Magnetic and electric properties in the distorted tetrahedral spin chain system CuMoO
We study the multiferroic properties in the distorted tetrahedral quasi-one dimensional spin system CuMoO, in which the effects of the low dimensionality and the magnetic frustration are expected to appear simultaneously. We clarify that the antiferromagnetic order is formed together with ferroelectric properties at K under zero magnetic field and obtain the magnetic-field-temperature phase diagram by measuring dielectric constant and spontaneous electric polarization. It is found that the antiferromagnetic phase possesses a spontaneous electric polarization parallel to the axis when the magnetic field is applied parallel to the axis. On the other hand, there are three different ferroelectric phases in the antiferromagnetic phase for parallel to the axis.
Recently, the discovery of the strong magnetoelectric effect in TbMnO  has rekindled significant interest in multiferroics displaying the interplay between ferromagnetic and ferroelectric properties. After that, the multiferroism has been extensively studied  in transition metal oxides and a few microscopic mechanisms of this phenomenon have been proposed. The inverse Dzyaloshinskii-Moriya interaction and the inverse Kanamori-Goodenough interaction induce multiferroic properties in the spiral spin and collinear structures, respectively, where the magnetic superlattices are formed.[3, 4, 5] The geometrical magnetic frustration also plays an important role as the origin of the nontrivial spin configuration which breaks the spatial inversion symmetry. Recently we reported a possibility that CuMoO shows multiferroic behaviors without any magnetic superlattice formation. In ref., we focused on the dielectric properties and the electric polarization induced by an antiferromagnetic (AFM) spin order when the magnetic field is applied along the axis. In the present work, we report mainly the results for parallel to the axis.
CuMoO has two distorted tetrahedral quasi-one dimensional quantum spin systems made from spins along the b axis in its orthorhombic unit cell (see Figs. 1(a) and (b)).[8, 9] This compound has magnetic frustrations due to the tetrahedral spin alignment and the quasi-one dimensionality simultaneously. This compound undergoes an AFM phase transition at = 7.9 K at zero magnetic field and shows a weak ferromagnetic order due to the spin canting at low temperatures.[8, 9] The inelastic neutron scattering study shows the hybridization effects due to the and superexchange interactions between two elemental magnetic excitations, i.e., that of the quasi-one dimensional AFM spin system made from the (= 4.0 meV) superexchange interactions and that of the isolated AFM spin dimers made from the (= 5.8 meV) ones.[10, 11]
We measured the temperature and magnetic-field dependences of the dielectric constant and in CuMoO when is applied along the and axes. We prepared the plate-like single crystals of CuMoO of which cross sections and thicknesses are typically about 60 mm and 0.4 mm, respectively. To form a capacitor, the faces were coated with gold and attached using gold wires. The capacitance, of which the typical value was on the order of 10 pF, was measured using the impedance analyzer (Yokogawa-Hewlett-Packard 4192A). ( or ) was obtained from the capacitance at 100 kHz with a peak voltage of 1 V. The magnetic field was applied using a superconducting magnet (Oxford Instruments, Teslatron S14/16), of which the maximum magnetic field was 16 T.
3 Results and Discussion
Figures 2(a) and (b) show the typical dependences of ( or ) under a fixed along the axis (), (the - curves), respectively, each of which has a (local) maximum value at . increases at 6 T, but it decreases at 16 T. at 16 T shows two anomalies consisting of two peaks, as shown in Fig. 2(a). As shown in Fig. 2(c), the detailed - curves under magnetic fields between 12 and 16 T, the above 15 T has two peaks indicated by arrows. The values of against are plotted in the - phase diagram in Fig. 3(a) by the solid symbols. Figure 2(d) shows the typical dependences of from 8 to 12 K (the - curves). The - curves have a cusp between 8.3 and 9 K and two ones between 9.5 and 10 K, respectively. These are plotted in the phase diagram in Fig. 3(a) by the open symbols.
The inset of Fig. 3(a) shows the polarization-electric field (-) loops at 3 K under 0 and 13 T when the electric field and the magnetic field are applied along the and axes, respectively. Typical ferroelectric - hysteresis loops were observed, indicating that the AFM phase is ferroelectric and has a spontaneous electric polarization parallel to the axis. This result is consistent with the fact that the peak height of is about ten times larger than that of , as seen in Figs. 2(a) and (b). At 13 T, all of the saturated polarization, the spontaneous polarization and the coercive electric field are larger than the values at 0 T. These results indicate that the ferroelectric correlation increases with increasing . These magnetic-field dependences of electric polarization are different from the ones when the magnetic field is applied along the axis. The magnetic-field dependence of magnetization also depends on the direction of the magnetic field. We consider that the anisotropic electric property of CuMoO is related to the anisotropic magnetization of this compound.[8, 9] And it suggests the ferroelectricity originating from the frustrating spin configuration as an origin of the multiferroic behavior.
Together with the phase boundary obtained from the dependence of the specific heat under , we obtain the (-) phase diagram in Fig. 3(a) when is applied parallel to the axis. The obtained by the specific heat is little bit lower than .
We compared Fig. 3(a) to the - phase diagram from ref.  (Fig. 3(b)), which is obtained under along the axis. There are three different ferroelectric phases in the AFM phase of Fig. 3(b), indicating that the phase diagram for is simpler than that for . When , a change in direction of the spontaneous electric polarization occurs at the phase boundary running from () = (8 T, 2 K) to (10 T, 8 K). Around the tricritical point at 10 T and 8 K, the change of the direction in the electric polarization causes a colossal magnetocapacitance effect. When , the - curve shows two peaks under magnetic fields above 14 T, as shown in Fig. 2(c), suggesting that a new phase appears in the narrow region. Then, another tricritical point may exist around (9 K, 14 T). At this tricritical point, the strong magnetocpapacitance effect has not been observed in the present work. This suggests that the strong magnetocapacitance effect originates from the change in the direction of the spontenous electric polarization. We conclude that much different multiferroic behaviors occur when // and //. At present we are interested in the multiferroic behaviors under high magnetic fields.
This work is partly supported by a Grants-in-Aid for Scientific Research (C) (No. 40296885) and on Priority Area (No. 19052005) from the Ministry of Education, Culture, Science and Technology of Japan (MEXT). We also wish to acknowledge the technical assistance of Mr. R. Kino and Mr. M. Suzuki.
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