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Low-magnetic-field control of dielectric constant at room temperature realized in Ba0.5Sr1.5Zn2Fe12O22

We show that room temperature resistivity of Ba0.5Sr1.5Zn2Fe12O22 single crystals increases by more than three orders of magnitude upon being subjected to optimized heat treatments. The increase in the resistivity allows the determination of magnetic field (H)-induced ferroelectric phase boundaries up to 310 K through the measurements of dielectric constant at a frequency of 10 MHz. Between 280 and 310 K, the dielectric constant curve shows a peak centered at zero magnetic field and thereafter decreases monotonically up to 0.1 T, exhibiting a magnetodielectric effect of 1.1%. This effect is ascribed to the realization of magnetic field-induced ferroelectricity at an H value of less than 0.1 T near room temperature. Comparison between electric and magnetic phase diagrams in wide temperature- and field-windows suggests that the magnetic field for inducing ferroelectricity has decreased near its helical spin ordering temperature around 315 K due to the reduction of spin anisotropy in Ba0.5Sr1.5Zn2Fe12O22.


Introduction
Recently, there has been an increase in the number of researches-both basic and applied researches-on a new class of materials called multiferroics, wherein ferroelectric (FE) and magnetic orders coexist or large magnetoelectric effects are seen [1,2]. For the practical realization of a multifunctional device, it is required to control the electric polarization (P) or dielectric constant ( ) under a small magnetic field (H), particularly near room temperature [2]. However, large magnetoelectric or magnetodielectric effects in single phase multiferroic materials have been so far observed mostly at low temperatures [3,4]. Zn 2 Y-type hexaferrite Ba 0.5 Sr 1.5 Zn 2 Fe 12 O 22 is a good candidate for improving the current situation because it is predicted that the compound can exhibit H-induced ferroelectricity at room temperature under a rather small H of~0.8 T [5]. Below the Nèel temperature (T N ) of 326 K, the compound is known to develop the helical spin ordering, in which the spin moments lie and rotate in the hexagonal ab-plane. When H is applied in the ab-plane, the compound undergoes several magnetic transitions, among which the so-called intermediate-III phase is found to have a finite value of P. Furthermore, on the basis of the H-dependent magnetization M(H) measurements, the intermediate-III phase, i.e., the FE phase, has been suggested to exist up to T N = 326 K , while both P(H) and (H) measurements have provided evidence for the occurrence of ferroelectricity only up to 130 K. Above 130 K, those electrical measurements could not be carried out to confirm the occurrence of ferroelectricity due to the low resistivity of the specimen [5]. Thus, it is necessary to increase the resistivity of this hexaferrite system in order to corroborate the occurrence of H-induced ferroelectricity through electrical measurements and to observe magnetoelectric coupling around room temperature.
In this paper, we report the effect of heat treatments on both resistivity ( ) and FE phase boundaries of Ba 0.5 Sr 1.5 Zn 2 Fe 12 O 22 single crystals. By optimizing the heat treatment conditions, we achieve an increase in the resistivity by more than three orders of magnitude at 300 K. This increase enables us to determine the magnetic field-induced FE phase boundaries up to 310 K.

Experimental details
Single crystals of Ba 0.5 Sr 1.5 Zn 2 Fe 12 O 22 were grown from Na 2 O/Fe 2 O 3 flux in air. After being melted at 1420°C in a Pt crucible, the flux mixture was subjected to several thermal cycling to avoid impurity phase [6] and cooled to room temperature at a rate of 50°C/h. X-ray diffraction of the as-grown crystals showed lattice parameters consistent with the literature values [6]. obtained at room temperature in a sample treated with 8 day-annealing and slow cooling, which will be called as the 'most insulating'-sample below (See, section 3 for resistivity data).
A standard four-probe method was used to obtain the temperature-dependent of all the as-grown crystals in the ab-plane. Due to the high resistance of the heat-treated crystals, a twoprobe method was employed to measure their (T). The samples for dielectric measurements are polished into wide and thin plates in a way that electric field (E) and H are in the ab-plane and perpendicular to each other (as depicted in figure 3(c) inset). A typical dimension of the sample used is 2×0.3×1 mm 3 . Dielectric constant was measured with an LCR meter (Hewlett-Packard 4275A) at a frequency of 10 MHz. In order to trace ferroelectric phase boundary by measuring ε(Η) peaks under minimal influence of dielectric loss, we have measured complex dielectric constant of each crystal, ε + iε 2 , in a broad frequency range to choose the frequency with the minimum loss. From this investigation, we have found that the dielectric loss of most samples including the 'most-insulating' one becomes more or less minimum, particularly at the frequency of 10 MHz near room temperature.
We have also measured the magnetoelectric current (J ME ) by using an electrometer (Keithley 6517) while sweeping magnetic field at a rate of 20 Oe/sec at each temperature. Before the J ME measurement, we have poled each sample with E=250 kV/m in its paraelectric state (at µ 0 H=4 T), and then adjusted µ 0 H=1 T to drive the sample into the ferroelectric state. After these processes, E is removed and J ME is measured while sweeping H up or down. Therefore, in the case of our crystals grown from Na 2 O/Fe 2 O 3 flux, we postulate that the annealing period of 8 days is effective in removing oxygen deficiencies before the counter effect from the Na impurities increase considerably.

Results and discussion
Furthermore, we observe that controlling the cooling rate is crucial to obtain an increase in the resistivity (see, figure 1(b)). An increase in the cooling rate results in a reduction in (300 K) and . Recent band structure calculations for Ba 2−x Sr x Zn 2 Fe 12 O 22 have indicated that the fraction of Zn at the tetrahedral sites in the magnetic L blocks, denoted by ( figure 2(a)), is a critical parameter controlling the electrical properties of this system [8,9]; when increases, the compound becomes more insulating. In our study, after the elimination of the oxygen deficiency in the crystal by annealing under O 2 gas, the cooling rate is likely to control the distribution of Zn ions, i.e., . At 900°C, is presumably close to a random distribution value of 0.5, and quenching will enable the crystal to maintain the high temperature value down to room temperature. For the slow cooling condition, the crystal will have an equilibrium value of temperatures lower than 900°C, which seems to be larger than 0.5 in this material system. This is consistent with the reported value of (0.661) in Ba 0.5 Sr 1.5 Zn 2 Fe 12 O 22 single crystals [10,11] grown under slow cooling condition [10]. From these results, we conclude that the combination of the 8-day O 2 annealing and the slow cooling is close to the optimal condition for obtaining the highest resistivity at 300 K (most-insulating sample).
The high resistivity of the most-insulating sample enabled us to detect the key features of the H-induced FE phase boundary, i.e., peaks in the (H) data, even above room temperature as plotted in figure 3(a) and (b). Two main peaks in the (H)/ (0) curve (black ticks) clearly exist from 10 K to 310 K and then suddenly disappear at 315 K, indicative of ferroelectricity onset, in the most-insulating sample. The continuous evolution of these peak fields from low to high temperature regions supports that the most-insulating sample has indeed the H-induced FE transitions up to the 310 K. The corresponding ε 2 vs H curves are also plotted at 10 and 300 K in figure 3(c). At the two critical magnetic fields for the ferroelectricity onset, there exist sharp peaks or dips in the ε 2 (Η) curves. Particularly at 300 K, while a gradual increase of ε 2 exists in the background possibly due to increased leakage with H, we find dips at the expected FE phase transition fields. For this most-insulating sample, the loss tangent, tan δ≡ε 2 /ε was about 1 at 300 K. In contrast, a typical as-grown sample had larger value of tan δ≅10 at 300 K, and it did not show any dip or peak feature in the (H) and 2 (H) curves above 130 K at the expected FE phase transition fields, presumably due to the increased leakage.
To directly confirm the development of ferroelectric polarization at the ε−peak-fields, we have tried to measure the magnetoelectric current J ME . However, as we have prepared a relatively small piece of crystal for homogeneous heat treatments, we could not easily measure J ME reliably in the heat-treated sample in general. As a result, in the most-insulating sample, we could only confirm the existence of P below 30 K through the peaks of J ME , which almost match with the corresponding (H) peaks. However, as the sample treated with 14 day-annealing and slow cooling had a little larger surface area, we could observe the clear peak features in the J ME curves up to 70 K.  figure 4(a), particularly above 220 K and in the low-H regions. For example, the FE phase boundaries at 300 K starts at almost zero magnetic fields while those of intermediate-III still remain above 0.7 T at 300 K. The deviation becomes more significant as temperature approaches the T N . We note, however, that below 220 K, both FE and intermediate-III phases almost coincide each other in the most-insulating crystal. Even in the as-grown crystal, the phase boundaries of intermediate-III almost match with the FE ones below 220 K although they are narrower than those in Ref. [5] (solid lines). Therefore, the electric phase boundaries closely match with magnetic (intermediate-III) ones below 220 K, regardless of the heat treatment. This is also consistent with the results in Ref. [5], in which the FE and magnetic phase boundaries mostly match each other below 130 K. All these observations consistently suggest that the FE phase-coinciding with the intermediate-III phase at low temperatures-becomes independent of the intermediate-III phase, particularly near the spin ordering temperature and that it is a generic property of this hexaferrite system.
To explain the difference between the phase boundaries of ferroelectricity and intermediate-III observed in the most-insulating crystal, we employ the spin-current model [12], which predicts the direction of P to be along e × Q. Here, e is the spin rotation axis and Q is the propagation vector of the spiral ordering. Q in Ba 0.5 Sr 1.5 Zn 2 Fe 12 O 22 is known to be parallel to the c-axis [10,11]. To generate a nontrivial P in the ab-plane, e for the helimagnetic spin ordering should have a net component perpendicular to the c-axis. Then, such a spin ordering pattern is likely to have a canted conical spin structure with a cone axis that tilts off the c-axis, as shown in figure 2(b). It is noted that the suggested pattern is similar to the one recently proposed for Ba 2 Mg 2 Fe 12 O 22 [13,14]. Therefore, the appearance of the FE phase in Ba 0.5 Sr 1.5 Zn 2 Fe 12 O 22 can also be associated with the canted conical spin configuration, similar to the case of Ba 2 Mg 2 Fe 12 O 22 . At temperatures below 220 K, the intermediate-III phase seems to almost coincide with this canted conical phase in the most-insulating crystal. However, as the temperature increases, the spin anisotropy required to confine the spin-moments within the abplane will be naturally weakened. In such a situation, it is highly likely that the canted conical spin structure starts to appear at a much lower H than the intermediate-III phase, explaining why the FE phase boundary in the most-insulating crystal moves to zero magnetic field near T N . Therefore, we suggest that the canted conical spin state is uniquely realized in Ba 0.5 Sr 1.5 Zn 2 Fe 12 O 22 between 280 K and 315 K under a rather small H value of 0.1 T. In particular, the temperature region to stabilize the canted conical structure is much higher for this compound than for Ba 2 Mg 2 Fe 12 O 22 , in which such a similar magnetic phase can only exist below its helical ordering temperature of 195 K [13].

Conclusions
We have observed the stabilization of the FE phase under a low magnetic field of 0.1 T up to the temperature of 310 K in optimally heat-treated Ba 0.5 Sr 1.5 Zn 2 Fe 12 O 22 . As a consequence, there appears a magnetodielectric effect of 1.1% under an H value of 0.1 T at 300 K. The remarkable lowering of the critical magnetic field for switching ferroelectricity is understood as the result of a reduction in the spin anisotropy near T N . The same mechanism can indeed be applied to a broader class of helimagnet and may further help to find new magnetoelectric phenomena in low magnetic-field and high temperature environment.     Intermediate-III phase diagrams of the as-grown and most-insulating crystals, derived from the M(H) measurements as illustrated in figure 5(b). The intermediate-III phase boundary in Ref. [5] is plotted again for comparison.