Low-temperature magnetism in the honeycomb systems SrLn₂O₄ (Review Article)
Recent progress in the understanding of the complex magnetic properties of the family of rare-earth strontium oxides, SrLn₂O₄, is reviewed. These compounds consisting of hexagons and triangles are affected by geometrical frustration and therefore exhibit its characteristic features, such as a signif...
Gespeichert in:
| Datum: | 2014 |
|---|---|
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2014
|
| Schriftenreihe: | Физика низких температур |
| Online Zugang: | http://dspace.nbuv.gov.ua/handle/123456789/119413 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Low-temperature magnetism in the honeycomb systems SrLn₂O₄ (Review Article) / O.A. Petrenko // Физика низких температур. — 2014. — Т. 40, № 2. — С. 139-147. — Бібліогр.: 28 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-119413 |
|---|---|
| record_format |
dspace |
| spelling |
irk-123456789-1194132017-06-07T03:03:28Z Low-temperature magnetism in the honeycomb systems SrLn₂O₄ (Review Article) Petrenko, O.A. Recent progress in the understanding of the complex magnetic properties of the family of rare-earth strontium oxides, SrLn₂O₄, is reviewed. These compounds consisting of hexagons and triangles are affected by geometrical frustration and therefore exhibit its characteristic features, such as a significant reduction of magnetic ordering temperatures and complex phase diagrams in an applied field. Some of the observed features appear to be rather remarkable even in the context of the unusual behavior associated with geometrically frustrated magnetic systems. Of particular interest is the coexistence at the lowest temperature of different magnetic structures (exhibiting either long or short-range order) characterized by different propagation vectors in materials without significant chemical or structural disorder. 2014 Article Low-temperature magnetism in the honeycomb systems SrLn₂O₄ (Review Article) / O.A. Petrenko // Физика низких температур. — 2014. — Т. 40, № 2. — С. 139-147. — Бібліогр.: 28 назв. — англ. 0132-6414 PACS 75.25.–j, 75.50.Ee, 75.47.Lx http://dspace.nbuv.gov.ua/handle/123456789/119413 en Физика низких температур Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
Recent progress in the understanding of the complex magnetic properties of the family of rare-earth strontium oxides, SrLn₂O₄, is reviewed. These compounds consisting of hexagons and triangles are affected by geometrical frustration and therefore exhibit its characteristic features, such as a significant reduction of magnetic ordering
temperatures and complex phase diagrams in an applied field. Some of the observed features appear to be rather remarkable even in the context of the unusual behavior associated with geometrically frustrated magnetic systems. Of particular interest is the coexistence at the lowest temperature of different magnetic structures (exhibiting
either long or short-range order) characterized by different propagation vectors in materials without significant chemical or structural disorder. |
| format |
Article |
| author |
Petrenko, O.A. |
| spellingShingle |
Petrenko, O.A. Low-temperature magnetism in the honeycomb systems SrLn₂O₄ (Review Article) Физика низких температур |
| author_facet |
Petrenko, O.A. |
| author_sort |
Petrenko, O.A. |
| title |
Low-temperature magnetism in the honeycomb systems SrLn₂O₄ (Review Article) |
| title_short |
Low-temperature magnetism in the honeycomb systems SrLn₂O₄ (Review Article) |
| title_full |
Low-temperature magnetism in the honeycomb systems SrLn₂O₄ (Review Article) |
| title_fullStr |
Low-temperature magnetism in the honeycomb systems SrLn₂O₄ (Review Article) |
| title_full_unstemmed |
Low-temperature magnetism in the honeycomb systems SrLn₂O₄ (Review Article) |
| title_sort |
low-temperature magnetism in the honeycomb systems srln₂o₄ (review article) |
| publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| publishDate |
2014 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/119413 |
| citation_txt |
Low-temperature magnetism in the honeycomb systems SrLn₂O₄ (Review Article) / O.A. Petrenko // Физика низких температур. — 2014. — Т. 40, № 2. — С. 139-147. — Бібліогр.: 28 назв. — англ. |
| series |
Физика низких температур |
| work_keys_str_mv |
AT petrenkooa lowtemperaturemagnetisminthehoneycombsystemssrln2o4reviewarticle |
| first_indexed |
2025-07-08T15:50:04Z |
| last_indexed |
2025-07-08T15:50:04Z |
| _version_ |
1837094463483150336 |
| fulltext |
Low Temperature Physics/Fizika Nizkikh Temperatur, 2014, v. 40, No. 2, pp. 139–147
Low-temperature magnetism in the honeycomb systems SrLn2O4
(Review Article)
O.A. Petrenko
University of Warwick, Department of Physics, Coventry CV4 7AL, UK
E-mail: o.petrenko@warwick.ac.uk
Received August 2, 2013
Recent progress in the understanding of the complex magnetic properties of the family of rare-earth strontium
oxides, SrLn2O4, is reviewed. These compounds consisting of hexagons and triangles are affected by geomet-
rical frustration and therefore exhibit its characteristic features, such as a significant reduction of magnetic order-
ing temperatures and complex phase diagrams in an applied field. Some of the observed features appear to be ra-
ther remarkable even in the context of the unusual behavior associated with geometrically frustrated magnetic
systems. Of particular interest is the coexistence at the lowest temperature of different magnetic structures (ex-
hibiting either long or short-range order) characterized by different propagation vectors in materials without sig-
nificant chemical or structural disorder.
PACS: 75.25.–j Spin arrangements in magnetically ordered materials (including neutron and spin-polarized
electron studies, synchrotron-source x-ray scattering, etc.);
75.50.Ee Antiferromagnetics;
75.47.Lx Magnetic oxides.
Keywords: rare-earth strontium oxides, magnetic properties.
Contents
1. Introduction .......................................................................................................................................... 139
2. Zero field magnetic properties of SrEr2O4, SrHo2O4 and SrDy2O4 ...................................................... 140
2.1. SrEr2O4 ......................................................................................................................................... 140
2.2. SrHo2O4 ........................................................................................................................................ 142
2.3. SrDy2O4 ........................................................................................................................................ 142
3. Field-induced behavior of SrEr2O4, SrHo2O4 and SrDy2O4 ................................................................. 142
4. Further considerations .......................................................................................................................... 144
4.1. Other SrLn2O4 compounds ........................................................................................................... 144
4.2. Crystalline electric field effects .................................................................................................... 145
5. Summary .............................................................................................................................................. 145
Acknowledgements .................................................................................................................................. 146
References ................................................................................................................................................ 146
1. Introduction
Frustrated magnets have been a focal point of the re-
search on magnetism for the past two decades. In this arti-
cle, the influence of geometrical frustration on the magnet-
ic properties of the family of rare-earth strontium oxides,
2 4SrLn O , (where Ln = Gd, Dy, Ho, Er, Tm and Yb) is
discussed. Given the nature of this special issue of Low
Temperature Physics on antiferromagnetism an extensive
general introduction to magnetically frustrated systems is
omitted and the reader is instead referred to a collection of
reviews available on the subject [1]. We start with a de-
scription of the crystal structure and general properties of
2 4SrLn O and other closely related compounds and then
present the recently obtained experimental results on their
low-temperature magnetic properties by our group and
others. Particular attention is paid to the zero-field ground
state of 2 4SrEr O , 2 4SrHo O and 2 4SrDy O (Sec. 2), as well
as the field-induced behavior of these compounds (Sec. 3).
The penultimate section briefly reviews the other 2 4SrLn O
compounds and discusses the importance of crystal field
effects. The concluding section compares different mem-
bers of the family and includes a brief summary.
The members of the 2 4SrLn O family crystallize in the
form of calcium ferrite [2], with the space group Pnam ;
the crystal structure of these materials (see Fig. 1) can be
© O.A. Petrenko, 2014
O.A. Petrenko
viewed as a network of linked hexagons and triangles [3,4].
The most important feature of the linked hexagon (or
“honeycomb”) lattice is that it has the lowest coordination
number, 3, in two dimensions. This feature attracts a lot of
theoretical attention to the lattice, but being bipartite, the
honeycomb lattice is not frustrated if only the nearest-
neighbor interactions are considered. The frustration in a
honeycomb lattice can be induced by further neighbor in-
teraction and numerous models of frustrated honeycomb
lattices which include Heisenberg, XY or Ising 1 2 3J J J− −
interactions have been extensively studied theoretically,
particularly for the = 1/ 2s quantum case.
In the 2 4SrLn O family, however, the cause of frustra-
tion is different; it arises from the triangular (or “zigzag”)
ladders running along the c axis which link the honeycomb
layers. In this respect 2 4SrLn O compounds are similar to
recently reported 2 4-CaCr Oβ [5] and perhaps to 4 8LnV O
compounds [6]. The term “zigzag” has also been used to
describe the spin-chain structure of another honeycomb
lattice compound 2 3Na IrO [7,8], but in a different context —
to describe the arrangement of magnetic moments formed
there.
The orthorhombic unit cell of the 2 4SrLn O compounds
contains 4 Sr atoms on a single site, 8 Ln atoms (split equal-
ly between two sites) and 16 oxygen atoms occupying 4
sites; all sites are of the 4c type with the coordinates
( , ,1 / 4)x y [4]. The a and b axes of the unit cell are typically
quite long, about 10 and 12 Å respectively, while the c axis
is the shortest, at around 3.4 Å on average. The magnetic Ln
atoms are surrounded by the distorted oxygen octahedra,
forming the chains running along the c-axis. The shortest
Ln–Ln separation is along the chains; there is a slightly
larger separation between the chains formed by the Ln at-
oms occupying the same sites (which are shown in Fig. 1 in
the same color), while the distance between Ln atoms from
different sites (red and green in Fig. 1) is much greater [4].
Such a crystal structure predetermines the quasi one-
dimensional magnetic properties of the 2 4SrLn O com-
pounds, as for rare-earth ions in insulating materials direct
exchange is often the most important mechanism for mag-
netic coupling. It is rather useful to note the equivalence of
the well-studied linear chain model with nearest and next-
nearest interactions [9] and the ladders of rare-earth ions
described here if these were “stretched” along the c axis.
An important observation to make prior to the descrip-
tion of their properties is that both polycrystalline and sin-
gle crystal samples of the 2 4SrLn O compounds have been
used for investigations. The progress achieved to date in
the understanding of their complex behavior is, however,
largely due to the availability of high quality single crys-
tals. Crystals of magnetic 2 4SrLn O oxides and their non-
magnetic analogues (with Ln = Lu or Y) have been syn-
thesized by the floating zone technique by our group and
others [10–12]. Examples of the single crystals grown [10]
are shown in Fig. 2; the size of the crystals available is
certainly sufficient for neutron scattering experiments, in-
cluding inelastic studies. In comparison, the magnetic
properties of structurally similar 2 4BaLn O (Ref. 13),
2 4EuLn O (Refs. 14,15) and 2 4BaLn S (Ref. 16) com-
pounds have not yet been probed to a significant degree, as
only polycrystalline samples are available.
2. Zero field magnetic properties of SrEr2O4, SrHo2O4
and SrDy2O4
2.1. SrEr2O4
2 4SrEr O is found to order magnetically at = 0.75NT K
with a = 0k antiferromagnetic (AFM) structure (depicted
in Fig. 3) consisting of ferromagnetic chains running along
the c axis, with adjacent chains arranged antiferromag-
netically [17]. The refinement of the powder neutron dif-
fraction (PND) data suggested that the moments point
along the c direction and that only one of the two 3Er +
sites possesses a sizeable magnetic moment. It was not
possible to determine which particular site contributed to
the ordering, as the magnetic moments may be swapped
between the two sites without changing the calculated
PND pattern significantly [17].
bb
c
aa
Fig. 1. (Color online) Positions of the magnetic rare-earth 3Ln +
ions within the 2 4SrLn O compounds, with the two
crystallographically inequivalent 3Ln + sites shown in different
colors. The left-hand panel emphasizes the honeycomb arrange-
ment of the 3Ln + ions when viewed along the c axis, while the
right-hand panel demonstrates the formation of zigzag ladders
running along the c axis which link the honeycomb layers and
give rise to geometric frustration. The blue box represents a crys-
tal unit cell of the Pnam space group.
Fig. 2. (Color online) As grown boules of 2 4SrHo O (left panel)
and 2 4SrDy O (right panel) single crystals, using growth speeds
of 6 to 8 mm/h. Figure is from Ref. 10.
140 Low Temperature Physics/Fizika Nizkikh Temperatur, 2014, v. 40, No. 2
Low-temperature magnetism in the honeycomb systems SrLn2O4
The situation with the low-temperature magnetic struc-
ture of 2 4SrEr O became much clearer after the publication
of single crystal polarized neutron diffraction results [18],
which are summarized in Fig. 4. The presence of a magnet-
ic component with long-range order (LRO) below 0.75 K
was confirmed by the observation of sharp resolution-
limited Bragg peaks at integer ( )hkl positions (see
Fig. 4(a)). These peaks are replaced by broad and much
weaker diffuse scattering features above NT (see Fig. 4(b)).
Surprisingly, another distinct magnetic component corre-
sponding to a short-range incommensurate structure was
also detected. This component manifests itself by the pres-
ence of a strong diffuse signal, forming the undulated
planes of scattering, which are seen as “rods” in a particu-
lar scattering plane. Fig. 4(c), for example, clearly shows
the two rods are at positions (0, ,1/ 2 )k + δ and
(0, ,3 / 2 )k − δ , where δ is dependent upon k. A Monte Car-
lo simulation [18] showed that a simple model based on a
ladder of triangles in which the nearest-neighbor interac-
tions are approximately five times stronger than the next-
nearest-neighbor interactions satisfactorily mimics the ob-
served diffuse scattering patterns.
Fig. 3. (Color online) Magnetic structure of 2 4SrEr O as deter-
mined from Rietveld refinements of the neutron-diffraction pat-
tern at = 0.55T K. The same structure is shown twice to empha-
sise different arrangements of the magnetic moments along the c
axis and with respect to the hexagons in the orthogonal plane.
Two different Er sites and their surroundings are shown in differ-
ent colors. Only one of the sites carries a significant magnetic
moment. Figure is from Ref. 17.
a
b
c
c
Fig. 4. (Color online) Reciprocal space intensity maps of the magnetic scattering from 2 4SrEr O in the ( 0)hk plane (top panels) and
in the (0 )kl plane (bottom panels) at 0.06 K (left panels) and 0.8 K (right panels). The highlighted area 1.3 < < 1.3h− , 0.7 < < 5.3k
in panel (a) has 10 times lower intensity scale to emphasize the presence at the lowest temperature of a weak diffuse scattering other-
wise obscured by the much more intense Bragg peaks. The magnetic scattering is isolated from the nuclear and spin-incoherent contri-
bution by full XYZ polarization analysis using D7 diffractometer for the ( 0)hk plane. In the case of maps of the (0 )kl plane, the intensi-
ty shown is obtained by removing the nuclear contribution from the non-spin-flip measurement with neutrons polarized orthogonal to
the scattering plane, following Ref. 21. Figure is from Ref. 18.
0.06 K 0.80 K
(a)
6
5
4
3
2
1
0
–1
(0
0)k
(b)
1.0
1.0
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0
0
–1
–1
–1
–1
0
0
0
0
1
1
1
1
2
2
2
2
3
3
3
3
4
4
4
4
5
5 6
5
5 6
( 00)h ( 00)h
1.5
1.0
0.5
0
(0
01
)
(с) ( )d
(0 0)k (0 0)k
Low Temperature Physics/Fizika Nizkikh Temperatur, 2014, v. 40, No. 2 141
O.A. Petrenko
From the width of the diffuse “rods” at the base tem-
perature, the estimates for correlation length along the c
axis vary from 130 to 70 Å depending on which “rod” is
considered [18], but in any event the AFM correlations are
rather long and include more than 20 magnetic ions. The
interpretation of these data is that apart from the = 0k
(LRO component shown in Fig. 3) the magnetic structure
of 2 4SrEr O consists of highly correlated AFM chains run-
ning along the c axis, but the correlations between the
chains are rather weak.
On warming from the base temperature of a dilution
cryostat to much higher temperatures, the partially ordered
component does not undergo a pronounced phase transition
unlike the = 0k component. Instead it gradually loses the
intensity, but it could be easily seen at 0.8 K (see Fig. 4(d))
and in fact much higher temperatures (not shown).
From the polarization analysis [18], the magnetic mo-
ments in the long-range commensurate and short-range
incommensurate structures are found to be predominantly
pointing along the c and a axes, respectively.
2.2. SrHo2O4
At a first glance, a refinement of the low-temperature
magnetic structure of 2 4SrHo O looks very similar to
2 4SrEr O . The PND data [19] returned a collinear AFM
= 0k component, very similar to the one shown in Fig. 3,
below the ordering temperature of 0.68 K, with only a half
of the 3Ho + ions carrying a significant moment. The pres-
ence of another magnetic component was also observed as
a pronounced scattering around the (0,0,1/ 2) positions.
Further single crystal diffraction data [20], however, re-
vealed a more complicated picture.
The observed broad diffraction peaks show that the
= 0k component (corresponding to a collinear antifer-
romagnetically coupled structure) is of short-range order
type. The planes of diffuse scattering corresponding to
another kind of magnetic order appear to be nearly perfect-
ly commensurate, i.e., the parameter δ is almost zero for
them, although the variations of the intensity have been
seen in both the ( 0 )h l and (0 )kl planes in reciprocal space.
This observation suggests that the second type of short-
range order present in 2 4SrHo O is principally one-dimen-
sional in nature, that is the magnetic structure is essentially
a collection of AFM coupled chains running along the c axis
with the intrachain correlations remaining rather weak
down to lowest temperatures. Similarly to what have been
observed in 2 4SrEr O , a magnetic component with the
propagation vector = 0k exists below a well-defined tran-
sition temperature, while the one-dimensional scattering is
observed at much higher temperatures.
Correlation lengths associated with the broad peaks are
about 150 Å in the ab plane and about 190 Å along the c
axis, while the correlation length associated with the dif-
fuse scattering planes is 230 Å along the c axis at the low-
est temperature. From the polarization analysis [20], the
magnetic moments in the = 0k and quasi one-dimensional
structures are found to be pointing along the c and b axes,
respectively.
2.3. SrDy2O4
In contrast to the other members of the 2 4SrLn O family
investigated so far, 2 4SrDy O does not show any sign of
magnetic phase transition down to the lowest available
temperatures. In zero field, heat capacity ( )C T measure-
ments indicate that this compound appears to be magneti-
cally disordered down to at least 0.39 K (see Fig. 5). The
( ) /C T T curve shows a very broad maximum at 0.77 K
and a nearly linear temperature dependence below this
peak. There are no sharp features in the heat capacity curve
which can be attributed to a phase transition to a magneti-
cally ordered state. PND data for 2 4SrDy O show no signs
of any long-range magnetic order down to 20 mK, as the
scattering pattern in zero field is dominated by broad dif-
fuse scattering peaks [24].
The magnetic entropy recovered in 2 4SrDy O between
zero temperature and = 5 KT (see inset in Fig. 5) amounts
to 2 ln 2R , which suggests that at the lowest temperature
the system is essentially a doublet with the magnetic mo-
ments restricted to point only along the easy axis (Ising)
direction.
3. Field-induced behavior of SrEr2O4, SrHo2O4 and
SrDy2O4
The higher-temperature magnetization curves for the
polycrystalline samples of these compounds have been
reported by Karunadasa et al. [4] and revealed non-linear
behavior of magnetization in field with pronounced maxi-
Fig. 5. (Color online) Temperature dependence of the specific heat
divided by temperature of 2 4SrDy O in zero field. The inset shows
the temperature dependence of the entropy, S (solid line), calculat-
ed as the area under the ( ) /C T T curve which has been extended
linearly down to = 0 KT . The dashed line indicates the position of
2 ln 2R , which corresponds to the magnetic contribution for
a system with an effective = 1 / 2s . Figure is from Ref. 22.
0 1 2 3 4 5
2
4
6
8
0 1 2 3 4 5
5
10
Temperature, K
Temperature, K
2 ln 2R
C
T/
, J
/(m
ol
·K
)2
S,
J/
(m
ol
·K
)
142 Low Temperature Physics/Fizika Nizkikh Temperatur, 2014, v. 40, No. 2
Low-temperature magnetism in the honeycomb systems SrLn2O4
ma in the derivatives, /dM dH as a function of applied
field. Further single crystal magnetization [23] and heat
capacity [22] measurements, however, revealed highly
anisotropic behavior, which is partially masked in the pol-
ycrystalline samples. We therefore summarize in this sec-
tion the results obtained on single crystal samples.
Magnetization versus field curves ( )M H and their field
derivatives /dM dH obtained for 2 4SrHo O for a field ap-
plied along the principal symmetry axes are shown in
Fig. 6. For H a (which is a hard magnetization direc-
tion), ( )M H remains rather small in any field. For other
two directions of an applied field, a significant portion of
the total magnetic moment is recovered, although no com-
plete saturation of magnetization is observed, as the /dM dH
values remain nonzero even in a field of 70 kOe [23]. This
implies that the spins of the 3Ho + ions are not fully aligned
at this field. For H b the magnetization process is char-
acterized by a double phase transition (seeing most clearly
as two maxima in the /dM dH curves in the bottom-left
panel of Fig. 6) indicative of the appearance of magnetiza-
tion plateau. Although the plateau is not well-pronounced,
i.e. the derivative /dM dH remains positive and relatively
large between the maxima, one has to remember that the
temperature for these measurements was relatively high,
0.5 K. For = 2.0 KT (see right-hand panels in Fig. 6),
the plateau in the magnetization disappears. Therefore, it is
likely that at the temperatures approaching 0 K the plateau
will be much more obvious. The value of the magnetization
on the plateau is about a third of the value observed in high-
er field. This fact allowes to conjecture [23] that the mag-
netic structure on the plateau is of collinear up-up-down
type, where on each triangle the two moments are pointing
along the applied field and the third moment is antiparallel
to them.
For H c the magnetization process in 2 4SrHo O is
characterized by a single, relatively sharp phase transition,
above which the magnetization remains practically con-
stant. For = 2.0 KT (see right-hand panels in Fig. 6), the
plateau in the magnetization disappears, the maximum in
/dM dH for H c broadens and shifts to slightly higher
fields, while the ( )M H curve for H a remains un-
changed.
In 2 4SrEr O and 2 4SrDy O the field dependence of the
magnetization looks rather similar to what have been ob-
served in 2 4SrHo O , but the directions of applied field
along which the plateau and sharp single phase transitions
appear (as well as the actual values of critical fields) are
different. In all three compounds a single and relatively
sharp increase in magnetization is seen for H c , a di-
rection along which the magnetic moments are pointing
Fig. 6. (Color online) Field-dependent magnetization curves (top panels) for 2 4SrHo O obtained at 0.5 K (left) and 2.0 K (right)
in the range of fields 0 to 40 kOe. (Bottom panels) The field derivatives of the magnetization at 0.5 K (left) and 2.0 K (right). Figure is
from Ref. 23.
0
1
2
3
4
5
6
7
0 0 55 1010 1515 2020 2525 3030 3535 40
SrHo O 2 4 SrHo O 2 4
0.6
0.2
0.4
dM
dH/
,µ
/(H
o
·k
O
e)
B
3+
M
, µ
/H
o
B
3+
T = 2.0 KT = 0.5 K
|| H a
|| H b
|| H c
H, kOeH, kOe
Low Temperature Physics/Fizika Nizkikh Temperatur, 2014, v. 40, No. 2 143
O.A. Petrenko
in the = 0k structures of 2 4SrEr O and 2 4SrHo O . In 2 4SrEr O
the application of field along the a axis results in a magnet-
ization plateau, while the b axis seems to be a hard mag-
netization direction. In 2 4SrDy O a magnetization plateau
appears for H b , while the a axis seems to be a hard
magnetization direction.
The fact that in all three compounds the observed plat-
eaux in magnetization appear at approximately a third of
the magnetization saturation values suggests that for the
field applied along either the a or b axes the contribution
from the = 0k structures remains rather weak, that is, the
magnetic moments in these structures remain pointing
along the c axis.
Further insight into the field-induced properties of
2 4SrDy O can be gained from the heat capacity measure-
ments [22]. Figure 7 (where the value of the heat capacity
divided by temperature is represented by the color scale
shown on the right of the figure) shows a magnetic phase
diagram of 2 4SrDy O obtained by combining the heat ca-
pacity field-scans for H b . At the lowest experimentally
available temperature of 0.39 K, a sharp double peak at
about 20 kOe is the main feature in the ( )C H curve. The
peaks indicate multiple magnetic field-induced transitions
in 2 4SrDy O for this direction of an applied field, but from
the bulk-property measurements alone it is impossible to
determine whether any of the field-induced phases are
long-range in nature. Therefore further neutron diffraction
experiments are required to answer this question. Remark-
ably for H c the application of a magnetic field does not
result in any features in the ( )C H curves sharp enough to
be indicative of a phase transition [22] which emphasizes
once again the highly anisotropic nature of the magnetiza-
tion process in the 2 4SrLn O compounds.
4. Further considerations
4.1. Other SrLn2O4 compounds
Apart from 2 4SrEr O , 2 4SrHo O and 2 4SrDy O reviewed
above, the only other family-member for which the low-
temperature properties have been reported is 2 4SrYb O .
Heat capacity measurements [12] revealed a magnetic
phase transition to LRO at = 0. K92NT . Neutron diffrac-
tion measurements [12] (see Fig. 8(a)) showed that the
structure is a noncollinear = 0k antiferromagnet in which
the magnetic moments of two inequivalent 3Yb + ions lie in
the ab plane, but have different moment sizes and direc-
tions. Both moments are reduced from the fully ordered
moment of 3Yb + (see Figs. 8(b) and 8(c)). Similarly to
what has been observed for other 2 4SrLn O compounds, the
application of a relatively strong field, 140 kOe, along any
direction does not result in a recovery of a full moment
expected for the 3Yb + ions [12].
Very interesting and highly anisotropic magnetic phase
diagrams (see Fig. 9) have been reconstructed for 2 4SrYb O
from the magnetocaloric and the magnetization measure-
ments [12]. A large number of transitions and crossovers
were found which has been taken as an indication of the
presence of various phases due to spin-flip and spin-flop
processes as well as possible competition between ex-
change interactions and magnetic anisotropy, however, the
exact nature of the field-induced phases in 2 4SrYb O re-
mains presently unknown.
Fig. 7. (Color online) Magnetic H T− phase diagram of
2 4SrDy O for [010]H obtained from the heat capacity meas-
urements. Color represents the heat capacity divided by tempera-
ture in the units of J/(mol·K2). Figure is from Ref. 22.
0 1 2 3 4
10
20
30
40
50
Temperature, K
Fi
el
d,
k
O
e
0.50
2.5
4.5
6.5
8.5
9.5C T T H ||( )/ – [010]
Fig. 8. (Color online) (a) Magnetic powder pattern of 2 4SrYb O
collected on D7 at 30 mK. The magnetic structure where the ar-
rows represent the 3Yb + ions spins (Yb1 blue, Yb2 red) (b)
along the zigzag chains and (c) projected onto the ab plane. The
2Sr + and 2O − ions are represented by yellow and red circles,
respectively. Figure is from Ref. 12.
(a)
(0
20
)
(1
20
) (2
00
)
(2
20
)
(1
30
)
(0
01
) (3
00
)
(1
00
) (1
10
)
(0
10
) (2
10
)
b
a
c
(b) ( ) с
c
Yb2 Yb1
Ja
Jb
0
J1-2
J1-1
J1-2 J1-1
J2-2 J2-1
Jb Jb
Jb
b
144 Low Temperature Physics/Fizika Nizkikh Temperatur, 2014, v. 40, No. 2
Low-temperature magnetism in the honeycomb systems SrLn2O4
We have recently started investigations of the magnetic
properties of 2 4SrGd O and from the heat capacity meas-
urements have found [25] that the compound undergoes
two magnetic transitions at 2.72 and 0.47 K. The initial
characterization of 2 4SrGd O by Karunadasa et al. [4]
missed the higher temperature transition. Since 3Gd + is
expected to be nearly isotropic, it is quite surprising that
the transition temperature of 2 4SrGd O is much higher than
that of the other members of the family. The higher order-
ing temperature of 2 4SrGd O is, however, consistent with
the properties of structurally similar 2 4BaLn O family, in
which 2 4BaGd O orders at 2.6 K, while the rest of the
compounds do not order down to at least 1.7 K [13]. In the
absence of neutron diffraction data the magnetic structure
of 2 4SrGd O remains unknown at present. The only other
established fact about low-temperature properties of
2 4SrGd O is that it undergoes a field-induced transfor-
mation at 20.5 kOe (for = 0.48 KT ) in a field applied
along the c axis [25].
It would certainly be interesting to expand the 2 4SrLn O
family and to test the magnetic properties of Tm, Tb, Sm,
Nd containing compounds provided that single crystal
samples can be prepared.
4.2. Crystalline electric field effects
From the findings presented above for the 2 4SrLn O
compounds, which vary greatly from one Ln ion to anoth-
er, it is rather obvious that the low-lying crystalline electric
field (CEF) levels must play an important role in the for-
mation of the highly anisotropic magnetic properties. At
present the CEF schemes remain unknown and the task of
establishing them may not be trivial: there are 8 Ln ions on
two district crystallographic sites in the unit cell. The sym-
metry is rather low, therefore the number of CEF levels is
expected to be large. Also, the positions of the levels at
lower temperature can potentially be influenced by the de-
velopment of short-range magnetic order. Inelastic neutron
scattering (INS) data for 2 4SrDy O and 2 4SrHo O have
been collected back in 2005 by Kenzelman et al. [26]. The
more recent INS results reported for 2 4SrHo O by Ghosh
et al. [11] are largely in agreement with the previous data.
We have also collected further INS data for 2 4SrEr O [27],
but to date neither group have reported any CEF schemes.
Moreover, there are further indications [28] that the prob-
lem could prove to be difficult to solve. An additional mo-
tivation for preparing this review was to alert the frustrated
magnetism community to the presence of such a challeng-
ing, but potentially very important problem.
5. Summary
We conclude this review by listing in Table 1 the most
important magnetic parameters of the 2 4SrLn O com-
pounds, such as Weiss temperature WΘ , effective moment
effp in Bohr magnetons Bµ , magnetic ordering tempera-
ture NT as well as indicating the nature of the zero field
ground state and the presence of critical fields cH for dif-
ferent directions of an applied field.
Important pieces of information missing from Table 1
include the values of the various exchange interactions and
details on the magnetic anisotropy in the 2 4SrLn O com-
pounds. This information which is typically obtained from
inelastic neutron scattering experiments is so far unavaila-
ble. Only after establishing the absolute values (including
signs) and relative strengths of the relevant exchange inter-
actions, as well as details of the magnetic anisotropy, could
one classify the 2 4SrLn O compounds as a collection of
weakly interacting chains of magnetic moments, or as a
network of ladders consisting of triangles. Apart from neu-
tron scattering, further Monte Carlo simulations, both di-
rect and reverse, as well as density-functional theory band-
structure calculations may play an important role in deter-
mining the magnetic interactions.
In 2 4SrEr O the LRO = 0k AFM phase (see Fig. 3) in
which the magnetic moments point along the c axis ap-
pears below 0.75 K while in 2 4SrHo O a very similar phase
appearing below 0.68 K remains short-range ordered down
at least 50 mK. Apart from this phase, a SRO quasi one-
dimensional AFM component is found in both compounds,
Fig. 9. (Color online) Magnetic phase diagram of 2 4SrYb O with
magnetic field along a (a), b (b), and c (c) axes. The colors indi-
cate the heat capacity in units of J/K. The circles indicate the
critical fields extracted from magnetocaloric effect measurements
and the triangles the critical fields extracted from magnetization
measurements. Black solid lines show second-order phase transi-
tions. Dash-dot black lines indicate the transition from the AFM
phase to a less ordered one. Dashed black lines show metamag-
netic crossovers. For the phase diagram along the c axis, above
4.5 T there are just three heat capacity scans at 6, 9, and 12 T,
the colors between them result from the interpolation of the data.
Below 4.5 T, the data were collected every 0.2 T. The tempera-
ture axis is in logarithmic scale. Figure is from Ref. 12.
(a) (b) B|| a
AFM
Short range order
Temperature, K
Temperature, K
Temperature, K
12
10
8
6
4
2
0
4
3
2
1
0
12
10
8
6
4
2
0
0.3 0.5 0.7 0.9 1.1
0.5 0.6 1.0 2.0 4.0 10
0.01
0.008
0.006
0.004
0.002
0
M
ag
ne
tic
fi
el
d,
T
M
ag
ne
tic
fi
el
d,
T
M
ag
ne
tic
fi
el
d,
T
5
0.4 0.6 0.8 1.0
(c)
C
p,
J/
K
B|| b
B|| c
Low Temperature Physics/Fizika Nizkikh Temperatur, 2014, v. 40, No. 2 145
O.A. Petrenko
but the direction along which the spins are pointing is dif-
ferent — it is parallel to the a axis in 2 4SrEr O and parallel
to the b axis in 2 4SrHo O . In 2 4SrEr O the diffuse scattering
signal corresponding to the quasi 1D component appears to
be much more structured compared to the 2 4SrHo O , which
could be indicative of the importance of further neighbor
exchange interactions. In 2 4SrYb O the magnetic moments
are confined to the ab plane (see Figs. 8(b) and 8(c)), with
the two different 3Yb + sites having very different moment
sizes and directions [12]. No long-range magnetic order
has been found in 2 4SrDy O down to 20 mK. Despite hav-
ing the weakest magnetic interactions (as demonstrated by
the lowest Weiss temperature) 2 4SrGd O orders at the
highest temperature of 2.72 K and undergoes another tran-
sition at 0.47 K. This observation suggests an immense
importance of the magnetic anisotropy in establishing the
ground state of the 2 4SrLn O compounds and the potential
competition between the exchange interactions and the
single-ion effects.
For all the 2 4SrLn O compounds the application of an
external magnetic field results in the appearance of com-
plex and highly anisotropic phase diagrams revealing mul-
tiple phase transitions, magnetization plateau and cross-
over regions. The magnetic structure of the field-induced
phases remains presently unknown.
We hope that this review will stimulate further research
on the magnetic properties of the 2 4SrLn O and related
honeycomb lattice compounds.
Acknowledgements
The author is very grateful to G. Balakrishnan,
M.R. Lees, D.McK. Paul, N.R. Wilson, T.J. Hayes,
O. Young, T.H. Cheffings, P. Manuel, D.D. Khalyavin,
D.T. Adroja, F. Demmel, B.D. Rainford, A.R. Wildes,
B. Ouladdiaf, L.C. Chapon, S. de Brion, E. Suard, C. Ritter,
P.P. Deen, R.J. Mason, A.K.R. Briffa, M.W. Long,
J. Mercer, M.L. Plumer, A. Desilets-Benoit, A.D. Bianchi,
and D.L. Quintero-Castro for the collaborations on the
projects involving the magnetic properties of the 2 4SrLn O
compounds.
References
1. A.P. Ramirez, Annu. Rev. Mater. Sci. 24, 453 (1994); M.F.
Collins and O.A. Petrenko, Can. J. Phys. 75, 605 (1997);
S.T. Bramwell and M.J.P. Gingras, Science 294, 1495 (2001);
Frustrated Spin Systems, H.T. Diep (ed.), World Scientific,
Singapore (2005); J.S. Gardner, M.J.P. Gingras, and J.E.
Greedan, Rev. Mod. Phys. 82, 53 (2010); Introduction to
Frustrated Magnetism, C. Lacroix, P. Mendels, and F. Mila
(eds.), Springer Series in Solid-State Sciences (2011), Vol. 164.
2. B.F. Decker and J.S. Kasper, Acta Crystallogr. 10, 332 (1957).
3. L.M. Lopato and A.E. Kushchevskii, Ukr. Khim. Zh. 39, 7
(1973).
4. H. Karunadasa, Q. Huang, B.G. Ueland, J.W. Lynn, P. Schif-
fer, K.A. Regan, and R.J. Cava, Phys. Rev. B 71, 144414
(2005).
5. F. Damay, C. Martin, V. Hardy, A. Maignan, G. Andre, K.
Knight, S.R. Giblin, and L.C. Chapon, Phys. Rev. B 81,
214405 (2010); F. Damay, C. Martin, V. Hardy, A. Maignan,
C. Stock, and S. Petit, Phys. Rev. B 84, 020402 (2011).
6. S. Das, A. Niaz, Y. Mudryk, V.K. Pecharsky, and D.C. John-
ston, Phys. Rev. B 81, 104432 (2010).
7. F. Ye, S. Chi, H. Cao, B.C. Chakoumakos, J.A. Fernandez-
Baca, R. Custelcean, T.F. Qi, O.B. Korneta, and G. Cao,
Phys. Rev. B 85, 180403 (2012).
8. J. Chaloupka, G. Jackeli, and G. Khaliullin, Phys. Rev. Lett.
110, 097204 (2013).
Table 1. Summary of the magnetic properties of the 2 4SrLn O compounds. WΘ is Weiss temperature and effp is an effective mag-
netic moment. Both parameters were determined from the higher-temperature susceptibility measurements. For the transitions fields cH
the corresponding measurement temperatures are indicated in the brackets
Ln WΘ , K effp , Bµ NT , K Magnetic structure (in zero field) cH , kOe
Er –13.5 [4] 9.176 [4] 0.75 [17]
= 0k LRO AFM (moments || c axis) [17]
&
quasi 1D SRO AFM (moments || a axis) [18]
||H c: 5.4 (0.5 K) [23]
H a : 2.0 & 12.5 (0.5 K) [23]
Ho –16.9 [4] 10.50 [4] 0.68 [19]
= 0k SRO AFM (moments || c axis)
&
quasi 1D SRO AFM (moments || b axis) [20]
H c : 4.0 (0.5 K) [23]
H b : 5.9 & 12.0 (0.5 K) [23]
Dy –22.9 [4] 10.35 [4] < 0.02 [22]
only SRO above 0.02 K [22] H b : 1.6 & 20.3 (0.5 K) [23], 20 (0.39 K) [22]
H c : 12.0 (0.5 K) [23]
Gd –9.0 [4] 8.02 [4] 0.47 & 2.72 [25] unknown H c : 20.5 (0.48 K) [25]
Yb –99.4 [4] 4.348 [4] 0.92 [12]
noncollinear = 0k AFM
with different moment sizes and directions [12]
H a : 45 (1.0 K) [12]
H b : 15 & 60 (0.6 K) [12]
H c : 11 & 45 (0.6 K) [12]
146 Low Temperature Physics/Fizika Nizkikh Temperatur, 2014, v. 40, No. 2
Low-temperature magnetism in the honeycomb systems SrLn2O4
9. A. Yoshimori, J. Phys. Soc. Jpn. 14, 807 (1959).
10. G. Balakrishnan, T.J. Hayes, O.A. Petrenko, and D. McK.
Paul, J. Phys.: Condens. Matter 21, 012202 (2009).
11. S. Ghosh, H.D. Zhou, L. Balicas, S. Hill, J.S. Gardner, Y. Qiu,
and C.R. Wiebe, J. Phys.: Condens. Matter 23, 164203 (2011).
12. D.L. Quintero-Castro, B. Lake, M. Reehuis, A. Niazi, H.
Ryll, A.T.M.N. Islam, T. Fennell, S.A.J. Kimber, B. Klemke,
J. Ollivier, V. Garcia Sakai, P.P. Deen, and H. Mutka, Phys.
Rev. B 86, 064203 (2012).
13. Y. Doi, W. Nakamori, and Y. Hinatsu, J. Phys.: Condens.
Matter 18, 333 (2006).
14. K. Hirose,Y. Doi, and Y. Hinatsu, J. Solid State Chem. 182,
1624 (2009).
15. O. Ofer, J. Sugiyama, J.H. Brewer, E.J. Ansaldo, M. Må nsson,
K.H. Chow, K. Kamazawa, Y. Doi, and Y. Hinatsu, Phys.
Rev. B 84, 054428 (2011).
16. Y. Misawa, Y. Doi, and Y. Hinatsu, J. Ceram. Soc. Jpn. 117,
85 (2009)
17. O.A. Petrenko, G. Balakrishnan, N.R. Wilson, S. de Brion,
E. Suard, and L.C. Chapon, Phys. Rev. B 78, 184410 (2008).
18. T.J. Hayes, G. Balakrishnan, P.P. Deen, P. Manuel, L.C. Cha-
pon, and O.A. Petrenko, Phys. Rev. B 84, 174435 (2011).
19. O. Young, L.C. Chapon, and O.A. Petrenko, J. Phys.: Conf.
Ser. 391, 012081 (2012).
20. O. Young, A.R. Wildes, P. Manuel, B. Ouladdiaf, D.D. Kha-
lyavin, G. Balakrishnan, and O.A. Petrenko, Phys. Rev. B 88,
024411 (2013).
21. J.R. Stewart, P.P. Deen, K.H. Andersen, H. Schober, J.-F. Bar-
themy, J.M. Hillier, A.P. Murani, T. Hayes, and B. Lindenau,
J. Appl. Crystallogr. 42, 69 (2009).
22. T.H. Cheffings, M.R. Lees, G. Balakrishnan and O.A. Pet-
renko, J. Phys.: Condens. Matter 25, 256001 (2013).
23. T.J. Hayes, O. Young, G. Balakrishnan, and O.A. Petrenko,
J. Phys. Soc. Jpn. 81, 024708 (2012).
24. O.A. Petrenko, L.C. Chapon, and T.J. Hayes, ILL Exp. Rep.
5-31-1695.
25. O. Young, G. Balakrishnan, and O.A. Petrenko, unpublished
(2013).
26. M. Kenzelmann and B. Rosendahl Hansen, ISIS Exp. Rep.
510364.
27. O.A. Petrenko, T.J. Hayes, and F. Demmel, ISIS Exp. Rep.
920327.
28. A. Desilets-Benoit, Thesis, Universite de Montreal (2010).
Low Temperature Physics/Fizika Nizkikh Temperatur, 2014, v. 40, No. 2 147
1. Introduction
2. Zero field magnetic properties of SrEr2O4, SrHo2O4 and SrDy2O4
2.1. SrEr2O4
2.2. SrHo2O4
2.3. SrDy2O4
3. Field-induced behavior of SrEr2O4, SrHo2O4 and SrDy2O4
4. Further considerations
4.1. Other SrLn2O4 compounds
4.2. Crystalline electric field effects
5. Summary
Acknowledgements
References
|