Spin-reorientation in YbFeO_3

Abstract

Precise measurements of YbFeO_3 magnetization in the spin-reoirentation temperature interval are performed. It is shown that ytterbium orthoferrite is well described by a recently developed modified mean field theory developed for ErFeO_3. This validates the conjecture about the essential influence of the rare earth ion's anisotropic paramagnetism on the magnetization behavior in the reorientation regions of all orthoferrites with Gamma{4} -> Gamma{24} -> Gamma{2} phase transitions.

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arXiv:cond-mat/0503060v1 [cond-mat.mtrl-sci] 2 Mar 2005
Spin-reorientation in YbFeO3
Ya. B. Bazaliy,1,2L. T. Tsymbal,2,3, ∗G. N. Kakazei,3,4V. I. Kamenev,2and P. E. Wigen3
1IBM Almaden Research Center, 650 Harry Rd., San Jose, CA 95120
2O.Galkin Donetsk Physics & Technology Institute,
National Academy of Science of Ukraine, R.Luxemburg St. 72, Donetsk, 83114 Ukraine
3Ohio State University, Department of Physics, 174 W. 18th Ave. Columbus, OH 43210
4Institute of Magnetism, National Academy of Science of Ukraine, 36-B Vernadskii Blvd., Kyiv, 03142 Ukraine
(Dated: February 2, 2008)
Precise measurements of YbFeO3 magnetization in the spin-reoirentation temperature interval
are performed. It is shown that ytterbium orthoferrite is well described by a recently developed
modified mean field theory developed for ErFeO3. This validates the conjecture about the essential
influence of the rare earth ion’s anisotropic paramagnetism on the magnetization behavior in the
reorientation regions of all orthoferrites with Γ4 → Γ24 → Γ2 phase transitions.
I.INTRODUCTION
Rhombic rare-earth orthoferrites RFeO3with R being
a rare-earth ion or an yttrium ion are magnetic insulators
that provide a classic example of the second order ori-
entation phase transitions. Orthoferrites have two mag-
netic subsystems: one of the rare-earth ions, and another
of the iron ions. Magnetic properties of the subsystems
and interaction between them depend on the external
parameters, e.g. temperature, field, pressure, etc., and a
series of phase transition is observed upon the parameter
change.
In the temperature interval where phase transitions
discussed in this work take place, the iron subsystem is
ordered into a slightly canted antiferromagnetic structure
exhibiting a weak ferromagnetic moment F. The rare-
earth system is paramagnetic. For all orthoferrites the
antiferromagnetic structure below the Neel temperature
TN (TN = 620 ÷ 740K) corresponds to the Γ4(Gx, Fz)
irreducible representation with magnetic vector F point-
ing along the c axis of the crystal and antiferromagnetic
vector G pointing along the a axis. The coordinates are
chosen so that c = ˆ z and a = ˆ x. In orthoferrites with
non-magnetic rare-earth ions (R = La, Lu, or Y) the
Γ4(Gx,Fz) configuration persists to the lowest tempera-
tures. For many other orthoferrites a reorientation tran-
sition with the sequence Γ4(Gx,Fz) → Γ24(Gxz,Fxz) →
Γ2(Gz,Fx) is observed. Upon cooling vector F starts to
rotate away from the c axis at temperature T1. Its con-
tinuous rotation towards the a axis happens in the (a,c)
plane between temperatures T1and T2< T1. Below T2,
the system stays in the Γ2(Gz,Fx) phase with F||a.
Although the spin reorientation region [T2,T1] has
been studied for many orthoferrites by different exper-
imental techniques, not enough is known about the
specifics of the rotation. Relevant experimental results
are often incomplete, lack accuracy, tend to contradict
each other, and do not correspond to either conven-
tional Landau theory1,2,3or its suggested modifications.
Recently4,5the temperature dependence of both a and
c axis projections of the magnetic moment was mea-
sured with high accuracy for the single crystal samples
of ErFeO3. These measurements gave the temperature
dependence of the absolute value of the magnetization
M(T) and its rotation angle θ(T) with respect to the c
axis in the [T2,T1] temperature interval at zero external
magnetic field. The results were in very good agreement
with the proposed modified mean field model,4that em-
phasized the anisotropy of the rare-earth ions paramag-
netic susceptibility. It was conjectured that this model
would be suitable for other magnetic materials with sim-
ilar phase transitions.
The present study is aimed at the detailed measure-
ments of M(T) and θ(T) behavior in single crystals of
YbFeO3, that exhibit the same Γ4 → Γ24 → Γ2 tran-
sition, with the purpose of checking this conjecture on
another material. It is shown that the modified field the-
ory of Refs. 4,5 works well for YbFeO3, even though in
this orthoferrite the reorientation happens at an order of
magnitude lower temperatures (T ≈ 8K), than in ErFeO3
(T ≈ 90K), while the Neel temperature remains roughly
the same TN≈ 630K.
II.EXPERIMENTAL RESULTS
Measurements were performed on two single crystals
of YbFeO3. Cubic sample A, weighting 0.0485 g, was
made of a single crystal grown by spontaneous crystal-
lization in the melt-solution. Ellipsoid sample B, weight-
ing 0.0715 g, was made of a single crystal grown by the
no-crucible zone melting technique with radiation heat-
ing. The results for both samples are very similar. The
temperature was varied in the 2 K to 10 K interval, and
both Ma and Mc projections of the magnetic moment
were measured by a Quantum Design MPMS-5S SQUID
magnetometer.
The M(T) dependence at zero external magnetic field
was found through the analysis of magnetization curves
analogous to those shown in Fig. 1,2. To analyze the data
we recall, that the (H−T) phase diagrams in the vicinity
of the Γ4→ Γ24→ Γ2transition for H||c and H||a field
directions are well known. According to them, as the
magnetic field is swept through H = 0 inside the [T2,T1]

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reorientation interval, a first order transition happens for
both directions of the field and manifests itself as a jump
of magnetization component parallel to the applied field.
First order transitions also happen above T1for H||c and
below T2for H||a orientations, while no transitions are
predicted below T2for H||c and above T1for H||a. In a
real experiment exact orientation of the field direction is
obviously impossible. A three-dimensional diagram valid
for the arbitrary field direction4,6shows that for a tilted
field a first order transition happens at any temperature
and a jump of at least one magnetic moment projection
should be observed. In the case of single-domain switch-
ing that would produce a rectangular hysteresis loop.
Well-developed rectangular loops were indeed observed
in experiments on ErFeO3 outside of the reorientation
interval.4Inside the [T2,T1] interval (T1≈ 88K and T2≈
97K for erbium orthoferrite) they transformed into the
S-shaped magnetization curves. Such modification was
attributed to the multi-domain state formation, possibly
connected to the abrupt change in domain wall mobility.7
In contrast with the case of ErFeO3, magnetization
curves in YbFeO3are S-shaped at all temperatures stud-
ied here for both H||a and H||c field orientations. The
width of the magnetization curves for the magnetic field
directed along the a axis is larger then for the field along
the c axis. In general, the total width of the loops is
considerably larger than in the case of ErFeO3.4In ac-
cord with the phase diagrams discussed above, magneti-
zation curves become straight lines passing through the
origin above T1 for the H||a orientation and below T2
for the H||c orientation. Their slope in these regions
corresponds to the paramagnetic contribution of the yt-
terbium ions (see Fig. 1,2). Importantly, magnetization
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FIG. 1:
YbFeO3, sample B, with H||a, at different temperatures.
Magnetization curves Ma(H) obtained on the
curves obtained for different samples are very similar.
We extract the a and c projections of the bulk magne-
tization at zero external field by extrapolating their ob-
served linear dependence at higher fields, H>
by Ma,c(H,T) = Ma,c(T) + χa,c(T)H and extracting
the vertical intercept Ma,c(T).
and Mc(T) obtained through this procedure are shown
in Fig. 3.
It is interesting to note, that while being very small
everywhere, the hysteresis of S-shaped loops visibly in-
creases in the reorientation region of YbFeO3. This fact
is illustrated by the following measurement. First, a sat-
urating magnetic field H = 650Oe was applied either
along the a- or along the c-axis. Then, the field was
reduced to zero and the projection of the remnant mag-
netic moment Mremnanton the same axis was measured.
Two series of measurements, one for Mremnant
other for Mremnant
a
were made. The results for the H||c
case are shown on Fig. 4. For S-shaped hysteresis loops
the remnant magnetic moment grows with the width of
the loop. The figure clearly demonstrates how the small
hysteresis observed in the high-temperature symmetric
phase T ≥ T1grows inside the reorientation region and
than drops to zero for T ≤ T2.
obtained for H||a. This property of hysteresis loops in
YbFeO3turns out to be useful for the determinations of
the critical temperatures T1,2: they are clearly marked
by the kinks of the curve on Fig. 4 and give T1= 8K and
T2= 6.6K.
The shape of the magnetization curves and the pres-
ence or absence of hysteretic behavior depends on the
quality of the samples, energy of the domain walls, etc.
The observed difference between erbium and ytterbium
∼650 Oe,
The values of Ma(T)
c
and an-
Similar results were
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FIG. 2:
YbFeO3, sample A, with H||c, at different temperatures.
Magnetization curves Mc(H) obtained on the

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FIG. 3: Magnetization projections Ma,c(T) obtained from the
magnetization curves: empty circles - Ma(T) for sample B,
empty triangles - Ma(T) for sample A, filled triangles - Mc(T)
for sample A.
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FIG. 4: Temperatue dependence of remnant magnetization
along the c-axis. Remnant magnetizations serves as a measure
for the width of the hysteresis loops. Increase of hysteresis in
reorientation region is clearly seen. The kinks of the curve
mark the transition temperatures T1,2
orthoferrites may result from the order of magnitude dif-
ference in the temperature of the reorientation transition.
This question requires a separate study beyond the scope
of the present paper.
The absolute value of magnetization M and rotation
angle θ were extracted from the experimental data ac-
cording to the expressions
M =
?
M2
a+ M2
c,θ = arctan
?Ma
Mc
?
and are shown in Fig. 5 and Fig. 6. Experimental results
presented in Fig. 3 and Fig. 5 show that as the tempera-
ture is lowered from TN to T1, the magnetization of the
crystal gradually grows. This reflects the build up of the
iron moment near TNand subsequent development of the
ytterbium moment along iron moment8at lower temper-
atures. In the narrow reorientation region [T2,T1] the
magnetization rapidly grows almost two-fold. Below T2
the magnetization continues to grow. This supports the
result of Ref. 9, suggesting that the ytterbium moment
remains parallel to the iron moment, and does not switch
to the antiparallel direction as stated in Ref. 8.
III. THEORETICAL ANALYSIS
Our experimental results can be explained by the mod-
ified mean field theory suggested in Refs. 4,5. As the
conventional Landau theory,1,2,3the modified theory as-
sumes that the magnetization of iron subsystem is sat-
urated at T<
∼T1,2≪ TN. The free energy of the iron
subsystem is taken in the form
F(θ,T) = F0(T) +Ku(T)
2
cos(2θ) + Kbcos(4θ) .(1)
With minimal assumptions about the temperature de-
pendence of phenomenological constants inside the reori-
entation region, namely constant Kb, and Ku(T) linearly
varying with temperature and going through zero inside
the reorientation interval, the minimization of the con-
ventional energy functional (1) gives1,2,3
tanθ =
?
1 + ξ
1 − ξ,
ξ(T) =(T1+ T2)/2 − T
(T1− T2)/2
(2)
Figs. 5, 6 show that experimental results neither support
the constancy of M(T), nor give a θ(T) dependence con-
sistent with Eq. (2)
According to the modified mean field model, paramag-
netic susceptibility of ytterbium subsystem should also
be taken into account to adequately describe the mag-
netic behavior of the orthoferrite. It is assumed, that in
the molecular field of iron the rare-earth ion acquires a
magnetic moment m = ˆ χYbF, while the absolute value
of the iron moment F remains constant.2,8,10,11Experi-
mentally measured magnetization is the sum of the iron
and rare-earth contributions M = F+m. The magnetic
susceptibility ˆ χYbof the rare-earth ions is assumed to be
anisotropic. This assumption naturally explains the large
change of M inside a narrow temperature interval, since
rotation of F leads to the change of m and thus changes
M as well.4The anisotropy of the rare-earth suscepti-
bility has been reported in the literature.2,8,10,11The key
point of Ref. 4 was the proper account of such anisotropy
in the calculation of the rotation angle and absolute value
of the magnetization, with the result:
tanθ = r
?
1 + ξ
1 − ξ,
r =Ma(T2)
Mc(T1)
(3)
M = Mc(T1)
?
r2(1 + ξ) + (1 − ξ)
2
. (4)
Since Ma(T2) and Mc(T1) are measurable magnetizations
of the sample at temperatures T2and T1respectively, the
value of r is known and expressions (3) and (4) have no
fitting parameters.
According to our measurements, the cubic sample A,
for which most of the measurements were done, had
T1= 8.0 K and T2= 6.6 K. Using the values of Ma(T2)
and Mc(T1) at these temperatures we find r = 1.78. The-
oretical curves given by Eqs. (3) and (4) are shown in

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FIG. 5: Absolute value of the magnetization M(T) calculated
from experimental data. Solid curve - theory Eq. (4)
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FIG. 6: Magnetization rotation angle θ(T) calculated from
experimental data in the reorientation region [T2,T1] at zero
external magnetic field. Solid curve - theory Eq. (3), dash
curve - conventional theory Eq. (2)
Figs. 5 and 6 by solid lines. A convincing correspondence
between the theory and experiment is evident.
Note, that the analysis of experimental data in terms
of the model introduced in Refs. 4,5 is only valid inside
the reorientation region. However, it is important that
inside the region of its validity such analysis is indepen-
dent of the driving mechanism of the transition, be it the
interactions in the iron subsystem, the R-Fe interactions,
the behavior of the rare-earth magnetic succeptibility, or
any other process. The approach of Refs. 4,5 only re-
quires the effective anisotropy constant Ku(T) to be a
linear function of temperature. Since precisely that be-
havior of Ku(T) was measured in Refs. 12,13, and Ref. 14
shows that such behavior follows from the microscopic
model of Ref. 15, the modified mean field theory4,5can
be applicable for a wide variety of orthoferrites.
IV.CONCLUSION
In this paper we report direct measurements of the
magnetization aboslute value |M|(T) and rotation angle
θ(T) during the Γ4→ Γ24→ Γ2spin-reorientation tran-
sition in YbFeO3single crystals. The results favor the im-
portance of strongly anisotropic rare-earth contribution
to the magnetization of the material. They give a con-
vincing argument if favor of the spin reorientation model
suggested in Ref. 4 and its applicability to Γ4 (Gx,Fz)
→ Γ24 (Gxz,Fxz) → Γ2 (Gz,Fx) orientation transitions
in different materials.
V.ACKNOWLEDGEMENTS
The work at O.Galkin Physics & Technology Institute
was partially supported by the State Fund for Fundamen-
tal Research of Ukraine, project F7/203-2004. Ya.B. was
supported by DARPA/ARO, Contract No. DAAD19-01-
C-006.
∗Electronic address: tsymbal@sova.fti.ac.donetsk.ua
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