Anisotropic magnetization and sign change of dynamic susceptibility in NaCoO single crystal
The DC and AC magnetic susceptibilities of NaCoO single
crystals were measured for the different crystal orientations of
(ab)- and (c)-axis. The DC-magnetic
susceptibility for (c)-direction exhibited the
antiferromagnetic transition at 22 K. The thermal hysteresis
between the zero-field-cooled (ZFC) and the field-cooled (FC)
magnetization below and the large frustration parameter
indicated the spin frustration along the -axis. For an applied
magnetic field in (ab)-plane, the DC magnetic
susceptibility exhibited the logarithmic divergent behavior at low
temperatures ( 6.8 K). This could be understood by the
impurity spin effect, dressed by the spin fluctuation. From the AC
magnetic susceptibility measurements, the real part of the
AC-susceptibility for (ab) exhibited the spin glass-like
behavior at low temperatures ( 4 K). Remarkably, for an
applied AC magnetic field with (c)-axis, the sign of the
AC magnetic susceptibility changed from a positive to a negative
value with increasing AC magnetic field frequency ( 3 kHz) at
low temperatures ( 7 K). We interpret the sign change of AC
magnetic susceptibility along the c-axis in terms of the
sudden sign reversal of the phase difference from in-phase to
out-of-phase response with an applied AC magnetic field in the
AC-susceptibility phase space.
Corresponding author: firstname.lastname@example.org (J.S.R.)
Request for materials should be addressed to: email@example.com (C.T.L.)
Since the discovery of superconductivity ( 4.5 K) in the hydrated compound of NaCoOHO ( 0.35, 1.3), much attention has been devoted to the Na cobaltate series compounds of NaCoO.Takada03 () Nonhydrated compounds of the Na cobaltate system NaCoO (0.3 1.0) exhibit various physical properties depending upon the Na nonstoichiometry, such as high thermoelectric power,Wang03 (); Lee06 () quantum criticality,Rivadulla06 () charge ordering,Foo04 (); Mukhamedshin04 () spin density wave,Bayrakci05 () magnetic polaron,Bernhard04 () etc. The variety of physical properties exhibited by this system may originate from the strong correlation among electron, spin, and orbital degrees of freedom. Since few years, intense investigations have been carried out on the magnetic ground state of NaCoO (0.75 0.85, P2 phase) compounds. In the neutron scattering experiments of NaCoO ( 0.75 and 0.85) compounds, ferromagnetic interaction was revealed within the CoO layers while antiferromagnetic (AF) ordering was observed perpendicular to the CoO layers (A-type AF).Helme05 (); Helme06 () Bulk antiferromagnetism was observed at the Néel temperature 19.8 K along the -axis in a NaCoO crystal with two-dimensional antiferromagnetic fluctuation near 30 K. In addition, from the susceptibility, specific heat, and muon spin rotation measurements, a spin density wave was observed, which is an indication of the two-dimensional spin state.Bayrakci04 (); Bayrakci05 ()
The two-dimensional characteristics of magnetic interaction and various magnetic and electronic ground states are mainly due to the layered structure of the CoO layer and the unconventional spin state of the Co ion in NaCoO. The crystal structure of the CoO sublattice is a triangular network of edge-sharing oxygen octahedra.Jorgensen03 () The magnetic ground state of NaCoO is very sensitive with respect to the Na nonstoichiometry. It may be affected by both the charge or the spin state of the Co ion and the crystal structure of the CoO sublattices. The detailed crystal structure variation of NaCoO is very complex with respect to Na concentration .Viciu06 () In particular, the NaCoO crystal is in the upper bound region of the phase type structure. It had the highest value of the Seebeck coefficient in addition to exhibiting the strong spin frustration behavior expected.Lee06 () Significant dynamical spin behavior is usually observed in a strong spin frustration system. Because the strong spin frustration was expected, the measurement of the dynamical spin property would be helpful in understanding the frustration behavior of the NaCoO compound.
Therefore, we measured the anisotropic DC and AC magnetic susceptibilities of a NaCoO single crystal in order to study the anisotropic behaviors of the static and dynamic spin response of the Co ion. From the measurement of the DC magnetic susceptibility, it was found that there existed a thermal hysteresis between the zero-field-cooled (ZFC) and the field-cooled (FC) magnetization at low temperatures ( 20 K), which implied an unstable magnetic background. On the other hand, an antiferromagnetic (AF) transition was observed at 22 K for along the (c) direction. Exotic behaviors of - logarithmic divergent DC magnetic susceptibility at low temperatures ( 7 K) and power law dependence (0.078) at high temperatures ( 100 K) - were also observed. In addition, from the measurement of the AC magnetic susceptibility, we observed an unconventional sign change from positive to negative of the dynamic spin susceptibility with respect to frequencies and temperatures. In this paper, we have discussed the unusual anisotropic magnetic state and AC frequency response of the dynamic magnetic susceptibility of the NaCoO crystal.
Ii Experimental Details
The single crystalline compound of NaCoO was grown by the traveling solvent floating zone method using an optical image furnace.Chen04 () The crystal was cleaved into a lamellar hexagonal shape. The chemical concentration of NaCoO was carefully analyzed by energy dispersive X-ray spectroscopy (EDX) and inductively coupled plasma-atomic emission spectroscopy (ICP-AES). The chemical distribution images by EDX confirmed that the chemical inhomogeneity of the Na ion was less than 2 at.%. The single crystalline property was determined by using the Laue back-scattering and X-ray diffraction techniques. Figure 1 shows well-aligned peaks on the -axis, perpendicular to the crystal plane; the major sharp (00l) peaks indicate the -phase NaCoO (P63/mmc). The -axis lattice parameter was determined to be 10.71 Å from the powder X-ray diffraction measurements. We found a minor impurity phase of NaCoO (R-3) of less than 2 at.%. The double phases of and NaCoO were not extrinsic impurity but intrinsic property in the Na range of 0.85 0.95.Lee06 () The minor phase (less than 2 at.%) of NaCoO might not affect the magnetic property because NaCoO is a nonmagnetic material. The temperature-dependent DC magnetization was measured by the magnetic property measurement system (Quantum Design, U.S.A.) in a temperature range of 2 K 300 K under fixed magnetic fields of 0.1, 1.0, 3.0, and 5.0 T. The frequency- and temperature-dependent AC magnetic susceptibilities were measured by the Physical Property Measurement System (Quantum Design, U.S.A.) with the AC magnetic susceptometer (ACMS) probe at low temperatures ( 20 K) and various frequencies of 0 Hz 10 kHz with the excitation magnetic field 10 Oe.
Iii Result and Discussion
iii.1 Static magnetic susceptibility
Figure 2 presents the temperature-dependent static magnetic susceptibility of NaCoO under a magnetic field of 1 T for different crystal orientations of (ab) and (c) in the temperature range of 2 K 300 K. The magnetic susceptibility for (c)-axis exhibits an antiferromagnetic (AF) transition at 22 K, which is comparable with that in the case of NaCoO ( 20 K).Lin07 () It follows the Curie-Weiss law from 300 K to 150 K as shown in the inset of Fig. 2 (red square, red line). From the Curie-Weiss fitting, the effective magnetic moment and Weiss temperature are estimated to be 0.91 /f.u. and 196.8 K, respectively. Under the assumption of a low spin state (LS), the magnetic moments of Co (3d, 1/2) and Co (3d, 0) are 1.732 and zero, respectively. If we consider only the Co low spin-state, the partial fraction of Co is 52 at.%, which is identical to the average valence of Co (3.52). The average Co valence, estimated by the effective magnetic moment, is a little higher than both the value (3.15) and the value determined by a redox titration.Maarit05 () From the wet chemical analysis of the Co valence for NaCoO, the Co valence was estimated to be 3.15. The Co valence higher than our estimation implies that the spin state of Co is not a low-spin state. The spin state transition of the Co ion is widely observed in the cobaltates, for example, perovskite cobaltates RACoO (R: rare earth and A: alkaline earth elements).Wang06 () In this system, the Co spin state is changed by the spin state transition from a low-spin (LS, , 0) to an intermediate-spin (IS, , 1) or high spin state (HS, , 2) with respect to temperatures. From the optical conductivity measurement of the NaCoO single crystal, the charge ordering of Co and Co was revealed in the CoO layers.Bernhard04 () The mixed valence of Co and Co in cobaltates easily invoke the spin state transition. The Co ion lowers the local symmetry of the Co ion, which induces the band splitting of the doublet and triplet states. If the energy gap between and orbitals is smaller than the Hund coupling, the intermediate- or high-spin states are favorable because electrons can be transferred from the highest level to the lowest level. The intermediate- or high-spin states of Co ions are not experimentally observed directly. A direct experimental observation of the spin state of Co in -NaCoO system would be of considerable interest.
The static magnetic susceptibility under a magnetic field of 1 T parallel to the (ab)-plane monotonically increases with decreasing temperatures from 300 K to 60 K. With decreasing temperatures, a peak is observed near 50 K with a subsequent increase in susceptibility at low temperatures ( 10 K). Even though this peak (near 50 K) is sharper than that in the other case,Lin07 () the broad shoulder of in the intermediate temperature region (20 K 50 K) is commonly observed for high Na concentration compounds of NaCoO.Bayrakci04 () The authors argue that this may be a signal of a valence fluctuation between Co and Co.Rhyee () The inverse magnetic susceptibility (black circle, black line), as shown in the inset of Fig. 2, follows the power-law behavior in the temperature range of 100 K 300 K according to the following equation: , where the zero-temperature susceptibility 0.0028 emu/moleOe, pre-factor 0.0046 emu/moleOeK, and power exponent 0.078. The non-Curie-Weiss behavior of a magnetic ordered system is an indication of the strongly correlated electron behavior. One possible scenario of the power-law behavior in the magnetic susceptibility is the multichannel Kondo effect.Stewart01 () The multichannel Kondo model is based on the strong correlation between the local impurity spin and the conduction electron spin. The spins of the conduction electron near the local impurities are paired with a singlet state due to the antiferromagnetic coupling by Pauli matrices.Schlottmann95 () When the total number of electrons overcompensates the local spin (where is the number of degenerate orbital channels and is the local spin), the power-law or logarithmic divergent behaviors of magnetization, resistivity, or specific heat are observed. The exact solution of the multichannel Kondo model for dilute impurities show that the magnetic susceptibility should have the power-law dependence with temperatures: , where . Under this consideration, the exponent parameter is estimated to be 0.078 from the magnetic susceptibility at high temperatures ( 100 K). The total number of electron channels is obtained as 2.34, which is the case of overcompensation (where 1/2 or 1). The multichannel Kondo effect can be manifested at high temperatures ().Pantke98 () In order to clarify the unconventional power-law behavior of at high temperatures ( 100 K), more detailed investigations need to be carried out by using the electrical resistivity, heat capacity, and thermopower measurements.
The logarithmic divergent behavior of is observed at low temperatures ( 7 K), which is different from the Fermi liquid behavior. It may be argued that the impurity spin effect of is significant due to the symmetrically coupled half-integer spin impurity with the valence fluctuation. Figure 3 (a) shows the temperature-dependent magnetic susceptibility for different magnetic fields as indicated with (ab). The increases logarithmically at low temperatures (2 K 7.5 K) as shown in the inset of Fig. 3(a). When an impurity spin is coupled with an antiferromagnetic background, the sublattice symmetric impurity spin 1/2 forms a collective spin state of spinon by pulling two spins, resulting in an orthogonal pair of degenerated ground states. If the symmetric impurity spin 1/2, which is coupled with an antiferromagnetic ground state, is dressed by the valence fluctuation, the impurity spin susceptibility would have a non-Curie divergence given by the following relation: , where () is the characteristic temperature with the energy scale of for weak coupling () ( is the transfer integral and is the coupling strength).Clarke93 () From the fitting of the above relation, the zero temperature susceptibility and characteristic temperature are estimated to be 0.0003 emu/moleOe and 10,451.02 K 0.90 eV for 0.1 T and 0.0004 emu/moleOe and 5,263.16 K 0.45 eV for 1.0 T. For high magnetic fields ( 3 T and 5 T), the above relation is not fitted. The spin impurity effect is suppressed with increasing magnetic fields as shown in Fig. 3(a). The suppression of the impurity spin effect with increasing magnetic fields might have been caused by the decreasing coupling strength between the impurity spin and the antiferromagnetic background.
Figure 3(b) depicts the magnetic susceptibility for (c)-axis at low temperatures (2 K 30 K) for different magnetic fields as indicated. The antiferromagnetic transition 22 K is not changed significantly with increasing magnetic fields. The important feature is the strong thermal hysteresis between the zero-field-cooled (ZFC) and the field-cooled (FC) magnetic susceptibility at 0.1 T as shown in the Fig. 3(b). While the Néel temperature 22 K is relatively low, the derived value of the Weiss temperature 196.78 K from the Curie-Weiss fitting is very large, which implied a strong antiferromagnetic interaction. The significant discrepancy between the Néel temperature and the Weiss temperature is the evidence of the spin frustration. The frustration parameter, defined by , is equal to 8.9, which is much larger than that of a conventional antiferromagnet. The antiferromagnetic compounds of NaCoO may have the geometrical spin frustration for a wide range of Na concentrations ( 0.78) due to the triangular crystal structure of the CoO sublattice. The SR study of NaCoO ( 0.78, 0.87, and 0.92) provided the evidence for the strong spin frustration.Bernhard07 () A small thermal hysteresis between ZFC and FC is also observed for the magnetic susceptibility with applied magnetic field in the (ab)-plane at low temperatures ( 20 K) under a magnetic field of 0.1 T (not shown here). The thermal hysteresis between ZFC and FC for different crystal orientations implies the unstable antiferromagnetic background of the NaCoO compound.
iii.2 Dynamic magnetic susceptibility
In order to study the dynamic spin behavior of this compound, we measured the AC magnetic susceptibility for the crystal orientations of both (ab)- and (c)-axis. Figure 4(a) and (b) represent the temperature-dependent real and imaginary (insets) parts of the AC magnetic susceptibility for various magnetic field frequencies as indicated with different crystal orientations of (ab)- and (c)-directions, respectively, where is the excitation AC magnetic field of 10 Oe. Here, the demagnetization factor ( 1) for (c) was considered for the following equations because we used the plate-like single crystal.
where and are the measured and intrinsic AC magnetic susceptibilities, respectively.
In the plot of the dynamic magnetic susceptibility for the (ab)-plane, as shown in Fig. 4(a), a broad peak is observed near 4.5 K for the magnetic field frequency 500 Hz. With increasing magnetic field frequency, the temperatures at which the broad peak is observed increase slightly from 4.5 K for 500 Hz to 6.0 K for 10 kHz. The frequency-dependent antiferromagnetic-like transition of the real part of the AC magnetic susceptibility is not a characteristic of an antiferromagnet but a characteristic of the spin glass-like behavior. The AC magnetic susceptibility behavior of the glass-like transition at 4.5 K without a phase transition near the antiferromagnetic temperature 22 K is similar to that observed in the case of the NaCoO compound.Wooldridge05 () The glass freezing temperatures are defined by the cusp points of . It is not a conventional spin glass system because of the strong energy dissipation of the AC magnetic susceptibility. The imaginary part of the AC magnetic susceptibility () along the (ab)-plane increases with decreasing temperatures and increasing magnetic field frequencies as shown in the inset of Fig. 4(a). The significant increase in with respect to decreasing temperatures and increasing frequencies is an uncommon behavior of the spin glass system. The out-of-phase part is much larger than the in-phase part at low temperatures. In a conventional spin glass system, the has broad peaks near the spin glass transition with a weaker signal than that of .Binder86 (); Hanasaki07 () However, in this compound, the energy dissipation part () of the dynamic spin susceptibility significantly enhanced with decreasing temperatures and increasing frequencies. Therefore, it is concluded that this system is not a simple spin glass system but an exotic system that exhibits strong energy dissipation. Moreover, the real part of the AC magnetic susceptibility along the (c)-direction (c) exhibits an unconventional sign change from positive to negative with decreasing temperatures ( 7 K) and increasing excitation field frequencies ( 3 kHz) as shown in Fig. 4(b). This system is quite different from that of the NaCoO compound as well as the conventional spin glass system.Wooldridge05 () In an usual case, the negative sign of implies a diamagmetic signal. However, this compound is neither a diamagnet nor a superconductor. First, it displays the strong antiferromagnetic transition at 22 K for the (c)-axis as shown in Fig. 3(b). Second, like , the energy dissipation of magnetic susceptibility is very significantly large. Compared to (6.010 dimensionless in CGS unit at 2 K and 10 kHz), the value of (5.810) is larger by two orders of magnitude than that of . In superconducting materials, the energy dissipation of the dynamic spin susceptibility diminishes below the transition temperature.
In order to understand the unusual dynamical spin susceptibility behavior of , we measured the isothermal frequency-dependent AC susceptibility at the temperatures of 2 K and 6 K, as shown in Fig. 5(a). With increasing AC field frequency at 2 K, decreases and the sign changes at 1.8 kHz. The small peaks at 1.2 kHz for 2 K and 6 K have not been understood as yet. The imaginary part of the AC susceptibility increases linearly with increasing AC field frequency, as shown in the inset of Fig. 5(a), which means the linear increase in energy dissipation. The out-of-phase part of the AC susceptibility is much more significant than the in-phase part of . The sign change of from positive to negative with increasing AC field frequency can be understood by the abrupt sign change of the phase difference with respect to the AC field frequency. From the definition of AC susceptibility , the magnitude of AC susceptibility and the phase difference can be represented by and , respectively. The phase difference is the relative phase shift between the applied AC magnetic field and the derived magnetic signal. Because the increases linearly with increasing field frequency and the orders of magnitude of is much larger than that of , increases linearly with AC field frequencies (not shown). The phase difference exhibits an abnormal abrupt sign change from 1.56 rad (89.4) to 1.56 rad (90.6) at the frequencies of the sign change, as shown in Fig. 5(b). The schematic view of the magnetic susceptibility in the complex phase space is shown in the inset of Fig. 5(b). At low frequencies ( 1.8 kHz at 2 K), these insets exhibit the in-phase response of magnetic susceptibility (red triangle) to the applied AC magnetic field (black rectangle) with 1.56 rad. However, at high frequencies, the phase difference abruptly changes to 1.56 rad (blue circle) due to a significant increase in the out-of-phase response . The in-phase to out-of-phase shift of the response of the AC magnetic susceptibility may be a result of the strong energy dissipation of this compound. Due to the fact that is much larger than , the phase difference is on the boundary between the in-phase and the out-of-phase regions in the magnetic susceptibility complex space ( rad) (right inset of Fig. 5(b)). At present, why the imaginary part of the magnetic susceptibility is much stronger than the real part of the susceptibility is not clear. The dynamical spin property of this compound may be related to the strong spin frustration in the (c)-axis.
In summary, we synthesized a high-quality single crystalline compound of NaCoO by the travelling solvent floating zone method. It was observed from the in-plane and the out-of-plane measurements that the DC magnetic susceptibility showed significant crystal anisotropic properties upon the application of a magnetic field. The DC magnetic susceptibility along the c-axis followed the typical Curie-Weiss behavior with a stable antiferromagnetic transition at 22 K. The strong thermal instability between the zero-field-cooled (ZFC) and the field-cooled (FC) magnetization and the high frustration index indicated a strong spin frustration along the c-axis. The in-plane magnetization exhibited the anomalous power-law behavior at high temperatures ( 100 K) and the logarithmic divergent behavior () at low temperatures ( 10 K). The high temperature power-law behavior may be related with the multichannel Kondo effect. The logarithmic divergence can be understood by the impurity spin effect, dressed by the valence fluctuation. Remarkable behavior of the AC magnetic susceptibility was observed at high excitation field frequencies ( 3 kHz) along the c-axis. The sign of the real part of the AC magnetic susceptibility along the c-axis changed from positive to negative with decreasing temperatures (near 7 K). We argued that the sign change may due to the abrupt sign change of the phase difference between the applied AC magnetic field and the magnetic susceptibility from 1.56 rad (89.4) to 1.56 rad (90.6). Because the imaginary part of the AC magnetic susceptibility was significantly larger than the real part one, the phase difference was on the boundary between the in-phase and the out-of-phase regions. A fundamental question remains as to why the energy dissipation was so significant at high frequencies and low temperatures of this compound. Further investigations would help in clarifying this behavior.
Acknowledgements.We would like to express our sincere gratitude to G. Götz and Christof Busch for their technical assistance.
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