Magnetostructural transitions in a frustrated magnet at high fields.
ABSTRACT Ultrasound and magnetization studies of bond-frustrated ZnCr(2)S(4) spinel are performed in static magnetic fields up to 18 T and in pulsed fields up to 62 T. At temperatures below the antiferromagnetic transition at T(N1)≈14 K, the sound velocity as a function of the magnetic field reveals a sequence of steps followed by plateaus indicating a succession of crystallographic structures with constant stiffness. At the same time, the magnetization evolves continuously with a field up to full magnetic polarization without any plateaus in contrast to geometrically frustrated chromium oxide spinels. The observed high-field magnetostructural states are discussed within a H-T phase diagram taking into account the field and temperature evolution of three coexisting spin structures and subsequent lattice transformations induced by the magnetic field.
arXiv:1105.5220v1 [cond-mat.str-el] 26 May 2011
Magneto-structural transitions in a frustrated magnet at high fields
V. Tsurkan,1,2S. Zherlitsyn,3V. Felea,2,4S. Yasin,3Yu. Skourski,3J.
Deisenhofer,1H.-A. Krug von Nidda,1P. Lemmens,4J. Wosnitza,3and A. Loidl1
1Experimental Physics 5, Center for Electronic Correlations and Magnetism,
Institute of Physics, University of Augsburg, D 86159, Augsburg, Germany
2Institute of Applied Physics, Academy of Sciences of Moldova, MD 2028, Chisinau, R. Moldova
3Hochfeld-Magnetlabor Dresden (HLD), Helmholtz-Zentrum Dresden-Rossendorf, D-01314 Dresden, Germany
4Institute for Condensed Matter Physics, TU Braunschweig, D-38106 Braunschweig, Germany
(Dated: 24.05.2011 [Received: date / Revised version: date ])
Ultrasound and magnetization studies of bond-frustrated ZnCr2S4 spinel are performed in static
magnetic fields up to 18 T and in pulsed fields up to 62 T. At temperatures below the antiferromag-
netic transition at TN1 ≈ 14 K the sound velocity as function of magnetic field reveals a sequence
of steps followed by plateaus indicating a succession of crystallographic structures with constant
stiffness. At the same time, the magnetization evolves continuously with field up to full magnetic
polarization without any plateaus in contrast to geometrically frustrated chromium oxide spinels.
The observed high-field magneto-structural states are discussed within a H-T phase diagram taking
into account the field and temperature evolution of three coexisting spin structures and subsequent
lattice transformations induced by magnetic field.
PACS numbers: 43.35.+d, 62.65.+k, 72.55.+s, 75.50.Ee
Frustrated magnets with spinel structure AB2X4man-
ifest an intriguing behavior and unusual ground states,
such as composite spins , spin dimerization [2, 3],
heavy-fermion properties [4, 5], spin-orbital liquid ,
and orbital glass [7, 8] which originate from magnetic
frustration but also from the intimate interplay of spin,
charge and orbital degrees of freedom and their coupling
to the lattice. In the magnetic B-site Cr spinels with
strong spin-phonon coupling, a novel type of structural
transformation has been identified experimentally, the
so called spin Jahn-Teller effect [9–12]. In an octahe-
dral crystal field the t2g levels of the Cr3+ions are half
filled and the spin-orbit coupling is negligible. Therefore,
the conventional Jahn-Teller scenario related to magnetic
ions with an orbitally degenerate state is not applicable
here, and the structural deformation is believed to be
driven purely by spin ordering. The ground-state prop-
erties of frustrated magnets are characterized by a large
degeneracy and are highly susceptible to external pertur-
bations. An external magnetic field can change the bal-
ance between the competing interactions, and unusual
phenomena, such as magnetization plateaus at half or
fractional saturation are observed [13, 14].
In geometrically frustrated ACr2X4 oxide (X=O)
spinels the Cr ions forming a pyrochlore lattice of corner-
sharing tetrahedra are strongly coupled by direct anti-
ferromagnetic (AFM) interactions of the order of 100 -
400 K. Emerging phenomena in geometrically frustrated
oxides are dominated by local ”tetrahedron” physics
[15, 16]. In sulphide (X=S) and selenide (X=Se) spinels
the direct AFM exchange is reduced due to the increas-
ing distance between the magnetic ions and at the same
time 90oferromagnetic (FM) exchange becomes impor-
tant. Where FM and AFM exchanges are of comparable
strength, the ground state again is strongly frustrated, a
situation which has been named bond frustration .
In ZnCr2S4, subject of the present study, competing
FM and AFM interactions indeed are of equal strength
resulting in a Curie-Weiss temperature close to zero
.Neutron-diffraction measurements [18–20] estab-
lished two subsequent magnetic transitions in ZnCr2S4:
the first one to an incommensurate helical AFM order
at TN1≈ 14 K, and the second one, to coexisting com-
mensurate spin order at TN2≈ 7 K. The helical state is
characterized by a spin spiral with a propagation vector
k1 ≈ (0,0,0.787) along the crystallographic c direction
and with the spins rotating in the a-b plane. This is also
the ground-state structure of the bond-frustrated AFM
ZnCr2Se4 with increased FM exchange as compared to
ZnCr2S4 .At temperatures below TN2 the spiral
phase coexists with two additional collinear spin struc-
tures with propagation vectors k2 ≈ (0.5,0.5,0) and k3
≈ (1.0,0.5,0) . These collinear ordering wave vectors
resemble those of geometrically frustrated AFM ZnCr2O4
which exhibits composite spin structures of weakly inter-
acting self-organized spin clusters [1, 21]. The magnetic
ground state of ZnCr2S4can be regarded as a combina-
tion of spin orders known from geometrically frustrated
ZnCr2O4 and bond frustrated ZnCr2Se4. An external
field favors the parallel spin alignment and one can ex-
pect that the system passes through a sequence of exotic
states when frustration is released via strong magneto-
Several bulk properties of ZnCr2S4, such as specific
heat and thermal expansion exhibit significant anomalies
at the magnetic transitions. Also, a pronounced splitting
of the phonon modes in the IR reflectivity spectra below
the magnetic transitions was found clearly indicative for
broken symmetry . These anomalies suggest struc-
tural transformations due to a strong spin-phonon cou-
pling . Recent high-resolution synchrotron x-ray pow-
der diffraction measurements indeed revealed two subse-
quent structural transformations in ZnCr2S4from a cu-
bic Fd¯3m to a tetragonally distorted intermediate phase
(space group I41/amd) below TN1and a further transi-
tion into a low-temperature orthorhombic phase (space
group Imma) below TN2.
In this Letter, we report on ultrasound and magneti-
zation studies on ZnCr2S4 single crystals performed in
static (up to 18 T) and pulsed magnetic fields (up to
62 T). We explore the unique case of almost fully compen-
sated AFM and FM exchange interactions in the spinel
ZnCr2S4with strong spin-lattice coupling and several co-
existing magnetic structures with different spin arrange-
ment. We expected that strong spin-phonon coupling
leads to significant fingerprints in the temperature and
magnetic field dependence of sound waves. Ultrasound
techniques are known to be highly sensitive probes for
magneto-elastic interactions .
strated by L¨ uthi et al. that the magnetic phase tran-
sition in ZnCr2O4, recognized now as spin Jahn-Teller
effect, is accompanied by pronounced anomalies in the
temperature dependence of sound waves .
ZnCr2S4single crystals were grown by chemical trans-
port reactions. The magnetic susceptibility reveals a
sharp peak at TN1 = 13.8 K in good agreement with
published data . The measurements of the velocity
and attenuation of longitudinal waves with wave vector
k and polarization u parallel to the ?001? axis (corre-
sponding to c11acoustic mode for a cubic crystal) were
performed for temperatures between 1.5 and 300 K and
in static magnetic fields utilizing an experimental setup
similar to that in  with a phase-sensitive detection
technique based on a pulse-echo method. The measure-
ments in pulsed fields with a rise time of 35 ms and a
pulse duration of 150 ms were done in the range 1.5 –
In Fig. 1 the relative changes of the sound veloc-
ity and attenuation for different static magnetic fields
are presented as function of temperature. In zero field,
the sound velocity exhibits significant softening on de-
creasing temperature below 60 K and a well-defined
anomaly at TN1 = 13.8 K, in agreement with suscep-
tibility and thermal-expansion data . The sound at-
tenuation raises sharply approaching TN1 and exhibits
a well-defined peak. With increasing magnetic field the
magnitude of the anomalies in the sound velocity and
attenuation at TN1are reduced and shifted to lower tem-
peratures. We recall that at TN1the sample transforms
from the cubic paramagnetic state into the tetragonal he-
limagnetic phase . The softening of the sound velocity
probably results from strong spin fluctuations in the co-
operative paramagnetic state where the thermal energy is
lower than the leading frustrated magnetic exchange. In
It has been demon-
FIG. 1: (color online) Temperature dependencies of the rel-
ative change of the sound velocity ∆v/v0 (upper panel) and
sound attenuation ∆α (lower panel) for ZnCr2S4 measured in
different static magnetic fields. The vertical dashed lines mark
the magnetic phase transitions TN1 and TN2 in zero field. The
horizontal dashed line shows the extrapolated undisturbed
sound velocity estimated from a fit to the data above 60 K
(see text for details).
contrast, at TN2= 7.3 K where ZnCr2S4transforms into
the orthorhombic structure, only a smooth change of the
sound velocity is found, and a broad peak in the atten-
uation appears. According to  the collinear structure
evolves already at 12 K which could explain the observa-
tion of two peaks in the attenuation below TN1and of a
weak anomaly in the sound velocity at TN2. The anomaly
in the attenuation at 11 K shifts to lower temperatures
with increasing fields. Its magnitude first increases with
field up to 5 T but then decreases at higher fields.
Figure 2 documents the main results of the pulsed field
studies presenting the relative change of the sound veloc-
ity, ∆v/v0, attenuation, ∆α, and magnetization, M, as
function of applied field for different temperatures. We
notice rather significant changes of the sound velocity
with field of the order of 3-5% which prove the strong
magneto-elastic coupling in ZnCr2S4.
sound velocity shows a non-monotonous behavior with
field; ∆v/v0 first decreases and beyond 30 T increases
again with increasing fields. Both, the sound velocity
and the attenuation exhibit four prominent anomalies at
7, 27, 38, and 44 T suggesting changes in the spin state
and structural phase transitions. The anomalies (labeled
respectively from 4 to 1) are visible as minima or clear
changes of slope in the sound velocity, and as maxima
in the attenuation. The anomalies 1-3 (at 1.5 K) in the
At 1.5 K, the
FIG. 2: (color online) Relative change of the sound velocity, ∆v/v0 [(a) and (b)] and attenuation, ∆α [(d) and (e)] in ZnCr2S4
vs. magnetic field at 1.5 K, 10 K (left scale) and 6.8 K, 20 K (right scale). The vertical arrows mark the magneto-structural
anomalies labeled from 1 to 4. (c) Magnetization curves with field aligned along the ?001? axis and (f) derivatives of the
magnetization dM/dH for 1.5, 6.8, and 10 K. For clarity the curves are shifted along the vertical axis. Data for field sweep up
and down are shown.
sound velocity at fields above 27 T are free of hysteresis,
whereas anomaly 4 shows a marked hysteresis on increas-
ing and decreasing fields. Such hysteretic behavior indi-
cates first-order transformations induced by the magnetic
field. With increasing temperature all anomalies in the
sound velocity shift to lower fields. At 10 K, the sound
velocity develops into distinct plateaus with step-like fea-
tures at 16.5, 30, and 40 T. This signals abrupt changes of
the lattice stiffness, probably induced by structural phase
transitions, which are followed by plateaus with a given
structure and, therefore, constant stiffness [Fig. 2(b)]. At
the same time, between 7.5 and 40 T the changes of the
magnetization M with field are rather gradual [Fig. 2(c)]
and occur with two different slopes below and above 27 T
[Fig. 2(f)]. This indicates that the structural changes
are not accompanied by significant changes in the spin
structure. In Fig. 2(f) the field derivatives of the mag-
netization dM/dH for different temperatures are shown.
The sharp maximum in dM/dH at 44 T (at 1.5 K) corre-
lates well with the anomaly 1 in ∆v/v0and ∆α. Finally,
at 47 T the full saturated polarization is achieved with
the net ordered moment close to 6 µB. A well-defined
change of slope in M appears just before reaching full po-
larization. With increasing temperature, the maximum
in dM/dH is shifted to lower fields and broadens consid-
The magnetic-field dependence of the sound velocity
and attenuation below 15 T is dominated by dynamic
effects as revealed by measurements in static fields. A
comparison of ∆v/v0in pulsed and static fields shows a
general agreement. However, below 7 T the variations
of ∆v/v0in static fields are much smaller than in pulsed
fields which can be attributed to the relaxation dynamics
of domains reorientations that should be comparable to
the high sweep rate in pulsed fields.
The observed temperature and field evolution of the
anomalies in the sound characteristics detected both in
static and pulsed fields is summarized in a tentative
phase diagram in Fig. 3. We interpret it within the sce-
nario which considers the interplay of different magnetic
phases with structural transformations.
at T = 1.5 K (phase V), two commensurate collinear
(k2+k3) spin structures coexist with an incommensurate
helical (k1) spin structure and the crystal structure is or-
thorhombic . At fields above 7.5 T (phase IV), the
commensurate structure (k3) becomes suppressed but the
second commensurate structure (k2) survives and coex-
ists with the helical spin structure (k1). At the same time
the suppression of the splitting of the lowest phonon by
this field strength observed in the IR experiments [11, 17]
indicates the change of the lattice symmetry, from or-
thorhombic to tetragonal which identifies the origin of
the anomaly 4 in the ultrasound data.
In zero field
The transition from the phase IV into the phase III
can be traced by the anomaly in the attenuation (Fig. 1,
static data) and by the anomaly 3 in the pulsed-field
scans in Fig. 2. Above 7 K in the static fields this tran-
sition is clearly defined, whereas in the pulsed fields the
boundary between phases IV and III is much broader
probably due to relaxation effects. But we cannot ex-
clude an intermediate phase in between phases III and
IV for temperatures 7 K < T < 12 K. The phase III cor-
responds to a tetragonal phase with the Cr spins forming
a spiral, such as in ZnCr2Se4.
FIG. 3: (color online) H-T phase diagram of ZnCr2S4. Cir-
cles correspond to ultrasound data for pulsed fields, squares
for static fields; up triangles to magnetization data for pulsed
fields, down triangles for static fields.
up sweeps in field (temperature), closed symbols for down
sweeps.Anomalies 1-4 and different magneto-structural
phases I-V are described in the text.
Open symbols for
The best defined features in the sound velocity and in
the attenuation both in temperature and field dependen-
cies are reflected by anomaly 2. Its step-like shape is
only slightly affected by temperature indicating a well-
defined phase transformation. Since the magnetization
shows only a gradual change in this temperature and field
range, and taking into account neutron diffraction and
x-ray data [18–20] we associate the anomaly 2 with the
second structural transition from the tetragonal phase III
to the cubic phase II. It is also important to note that
the magnitude of the total change of ∆v/v0by magnetic
field is close to that expected for the full recovery of the
cubic state estimated from a fit to the experimental data
in the true paramagnetic state (above 60 K) shown by
the dashed line in Fig. 1, using an anharmonic approx-
imation according to Ref. 25. We suppose that at zero
temperature in fields close to 40 T the AFM spin spiral
arrangement becomes fully suppressed and the system
enters into a strongly polarized cubic paramagnetic state
because no additional phase boundary to the paramag-
netic phase above TN1 is evidenced in the ultrasound
data. The anomaly 1 in the ultrasound and magnetiza-
tion data probably has a purely magnetic origin. Finally,
phase I corresponds to a state with full polarization in-
duced by magnetic field.
In conclusion, ultrasound and magnetization studies in
magnetic fields up to 62 T of bond-frustrated ZnCr2S4
with strong magneto-elastic coupling revealed a sequence
of magneto-structural states. We evidenced novel effects,
namely, plateaus in the sound velocity on the way to-
wards the recovery of the lattice symmetry in the polar-
ized state which are ascribed to different crystallographic
phases with constant stiffness. In contrast to geometri-
cally frustrated antiferromagnets ACr2O4 (A= Zn, Cd,
Hg) which reveal magnetization plateaus accompanied
by lattice distortions [13, 14, 26–28], the magnetization
of bond-frustrated ZnCr2S4evolves continuously without
any anomalies up to full polarization. Our study provides
a new insight into the physics of bond-frustrated spinels
which is clearly distinct from that of the geometrically
frustrated oxides. The origin of the observed intriguing
effects, in particular, of the anomalies 1-3, as well as of
the coupling mechanism of different magnetic structures
to lattice strain which generates crystal structures of dif-
ferent symmetry is yet to be clarified and demands for
further experimental and theoretical studies.
This research has been supported by the DFG via TRR
80 (Augsburg - Munich) and FOR 960 (Quantum phase
transitions), LE 967/6-1 (Braunschweig) and by Euro-
MagNET II under the contract 228043.
 S.-H. Lee et al., Nature (London) 418, 856 (2002).
 P.G. Radaelli et al., Nature (London) 416, 155 (2002).
 M. Schmidt et al., Phys. Rev. Lett. 92, 056402 (2004).
 S. Kondo et al., Phys. Rev. Lett. 78, 3729 (1997).
 A. Krimmel et al., Phys. Rev. Lett. 82, 2919 (1999).
 V. Fritsch et al., Phys. Rev. Lett. 92, 116401 (2004).
 R. Fichtl et al., Phys. Rev. Lett. 94, 027601 (2005).
 V. Tsurkan et al., J. Phys. Chem. Solids 66, 2036 (2005).
 S.-H. Lee et al., Phys. Rev. Lett. 84, 3718 (2000).
 A.V. Sushkov et al., Phys. Rev. Lett. 94, 137202 (2005).
 J. Hemberger et al., Phys. Rev. Lett.97, 087204 (2006).
 J. Hemberger et al., Phys. Rev. Lett. 98, 147203 (2007).
 H. Ueda et al., Phys. Rev. Lett. 94, 47202 (2005).
 M. Matsuda et al., Nature Physics 3, 397 (2007).
 Y. Yamashita et al., Phys. Rev. Lett. 85, 4960 (2000).
 O. Tchernyshyov et al., Phys. Rev. Lett. 88, 067203
 T. Rudolf et al., New J. Phys. 9, 76 (2007).
 M. Hamedoun et al., J. Phys. C 19, 1783 (1986).
 M. Hamedoun et al., J. Phys. C 19, 1801 (1986).
 F. Yokaichiya et al., Phys. Rev. B 79, 064423 (2009).
 S. Ji et al., Phys. Rev. Lett. 103, 037201 (2009).
 B. L¨ uthi, Physical Acoustics in the Solid State, Springer,
 Y. Kino and B. L¨ uthi, Solid State Comm. 9, 805 (1971).
 B. Wolf et al., Physica B 294-295, 612 (2001).
 Y.P. Varshni, Phys. Rev. B 2, 3952 (1970).
 S. Zherlitsyn et al., J. Low Temp. Phys. 159, 134 (2010).
 E. Kojima et al., J. Low Temp. Phys. 159, 3 (2010).
 H. Mitamura et al., J. Phys. Soc. Jpn. 76, 085001 (2007).
 S. Bhattacharjee et al., Phys. Rev. B 83, 184421 (2011).