Magnetoelectric coupling tuned by competing anisotropies in Mn{}_{1-x}Ni{}_{x}TiO{}_{3}

Magnetoelectric coupling tuned by competing anisotropies in MnNiTiO

Abstract

A flop of electric polarization from () to () is observed in MnTiO as a spin flop transition is triggered by a -axis magnetic field, =7 T. The critical magnetic field for is significantly reduced in MnNiTiO (x=0.33). and have been observed with both and . Neutron diffraction measurements revealed similar magnetic arrangements for the two compositions where the ordered spins couple antiferromagnetically with their nearest intra- and inter-planar neighbors. In the x=0.33 system, the uniaxial and planar anisotropies of Mn and Ni compete and give rise to a spin reorientation transition at . A magnetic field, , aligns the spins along for . The rotation of the collinear spins away from the -axis for alters the magnetic point symmetry and gives rise to a new ME susceptibility tensor form. Such linear ME response provides satisfactory explanation for the behavior of the field-induced electric polarization in both compositions. As the Ni content increases to x=0.5 and 0.68, the ME effect disappears as a new magnetic phase emerges.

pacs:
78.70.Nx,61.05.fm,74.70.-b,75.30.Fv

The multiferroics that show strong magnetoelectric (ME) effect are among the most saught-after materials due to their multi-functionality of inducing polarization with magnetic field or magnetization with electric field. Fiebig (2005); Cheong and Mostovoy (2007); Eerenstein et al. (2006); Khomskii (2006); Kleemann et al. (2010); Kimura (2012) The linear ME effect occurs in a crystal when the term in the expansion of its Gibbs free energy is nonzero. Here is a second rank tensor which changes sign under space or time inversion, but is invariant when the occurrences of the two inversions are simultaneous. Agyei and Birman (1990); Rivera (2009) The magnetic symmetries that meet such conditions are allowed to have linear ME response. Therefore in exploring magnetoelectrics among materials with long range magnetic order, symmetry analysis serves as a reliable guide. Harris (2007); Zvezdin and Pyatakov (2010); Bousquet and Spaldin (2011) Such predictability can be obscured when extra microscopic complications, such as magnetic anisotropy, spin frustration and spin-lattice coupling, have been introduced. However, these extra variables sometimes help to increase the magnitude of Mostovoy et al. (2010); Bousquet and Spaldin (2011); Bousquet et al. (2011) or even give rise to new ME coupling mechanisms. Hornreich and Shtrikman (1967); Wojde†and iguiez (2009); Yamauchi et al. (1983)

Figure 1: (Color online) Primitive cells of the hexagonal lattice of the compounds MnNiTiO. (a) The top view of the hexagon of cations with respect to the rhombic cross section as shaded in (b). Note the vacant octahedral site and a cation displacement from the ab-plane. Two types of magnetic structures, G-type with real spin directions unspecified and A-type, are shown in (b) for Mn-rich compounds and (c) for the Ni-rich compounds. in (b) is the angle between the spins and the hexagonal -axis.

MnNiTiO is such a system where more than one ME mechanism has emerged. MnTiO and NiTiO have the same ilmenite structure (Fig. 1) Ishikawa and Akimoto (1958) but different spin arrangements and easy axes, Shirane et al. (1959) which compete in the mixed compounds. Also competing are the energy loss from single ion anisotropy and that from the frustration of the exchange interactions. Yoshizawa et al. (1992) Various new magnetic phases including spin glass (SG) phase emerge as a result, forming a rather complex phase diagram. Ito et al. (1992); Yoshizawa et al. (1992); Kawano et al. (1993) While the linear ME effect was observed in MnTiO as its magnetic symmetry permits, Mufti et al. (2011) a new ME response is induced by the toroidal moments in the SG state of the mixed compounds. Yamaguchi et al. (2012) On both sides of the SG phase, the unexplored spin flop transitions, short range magnetic correlations and the Ti ions with empty 3 shells, Cohen (1992); Deng et al. (2012) are all potential hosts of yet another novel ME mechanism. Although the magnetic structures of the end-member compounds have been studied, Shirane et al. (1959) the details of the magnetic evolution in the mixed compounds and its effect on the electric polarization are still lacking. This report presents a systematic investigation of the ME effects and the magnetic orders in MnNiTiO. New components of the ME tensor and an anomaly in their temperature dependence under a low magnetic field have been observed. Neutron diffraction measurement on the x=0.33 compound under an applied magnetic field reveals the effect of the field on the spin orientation and therefore, on the nature of the new ME coupling. Details of the magnetic orders in 4 typical compositions and corrections to the phase diagram are reported.

Single crystals of MnNiTiO (x=0, 0.33, 0.50 and 0.68) were grown by the traveling-solvent floating zone technique. For electric polarization measurements, silver epoxy was pasted on the crystals cut into thin plates. The pyroelectric current was measured using a Keithley 6517A electrometer on warming after poling the crystal in an electric field of 800 kV/m while cooling down from above . The spontaneous polarization was obtained by integration of the pyroelectric current with respect to time.The single crystal neutron diffraction measurements were carried out at the High Flux Isotope Reactor of the Oak Ridge National Laboratory. The HB-2C Wide Angle Neutron Diffractometer (WAND) with wavelength of 1.482 Šwas used for reciprocal space and diffuse scattering surveys. The collections of reflections for structural determination were carried out at HB-3A four circle diffractometer where the wavelength of 1.542 Šwas chosen. An assembly of permanent magnets that provides 0.7 Tesla at the sample position was employed in the magnetic field measurement on HB-3A. Closed-cycle refrigerators were used on both diffractometers. The Rietveld refinements on the crystal and magnetic structures were conducted using the FullProf Suite. Rodr´ıguez-Carvajal (1993)

III.   RESULTS

A.   Pyroelectric measurements under magnetic field

Figure 2: (Color online) Temperature dependence of the electric polarization of MnTiO at various magnetic fields measured with and (a) , and (b) . The temperature dependence of for the x=0.33 compound with and (c) , and (d) .
Figure 3: (Color online) Temperature dependence of the electric polarization of MnNiTiO at various magnetic fields measured with and (a) , and (b) . The temperature dependence of for the x=0.33 compound with and (c) , and (d) . The dotted red lines mark the Nel temperature and the onset temperature of the spin rotation under the magnetic field of 0.7 T.

The ME effect was observed in x=0 and 0.33. In both cases the pyroelectric current anomaly signaling the onset of polarization appears only when finite magnetic field is applied along . Fig. 2 shows the temperature dependence of the spontaneous polarization () under various magnetic fields for the x=0 sample. The previous study Mufti et al. (2011) only reported the observation of in this compound. As shown in Fig.2(a), increases monotonically with increasing field until =6.5 T, then starts to decreases quickly and disappears above 7 T. The maximum value of is about 12 , which is consistent with ref Mufti et al. (2011). The intensity of , on the other hand, appears and starts to grow only above 7 T, as shown in Fig. 2(b). Magnetic field of 7 T along is where a spin flop in the magnetization was reported. Yamauchi et al. (1983) The magnetic field induced can be attributed to linear ME effect for several reasons: (1) Polarizations for both directions are linearly dependent on . (2) The G-type magnetic structure with spins along belongs to point group which does permit a non-zero . (3) A dielectric anomaly appears in the vicinity of . Mufti et al. (2011) The switch of polarization from to signifies the change of the ME tensor, and therefore of the magnetic symmetry. The ME coefficient and , deduced from the slope of the - curve, are 4.44 and 5.1 (CGS unit), respectively. These values are about an order of magnitude smaller than those of CrO. Popov et al. (1999); Rivera (1994)

In the x=0.33 compound, the magnetic field induced polarization persists, but its behavior differs from that in undoped compound. The threshold of field for disappears. Both and start to increase as soon as is turned on, as shown in Fig.3(a) and (b). linearly increases with (Fig.3(b)), but increases first then decreases to 1 and remains unchanged from 4 T to 7 T (Fig.3(a)). The polarizations along the two different directions also have different temperature dependence. The onset temperature of is at about 20 K while that of is 27 K. Moreover, at =1 T the initial increase of on cooling is considerably suppressed below 20 K, as shown by the red circle in Fig.3(a). Such an anomaly is absent for higher fields. Additionally, the and can also be induced by (Fig. 3(c) and (d)), which does not give rise to any polarization in the x=0 compound. Compared to the -induced polarizations, the onset temperature for the palarizatoin with -axis field is different though. In Fig.3(c) and (d), and both appear below 17.5 K. Different critical values of are required for and , which are around 2 Tesla and 4 Tesla, respectively. Above the critical , the polarization increases with the in both cases. The polarization was not observed in the x=0.50 and 0.68 crystals regardless of the directions and magnitudes of the applied magnetic field. The knowledge of detailed spin structures in these mixed compounds and their evolution with temperature and magnetic field is needed to understand the coupling of the ferroelectric order with the magnetic one.

Figure 4: (Color online) The contour plot of the diffraction pattern in the (H,0,L) plane for x=0 at (a) 5 K, (b) 25 K, (c) 50 K, and (d) 75 K. (e)-(h) show the same plane for x=0.33 at 5 K, 25 K, 50 K and 75 K, respectively. The intensity scale in (h) is different from other panels to show the diminishing diffuse scattting.

1.  The G-type AFM phase

The structural refinements show that the 4 compositions of MnNiTiO compounds all crystallize in space group . Their ilmenite structure and the two generalized spin configurations are depicted in Fig.1. Along the -axis of the hexagonal lattice, Mn/Ni and Ti layers alternate and every third octahedral site is vacant. The magnetic structure of MnTiO is G-type where nearest inter- and intra-planar neighbor spins are antiparallel, Shirane et al. (1959) which has the propagation wave vector =(0,0,0). The magnetic peaks coincide with the allowed nuclear ones (-++=, is integer). The contour plots of the magnetic diffraction in the () scattering plane, obtained by subtracting the high temperature (140 K) data as background, are shown in Fig. 4(a-d). The temperature dependence of the (1,0,1) position gives the Nel temperature 64 2.4 K. The absence of peaks along [0,0,L] implies that the Mn moments are along . The ridge-like diffuse scattering along starts to develop around 90 K. Fig.4(d) show the diffuse peaks at 75 K, which center on the magnetic Bragg peak positions such as (1,0,1), instead of (1,0,0). Akimitsu and Ishikawa (1977) On cooling the diffuse scattering intensity reaches its maximum at , then quickly decreases. Akimitsu et al. (1970) Before Lorentzian peaks completely disappear at 4 K, they coexist with the Gaussian line shape, suggesting the coexistence of long-range AFM order and short range 2D AFM correlations.

Figure 5: (Color online) (a) The intensity of the magnetic peak (1 0 1) as a function of temperature in x=0 and x=0.33. (b) The integrated intensity of the diffuse scattering and short-range correlation length along as a function of temperature in x=0.33.

The spin structure of x=0.33 system remains G-type as suggested by the unchanged magnetic peak positions in Fig. 4(e). The onset temperature of the AFM order is suppressed by Ni-doping to 27.6 K (Fig. 5(a) and Fig. 6(a)). However, the temperature dependence of the magnetic peaks, shown in Fig.5(a) and Fig.6(a), indicates an extra phase transition at =17.5 K. Both (0,1,2) and (1,0,1) show a kink at this temperature and (0,0,3) suddenly gains intensity below suggesting the spins rotate away from the -axis and obtain the component of the moment perpendicular to the wavevector. To accurately characterize the magnetic configuration and monitor the changing spin directions, 116 magnetic Bragg peaks were collected for every 1 K between 5 K and . In the magnetic structure refinement using FullProf, three equivalent magnetic domains were taken into account, only one of which is presented here. The component of the ordered moment in the -plane at all measured temperatures lies in the -direction. So the spin directions are specified by , the angle between the spin and the -direction in the -plane, as shown in Fig.1(b). The blue up-triangles in Fig.6(d) show the spin orientation as a function of temperature. The ordered spins between and are close to but not quite along (=14.26 at 20.5 K). Cooling across the spins abruptly rotate by more than 60 degrees toward . The angle reaches 80.1 at 4 K. These results are different from the established phase diagram which shows spins lying exactly along between and and exactly along below . Ito et al. (1992); Yoshizawa et al. (1992) Fig. 6(c) shows the refined ordered moment as a function of temperature, which is a smooth decrease and proves that the kinks of the magnetic peak intensities at 20 K in Fig. 6(a) are solely caused by the reorientation of the spins.

The diffuse scattering at this composition becomes more prevalent: The ridge along persists to the lowest measured temperature, extends high above , and becomes broader than the undoped system (Fig.4(g)). The integrated intensity of the diffuse component around (1,0,1) also reaches its maximum at and decreases quickly on both sides (Fig.5(b)). In addition, the Lorentzian line width does decrease on cooling. The inter-plane spin correlation length is smaller than the nearest neighbour interlayer distance above , implying the short range order is basicaly 2-dimensionl (2D). The crossover from 2D to 3D occurs close to when the correlation length becomes bigger than the distance between neighbouring Mn/Ni layers. does not diverge at but continues to increase on cooling to the base temperature. With some short-range correlated spins participating in the establishment of 3-dimensional long range order, some remain short-ranged at low temperature.

Figure 6: (Color online) Temperature dependence of (a) various magnetic reflections of the x=0.33 compound without magnetic field, (b) magnetic peaks with applied external magnetic field of 0.7 T, (c) the refined ordered moment and (d) the angle between the ordered spins and .

2. Magnetic field effect on the AFM order (x=0.33)

The onsets of and occur at and , respectively. The anomalous suppression of under low field also coincides with . Given that there is no detectable structural transitions at these temperatures, the electric polarization in the x=0.33 system apparently originates from the magnetic order. To investigate if this is linear or higher order ME effect, it is critical to know the effect of -direction magnetic field on the symmetry of the AFM order. The same crystal was aligned and mounted in the permanent magnet set which were mounted in a CCR with the c-axis parallel to the field direction. The selected magnets provided a field of 0.7 T at the sample position, which was measured by Gauss meter. The actual angle between and the field was determined to be 6 using the observed angle of the Bragg peak (0,0,6). The temperature dependence of the magnetic peak intensities is shown in Fig.6(b). Due to the geometrical restrictions imposed by the magnets, fewer magnetic peaks were accessible, but enough were collected for an unambiguous refinement of the spin structure at each temperature. The field kept the spin structure and intact, but increased from 17.5 K to about 20 K, making it the same as the onset temperature for . The result of spin structure refinements shows that the spins were pulled toward by the field, both below and above . is reduced to about 5 above and around 30 below. It is reasonable to assume that the spins would have been aligned along the -axis had a higher field been perfectly applied along . The spin-rotation transition is made sharper by the small field. Another effect of this field is suppressing the moment as shown in Fig. 6(c).

Figure 7: (Color online) (a) Contour plot of the (H,0,L) scattering plane collected at 4 K with the 25 K data subtracted as the background. The visible (0,0,3) and (0,0,6) peaks do not show temperature dependence. The temperature dependence of the magnetic peak (1,0,2.5) for the (b) x=0.5 and (c) x=0.68 compound.

3. A-type AFM structure (x=0.50 and 0.68)

The SG state forms between x=0.4 and 0.48 according to the established phase diagram. Yoshizawa et al. (1992); Ito et al. (1986); Yamaguchi et al. (2012) The contour plot of the (H,0,L) scattering plane for x=0.5 is taken at 4 K with 20 K data subtracted and shows a new magnetic wave vector =(0,0,1.5), indicating the A-type magnetic order has taken over at this composition. There is no sign of diffuse scattering along . The Bragg peak (1,0,2.5), shown in Fig.7(b), decreases smoothly in intensity without an abrupt transition and completely vanishes above 15 K. The smeared transition also shows hysteresis on cooling suggesting the spin glass phase still lingers at this composition. This is consistent with the magnetization measurement. Ito et al. (1986) The coexistence of long range AFM order with the spin glass order has been predicted Sherrington and Kirkpatrick (1975) in such a magnetically non-diluted system. Similar phonomena have been observed in MnFeTiO, where the dominant nearest neighbor interactions compete with each other and give rise to a strong magnetic frustration within the honeycomb layer. Yoshizawa et al. (1987); Katori and Ito (1993) The spin structure refinement agrees with the A-type model with the spins lying along -axis, as shown by Fig. 1(c). As the nickel content increases to 0.68, the arrangement of the ordered moments remains A-type. Both the Nel temperature and the size of the ordered magnetic moment at low temperature increase. increases to 21.5 K and the transition is abrupt and first-order like, contrasting with that of the x=0.5 sample. The structural parameters at 4 K and the magnetic orders in compounds of different Ni concentrations are summarized in Table 1.

refined x x=0.00 Kidoh et al. (1984) x=0.33 x=0.50 x=0.68 x=1.00 Boysen et al. (1995)
5.14 5.12 5.06 5.05 5.04
14.28 14.15 13.91 13.91 13.81
0.3600 0.347(2) 0.3471(2) 0.3509(5) 0.3509
0.1476 0.1504(5) 0.1466(2) 0.1426(8) 0.1450
0.3189 0.3188(6) 0.3166(2) 0.3161(8) 0.3142
0.031 0.0264(8) 0.0246(3) 0.0205(7) 0.016
0.2439 0.2449(3) 0.2459(1) 0.2458(3) 0.2465
magn.
struc. G-type G-type A-type A-type A-type
64 27.6 15 21.5 21.8 Shirane et al. (1959)
17.51
() 0 2.86(2) 1.36(3) 2.06(3) 2.25 Shirane et al. (1959)
() 4.55 Shirane et al. (1959) 0.5(1) 0 0 0
Nucl. 7.77 6.33 8.05
Magn. 3.97 15.2 9.6
Table 1: The lattice parameters, atom parameters, magnetic structures, magnetic phase transition temperatures, the ordered moments of the magnetic orders, and the R factors of the structure refinements in various MnNiTiO compounds. m and m denote the projected moment on the hexagonal - and -axes respectively. is calculated by =, where is the structure factor and the number of reflections used.

IV. DISCUSSION AND CONCLUSION

The ionic radius of Ni (0.70 Å) is smaller than that of Mn (0.80 Å), so the effect of increasing Ni content on the nuclear structure is to be expected. As exhibited in Table 1, and both decrease with increasing Ni-doping, so do the values of the atoms on sites (Mn, Ni, and Ti). The value of for the oxygen site, already small in MnTiO (0.031), is systematically reduced by the Ni-replacement and becomes 0.016 in NiTiO. However, its minuscule value keeps the crystal from having mirror planes, so is important for the crystallographic symmetry and consequently for the magnetic symmetry. The effective moment for Mn in MnTiO, 4.55 , is smaller than the spin-only value. This can be ascribed to the incomplete ordering of Mn and Ti or the existence of Mn. Shirane et al. (1959) Both the effective moment and the Nel temperature change with Ni concentration as a result of the competing anisotropies and frustrated exchange interactions . This change is more rapid on the Mn-rich region. Both values are considerably reduced at x=0.5, which is compatible with the observed spin glass behavior. In the x=0.68 compound, the intra-layer exchange interactions among the Ni ions become so dominant that and the ordered moment are very close to those in the pure NiTiO. Because of the similar radii of Ni and Ti ions, more incomplete ordering exists in NiTiO Ishikawa and Akimoto (1958), which is mainly responsible for the less-than-expected moment size of Ni. Shirane et al. (1959)

The Mn and Ni ions have distinct single ion anisotropies as manifested by their different easy axes in the ilmenites Ishikawa and Akimoto (1958); Shirane et al. (1959) and other compounds such as barium fluorides BaMnF Poole et al. (2011) and BaNiF. Cox et al. (1970) The added Ni cations randomly replace Mn on the octahedral sites and weaken the spin correlations, more so in the inter-planar direction, as indicated by the enhanced diffuse scattering in the x=0.33 system. Although the spin correlation starts to form high above , the electric polarization does not occur until the long range G-type magnetic order is established. When the spins are parallel to the -axis, the magnetic group symmetry is and the point symmetry is . As the collinear AFM moments tilt away from the axis, the emerged -axis components in the hexagonal layer loses the 3-fold rotation symmetry. The magnetic space group then becomes and the magnetic point symmetry becomes . Since the nonzero value keeps the crystal from having 2-fold rotation axis and mirror planes. Even if the spins completely lie in the -axis, the point group of the magnetic symmetry is not as it appears to be. The restrictions from the non-magnetic anion sites must be obeyed as the Neumann’s principle requires the physical property tensor be invariant under all the permissible operations of the crystallographic symmetry Birss (1964); Bhagavantam and Pantulu (1964).

This observation is the key to understand the observed electric polarizations summarized in Fig.2 and Fig.3 for x=0 and 0.33, respectively. Both and are among the 58 magnetic point groups that have non-zero elements in their ME susceptibility tensors. Rivera (2009) The former has both diagonal =, and off-diagonal components =-, while the latter does not impose any restrictions on the form of ME tensor and all tensor components are non-zero. The G-type structure with -axis spins (=0) in MnTiO, permits as indeed observed. In the x=0.33 system, the spins tilt away from while maintaining the -type structure and lowers the symmetry to . The symmetry remains as even for unless a -direction magnetic field pull the spins back along (Fig. 6(d)), which enables the recovery of the symmetry in this temperature range. This explains why , allowed by both symmetries, exist in the entire range. Cooling across at 20 K, arising from the collinear spin rotation triggers , which is prohibited by . At the same temperature, exhibits considerable suppression due to the reduced -component of the moment, as shown by the red triangle in Fig.6(d). The change of magnetic point symmetry satisfactorily explains the temperature dependence of the observed and . It is clear that coupling of the ferroelectric order and magnetic order is due to the linear ME effect. The case of x=0.33 system is different from a normal linear ME effect, as in x=0, in that the spin directions vary with external magnetic field, which fails the linear dependence of the polarization on magnetic field.

With the ties between the two orders established, one can use the polarization to predict the spin structures at higher fields, as they are difficult to determine experimentally. The representation analysis using SARAh program Wills (2000) shows that for the space group with magnetic propagation vector k=(0,0,0), the G-type is the only possible AFM spin arrangement. So if one assumes the magnetic wave vector remains unchanged, alone should be sufficient to describe all the spin structures under moderate magnetic field. With higher in the x=0.33 compound, remains different in the two temperature regions. The fact that only exists below (Fig.2(d)) suggests that up to =7 T, =0 for T and that 0 for . As the magnetic field is applied along , the observed (Fig.3(d)), prohibited by , suggests the magnetic point symmetry.

The electric polarization flop has been observed in a few multiferroic materials, including rare-earth manganites RMnO, Kimura et al. (2003); Strempfer et al. (2007) RMnO Fukunaga et al. (2009) and the mineral hbnerite MnWO, Tanigushi et al. (2006) which generally have incommensurate noncollinear spiral spin structures. In these materials the -flop is typically caused by the flop of spiral or cycloid plane. MnTiO is a rare case of magnetic field induced -flop with a collinear magnetic structure. In the x=0.33 system, the polarizations in the two directions are turned on by the same field and coexist for , so this is not a typical -flop. But the reciprocal interactions between and and their different on-set temperatures makes it a unique type of ME control. The Co-doped MnWO is another case of -flop caused by the competing single ion anisotropies, which is achieved by the flop of the spin helix. Liang et al. (2012); Ye et al. (2012) But the magnetic frustration and complex magnetic structure make this type of control difficult to repeat in other compounds in terms of materials design. In comparison, the collinear spin rotation in MnNiTiO can be easily created for a random mixture of two antiferromagnets with orthogonal easy axes. A new intermediate phase whose easy axis tilts oblique to the easy axes of the pure systems, and two second order transitions are all predicted by mean field approximation. Matsubara and Inawashiro (1977); Oguchi and Ishikawa (1978) Such predictions have also been fulfilled in other random mixtures such as KMnFeF Bevaart et al. (1978) and CoFeCl2HO. Kobayashi and Katsumata (1978)

V.   SUMMARY

The structural, magnetic and electric properties have been studied for 4 typical compositions of MnNiTiO. Magnetic field induced electric polarizations have been observed in the compositions x=0 and 0.33, both of which have the G-type magnetic order. In the x=0 system, the polarizatio flops from to as the spin flop transition is triggered at =7 T. In x=0.33, is turned on together with by . Additionally, and can also be induced by . By studying the magnetic structure and phase transition with and without magnetic field, the occurrence of the new ME coupling is attributed to the emergent point group symmetry as the antiferromagnetically coupled spins tilt collinearly toward the -axis. Such spin rotation results from the strong competition of single ion anisotropy of the transition metal elements and provides a new way to tune electric polarizations. The magnetic structure of the x=0.5 and 0.68 systems is the same as that of the NiTiO. No polarization was observed.

V.   ACKNOWLEDGMENTS

The research at Oak Ridge National Laboratory’s High Flux Isotope Reactor was sponsored by the Scientific User Facilities, Office of Basic Energy Sciences, US Department of Energy. The authors are grateful for fruitful discussions with Bryan C. Chakoumakos. H.D.Z thanks for the support from JDRD program of University of Tennessee. NHMFL is supported by National Science Foundation (DMR-0654118) , the State of Florida, and the U.S. Department of Energy.

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