron diffraction studies of isostructural pnictides AFe2As2
3.3. Helicoidal structure
(A ¼ Ca, Sr, Ba) [19]. Using the thus obtained average ratio
mFe z 92 kOe/mB, we estimated the possible value of the magnetic
moment to be Fe z 0.39 mB, which appears to be very close to the
values of 0.37e0.46 mB deduced from a neutron diffraction study of
FeP [5]. It should be noted that despite the small difference in the
values of mFe defined by different methods, all of them clearly point
at a significant decrease of the resultant spin of iron compared to
SFe ¼ 5/2 (mFe ¼ 5 mB) for high-spin cations Fe3þ(d5). Such a
reduction of SFe cannot be related to the effects of strong covalency
of the FeP bonds in (FeP6) polyhedra of iron phosphide.
a ≡ Hhf/
As long as the model with a unique iron site failed to completely
describe the experimental spectrum, in the next step of the analysis
at T < TN we used a more sophisticated model by taking into ac-
count the features associated with an incommensurate planar
elliptical structure for FeP, which is schematized in Fig. 1b. The
angle w, which gives the orientation of the hyperfine field Hhf in the
m
(ab) plane, is varying continuously between 0 and 2
expressions (w, ) and 4(w, ) connecting the spherical angles in
Hamiltonian Hm (1) with the rotation angle (w) of the magnetic
p. We found the
q
Q
Q
^
Q
moments of iron ions and also with the angle
Q that the principle
Our model suggests that the “spatial anisotropy of a hyperfine
field” refers to the angular dependency of the Hhf(w) in the (ab)
plane of the orthorhombic unit cell or Hhf(qw, 4w) field value in the
system defined by principal axes of the EFG tensor (Fig. 3a). The
strong spatial anisotropy of the magnetic hyperfine field Hhf,
particularly at T ¼ 11 K, Ha ¼ 35.9(1) kOe and Hb ¼ 5.6(1) kOe, is
related to the spatial anisotropy of magnetic moment values mFe(w)
VZZ component makes with the normal (the c-axis) to the helical
plane (Fig. 3b):
cos
q
¼ sin
Q
cosw
(2a)
(2b)
tan f ¼ tanw=cos
Q
~
[5] or hyperfine magnetic interaction constant A(w) (generally, a
The values wi(z) depend on the coordinates of iron atoms (z)
along the helix propagation, in particular, for the harmonic
~
tensor quantity) included in the expression Hhf ¼ A,mFe [20]. Fig. 5a
approximation w(z) ¼ qz þ
assumes a linear relation of the magnetic moment mFe and the
hyperfine magnetic field Hhf at 57Fe nuclei: Hhf
amFe (neglecting
t (where t is the phase shift). Our model
¼
the influence of magnetic neighbors e supertransferred hyperfine
field, HSTHF). To account for the possible spatial anisotropy of the
magnetic moment mFe(w) ¼ amacosw þ bmbsinw or the anisotropy of
~
the magnetic hyperfine tensor (A), both of which lead to anisotropy
of the Hhf field, we used the expression Hhf(w) ¼ Hacos2w þ Hbsin2w,
where Ha and Hb are the magnitudes of Hhf when the magnetic
moment of Fe3þ is directed along the a and b axis, respectively.
Finally, we used Jacobian elliptic function, sn[…], to describe
possible anharmonicity (bunching) of spatial distribution of Fe3þ
magnetic moments [18]:
coswðzÞ ¼ sn½ð 4KðmÞ=lÞz; mꢃ;
(3)
R
p
where KðmÞ ¼ =2 dw=ð1 ꢀ m cos2 wÞ1=2 is an elliptic integral of
the first kind,
l
0the helical period, and m is the anharmonicity
parameter that is found by minimization of the free-energy [18].
One of the main manifestations of anharmonicity is the depen-
dence of the angles (wij) between neighboring i-th and j-th iron
spins on the helicoid propagation (k). Without anharmonicity,
the angle wij defining the relative orientation of the spins for a
given wave vector k is constant wij (≡ kz). However, if anharmonicity
is present, the helicoid with w0 ≡ kz no longer describes the minimal
energy spin arrangement because the spins bunch along
the modulation propagation zjjc direction with modulated
57
€
Fig. 4. Fe Mossbauer spectra (experimental open circles) of FeP recorded at the
indicated temperatures. The solid red lines are simulations of the experimental spectra
as described in the text. (For interpretation of the references to color in this figure
caption, the reader is referred to the web version of this article.)
rotation angles wij ¼ w0
d(wij)/dz f 4 K(m)/
þ
Dwij and the spin distribution given by
l
(1ꢀmcos2w)1/2 [18]. The use of this model

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A.V. Sobolev et al. / Journal of Alloys and Compounds 675 (2016) 277e285
the value
D
Hanis
¼
aDmanis z 31.3 kOe that almost completely co-
incides with the experimental value 30.3(2) kOe. In addition, we
can not exclude the anisotropic part of the magnetic hyperfine
~
interaction constant A as the probable cause for the observed
anisotropy Hhf responsible for the mechanisms of formation of the
magnetic hyperfine structure [20]. One should also consider the
~
orbital contribution to A that is strongly dependent on the iron spin
direction with respect to the crystal axes.
Within the above model, the best description of all spectra
measured at 11К ꢄ T ꢄ 120 K (Fig. 4) may only be attained with
sufficiently high values of the anharmonicity parameter m that
remains almost unchanged (m z 0.96) in the entire temperature
range (T < 0.87,TN) of magnetic order (Fig. 5b). The obtained very
large and temperature independent anharmonicity parameter of
the helicoidal spin structure results from the bunching of the spins
along certain directions in the plane of the iron spin rotation. Such
type of bunching was suggested by Moon [21] for MnP having the
spiral structure with a bunching of the spins along easy axis in the
ab-plane. In the used model, the angle w of the iron moments
relative to the b-axis is w ¼ kz ꢀ2
xsin2(kz), where x is the bunching
parameter (x4.6K ¼ 0.022(2) for MnP [21]). The same model was
€
€
used by Haggstrom et al. [6] for the qualitative analysis of
€
Mossbauer data for FeP. However, no quantitative estimates of the
bunching parameter were performed. The inset in Fig. 5b shows the
dependence of the bunching parameter (
x) as a function of the
anharmonicity (m). According to our estimation,
x11K z 0.18 for FeP
that significantly exceeds the similar parameter for MnP [21] con-
taining high-spin Mn2þ ions with quenched orbital angular
momentum.
In order to visualize the effect of the uniaxial anisotropy that
distorts from circular helicoid, the asymmetric (p(Ha) >> p(Hb))
hyperfine field distribution p(Hhf) f (jvHhf(w)/vwj)ꢀ1 resulting from
simulation of the spectra is shown in Fig. 5b. In addition, a modu-
lation along the direction k(jjz) of the x-projection Hx ¼ Hhf(w),sn
[( 4 K(m)/
l
)z, m] (see Eq. (3)) of the Hhf field on the a(jjx)-axis is
shown in the inset to Fig. 6 (for comparison, the figure shows the
distribution p(Hhf) for a harmonic helicoidal magnetic structure
with w0 ≡ kz (blue area)). The anharmonicity is related to the con-
stant of magnetocrystalline anisotropy (Ku) [18]: m f (Ku/<J>)
Fig. 5. (a) Polar diagram demonstrating anisotropy of the hyperfine magnetic fields at
57Fe nuclei in FeP for selected temperatures; the symbol Ha denotes a hyperfine field
component on iron along the a-axis, while Hb stands for an iron hyperfine field
component along the b-axis. (b) Temperature dependences of the anharmonicity
parameter (m) and the difference
D
Hanis ¼ (HaeHb) extracted from least-squares fits of
€
the Mossbauer spectra. The inset shows the dependence of the bunching parameter (
x)
as a function of the anharmonicity (m).
represents experimental polar diagrams Hhf(w) at different tem-
peratures. Clearly, the difference (Ha - Hb) ≡ Hanis decreases
D
monotonically with increasing temperature (Fig. 5b). The anisot-
ropy of Hhf usually associates with the dipole contribution Hdip due
to the asymmetry of the local magnetic surrounding, but in our case
it cannot significantly influence Hhf because of the low mFe value. In
our case, the most probable cause of the anisotropy Hhf is related to
the anisotropy of the magnetic moment mFe(w) as it rotates in the
(ab) plane. This conclusion is consistent with the results of the FeP
neutron diffraction study [5], according to which the anisotropy of
magnetic moment is Dmanis z 0.34mB (T ¼ 4.6 K); that should lead to
Fig. 6. The hyperfine field distribution p(Hhf) resulting from a simulation of the spectra
(red area). For comparison, the figure shows the distribution p(Hhf) for a harmonic
helicoidal magnetic structure (blue area). Insert: modulation along the direction k(jjz)
of the x-projection (Hx ¼ Hhf,cosw) of the Hhf field on the a axis, derived from the
€
Mossbauer spectrum (red line); for comparison, blue line gives the theoretical curve
for harmonic (sin-modulated) spin structure. (For interpretation of the references to
color in this figure caption, the reader is referred to the web version of this article.)

A.V. Sobolev et al. / Journal of Alloys and Compounds 675 (2016) 277e285
283
RFeeFe, where <J> is the exchange integral and RFeeFe is the distance
between nearest iron atoms along the helicoid propagation. The Ku
constant contains two main contributions: Ku ¼ KD þ KSI [15],
where KD is a dipole contribution connected to dipoleedipole in-
teractions of magnetic moments mFe, which depend on their
orientation in a crystal, and KSI is the single-ion anisotropy deter-
mined by the effects of the spin-orbital interaction [22]. In the case
of FeP, the KD contribution should not play any significant role due
to the very low values of magnetic moment mFe(w). The manifes-
tation of single-ion anisotropy KSI by Fe3þ ions is possible only with
consideration of electronic states with a nonzero orbital angular
moment [15].
3.5. Low-spin model for Fe3þ
€
Thus, the above Mossbauer data suggest that the orbital angular
moment contribution should be taken into account while analyzing
the basic electronic state of the Fe3þ cations in iron phosphide FeP.
High-spin Fe3þ ions in the distorted octahedral environment of
6
phosphorus anions are characterized by the electronic term A1g
,
which requires orbital angular moment to be completely quenched.
Consideration of <L> s 0 is possible only within the second order
of perturbation theory that could hardly explain the low value of
hyperfine magnetic field Hhf, the high value of anisotropy
DHanis,
and strongly pronounced anharmonicity (m / 1) of magnetic he-
licoid observed in our experiments. A possible reason for all these
results is the stabilization of iron cations in a low-spin state (LS).
Examples of the high-spin to low-spin transition in isostructural
compounds were observed for FeAs and P-doped MnAs at 77 and
232 K, respectively [9,23]. In a strong crystal field of octahedral
symmetry, the ground state of the Fe3þ ions is 2T2g (t52g, SFe ¼ 1/2).
Considering the relation between holes and electrons, we have to
take the t52g electron configuration as a t21g hole configuration. If the
2
local symmetry is exactly octahedral, then the T2g state is sixfold
Fig. 7. (a) Low-spin Fe3þ orbital level scheme in the trigonal crystal field approxima-
tion; (b) Quadrupole coupling constant eQVZZ plotted versus temperature; fitting to the
experimental data (blue solid line) with the crystal field model (the region I e T < TN)
and using semi-empirical relation (see text) in the region II: T > TN. (For interpretation
of the references to color in this figure caption, the reader is referred to the web
version of this article.)
degenerate. However, under the influence of axial tetragonal or
trigonal distortions the sixfold degeneracy is removed (Fig. 7a).
According to our estimations, the negative sign of eQVZZ (<0), which
is observed at T << TN, is compatible with a crystal field with pre-
dominant tetragonal or very large (ε/
D > 0.4, see Fig. 7a) and
physically unreasonable trigonal distortion (small trigonal char-
acter gives a positive sign for the quadrupole interaction). Thus,
although there is no direct experimental evidence for the presence
of a fourfold local symmetry axis at the Fe3þ positions in the FeP
lattice, the sign of the measured EFG tensor shows that the iron ions
experience a quasi-tetragonal crystal field.
.D
E
Dh
i.
E
~
Hhf ¼ HF þ
l
L,SmB r3 þ 2mB 3rðS,rÞ ꢀ r2S r5
;
(5)
where HF is the Fermi contact term, which is created by the po-
larization of the s electrons by the 3d electrons of iron ions; the
second term (HL) is the contribution from the components of the
unquenched angular momentum, and the third dipole term (HD) is
due to the anisotropy of the spin density distribution. The dipole
term is related to the electronic contribution (~Vel/jej) to the EFG,
which arises from the aspherical charge distribution (see x1). Under
a small tetragonal distortion from the strict cubic symmetry the
degeneracy of the t2g triplet is partially removed giving rise to a
singlet a1g{dxy} and a doublet eg{dxz,dyz} (Fig. 7a). For the LS
configuration (dxz,dyz)4(dxy)1, ignoring the effects of crystal field of
lower than tetragonal symmetry, the components of the Hhf parallel
The hyperfine interactions in low-spin iron ions are consider-
ably modified as compared with those of high-spin iron ions. For
instance, despite the fact that the axial and rhombic distortions of
the (Fe3þP6) polyhedra causes the splitting of sub-levels t2g
/
a1g þ eg (Fig. 7a), a small difference in energies of the generated
terms 2A1g and 2Eg as well as the spin-orbital interaction (
lead to a partial “unfreezing” of the orbital moment <Li>
lLS) will
b
b
X
〈0jLijn〉〈njLjj0〉
En ꢀ E0
hLii ¼
l
LijSj ¼
l
,Sj;
(4)
n
b
(H ) and perpendicular (H⊥) to the OZ tetragonal axis (jj VeZlZ) are
where
l
is the spin-orbital interaction constant; Li is the orbital
jj
angular momentum operator; <0jand jn> are wave vectors of
given by
ground and exited electronic states, respectively; Е0 and Еn are the
energies of the corresponding states; Lij are the (L) tensor com-
~
n ꢀ
ꢁ
o
D
E
H ¼ HF þ 4 g ꢀ 2 ꢀ 4=7 mB rꢀ3
(6a)
ponents that define the anisotropy of the orbital moment. The
observed internal magnetic field Hhf at the 57Fe nucleus may be
discussed in term of three dominant contributions [24]:
jj
jj

284
A.V. Sobolev et al. / Journal of Alloys and Compounds 675 (2016) 277e285
including the magnetic transition temperature TN in comparison
D
E
H⊥ ¼ HF þ f4ðg⊥ ꢀ 2Þ þ 2=7gmB rꢀ3
;
(6b)
€
with the Mossbauer data for the isostructural phases will be a
subject of our next publication.
~
where g ≡ gzz and g⊥ ≡ gxx,yy are the main components of the g
jj
3.6. 31P NMR spectra
tensor: {gij} ¼ 2 þ
l
/2Lij. Using the above equations, one can write
the expression
D
Hanis z (H ꢀH⊥) ¼ {4(g ꢀg⊥)ꢀ6/7}mB<rꢀ3> ac-
jj
jj
The remaining question is whether the magnetic anisotropy
affects the hyperfine magnetic fields at 31P nuclei transferred from
the nearest magnetic Fe3þ ions. Fortunately, apart from the most
cording to which the dipole term HD is the main source of the
observed anisotropy (~DHanis) of the internal magnetic field Hhf at
the 57Fe nuclei in FeP. However, as the Fermi (HF) and orbital (HL)
contributions to the hyperfine magnetic field have opposite signs,
their partial canceling may lead to a significant decrease of the Hhf
value. In addition, since the value of the orbital moment <Li> is
mostly anisotropic (Lxx z Lyy s Lzz), the HL contribution induced
by this moment must be anisotropic as well. Finally, “mixing” the
main electronic state of low-spin cations FeIII and the term 2Eg leads
to the Ising-like anisotropy [22], which could manifest itself as a
high anisotropy level of spiral magnetic structures.
popular Mossbauer nuclei, 57Fe, the crystal structure of FeP con-
€
tains also very good NMR nuclei 31P (I ¼ 1/2,
g/2
p
¼ 17.235 MHz/T).
This enables us to probe the hyperfine interactions on the phos-
phorus site in FeP by 31P NMR spectroscopy.
The field-sweep 31P NMR spectrum of the FeP powder sample
measured at fixed frequency of 80 MHz in the paramagnetic state at
155
K is presented in Fig. 8a. The line is very narrow
(FWHM ~ 6,10ꢀ2 kOe) with the peak situated almost at the
diamagnetic Larmor field HLar ¼ 46.42 kOe.
The above assumption about the low-spin state of Fe3þ ions in
FeP provides good explanations for the main features of the
experimental temperature dependence of a quadrupole coupling
constant eQVZZ at T < TN (Fig. 7b). If in high-spin Fe3þ(t23geg2) com-
pounds the EFG acting on the iron nuclei is of lattice origin (Vlat),
then in the low-spin Fe3þ(t25g) state it is mainly produced by 3d5-
electrons of iron ions. The temperature dependent electron popu-
lation on t2g sublevels produces a relatively strong temperature
dependent electronic contribution (Vel) to the EFG [16,20]. Taking
into account the temperature dependent probabilities of a hole
With decreasing temperature below TN the 31P spectra change
dramatically. The spectrum measured at lowest temperature of
1.55 K is presented in the Fig. 8b. First of all, the spectrum is now
extremely broad with FWHM ~11.6(4) kOe and width at the line
basement ~ 16.4(4) kOe which is more than two orders of magni-
tude higher than the FWHM in the paramagnetic state. This result
unambiguously indicates that in the magnetically ordered state the
effective magnetic field on 31P nuclei is strongly affected by the
hyperfine field transferred from Fe3þ cations. The spatial distribu-
tion of these transferred fields with respect to external magnetic
field is reflected in the characteristic trapezoidal 31P line shape.
The trapezoidal distribution of the resonance fields Hres in an
antiferromagnet can be modeled based on the superposition of the
internal magnetic field Hint and the externally applied magnetic
field H [32,33]:
occupying the A1g and 2Eg levels, the temperature dependence of
2
the electronic EFG can be described as [16].
VZZðTÞ ¼ VZZð0Þ½ð1 ꢀ expðꢀε=RTÞÞ=ð1 þ 2 expðꢀε=RTÞÞꢃ;
(7)
From the thermal variation of eQVZZ we can give an evaluation of
the crystal field splitting (ε) between the two lowest orbitals of the
low-spin Fe3þ ions (Fig. 7a) in the FeP structure. The EFG is a
decreasing function of increasing temperatures; this effect, which
arises from the fact that the EFG is a thermal average between the
values corresponding to the lowest orbital doublet and singlet. The
axial case (only one free parameter, ε) proved to be the best in all
fitting procedures. Using the data of Fig. 7b and the simple formula
(8) one gets ε ¼ 2.61 kJmolꢀ1. As can be seen (Fig. 7b), the agree-
ment of calculated curve with experimental results is quite satis-
factory. In the paramagnetic range T > TN, the temperature
dependence of the quadrupole interactions is described using a
semi-empirical relation VZZ(T) ¼ A(1ꢀB,T3/2), where A ≡ VZZ(TN) is
the main EFG tensor component at T z TN, corresponding to the
D118K ¼ 0.61(1) mm/s value of quadrupole splitting, and B is a
constant with positive value 1.17(6),10ꢀ5 K2/3. In this temperature
range (T > TN), the observed eQVZZ(T) dependence is mainly due to
the temperature variation of the lattice Vlat(T) contribution to the
EFG [20].
ꢂ
ꢂ
ꢂ
ꢂ
!
!
Hres
¼
u0
=
g
¼ H þ Hint
;
(8)
or, equivalently,
Hr2es ¼ H2 þ Hi2nt þ 2H,Hint,cos
a;
(9)
80 MHz
HL = 46.42 kOe
(a)
T = 155 K
-0.01
0 0.010.02
One notes that at T z TN the quadrupole splitting increases
60 MHz
sharply on cooling (Fig. 7b). Similar sudden change in
D(T) have
HL = 34.8 kOe
been observed in many compounds, for example, MnAs [1],
MnFeP1-xAsx [25], NaFeAs [26], FeAs [10], and FeS [27], thus
demonstrating a strong coupling magnetic ordering to the lattice
deformation. Various mechanisms have been examined in order to
interpret this transition, such as exchange magnetostriction
[27,28], biquadratic exchange [29] or spin-orbital coupling of
magnetization in the presence of orbital degeneracy (Jahn-Teller
distortions) [30,31]. However, due to the lack of sufficient struc-
tural and thermodynamic data for FeP we are unable to give a
definitive explanation of this unusual behavior of the temperature
(b)
T = 1.55 K
-10
-5
0
5
10
H - HL (kOe)
Fig. 8. (a) 31P NMR spectrum of FeP measured in the paramagnetic state at 155 K; (b)
31P NMR spectrum of FeP measured in the magnetically ordered state at 1.55 K. (the
red solid line is the simulation, see text). (For interpretation of the references to color
in this figure caption, the reader is referred to the web version of this article.)
dependence
D(T) at the magnetic phase transition. More detailed
analysis of hyperfine parameters in a wide range of temperatures

A.V. Sobolev et al. / Journal of Alloys and Compounds 675 (2016) 277e285
285
where
a
is the angle between H and Hint. In a powder sample, the
of hyperfine magnetic field Hhf(11 K) z 36 kOe and its high
anisotropy Hanis(11 K) z 30 kOe can be attributed to the stabili-
direction of H is randomly distributed with respect to Hint, and the
probability for an angle between H and Hint to be in an interval
between
D
zation of iron cations in the low-spin state (SFe ¼ 1/2). This
assumption is consistent with the high value of the anharmonicity
parameter of helical structure obtained from the spectra of interest.
Our preliminary 31P NMR measurements on FeP demonstrate
extremely broad spatial distribution of the transferred internal
magnetic fields on P sites in the magnetically ordered state.
a
and
a
þ
Da is proportional to the solid angle
N ¼ f(H) H which probe a
H is proportional to the solid
Da, giving the NMR line shape f(H):
DU ~ sin
a
,Da. The number of nuclei
D
D
resonance field between H and H þ
D
angle DU or f(H) H ~ sin
D
a,
d
dH
a
f ðHÞfsin
a
:
(10)
Acknowledgments
The latter term d
a/dH is given by the differentiation of Eq. (9)
using the relation:
This work is supported in part by the Russian Science Founda-
tion, grant # 14-13-00089 (nuclear resonance measurement), and
Russian Foundation for Basic Research, grant # 15-03-99628
(sample preparation and characterization). A.A.G., M.S., and N.B.
kindly acknowledge support from the German Research Society
DFG via TRR80 (Augsburg, Munich).
H2 ꢀ Hi2nt þ Hr2es
d
a
d cos
dH
a
1
sin a
,
¼ ꢀ
,
;
(11)
H
int,H2
d cos
a
This result, inserted into Eq. (10), gives f(H) which represents the
number of nuclei which are in resonance at a certain value of the
applied magnetic field H. As different values of Hres are only ob-
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D
this figure, the coincidence with the experimental 31P spectrum is
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decreasing of DHint.
4. Conclusions
The results obtained in the present study have shown the
effectiveness of the suggested approach to the complex hyperfine
magnetic structure analysis of the experimental spectra of iron
phosphide measured over a wide temperature range. The results
presented above show that a good fitting of the experimental
spectra can be achieved without assumptions of formation of two
nonequivalent crystallographic positions of the Fe3þ cations, as was
suggested earlier. The main reason for the observed asymmetry of
hyperfine structure is the spatial modulation of the rotation angles
w between adjacent moments mFe along the c axis, which induces
^
the modulation of the Hamiltonian Hm
(
Q
q,4) eigenvalues. Low value
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