V Babin

V Gorbenko

I Kondakova

T Kärner

V V Laguta

M Nikl

S Zazubovich

Yu Zorenko

Time-resolved spectroscopy of exciton states in single crystals and single crystalline films of YAlO 3 and YAlO 3 :Ce

Keywords: density functional calculations, NMR spectroscopy, perovskites, time-resolved luminescence spectroscopy PACS 78.20.-e, 78.47.jd, 78.66.-w, 78.60.Kn, 76.30.Kg, 76.60.-k

Luminescence characteristics of single crystals (SC) and single crystalline films (SCF) of YAlO 3 and YAlO 3 :Ce have been studied at 4.2-300 K under photoexcitation in the 4-20 eV energy range. The origin and structure of the intrinsic and impurity defects responsible for various exciton-related emission and excitation bands have been identified. The ≈5.6 eV emission of YAlO 3 SCF is ascribed to the self-trapped excitons. In YAlO 3 SC, the dominating 5.63 eV and 4.12 eV emissions are ascribed to the excitons localized at the isolated antisite defect Y 3+

Al and at the Y 3+ Al defect associated with the nearest-neighbouring oxygen vacancy, respectively. The thermally stimulated release of the electrons, trapped at these defects, takes place around 200 K and 280 K, respectively. The presence of Y 3+

Al -related defects and isolated oxygen vacancies (AlO 5 units) in YAlO 3 SC is confirmed by NMR measurements. The formation energies of various Y 3+ Al -related defects are calculated within the density functional theory. The influence of various intrinsic and impurity defects on the luminescence characteristics of Ce 3+ centers is clarified.

Introduction

Single crystals (SC) of Ce 3+ -doped yttrium-or lutetium-aluminum perovskite YAlO 3 (YAP) or LuAlO 3 (LuAP) were found to have favorable scintillation characteristics especially for medical applications [1,2] which stimulated intense studies of this material. Luminescence characteristics of Ce 3+ centers, as well as energy transfer and defects creation processes in YAP:Ce SC or LuAP:Ce SC were intensively studied [1][2][3][4][5][6]. The crystals grown from the melt at high temperatures (1900-2000 o C) contain antisite (e.g., Y 3+ Al -, Ce 3+ Altype) and vacancy-related defects which can negatively influence the scintillation characteristics of YAP:Ce SC. The concentration of these defects is strongly suppressed in the YAP single crystalline films (SCF) prepared by the low-temperature Liquid Phase Epitaxy (LPE) method [7]. However, at the preparation of the SCF with the use of the PbO-containing flux, lead ions are introduced into the SCF. As a result, various leadrelated centers appear with the luminescence in the UV spectral range [8][9][10].

Luminescence of undoped YAP SC was studied for more than thirty years (see, e.g., [7][8][9][11][12][13][14][15][16][17] and references therein). The two emission bands observed at 5.9 eV (FWHM=0.7 eV) and 4.2 eV (FWHM=0.9 eV) under excitation in the exciton absorption region were ascribed to the self-trapped excitons (STE) and recombination processes, respectively [12][13][14][15][16]. In [7][8][9]17] the role of antisite defects of the type of Y 3+ Al in Confidential: not for distribution. Submitted to IOP Publishing for peer review 17 June 2011 the formation of intrinsic luminescence centers was considered. After that, the highest-energy intrinsic emission of YAP SC was concluded to arise from the Y 3+ Al defect itself [7], or the exciton localized near the Y 3+ Al defect [8][9], or the STE [17]. In [17] the 5.28 eV emission was ascribed to the exciton localized near the Y 3+ Al defect, while the emission bands located in the 3.0-4.5 eV range, to the excitons localized near various vacancy-related defects.

Thus, in SC and SCF of YAP, several types of intrinsic defects can exist. This reduces the efficiency and speed of energy transfer from the host lattice to Ce 3+ centers. Photo-thermally stimulated disintegration of various exciton states into electron and hole centers and their subsequent tunnelling recombination can result in the appearance of slow luminescence decay components. The overlap of intrinsic emission bands with the absorption bands of Ce 3+ can allow for an effective energy transfer from the defect-related centers to Ce 3+ ions which negatively influences the scintillation response of Ce 3+ -doped YAP.

However, the origin of the defect-related states as well as the processes responsible for the luminescence of undoped YAP is not clear as yet. In different papers, different data are reported regarding the positions of the exciton, defect-related and impurity-related excitation bands in the exciton absorption region (see, e.g., table 1). Therefore, their detailed comparison is not always possible. In the present work, the characteristics of various emission bands measured for the same undoped and Ce 3+ -doped YAP SC and YAP SCF samples at the same experimental conditions are compared. The aim of the work was to clarify the origin and structure of the defects responsible for the nonrelaxed (denoted further as perturbed) and the relaxed (localized) exciton states in the SC and SCF of YAP, and to obtain information on the processes of energy transfer from the defect-related centers to the luminescence Ce 3+ ones.

Experimental details

The single crystals of undoped and Ce 3+ -doped YAP were grown in CRYTUR Ltd., Turnov, Czech Republic, by the Czochralski method in a molybdenum crucible and studied in [3,6]. The single crystalline films of undoped YAP and YAP:Ce were prepared in Lviv University, Ukraine, by the LPE method from the PbO-B 2 O 3 flux in a platinum crucible [7][8][9]17] and investigated in [10]. The undoped YAP SC was used as a substrate. The YAP:Ce powder QM58/N-S1 with an average crystallite size of 6-8 µm was synthesized at Phosphor Technology Ltd, UK, through a solid state reaction and was not melted in the process of the preparation. Our XRD measurements showed that it has a perfect orthorhombic perovskite structure. Ce concentrations in YAP:Ce SC (measured using electron microprobe) and in YAP:Ce SCF (estimated from the comparison of the absorption coefficients of these two samples at the same photon energy) were, respect to Y content, 0.50 at% and 0.61 at%, respectively.

The luminescence characteristics were studied at 10 K under excitation by the synchrotron radiation at SUPERLUMI station (HASYLAB at DESY, Hamburg, Germany) with the time windows 1-9 ns and 96-149 ns. The excitation spectra of different emissions were measured in the 4-20 eV energy range at exactly the same conditions and corrected for the spectral dependence of the excitation intensity. The emission spectra were measured with the use of the monochromator ARC 0.3 m Spectra Pro300i, detected with the photomultiplier Hamamatsu R6358P, and were not corrected. The spectral width of the slits was 15 nm. The experiments at low temperatures were carried out with the use of a closed-cycle refrigerator.

Thermally stimulated luminescence (TSL) glow curves were measured with the heating rate 5 K/min after X-ray irradiation of a sample at 70 K for 30 min (40 kV, 15 mA). The sample located in an Oxford Instruments OptistatCF (Continuous Flow) helium cryostat was cooled and heated by He exchange gas. The heating rate was controlled with an ITC5205 temperature controller. The luminescence was registered using a Hamamatsu H8259-01 photon counting head.

Nuclear magnetic resonance (NMR) spectra of 89 Y and 27 Al were measured in a magnetic field B = 9.4 T, corresponding to a Larmor frequency 19.607 MHz and 104.264 MHz for 89 Y and 27 Al, respectively. Both single pulse and solid echo pulse sequences with phase cycling were used. Due to the long spin-lattice relaxation time, the repetition time between pulses for yttrium was about 45 min. Magic Angle Spinning (MAS) 27 Al NMR spectra were measured at spinning rates 10 and 14 kHz.

Results and Discussion

As the emission spectra were not corrected, their maxima positions and FWHM differ from the true ones, especially in the energy range >5 eV due to the decreasing sensitivity of the detection system with the increasing emission energy. In YAP SCF, all the intrinsic and defect-or impurity-related emissions are most effectively excited in the exciton absorption region. The emissions of YAP SC are effectively excited in the 7.80 [9]; 7.9

Self-trapped and localized exciton luminescence in YAP single crystalline films

As it was mentioned above, the number of the antisite and vacancy-related defects is strongly suppressed in SCF as compared with SC. Therefore, in the emission spectrum of YAP SCF, the STE band should be the dominating one. In the uncorrected emission spectrum of YAP SCF, measured at 10 K under excitation in the 8.40-7.95 eV range, the most intense band peaking at ≈5.6 eV is observed (figure 1 a, curves 1-3) which should arise from the STE. The excitation band of this emission is located at about 7.83 eV (figure 2 a) (see table 1). The band gap energy in YAP is E g =8.8 eV [START_REF] Kirm | Physics and Chemistry of Luminescent Materials PV 99[END_REF][START_REF] Tomiki | [END_REF]. Besides the STE emission, a complex band is observed in YAP SCF, consisting of at least three components with the maxima at 4.16 eV, 3.63 eV, and 3.15 eV (figure 1 a, curve 4). Two later bands arise from the single and dimer Pb 2+ -based centers [10]. A wide 4.16 eV emission, observed in [8] at 4.19 eV and ascribed to an exciton localized near a Pb 2+ ion, is excited around 7.6 eV (figure 2 b). The origin of the analogous (4.3 eV) emission in LuAG SCF was studied in detail [20]. By analogy with [20], we suggest that the 4.16 eV emission arises from an exciton localized near a Pt 4+ ion whose presence in SCF is caused by the use of a platinum crucible at their preparation. In the excitation spectrum of the 3.63 eV emission of the single Pb 2+ -based centers, the 7.66 eV band is observed (figure 3 a). In the excitation spectrum of the 3.15 eV emission of the dimer {Pb 2+ -V O -Pb 2+ } centers, the band located at 7.74 eV is present (figure 3 b). These bands can arise from the excitons perturbed by the single and the dimer Pb 2+ -related centers, respectively. The appearance of the intra-centre 3.63 eV and 3.15 eV emissions under excitation in the exciton 7.66 eV and 7.74 eV bands means that the excitation energy is effectively transferred to the corresponding lead centers. The different position of the excitation band of the 4.16 eV emission as compared with those of the lead-related 3.63 eV and 3.15 eV emissions (table 1) confirms our conclusion that the 4.16 eV emission is not connected with lead ions.

Intrinsic luminescence of YAP single crystals

In the uncorrected emission spectrum of YAP SC, the 5.63 eV and 4.12 eV emissions are observed (figure 1 b). As it was mentioned in the Introduction, different interpretations were given for the highest-energy intrinsic emission band [7][8][9][13][14][15][16][17]. As in SC, containing a lot of antisite and vacancy-related defects, the STE emission should be strongly suppressed, the 5.63 eV emission is surely connected with an antisite defect. In [17], a weak 5.28 eV emission was ascribed to ex 0 Y 3+ Al . However, this emission is not excited in the exciton absorption region (figure 1 b). This is evident also from the complete coincidence of the excitation spectra shown in figures 4 a and 4 b. The relative intensity of the 5.28 eV emission is much larger under Xray excitation. By analogy with the ≈4.3 eV emission of LuAG [20], we suggest that the 5.28 eV emission arises from recombination processes. The 4.2 eV emission found in [12] has been ascribed to the exciton-based center [15,16,21]. This emission was observed also in the thermally stimulated luminescence (TSL) spectra of undoped YAP SC [13,16,22] and ascribed [22] to an exciton localized around a single oxygen vacancy.

The results obtained indicate that the characteristics of the 5.63 eV and 4.12 eV emissions in YAP SC differ from the characteristics of the STE emission in YAP SCF. In the YAP SCF, these emissions are absent [8]. We conclude that both the 5.63 eV and the 4.12 eV emission arise from the excitons localized near Y 3+ Alrelated defects. As the positions of their lowest-energy excitation bands are different: the 5.63 eV emission is excited around 7.9 eV (figure 5 a), while the 4.12 eV emission at 7.13, 7.65 eV (figure 5 b), it means that the defects responsible for these emissions are different as well. One can suggest that these emissions arise from an exciton localized near a single antisite defect: ex 0 Y 3+ Al and from an exciton localized near the Y 3+ Al defect associated with an oxygen vacancy V O : ex 0 {Y 3+ Al -V O }. The presence of Y 3+ Al -V O defects in YAP SC has recently been confirmed by the ESR method [23] where the paramagnetic electron centers of the type of Y 2+

Al -V O were detected in the irradiated crystals. Their emission band is located at 2.45 eV [24]. Table 2. Structural parametres of YAlO 3 . Space group Pmna (53) and lattice parametres a = 5.334 Å, b = 7.375 Å, c = 5,180 Å were taken from the x-ray diffraction data [32]. The fractional atomic coordinates, Y (x,1/4, z), Al (0,0,1/2) O1 (x,1/4,z), O2 (x, y, z) are obtained by total energy minimization and compared with x-ray refinement (experiment). There are four formula units per primitive cell.

Other code [33] FPLO [3,12]. The reduction of the 5.63 eV emission intensity is accompanied with the enhancement of the 4.12 eV emission [3]. In YAP:Ce SC, the TSL peaks are observed at the temperatures ≈200 K and ≈280 K (figure 6, solid line, see also [22]) corresponding to the thermal quenching of the 5.63 eV and 4.12 eV emissions, respectively. Due to the effective positive charge of an oxygen vacancy, the thermal stability of the electron centers based on Y 3+

Al -V O defects should be larger as compared with the electron centers based on single Y 3+ Al defects. Therefore, the TSL peaks at ≈200 K and ≈280 K can arise from the recombination of electrons, thermally released from Y 3+ Al and Y 3+ Al -V O traps, respectively, with the hole Ce 4+ centers. Indeed, the thermal quenching of the 2.45 eV emission, caused by the electron release from Y 3+ Al -V O traps, takes place just around room temperature [24]. The conclusion on the origin of the ≈200 K and ≈280 K peaks is also confirmed by the fact that these peaks are absent in the YAP:Ce powder (figure 6, dashed line). Indeed, as this material was not melted at any preparation stage, the concentration of antisite defects in the YAP:Ce powder should be considerably lower as compared with the melt-grown YAP:Ce single crystals.

The existence of the defects of the type of Y 3+

Al -V O was suggested also for Y 3 Al 5 O 12 [25,26]. Clustering of Ce 3+ ions with Lu Al 3+ antisite defect was observed by the ESR method in Lu 3 AlO 12 :Ce SC [27], and clustering of Ce 3+ and oxygen vacancy was considered in Lu 2 SiO 5 :Ce single crystals [28]. Thus, such defect clusters are repeatedly considered or evidenced in complex oxides to explain the observed characteristics. On the contrary, the atomistic simulations [29] found a negative binding energy for the {Y Al 3+ -V O } defect in Y 3 Al 5 O 12 and the authors concluded that these defects would not exist. However, despite the fact that there is no electrostatic attraction between Y Al 3+ and V O , one should take into account that a large Y 3+ ion substitutes a much smaller Al 3+ ion and, hence, the location of Y 3+ Al defect close to V O can be preferable. Indeed, in Section 2.3. the density functional theory calculations of formation energies of various antisite-related defects in YAlO 3 showed that the formation of the associate of antisite defect with oxygen vacancy is more preferable as compared with a single antisite defect.

Calculation of the Y 3+

Al , {Y 3+ Al -V O }, and {Y 3+ Al -Ce 3+ } defects formation energies Ab-initio computations allow the determination of the total energy as a function of ionic coordinates and types of ions, and thus provide independent information about the microscopic structure of a defect and clarify some defect models. The density functional theory (DFT) calculations were performed by us within the local spin-density approximation (LSDA). We have used the all-electron full-potential local-orbital (FPLO)_ code _version 7.00-28 [30]. In our scalar relativistic calculations, the exchange and correlation potential of Perdew and Wang [31] was employed. The k-mesh gives the subdivision of the Brillouin zone along the three axes from which the k-space integration mesh is constructed. We have used the default value 12x12x12 for pure YAlO 3 and 6x6x6 for supercells with defects. The defect energy was calculated using 20-atom P nmasymmetry cell, where the lattice parameters were taken from x-ray diffraction data [32].

Using the supercell calculations, we have first obtained the formation energy of Y Al -Al Y antisite defect by comparing the ground state total energy of perfect cell with that of cells with single Y-Al interchanges. The structural parameters used are summarized in table 2. As it can be seen from the table obtained using the LSDA calculations, the relaxed structure is close to the experimentally found one [32] and is consistent with the density functional results published earlier [33].

The calculated energies for different configurations of antisite defects are summarized in table 3. We found the antisite defect formation energies in the presence of the nearest-neighbouring oxygen vacancy as well as in the presence of a Ce 3+ impurity ion. The formation of the antisite defect is more preferable in the cases where there is an oxygen vacancy nearby, which settles close to the direction Al -V O -Al. The formation energy of the such type defect is 25 % lower as compared with the energy of the antisite ion with an oxygen vacancy V O in a farther environment. We have also calculated the total energy for a supercell, in which a Ce 3+ ion substitutes for an Y ion, and found that the antisite defect formation is facilitated when Ce 3+ occupies the nearest Y 3+ site (see table 3).

Our calculations have also shown that the ground state energy of the Ce 3+ -doped YAP lattice with the oxygen vacancy near Ce 3+ is on 0.25 eV lower than the energy of the lattice in which the oxygen vacancy is located far from the Ce 3+ ion.

In the case where Y 3+ substitutes for the Al ion nearby the oxygen vacancy, the Y 3+ ion must be shifted towards the vacancy because the Y 3+ ion is much larger than the Al 3+ ion. The total energy dependence on the displacement of an Y 3+ antisite ion is presented in figure 7. One can see that the calculation predicts the Y 3+ ion displacement from the Al position in the direction towards the oxygen vacancy by a distance of about 0.34 Å.

Figure 7.

The total energy dependence on the displacement of an Y 3+ ion which replaces Al 3+ obtained for the case when the oxygen vacancy is close by.

It should be noted that the calculations of the defects formation energies were performed for the ideal stoichiometric YAP lattice. Commercial YAP single crystals are usually grown with a small excess of Y ions that prevents the substitution of Al ions for Y sites. Therefore, in general case, the probability of creation of different type defects depends also on technological parameters which have to be taken into account under analysis.

The excitons perturbed by Ce 3+ -related centers in SC and SCF of YAP:Ce

At 4.2 K, the emission spectrum of Ce 3+ centers in YAP:Ce consists of two components peaking at 3.30 eV and 3.55 eV (see, e.g., [3,6]). In SC and SCF of YAP:Ce, the excitation spectra of the Ce 3+ emission in the exciton absorption region are considerably different (see also [7,9]). The main exciton band is located at ~7.7 eV in SC (figure 8 a), but at about 7.9 eV, in SCF (figure 8 b). These bands are most probably arising from an exciton perturbed by a Ce 3+ -related defect. As the main difference between SCF and SC is in the absence of antisite defects in SCF, we assume that the 7.9 eV band arises from an exciton perturbed by a single Ce 3+ ion, while the band around 7.7 eV, from an exciton perturbed by a Ce 3+ ion associated with the antisite defect Y 3+ Al (see table 1). The preferable location of antisite defects close to Ce 3+ ions is confirmed by the calculations of the {Y 3+ Al -Ce 3+ } defect formation energy (see Section 2.3) and by the fact, that in LuYAP:Ce and LuAP:Ce where the content of antisite defects should be larger [34,35], the abovementioned difference in the excitation spectra in SC and SCF is also larger [9,17,35]. The presence of nonequivalent Ce 3+ centers in YAP:Ce and LuYAP:Ce has been noticed also earlier [6,36]. The comparison of the excitation spectra of the slow and fast decay components of the Ce 3+ emission in the exciton region (figure 8) indicates that in YAP SC, unlike YAP SCF, a competition exists between the processes responsible for these components (see also [7][8][9]). Indeed, the excitation spectrum maximum of the fast component coincides with the excitation spectrum minimum of the slow component. Similar competition was observed in YAP:Ce SC between the processes of defects creation and excitation of the Ce 3+ emission in the exciton absorption region [6]. As the absorption/excitation bands of Ce 3+ are strongly overlapped with the intrinsic emission bands of YAP SC and SCF (figure 1), one can assume that the appearance of the slow components in the Ce 3+ emission decay is caused by the energy transfer from the corresponding defects to Ce 3+ ions. However, the excitation bands of the defect-related emissions (figures 2b -5) do not coincide with the excitation spectrum of the slow component of the Ce 3+ -related emission in the exciton absorption region (figure 8). Only in the 7.6-7.7 eV range, the slow component of the Ce 3+ emission in YAP SC can arise from the above-mentioned energy transfer processes. Therefore, one can assume that the slow component of the Ce 3+ emission appears around 8.0 eV mainly due to the tunneling recombinations between the electron centers and hole Ce 4+ centers produced as a result of the photostimulated disintegration of the regular exciton state. The tunnelling recombination processes in YAP were considered also earlier [22,37]. In the energy range <7.5 eV, the slow component can appear in YAP SC due to the tunneling recombinations in the pairs consisting of an antisite-defect-related electron center and hole Ce 4+ center, both produced as a result of the photoionization of the higher-energy excited states of Ce 3+ or the photostimulated electron transfer processes [6].

The comparison of the lowest-energy exciton bands in the excitation spectra of the lead-related emission (figure 3) and the Ce 3+ emission (figure 8 b) indicates that there is no energy transfer from the lead-induced centers to Ce 3+ -related centers. However, the energy transfer from Ce 3+ to dimer lead centers can take place.

89 Y and 27 Al NMR study

In the previous study [23] we have shown high ability of NMR to detect the presence of the Y Al antisite ions. In particular, single crystal 89 Y NMR measurements have shown the presence in YAP SC of Y Al ions in the concentration of 2-3%. It is expected that in the YAP powder the concentration of irregular Y ions should be much smaller than in single crystals and NMR could prove this statement. However, unfortunately, 89 Y NMR in YAP powders is too weak and broad to resolve the irregular Y positions, and the Magic Angle Spinning (MAS) measurements for 89 Y were not possible due to low Larmor frequency (19.6 MHz) and long spinlattice relaxation time (45-60 min) of this nucleus.

In the present work, we have performed the studies of 27 Al NMR in YAP ground single crystals and in the commercial YAP powder QM58/N-S1 with the aim to look for Al antisite defects. In YAP single crystals or powders, 27 Al static NMR spectra are too broad to resolve the spectral component responsible for Al at irregular positions. However, the application of MAS technique enables effective narrowing of the NMR linewidth, so that inequivalent positions of ions can be resolved in MAS spectra. 27 Al NMR spectra measured in the ground single crystal and in the commercial powder are shown in figure 9. 27 Al chemical shifts are quoted with respect to the octahedral AlO 6 resonance of Y 3 Al 5 O 12 . Static linewidth of the central 1/2 ↔ -1/2 transition is large, about 3.5 kHz, while the MAS linewidth is only 0.3 kHz. Besides of the strong central transition at 10 ppm, the MAS spectrum consists of broad quadrupole sidebands visible at spinning frequencies and a weak intensity line which appears in ground single crystal at both spinning rates. Its position, 50-55 ppm, suggests that this resonance can originate from Al ions in five-fold coordinated AlO 5 positions. It is well known (see, e.g., [START_REF] Smith | Multinuclear Solid-State NMR of Inorganic Materials[END_REF]) that 27 Al chemical shift strongly depends on the Al coordination number. In Al-O environments, the 27 Al chemical shifts occur at about 60-90 ppm and -10 to 15 ppm for 4coordinated and 6-cordinated Al, respectively. The isotropic chemical shifts of 5-coordinated Al in welldefined crystalline compounds fall between these two ranges at about 30-50 ppm. Therefore, the weak resonance at 50-55 ppm can originate from Al in the octahedral position where one of the six oxygen ions is missing, i.e., oxygen vacancies are detected. Our assignment agrees with the fact that this spectral component is undetectable in commercial powder which was sintered at a much lower temperature than the temperature used in bulk crystals growth (about 2000 o C). Therefore, the powder should contain a much lower concentration of oxygen vacancies. The formation of oxygen vacancy defects is crucially dependent on the preparation temperature and is an inevitable consequence of using both the high growth temperature and the reducing atmosphere of the bulk crystals grown from the melt by Czochralski, Bridgman or similar methods. The relative concentration of AlO 5 units (isolated oxygen vacancies) in SC was estimated from the integral intensities of NMR lines as (0.3-0.5) %. However, the total concentration of oxygen vacancies is obviously larger as part of the vacancies is coupled to Y Al antisite ions and is not visible in 27 Al NMR. Possible 27 Al resonance from Al Y antisite positions (12-fold Al coordination) is expected be at the chemical shifts -40 to -90 ppm. To our best knowledge, actual of the chemical shifts of 12coordinated Al not been reported yet because such crystalline compounds probably do exist in a stable state. One can see from figure 9 that at the chemical shifts of to -100 ppm, there are no resonances. This means that the of Al Y antisite ions in SC is lower than the detection limits about 0.05-0.1 %. It is also worth mentioning that commercial YAP single crystals are usually grown with small excess of Y ions that obviously prevents the substitution of Al ions for Y sites. Finally, our single crystal NMR measurements of the 27 Al quadrupole transitions also did not reveal any additional resonances related to possible Al Y ions.

Conclusion

The detailed study of luminescence characteristics of undoped and Ce 3+ -doped SC and SCF of YAP and the analysis of published data has allowed us to identify the origin and structure of the defects responsible for various localized exciton emission bands. In YAP SCF, the relatively weak ≈5.6 eV emission of the STE is the dominating one. The antisite defects of the type of Y 3+

Al and Y 3+ Al -V O are absent. In YAP SC, the STE emission is practically absent, the 5.63 eV emission is assumed to arise mainly from ex 0 Y 3+ Al , while the 4.12 eV emission, from ex 0 {Y 3+ Al -V O }. In X-irradiated YAP:Ce SC, the thermally stimulated destruction of the Y 3+

Al -and {Y 3+ Al -V O }-related electron centers takes place around 200 K and 280 K, respectively. The recombination of the released electrons with Ce 4+ centers is accompanied with the Ce 3+ emission. An effective formation of the {Y 3+ Al -V O }-type defects in YAP single crystals is confirmed by the theoretical calculations. The presence in SC of Y 3+ Al -related defects and isolated oxygen vacancies (AlO 5 units) is confirmed by NMR measurements.

In the excitation spectra of various intrinsic, defect-related and impurity-related emission bands, the regular and various perturbed exciton bands are identified. The comparison of their positions allowed us to clarify the influence of various defects on the appearance of undesirable slow components in the decay kinetics of the Ce 3+ luminescence, which negatively influence the scintillation characteristics of YAP:Ce. The conclusion is made that the slow decay is mainly caused by the tunnelling recombination of electron and hole centers created at the disintegration of the regular exciton states and the photoionization of Ce 3+ ions. The contribution of the energy transfer processes between defect and Ce 3+ states is found to be smaller.

Figure 1 .

 1 Figure 1. a) Emission spectra of YAP SCF measured under 8.4 eV (curve 1), 8.15 eV (curve 2), 7.95 eV (curve 3) and 7.6 eV (curve 4) excitations. b) Time-resolved emission spectra of YAP SC measured under E exc =7.95 eV. T=10 K.

Figure 2 .

 2 Figure 2. Time-resolved excitation spectra of YAP SCF (shown in the 6-9 eV range) measured at 10 K for a) the STE emission and b) the 4.19 eV emission of the localized exciton.

Figure 3 .

 3 Figure 3. Time-resolved excitation spectra of YAP SCF (shown in the 4-10 eV range) measured at 10 K for a) the 3.63 eV emission of single Pb 2+ -based centers and b) the 3.15 eV emission of dimer Pb 2+ centers.

Figure 4 .

 4 Figure 4. Time-resolved excitation spectra of YAP SC measured at 10 K for a) E em =5.7 eV and b) E em =5.2 eV.

Figure 5 .

 5 Figure 5. Time-resolved excitation spectra of YAP SC (shown in the 6-9 eV energy range) measured for: a) E em =5.7 eV and b) E em =4.1 eV. T=10 K.

Figure 6 .

 6 Figure 6. TSL glow curves measured at the same conditions with the heating rate 5 K/min for the YAP:Ce single crystal (solid line) and YAP:Ce powder QM58/N-S1 (dashed line) after their X-ray irradiation at 70 K for 30 min (40 kV, 15 mA).

Figure 8 .

 8 Figure 8. Time-resolved excitation spectra of the Ce 3+ emission measured at 10 K for a) YAP:Ce SC and b) YAP:Ce SCF (shown only in the 6-9 eV range).

Figure 9 .

 9 Figure9.27 Al static (insert) and MAS NMR spectra measured in ground YAP single crystal and commercial powder: a) ground SC, spinning rate (SR) 10 kHz; b) ground SC, SR 14 kHz; c) powder, SR 14 kHz. The strong line at 10 ppm corresponds to resonance from regular Al ions in the AlO 6 octahedral coordination, while weak resonance at 50 ppm corresponds to Al in 5-fold coordination. The broad lines visible at spinning frequencies are quadrupole sidebands.

Table 1 .

 1 Luminescence characteristics of perturbed and localized excitons and defects in YAP SC and YAP SCF at 10 K. The maxima positions obtained in the present paper are shown in bold and labelled in the figures.

	Sample	Exciton		Exciton emission, eV	Defect	Lowest-energy exciton
							emission, eV	band, eV
	YAP	STE			5.69 [17]	7.89 [17]
	SC	ex 0 Y 3+	Al		5.9 [12]; 5.69 [8]; 5.28 [17]; 5.63	-	7.88 [8]; 7.95 [16]; ≈7.9
		ex 0 {Y 3+	Al -V O }	4.12	2.45 [29]	7.65; 7.13
		ex 0 V O		4.2 [22]	-	7.67 [17]; 7.6 [13]; 7.52 [8]
		ex 0 Ce 3+		no	Ce 3+	7.80 [9]; 7.9
		ex 0 {Ce 3+ -Y 3+	Al }	no	~Ce 3+	7.75 [9]; ≈7.7
	YAP	STE			≈5.6	-	7.91 [17]; 7.83
	SCF	ex 0 (Pt 4+ )		4.16	-	≈7.6
		ex 0 (Pb 2+ )		4.19 [8]	-	7.59 [8]
		ex 0 (Pb 2+ )		no	3.63 [8]	7.66
		ex 0 (Pb 2+ -V O -Pb 2+ }	no	3.15 [10]	7.74
		ex 0 Ce 3+		no	Ce 3+

Table 3 .

 3 Calculated LSDA total and defect energies of YAlO 3 based on 20-atom supercells.

	Type of defects	Energy of antisite	Total energy (Hartree) 1Hr=27.2 eV
					pair defect (eV)
			YAlO 3		-15394.773028
	Al Y -Y Al (antisite pair)	10.8	-15394.370739
	Al Y -Y Al (V O is nearby)	8.1	-15319.478418
	Al Y -Y Al (V O is far)	10.6	-15319.384259
	Al Y Y Al -Ce 3+	Y	10.2	-20871.244242
	Y Al (V O is far)	-18459.58375
	Y Al (V O is nearby)	-18459.66158
	Ce 3+	Y (V O is nearby)	-20796.646814
	Ce 3+	Y (V O is far)	-20796.637682

Acknowledgments

The work was supported by the projects of the Estonian (No. 8678), Czech (No. 202/08/0893 and GA AV IAA100100810), and Ukrainian (No. SF-28F) Science Foundations as well as by the II-20052049 EC project of DESY, Hamburg. The authors are very much grateful to Paul Ripley (Phosphor Technology Ltd) for useful technological information.


A Tkach

A Almeida
email: amalmeid@fc.up.pt

Agostinho Moreira

A Espinha

M R Chaves

J Perez

La Cruz

P M Vilarinho

J Agostinho Moreira

J Perez De La Cruz

Lithium-induced dielectric relaxations in potassium tantalate ceramics

Keywords: Quantum paraelectricity, Lithium doped potassium tantalate, Dielectric relaxtion properties, Microscopic mechanisms

come

I. INTRODUCTION

Among perovskites having general formula ABO 3 , there exist three compounds, SrTiO 3 , KTaO 3 (KT) and CaTiO 3 , 1 which possess polar soft modes but do not exhibit any ferroelectric phase transition down to 0 K. These materials are classified as incipient ferroelectrics and possess a highly polarizable lattice, thus their properties are very sensitive to defects, impurities, elastic and applied electric fields.

These factors can easily induce ferroelectricity, intermediate glass-or relaxor-like states, making such systems very attractive from both fundamental and technological point of view. In fact, they are attractive candidates for processing microwave devices, nonvolatile memories and photocatalytic water splitters. [2][3][4] Since KT is very sensitive to impurities, several kinds of substitution ions have been used to study their effect on its properties. In particular, K 1-x Li x TaO 3 (KLT) solid solutions with x<0. 16 has been intensively studied, wherein lithium ions substitute for K ions on perovskite A sites, having a coordination number (CN) of 12. The substitution of smaller Li + ions (r Li + = 1.25 Å extrapolated for CN = 12) for larger K + ions (r K + = 1.64 Å for CN = 12) 5 yields a displacement from the centre of A sites by about ~1.26 Å along the cubic [001] direction. 6 Displacements of Li ions generate strong local dipole moments (Li dipoles), which couple electrostatically to the KT polar soft mode. The combination of Li-dipoles relaxations, their interactions, and the soft mode leads to complex nature of the dielectric response in KLT. 7,8 Dielectric measurements on KLT single crystals with 0<x<0.02 reveal only one relaxational peak in (T) at low temperature, while for x>0.02, two peaks are observed. These two peaks have been associated with two distinct relaxational processes, termed low-T and high-T relaxations. [9][10][11] The low-T process with an activation energy of 78<U<125 meV has been associated with isolated Li ions hopping from one <001> position to another. 12 However, the high-T process with an activation energy of 181<U<241 meV is poorly understood. On the basis of acoustic measurements, it was suggested that this latter process could be due to 180°reorientations of Li ions within dipole pairs. 10 While K 1-x Li x TaO 3 single crystals have been intensively studied with considerable success in the last decades, to the best of our knowledge no systematic experimental work has yet been carried out in KLT-based ceramics, so far. This is because polycrystalline KTaO 3 is hard to process as a phase pure stoichiometric compound with relatively high density. However, there are several important advantages of ceramics, compared to single crystals: 1) ceramics are less expensive to be processed than single crystals; 2) the doping control in ceramics (including dopant amount and site occupancy) is easier than in single crystals; and 3) ceramics can be tailored by the processing in a large variety of shapes, sizes and other properties, making them distinctive candidates for a wider range of applications than single crystals. Currently, they are also highly requested as targets for processing and developing thin films and super-lattices for applications in emergent technologies. Thus, the aim of this work is a systematic study of K 1-x Li x TaO 3 by dielectric spectroscopy and polarization inversion, using ceramic samples. The experimental data will be further analyzed with comprehensive theoretical models, and the relaxation characteristic parameters obtained thoroughly compared with those earlier reported for single crystals.

II. EXPERIMENTAL PROCEDURE

KTaO 3 , K 0.98 Li 0.02 TaO 3 , K 0.95 Li 0.05 TaO 3 , and K 0.90 Li 0.10 TiO 3 ceramic samples were prepared by conventional mixed oxide method. Dried grade K 2 CO 3 , Li 2 CO 3 and Ta 2 O 5 reagents were weighed according to the aforementioned compositions with initial (K+Li)/Ta ratio = 1.05 in order to compensate the 5% loss of alkali ions during sintering. 13,14 After ball milling in alcohol for 5 h using teflon pots and zirconia balls in a planetary mill, the powders were dried, and then calcined at 875 °C for 8 h. The calcined powders were milled again for 5 h to obtain powders with particle size lower than 5 µm. Pellets of 10 mm in diameter were uniaxially pressed at 100 MPa, covered by powder of the same composition to decrease the loss of potassium, and sintered in closed alumina crucibles at 1300-1350 °C for 1 h with a heating and cooling rate of 5 °C/min.

The density of the sintered samples, measured by the Archimedes' method using diethylphthalat as the immersion liquid, is ~88%. Room temperature x-ray diffraction analysis did not detect any secondary phase. The grain size was obtained using scanning electron microscopy to be about 6 µm.

For the dielectric measurements, sintered samples were polished and gold electrodes were sputtered on both sides.

The real ( ') and imaginary ( '') parts of the dielectric permittivity in the frequency range of 10 2 -10 8 Hz, as well as the electric polarization versus electric field at 2.5 Hz were measured, using both a Precision LCR Meter (HP 4284A) and a RF Impedance Analyzer (HP 4191A), and a ferroelectric tester (TF analyzer 1000 AIXACT) with amplifier, respectively. The temperature could be altered from 10 to 300 K using a He closed cycle cryogenic system (Displex ADP-Cryostat HC-2), equipped with a digital temperature controller (Scientific Instrument Model 9650). The temperature was measured with a silicon diode with a precision of ~0.1 K.

III. RESULTS AND DISCUSSION

A. Dielectric anomalies induced by Li doping in KTaO 3

The temperature dependence of the real and imaginary parts of the dielectric permittivity ( '-j ''), as well as of the dissipation factor, tan = ''/ ', measured at a frequency of 10 kHz in a heating run on K 1-

x Li x TaO 3 (x = 0, 0.02, 0.05, and 0.10) ceramics, is presented in Figures 1a,1b, and 1c, respectively. As seen from Figure 1a, undoped KTaO 3 ceramics reveal a classic incipient ferroelectric behavior, i.e., a continuous increase of ' with temperature decrease similar to that of KTaO 3 single crystals. In contrast to undoped KTaO 3 , '(T) of Li-doped KT ceramics reveal a diffuse peak, which amplitude and position depend on Li content. As shown in Figures 1b and1c

B. Analysis of the dielectric relaxations of K 1-x Li x TiO 3 ceramics

The analysis of each dielectric relaxation was carried out assuming a Debye approximation.

Accordingly, the set of independent dipoles is characterized by a unique relaxation time ( ), which is equal to the inverse of the angular relaxation frequency ( ). All the parameters of the relaxation dynamics were deduced from the temperature dependence of ''. First, all the relaxations were described by an Arrhenius law:

= 0 exp(U/k B T), ( 1
)
where 0 is the relaxation time at infinite temperatures, and U is the activation energy of the dipolar process. In order to determine 0 and U a linear fitting to the experimental data plotted as ln( -1 ) versus 1000/T ''m is carried out in the frequency range of 10 2 -10 8 Hz.

As shown in Figure 5, dynamics of both contributions of peak A in all studied KLT ceramics is well described by the Arrhenius law with the relaxation time pre-exponents 0A1 , 0A2 ~10 -13 s, and activation energies U A1 ~77 meV and U A2 ~96 meV, as presented in Table 1.

Dynamics of peak B for x = 0.02 could be analyzed in the same way as referred to above (Figure 5), wherein 0B ~10 -15 s and U = 212 meV (see Table 2). However, when following the same procedure for peak B1 in K 0.95 Li 0.05 TaO 3 and peaks B1 and B2 in K 0.90 Li 0.10 TaO 3 ceramics, a 0 ~10 -18 s was obtained, which is too small to have any physical meaning. Conversely, dynamics of peak B could be achieved by using for the temperature dependence of the relaxation time the Vogel-Fulcher relation:

= 0 exp(U/k B [T-T f ]), (2)
where T f stands for the freezing temperature of the relaxation process. The fitting procedure yields 0 ~10 -13 s, U ~97 meV, and T f ~63 K for peak B1, as present in Table 2. For peak B2 in K 0.90 Li 0.10 TaO 3 ceramics, 0 ~10 -14 s, U ~81 meV, and T f ~94 K were obtained as shown in Table 2 as well.

Here we would like to notice that the relaxation processes following the Arrhenius law were widely observed in Li-doped KT single crystals by a number of techniques, but usually no more than two relaxations were found. characterized by a quadrupolar relaxation, i.e., reorientation of Li + between equivalent sites on orthogonal axes by 90°( /2 flipping). 10,12 Since these values of activation energy are close to those obtained in the current work for the relaxation A1, it can also be associated with individual /2 flipping of small lithium ions on the large potassium sites in KLT ceramics. The second group, with U = 86-125 meV obtained for KLT crystals with x = 0.011-0.070 (Refs. 9, 11, 12, 19-22) is related to dipolar relaxation, i.e., reorientation of Li + between equivalent sites on the same axis by 180°( flipping). 12 In this range of activation energy, also falls the relaxation A2, thus revealing that the corresponding relaxation mechanism is assigned to the flipping of off-central Li + K in KLT ceramics. The third group, with U = 181-241 meV obtained for KLT crystals with x = 0.025-0.160 (Refs. 9-11, 20, 22, 23) is ascribed to the reorientation of pairs of coupled dipoles in head-to-tail configurations along the same axis by 180°( pair flipping). 10 An activation energy inside that range is obtained in the current work for KLT with x = 0.02, revealing that relaxation B in this composition stems from the flipping of Li + K pairs. Regarding the fitting of the Vogel-Fulcher relation to the high-T experimental data in KLT ceramics with x = 0.05 and 0.10, the relaxation parameters obtained evidence the apparent off-centre displacements of small lithium ions on the large potassium sites within polar clusters. 7 Moreover, the similarity of the activation energy for relaxations A2 and B1 as well as A1 and B2 implies the same type of the Li reorientations. The difference is just that Li ions flipping is individual for low-T A relaxations, while it is collective for high-T B relaxations, which then become frozen on cooling down.

In contrast to Arrhenius law, there are only few works reporting applicability of the Vogel-Fulcher relation to KLT system. Laguta et al. obtained 0 ~10 -14 s, U A1 ~79 meV, and T f ~12 K for K 0.97 Li 0.03 TaO 3 , 17 whereas Yokota et al. reported parameters 0 ~10 -12 s, U A1 ~88 meV, and T f ~56 K for K 0.93 Li 0.07 TaO 3 . 24 The later parameters are close to those obtained in the current work for K 0.95 Li 0.05 TaO 3 and K 0.90 Li 0.10 TaO 3 . Applicability of the Vogel-Fulcher relation is a characteristic feature of relaxors. 17

C. Polar behavior of K 1-x Li x TaO 3 ceramics

The emergence of slim S-shaped P(E) hysteresis loops is a characteristic feature of disordered and frustrated systems like dipolar glasses and relaxors. 18 So, in order to figure out the actual nature of the dielectric relaxations in K Remnant polarization P r deduced from the loops obtained at electric field of 25 kV/cm is plotted on the bottom panel of Figure 1 as a function of temperature. P r (T) reveals a distinctive similarity to the behavior of the dielectric loss, despite the difference in the test signal frequency (10 kHz for dielectric measurements and 2.5 Hz for P(E) measurements). The temperature dependence of P r is actually characteristic of dipolar glasses and relaxors in unpoled state, revealing peaks around the maximum amplitude temperatures of A and B relaxations, and a smooth decrease of P r with increasing temperature, in evident contrast to classic ferroelectrics. For KLT single crystals, S-shape hysteresis loops were also reported for x = 0.035. 18

D. Crossover from dipolar glass to relaxor-like behavior

Three main distinct features of dipolar glass or relaxor-type behavior are observed on K 1-x Li x TaO 3 ceramics with x = 0.02, 0.05, and 0.10. Firstly, a rounded peak in the temperature dependence of ' is observed, in contrast to the sharp peaks at the phase transition temperatures characteristic for classic ferroelectrics. Moreover, the ' peak always occurs at a temperature higher than wherein the loss peak is observed (Figures 1, 2, 3, and 4). Secondly, as opposed to classic ferroelectrics both a frequency dispersion of ' in the radio-frequency range, and a rather slow relaxation time are evidenced (Figures 2, 3, and4). Finally, slim hysteresis loops were observed, as opposed to more squared-shaped loops of classic ferroelectrics (Figures 678). Furthermore, analysis of the experimental data presented above by Debye relaxation model, and both Arrhenius and Vogel-Fulcher relations, confirmed the possibility to obtain dipolar glass or relaxor phases in K 1-x Li x TaO 3 by just varying the lithium content. For weakly doped K 1-x Li x TaO 3 ceramics with x = 0.02, only Arrhenius law is valid, thus yielding a dipolar glass behavior for low lithium content. For moderately doped K 1-x Li x TaO 3 ceramics with x = 0.05 and 0.10, though a dipolar glass behavior is still apparent for A-type relaxations, a compliance with the Vogel-Fulcher relation is distinctly observed for the B-type relaxations. Hence, the dynamics in K 1-x Li x TaO 3 can be rather understood in the scope of a crossover from a dipolar glass to a relaxor-like behavior as the lithium content gradually increases.

IV. CONCLUSIONS

The dielectric and polar response of K 1-x Li x TiO 3 ceramics (x = 0-0.10), prepared by conventional method, was analyzed in wide frequency and temperature ranges. relaxor-like behavior as the lithium content gradually increases. Thus, relaxations A1 and A2 were attributed to quadrupolar ( /2) and dipolar ( ) reorientations of individual Li + K , respectively, whereas relaxation B (B1) is related to the -reorientation of Li + K pairs (for x = 0.02) or clusters (for x = 0.05 and 0.10). An additional relaxation B2, detected for the first time for x = 0.10, was assigned to /2reorientation of Li + K clusters. All the relaxations are accompanied by slim S-shape P(E) hysteresis loops. Thus, Li-doped KT ceramics studied in this work may be definitely considered as a reliable representative of K 1-x Li x TaO 3 system along with widely reported KLT single crystals.

Figure 4 .

 4 Figure 4. Relaxations B1 and B2 were detected for x = 0.05 as well, but the relaxation dynamics could be further defined only for the dominant contribution B1.

  Dielectric relaxations were induced by Li doping on the background of classic incipient ferroelectric behavior of undoped KTaO 3 . For weakly doped K 1-x Li x TiO 3 (x = 0.02), the relaxation dynamics follows well Arrhenius law with activation energies U A1 = 78 meV, U A2 = 102 meV and U B = 212 meV. For moderately Li-doped potassium tantalate (x = 0.05-0.10), the low-temperature relaxations also obeys Arrhenius law with U A1 = 76-78 meV and U A2 = 91-95 meV. Contrarily, the high-temperature relaxations follow Vogel-Fulcher relation with U B1 = 96-99 meV and U B2 = 81 meV together with freezing temperatures T fB1 = 59-66 K and T fB2 = 94 K. The change from an Arrhenius to a Vogel-Fulcher relation shows that the dynamics in K 1-x Li x TaO 3 can be apprehended in the scope of a crossover from a dipolar glass to a

Figure 1 .

 1 Figure captions

Figure 2 .

 2 Figure 2. Real ' (a) and imaginary '' (b) parts of the dielectric permittivity, and dissipation factor tan (c) of K 0.98 Li 0.02 TaO 3 ceramics at different frequencies from 10 2 to10 8 Hz as a function of temperature.

Figure 3 .

 3 Figure 3. Real ' (a) and imaginary '' (b) parts of the dielectric permittivity, and dissipation factor tan (c) of K 0.95 Li 0.05 TaO 3 ceramics at different frequencies from 10 2 to10 8 Hz as a function of temperature.

Figure 4 .

 4 Figure 4. Real ' (a) and imaginary '' (b) parts of the dielectric permittivity, and dissipation factor tan (c) of K 0.90 Li 0.10 TaO 3 ceramics at different frequencies from 10 2 to10 8 Hz as a function of temperature.

Figure 5 .

 5 Figure 5. Arrhenius plots ln( ) vs 1000/T ''m for relaxations A (a) and B (b) of K 1-x Li x TaO 3 ceramics with fits to Arrhenius law (solid lines) and Vogel-Fulcher relation (dash lines).

Figure 6 .

 6 Figure 6. Polarization P versus electric field E of K 0.98 Li 0.02 TaO 3 ceramics at 2.5 Hz at selected temperatures from 10 to 295 K.

Figure 7 .

 7 Figure 7. Polarization P versus electric field E of K 0.95 Li 0.05 TaO 3 ceramics at 2.5 Hz at selected temperatures from 10 to 295 K.

Figure 8 .

 8 Figure 8. Polarization P versus electric field E of K 0.90 Li 0.10 TaO 3 ceramics at 2.5 Hz at selected temperatures from 10 to 295 K.

Figure 1 Figure 2

 12 Figure 1

Figure 3

 3 Figure 3

Figure 4

 4 Figure 4

Figure 5 Figure 6

 56 Figure 5

Figure 7

 7 Figure 7

Figure 8

 8 Figure 8

  10,12 The exception is the early work by Prosandeev et al. on K 0.957 Li 0.043 TaO 3 single crystal, where relaxation processes with activation energies of 85, 104 and 241 meV (i.e., similar to 77, 96 and 212 meV obtained in the current work) were reported.11 First relaxation was associated with Fe-related defects, usually detected in KTaO 3 as 'an unavoidable impurity'.11 However, similar parameters obtained by Prosandeev et al. in weakly doped K 0.994 Li 0.006 TaO 3 single crystal were associated with the /2-relaxation.15 Moreover, our analysis of the dielectric response of undoped KTaO 3 ceramics prepared in the same way as Li-doped ceramics does not yield any relaxation process with such parameters, disproving the 'unavoidable impurity' mechanism. The second and third relaxations of K 0.957 Li 0.043 TaO 3 , observed in the single crystals, were associated with the off-centre /2-rotations of Li + , and the -rotations of Li + pairs, respectively.11 As referred to above, there are several works on Li-doped KT single crystals that report values of U and 0 parameters, obtained by fitting the Arrhenius law to the experimental data. According to the values of those parameters, several mechanisms have been proposed for the observed dielectric

relaxations. In this work, we have systematized the earlier reported results, as listed in Table

3

, to avoid any misinterpretations. Three main groups can be identified in terms of activation energies. The first group, with U = 78-86 meV obtained for KLT crystals with x = 0.006-0.050 (Refs. 9-12, 15-18) is

  1-x Li x TaO 3 ceramics, P(E) measurements were carried out over the

temperature range from 12 to 295 K. Figures

6, 7

, and 8 show several characteristic P(E) curves for x = 0.02, 0.05 and 0.10, respectively. Well developed S-shaped hysteresis loops with non-zero remnant polarization P r suggest the existence of either dipolar glass or relaxor-type states in KLT ceramics at low temperatures, as seen from Figures

6 to 8

. At room temperature the polarization vs electric field response is linear for all the samples.

Table 1 .

 1 Arrhenius law parameters for the dynamics of the dielectric relaxations A in K 1-x Li x TiO 3 ceramics.

	Relaxation	x	U, meV	0 , s
		0.02	78	2.7×10 -13
	A1	0.05	78	1.1×10 -13
		0.10	76	1.7×10 -13
		0.02	102	0.8×10 -13
	A2	0.05	91	2.2×10 -13
		0.10	95	2.4×10 -13

Table 2 .

 2 Parameters of Arrhenius law and Vogel-Fulcher relation for the dynamics of the dielectric relaxations B in K 1-x Li x TiO 3 ceramics.

	x	Relaxation	Arrhenius law	Vogel-Fulcher relation
			U, meV	0 , s	U, meV	0 , s	T f , K
	0.02	B	212	3.3×10 -15
	0.05	B1	292	6.1×10 -17	99	6.9×10 -13	59
	0.10	B1	328	4.7×10 -18	96	4.6×10 -13	66
	0.10	B2	416	4.6×10 -19	81	1.6×10 -12	94

Table 3 .

 3 Relaxation mechanisms observed in K 1-x Li x TaO 3 system and their Arrhenius-law parameters.

	Proposed mechanism x	U, meV	0 , s	Ref.
		0.006	78	1.4 × 10 -13	[15]
		0.009	86	1.3 × 10 -13	[16]
		0.010 0.016	84 86	4.1 × 10 -13 3.4 × 10 -13	[17]
	Quadrupolar relaxation -reorientation of Li + between equivalent sites on orthogonal axes by	0.011 0.015 0.035	86 86	0.2 × 10 -13 6.0 × 10 -13	[12] [10]
	90°( /2 flipping)	0.050 0.025 0.033	86 86	50 × 10 -13 8.0 × 10 -13	[9]
		0.035	86	1.6 × 10 -13	[18]
		0.043	85	0.5 × 10 -13	[11]
		0.011	98	1.0 × 10 -13	[12]
		0.012	125	16 × 10 -13	[19]
	Dipolar relaxation -	0.016 0.026	95 95	0.6 × 10 -13 0.6 × 10 -13	[20]
	reorientation of Li +	0.026	95	0.3 × 10 -13	[21]
	between equivalent sites on the same axis by 180°( 0.025 0.033 86 112	8.0 × 10 -13 0.8 × 10 -13	[9]
	flipping)	0.034
		0.050	99	1.0 × 10 -13	[22]
		0.070
		0.043	104	0.8 × 10 -13	[11]
	Reorientation of a pair of
	coupled dipoles in head-
	to-tail configurations

Acknowledgements

This work was supported by Portuguese Foundation for Science and Technology (FCT) through the Project PTDC/CTM/64805/2006. A. Tkach also acknowledges FCT for financial support (SFRH/BPD/34607/2007).


A Alija

A Hierro-Rodríguez

A Pérez-Junquera

J M Alameda

J I Martín

M Vélez
email: mvelez@uniovi.es

Crossed ratchet effects on magnetic domain walls: geometry and transverse field effects

Keywords: 75, 60Ch, 75, 60, Jk; 75, 75, -c Crossed ratchet effects on domain walls: geometry and transverse field effects

Domain wall propagation across a 2D array of asymmetric holes is strongly dependent on domain wall configuration: i.e. on whether the wall is flat or kinked. This results in interesting crossed ratchet and asymmetric accommodation effects that have been studied as a function of geometry and transverse field. Micromagnetic simulations have shown that the observation of crossed ratchet effects is easier for arrow than for triangular holes due to a larger field range in which kink propagation is the preferred mode for domain wall motion. Also, it has been found that dc transverse fields can produce a significant enhancement of the easy axis asymmetric accommodation and, also, that ac transverse fields can be rectified by the crossed ratchet potential.

Introduction

A good understanding of domain wall (DW) propagation in magnetic nanostructures is a key issue for device applications [1,2]. A case of particular interest is the study of ratchet effects that create an asymmetry between forward/backward domain wall propagation. This asymmetry can be of use for the design of DW diodes [3][4][5][6][7][8] and memory devices [9]. A DW ratchet appears whenever the relevant pinning potential is asymmetric either due to an asymmetric geometry as in magnetic nanowires of triangular section [3] or an asymmetric domain wall configuration as in Neel walls of different chirality [10]. Two different sorts of DW ratchets can be found depending on the nanostructure dimensionality: simple forward/backward ratchet in patterned 1D nanowires [3][4][5][6][7][8]10] and crossed ratchets in 2D arrays of asymmetric pinning centers [9,11]. In the first case the sign of the ratchet asymmetry is fixed by nanostructure geometry and/or DW chirality whereas in the second case the sign of the ratchet asymmetry depends on the applied field amplitude and DW configuration. Thus, crossed ratchets allow for a more complex control of DW propagation that can be tuned both by array geometry and external parameters.

Up to now crossed ratchet effects have only been experimentally demonstrated in arrays of arrow holes [9], whereas most of the theoretical analysis and simulations of this phenomenon have been performed using the simpler triangular geometry [11,12]. Also, the pinning interaction between a Neel wall and an array of symmetric patterned holes is known to be quite sensitive to changes in domain wall energy [13] that could be tuned by the application of a small transverse field. In this work we have combined micromagnetic simulations and magnetization measurements in order to analyze the role of two different factors on crossed ratchet effects created by an array of asymmetric holes: hole shape (comparing triangular and arrow holes) and the effect of transverse fields applied along the hard anisotropy axis.

Experimental and simulation details

500 µm × 500 µm arrays of asymmetric holes arranged in a 20 µm × 20 µm square lattice have been fabricated in 40 nm thick amorphous Co 73 Si 27 films by a combined e-beam lithography and etching process, as reported elsewhere [14]. The magnetic films show a well defined in-plane uniaxial anisotropy (K = 1000 J/m 3 ), low saturation magnetization (M S = 2×10 5 A/m) and low coercivity [13]. The asymmetric holes have an arrow shape pointing in a direction perpendicular to the easy axis, as shown in Fig. 1. The arrow shape defines the "forward" (i.e. left to right) propagation sense (correspondingly "backward" propagation indicates right to left DW motion). The magnetic behavior of the patterned films was characterized by Magnetooptical Transverse Kerr (MOTKE) effect, using a set up in which the laser beam is focused in a 300 µm spot, i.e. smaller than the patterned area [15]. The magnetic field H was always applied in the sample plane.

Micromagnetic simulations of DW propagation across similar patterned arrays have been performed with the OOMMF code [START_REF] Donahue | OOMMF User's Guide, Version 1.0[END_REF]. Square arrays of empty triangular/arrow holes have been defined in rectangular thin film elements with material parameters corresponding approximately with those of the Co-Si alloy: M S = 2×10 5 A/m, A = 3×10 -11 J/m and uniaxial anisotropy K = 1000 J/m 3 with the easy axis oriented in the y direction. Typical mesh sizes are 15 -35 nm, smaller than both the material exchange length, δ ex = (2A/µ 0 M S 2 ) 1/2 = 35 nm, and the Bloch parameter δ 0 = (A/K) 1/2 = 170 nm.

Asymmetric pinning potential and hole geometry: micromagnetic simulations

DW propagation across a 2D array of asymmetric defects is characterized by two different field scales corresponding to the softer propagation mode in each sense [9,11]: H F the field needed for forward flat wall propagation and H U the field needed for upward kink propagation in kinked walls which is equivalent to net backward wall motion (see sketches in Fig. 1). In the field range between H F and H U the system displays the typical signatures of crossed ratchet behaviour [9]: inverted asymmetry of minor hysteresis loops relative to major loops and asymmetric accommodation curves that keep memory of the sign of the last saturating state. In this section we will study domain wall propagation across identical arrays of 4 µm holes changing only hole shape (triangular vs. arrow) both for flat and kinked wall configurations.

Simulated magnetization curves and energy landscapes

Figure 2 shows the calculated magnetization curves as a flat DW crosses the sample for a square array of 4 µm triangular holes (Fig. 2(a)) and for a square array of 4 µm arrow holes (Fig. 2(b)). The simulations start from an initial zero field-zero magnetization state with a straight 180º Neel wall located at the film center (see frames I in Fig. 2). Then, this wall is pushed either forward or backward by a continuous positive/negative field H y of increasing amplitude applied along the easy axis for uniaxial anisotropy until positive/negative saturation is reached. The magnetization curves develop a series of steps that correspond approximately with the M y /M S values expected for a DW being pinned at each of the three lines of holes that form the patterned arrays (indicated as solid horizontal lines in Fig. 2). Also, the presence of the array of holes results in a significant enhancement of the saturation field H S in comparison with the behavior of an unpatterned Co-Si element (shown as a dotted line for comparison). In both cases (arrows and triangles), H S is clearly larger for backward than for forward propagation as expected from the individual hole asymmetry. It is interesting to note that backward magnetization curves are very similar for both kinds holes, which can be attributed to the similarities in the relevant backward DW propagation mode: DW depinning starts from the DW segment located between the lower film border and the last hole that, after reaching a critical curvature radius, slides along the vertical hole side (see frames B1 and B2 in Fig. 2). However, the differences in hole shape clearly show up in forward propagation curves that present broader steps for triangles than for arrows and a larger saturation field in the second case.

Further information on the DW propagation process can be obtained by energy landscapes calculated as the wall crosses the array of defects under a constant applied field, [12] that allow us to separate the different possible DW propagation modes in a more accurate way than with the global magnetization curves. starting from an initial kinked wall pinned in between two lines of arrows can be seen in Fig.

3(b)

. The energy landscape displays again a triangular potential well but with opposite asymmetry than for the flat wall depicted in Fig. 3(a): now the gradual slope corresponds to net backward DW motion (i.e. as the kink proceeds upward). This change in potential asymmetry depending on the geometrical DW configuration is the essential ingredient of crossed ratchet behavior and can only be observed in 2D systems.

Analysis of characteristic fields

In order to make a more quantitative analysis of the asymmetric domain wall propagation several characteristic fields can be defined from the calculated curves of Figs. 2 and 3 as indicated in Table 1. First, the global effect of the array of holes on DW propagation can be characterized by the hardening of the magnetization curve:

For backward propagation, the hardening induced by the arrays of holes is the same for arrows and triangles: µ 0 ∆H B (arrow) = µ 0 ∆H B (triangle) = 1.3 mT, and the differences in shape show up in forward depinning: µ 0 ∆H F (arrow) = 1 mT and µ 0 ∆H F (triangle) = 0.8 mT. These results can be understood using as a first approximation a simplified analytical model with only DW elastic energy and applied field pressure terms [11]. In this model, the critical field for propagation of a DW pinned in between two surfaces of arbitrary shape (such as in between two holes or in between a hole and a border) is inversely proportional to inter hole distance (or hole-border distance) and depends also on the angles made by the limiting surfaces: for triangle holes, the analytical model predicts H F /H B = sin(30º) = 0.5 roughly in agreement with the data in Table 1, ∆H F /∆H B = 0.61; on the other hand, for arrow holes, the results extracted from the simulated magnetization curves give ∆H F /∆H B = 0.77 which lies in between the asymmetry expected for depinning from the arrow base H F /H B = sin(68º) = 0.93 and from the arrow tip H F /H B = 4 µm/6µm = 0.67 (see frames F1 and F2 in Fig. 2(b)).

Table 1: Characteristic fields of the arrays of 4 µm arrow and triangular holes. Thus, the scaled range becomes µ 0 ∆H Cross CALC = 0.16 mT in quite a good agreement with the experimental µ 0 ∆H Cross EXP = 0.2 mT [9].

µ 0 ∆H F (mT) µ 0 ∆H B (mT) µ 0 H F (mT) µ 0 H U (mT) µ 0 ∆H Cross = µ 0 H F -µ 0 H U (mT)

Rectification enhancement in a transverse field

Neel walls, with their complex tail-core structure, are known to be quite sensitive to hard axis magnetic fields [START_REF] Hubert | Magnetic Domains[END_REF][START_REF] Bryan | [END_REF][19]. Thus, transverse magnetic fields could be of use to tune DW propagation across the array of asymmetric holes. In particular, one of the most interesting features in a crossed ratchet is the so called asymmetric accommodation [9]. This phenomenon appears when a DW is introduced in the array of asymmetric holes and, then, the system is excited by a small ac field. As shown previously [9], the walls enter flat into the array and develop kinks as they move forward due to small pinning center inhomogeneities and/or Barkhausen jumps. The ac field allows the pinned wall to relax to a lower energy state in a process governed by kink propagation under the asymmetric crossed ratchet potential.

Transverse field experiments

The influence of a transverse field on asymmetric accommodation can be clearly seen in M y (t). The experiment begins when a large negative field H y is applied to the array of holes at a time t = 0.06 s in order to saturate the array in the negative direction. Then, H y is increased up to the positive coercivity in order to introduce a DW in the array and, finally, it is reduced to zero at t = 0.11 s, in order to prepare a remanent state with a small magnetization indicative of a DW pinned inside the array. Now, after t = 0.16 s, a small oscillating field of increasing amplitude H y_ac is applied to the array so that the pinned wall is alternatively pushed forward and backward. For very low H y_ac the wall stays pinned but, when H y_ac is within ∆H Cross (i.e. H U < H y_ac < H F ) only kink propagation is allowed and the DW displays a net backward motion that results in the asymmetric accommodation of the magnetization towards its last saturating value (-M S in this case): that is, the ac field excitation produces a rectified backward DW propagation that gives rise to a constant magnetization change. This process takes place approximately within 0.16 s < t < 0.23 s and can be characterized by the small negative ∆M y that occurs during this time interval (see dashed horizontal lines in Fig. 4(b)). Eventually, H y_ac becomes large enough to allow extra DWs to be nucleated at the array limits (i.e. H F < H y_ac ) and large positive/negative magnetization oscillations are observed in the M(t) curve due to the growth and annihilation of domains within the patterned array. The accommodation ∆M y is quite different for the two curves plotted in Fig. 4(b), with a much higher value for the curve recorded with the larger transverse field µ 0 H x = 1.7 mT. Figure 4(c) shows the net magnetization increments during the accommodation process as a function of the transverse applied field. ∆M y is almost constant (about 0.05M S ) at low fields but is enhanced more than twofold up to 0.12M S for µ 0 H x above 1 mT.

Figure 5 shows the results of a different transverse field experiment: in this case, the system is first taken to its negative saturation by a large negative easy axis field, then H y is increased close to the positive coercivity in order to introduce a DW in the patterned area and, finally, it is reduced to zero so that a DW is left pinned at remanence inside the array of holes. Now a transverse ac field H ac_x of fixed amplitude is applied to the sample. The corresponding M y (t) signal shows a continuous decrease towards -M S modulated by a small ripple at a double frequency than the excitation field. This ripple is just a signature of the uniaxial film transverse susceptibility [START_REF] Chikazumi | Physics of Magnetism[END_REF]: the hard axis magnetization component is given by M x /M S = H x /H K and, 2 . This quadratic dependence of M y vs.

µ 0 H X (mT) ∆M Y /M S (c) correspondingly, M y /M S = [1-(M x /M S ) 2 ] 1/2 ≈ 1-½(H x /H K )
H x is responsible of the frequency doubling of the observed ripple. More interesting is the observed net magnetization decrease ∆M y produced by the ac hard axis field H ac_x : it is of the same sign as in the easy axis experiments of Fig. 4 and takes very similar values (in the 0.1M S -0.2M S range as shown in the inset of Fig. 5). These results suggest that the transverse field excitation is rectified by the crossed ratchet potential by a similar mechanism as in the easy axis case: i.e. by the net backward motion of the pinned wall due to low field kink propagation.

Discussion on transverse field effects

The experimental results presented in Figs. 4 and5 show a two fold effect of a transverse field on domain wall propagation inside the asymmetric array of holes: asymmetric

M Y /M S µ 0 H X (mT) ∆M Y /M S
accommodation is enhanced by the presence of a transverse dc field and, also, asymmetric accommodation can be produced by the application of a transverse ac field of small amplitude. This is quite interesting from the point of view of applications, since memory devices based on crossed ratchets rely on the observation of asymmetric accommodation [9] and transverse fields could be of use for sensitivity optimization.

In order to better understand the results presented above, we have performed a series of micromagnetic simulations to analyze the influence of a transverse field on a pinned kinked DW (see Fig. 6): we start from an initial zero field configuration of a kinked DW pinned in between two lines of arrows, then a positive/negative transverse field of constant amplitude is applied to the patterned film and, finally, H x is reduced again to zero and the system is allowed to relax to a new magnetization configuration (see and for a negative transverse field pulse (Fig. 6(d)). Initially the system starts from M y = -0.4 M S and a wall with a diagonal kink crossing the upper-left cell of the array of arrows. Then, upon application of the transverse field, there is a global rotation of the magnetic moments towards the applied field direction that produces a reduction of the absolute value of the easy axis magnetization down to M y = -0.1M S very similar both for positive/negative transverse fields (see frames II). This rotation is particularly intense in the shaded areas just below/above the arrow holes but it is reversible (i.e. it disappears as soon as the applied field is reduced to zero). It corresponds to the transverse susceptibility effect that showed up as the double frequency ripple in the experiments. On the other hand, there is an irreversible component in the simulated magnetization process that depends clearly on the sign of the transverse field: for µ 0 H x = 8 mT the kink has dissolved and there is only a very broad flat DW pinned at the first line of defects (see frame II in Fig. 6(c)), whereas for µ 0 H x = -8 mT the kinked wall stays pinned in the same place with a reduced wall thickness (see frame II in Fig. 6(d)). Therefore, when the transverse field is removed (see frames III), the system goes back to its initial magnetization state for µ 0 H x = -8 mT whereas for µ 0 H x = 8 mT it has reached a new state with a pinned flat wall. Thus, only in this case, there is a net ∆M y = -0.19M S between the initial and final magnetization states caused by the net backward motion of the pinned wall.

The sign dependence of the calculated rectification is directly connected to the chirality of the 180º pinned Neel wall: the transverse field promotes depinning of the kinked wall only when it is applied parallel to the magnetization within the wall core. This is because the influence of a transverse field on a Neel wall can be two fold: in the first place, a hard axis field reduces the overall DW angle and, correspondingly, the total DW energy mainly due to the smaller magnetostatic energy stored in the Neel wall tails. This is an even effect that would decrease the line tension associated to the kinked wall similarly for positive and negative transverse fields. In the second place, the energy of the Neel wall core is quite different depending on its orientation relative to the hard axis field. This results in a significant broadening of the Neel core for positive fields only (see frames II in Fig. 6) so that pinning by the patterned holes would be weakened by finite size effects [11][12][13]. This could allow upward kink propagation (which is the softer propagation mode of the system) driven by DW line tension in the presence of pinning centers of strongly reduced efficiency. For a Neel wall of opposite chirality the transverse field kink depinning would take place at negative fields but would again result in upward kink motion with the same sign of ∆M y given by the crossed ratchet potential. It is interesting to note that the sensitivity to the sign of the hard axis field is only experimentally found in the ac transverse accommodation experiments (Fig. 5) in which the same pinned DW is observed during the whole measuring sequence. However, for the dc experiments shown in Fig. 4, in which a constant transverse field is present both during DW nucleation and propagation the observed behavior is even in H x . This can be attributed to a preferred DW nucleation with a chirality such that core orientation is along the applied transverse field, i.e. opposite for positive/negative fields [START_REF] Eastwood | [END_REF]22].

Conclusion

In summary, the asymmetric DW propagation that gives rise to crossed ratchet behavior has been studied by micromagnetic simulations in square arrays of asymmetric holes with two

Figure 1 (Figure 2 (

 12 Figure 1 (colour online) SEM micrograph of a square array of arrow holes. Solid lines are sketches of a flat and a kinked DW. Arrows indicates forward DW propagation sense and upward kink propagation sense. Note that Upward kink propagation is equivalent to net backward DW motion.Flat DWKinked DW

Figure 3 (

 3 a) shows the difference between total energy E T and Zeeman energy E Z as a function of domain wall position (given approximately by M y /M S ) as a flat DW crosses a line of 4 µm arrow holes. The energy curve has the typical triangular shape of ratchet potentials with a much lower slope in the forward than in the backward propagation sense, i.e. forward is the easiest propagation sense. A similar calculation

Figure 3 (FORWARD

 3 Figure 3 (colour online) (a) Simulated energy landscape as a function of M y /M S as a flat wall crosses a line of 4 µm arrow holes propagating forward under a constant applied field of 3 mT. (b) Simulated energy landscape as a function of M y /M S as a kink proceeds upward along a wall pinned in between two lines of 4 µm arrow holes under a constant applied field of -3 mT. Frames correspond to selected wall configurations along the DW propagation process.

  must be noted that in the global characterization of the asymmetric behavior obtained from the equilibrium magnetization curves, different factors contribute to DW propagation (depinning from film borders, depinning from inter-hole regions, demagnetizing effects of the square Co-Si element…). This results in relatively broad transitions between DW pinning states at consecutive defect lines that make difficult a sharp definition of the critical field. Better defined depinning fields can be obtained for each particular DW propagation mode from the slopes of the triangular wells that appear in the energy landscapes shown in Fig.3. For flat walls, the results are µ 0 H F (arrows) = 0.9 mT and µ 0 H F (triangles) = 0.5 mT (dotted vertical lines have been plotted in Fig.2at these field positions and correspond roughly with the start of the DW transition from the central to the rightmost line of defects). For kink propagation, the upward propagation field H U estimated from the gradual slope is µ 0 H U = 0.3 mT for triangles and 0.5 mT for arrow holes, which are clearly lower values than the corresponding µ 0 H F .The interval between µ 0 H U (the critical field for the softer backward propagation mode) and µ 0 H F (the critical field for the softer forward propagation mode) is, then, the available range for observation of crossed ratchet effects dominated by kink motion. The calculated values are µ 0 ∆H Cross (arrow) = µ 0 H F -µ 0 H U = 0.4 mT and µ 0 ∆H Cross (triangle) = 0.2 mT, so that for a given array geometry the observation of crossed ratchet effects should be easier of arrays of arrow holes. In order to make a qualitative comparison of this calculation in square arrays of 4 µm arrow holes with experimental results in square arrays of 10 µm arrow holes, size effects can be considered by applying the proper scale factor between global array dimensions 4/10[11,12].

Figure 4

 4 Figure 4 in which the results of series of asymmetric accommodation experiments performed under different values of a constant transverse field H x are shown: Fig. 4(a) displays the easy axis applied field sequence H y (t) and Fig. 4(b) the measured easy axis magnetization response

Figure 4 (

 4 Figure 4 (colour online) Asymmetric accommodation under different values of a DC transverse field: (a) Easy axis µ 0 H Y (t) applied field sequence (b) measured easy axis M Y (t) response. Dashed horizontal lines indicate asymmetric accommodation ∆M under µ 0 H X = 1.7 mT. (c) Asymmetric accommodation ∆M Y /M S as a function of transverse field µ 0 H X .

Figure 5 (

 5 Figure 5 (colour online) (a) Applied field sequence in order to introduce a DW in the array and probe its response to an AC transverse field: µ 0 H Y (t), solid line; µ 0 H X (t), dashed line; (b) Measured time dependence of the magnetization under an AC transverse field. Dashed lines indicate the time interval for AC transverse field application and the induced asymmetric accommodation ∆M Y /M S . Inset shows ∆M Y /M S as a function of the amplitude of the transverse AC field.

  µ 0 H x (t) and M y (t) in Figs. 6(a) and (b), respectively). Snapshots of the resulting magnetization configuration are shown at different moments of the simulations labeled as I (initial), II (relaxed under a constant transverse field) and III (final configuration after removing the transverse field) for a positive transverse field pulse (Fig. 6(c))

Figure 6 (

 6 Figure 6 (colour online) (a) Transverse field pulses applied to a kinked wall for the micromagnetic simulations; (b) Calculated time dependence of the easy axis magnetization under a pulse of transverse field: M y (t) for positive field pulse is indicated by circles and M y (t) for negative field pulse is indicated by squares. (c) Simulated magnetization configurations at (I) initial stage, (II) relaxed under transverse field µ 0 H x = 8 mT and (III) remanence. (d) Simulated magnetization configurations at (I) initial stage, (II) relaxed under transverse field µ 0 H x = -8 mT and (III) remanence. Note the differences in domain wall width in frames II for positive/negative transverse field.

  different shapes: triangle and arrow. Triangle holes result in a stronger forward/backward asymmetry ∆H F /∆H B for flat wall propagation due to the smaller ∆H F in comparison with arrow holes. However, arrow holes are more suitable for the observation of crossed ratchet effects since they present a larger available field range µ 0 ∆H Cross = µ 0 H F -µ 0 H U in which the only DW propagation modes available correspond to kink motion. The simulated values µ 0 ∆H Cross of the order of 0.1 mT are in good agreement with experimental observations.Transverse field experiments have shown that domain wall propagation across the array of asymmetric defects is significantly affected by the presence of a hard axis field component: first, dc transverse fields of enough amplitude enhance the easy axis asymmetric accommodation and, also, ac transverse fields are found to be rectified by the crossed ratchet potential. These results can be attributed to the reduction in DW energy by the hard axis field and the polarity dependent broadening of the Neel wall core.

Acknowledgements

Work supported by Spanish MICINN (FIS2008-06249) and by Principado de Asturias FICYT (PCTI IB08-106).