Michael Rudolf Koblischka
email: m.koblischka@mx.uni-saarland.de

Alex Wiederhold

Muralidhar Miryala

Kazuo Inoue

Thomas Hauet

Bruno Douine

Kévin Berger

Masato Murakami

Uwe Hartmann

M Muralidhar

Development of MgB2-based, bulk supermagnets

Keywords: MgB 2, supermagnets, trapped fields, flux pinning forces. I

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

flow in the polycrystalline samples, and due to the porous character of the bulk samples. Therefore, we prepared a series of samples with a diameter of 20 mm at various reaction temperatures in order to determine the optimum preparation conditions for bulk MgB 2 samples.

II. EXPERIMENTAL PROCEDURE

Several samples were fabricated using a solid state reaction in pure Ar atmosphere from 750 to 950 o C in order to determine the optimum processing parameters to obtain the highest critical current density, j c , as well as large trapped field values. The X-ray analysis of these samples is presented elsewhere [START_REF] Muralidhar | Optimization of processing conditions towards high trapped fields in MgB 2 bulks[END_REF]. The magnetic characterization measurements were performed using SQUID magnetometry (Quantum Design MPMS) and the magneto-resistance charac-teristics were recorded using an Oxford Instruments 8 T Teslatron system. The critical current densities were calculated from the magnetization loops using the extended Bean model for rectangular samples. The trapped magnetic field was studied by magnetizing the bulk sample in a 10 T superconducting magnet over a wide temperature range between 20 K and 40 K. The transverse Hall sensor, which was directly glued at the center of the top and bottom surfaces of the bulk, has then only 0.5 mm distance between the probe and the surface of the sample. For SQUID measurements, small samples (2 × 2 × 1.5 mm 3 ) were cut from the big pellets. For the resistance measurements, small bars (10 × 1 × 1 mm 3 ) were prepared, and the contacts were fixed with silver paint. The AFM topography images were recorded using a Veeco/DI Nanoscope IV AFM employing micromachined Sicantilevers.

Development of

III. RESULTS AND DISCUSSION

As shown in Ref. [START_REF] Muralidhar | Optimization of processing conditions towards high trapped fields in MgB 2 bulks[END_REF], the samples prepared at temperatures lower than 775 °C are not pure MgB 2 phase, and the respective j c is lower. The irreversibility fields, H irr , are determined from the M(H)-loops using a criterion of 100 Acm -2 . Figure 1 indicates that the sample prepared at 775 °C exhibits the highest H irr (T) line, and also the highest trapped fields (measured only down to 20 K). H irr (T) and the trapped fields are then found to decrease when increasing the reaction temperature. However, the data of the sample processed at 950 °C show again an increase of H irr (T) and the trapped field (see the inset to Fig. 1). From the M(H)-loops recorded, we find that the sample processed at 775 o C showed the highest critical current density, j c , of 176 kAcm -2 and 55 kAcm -2 at 20 K in self-field and the trapped field of 1 T, respectively. The critical current density values are increasing further to 250 kA cm -2 and 150 kAcm -2 on decreasing the temperature further down to 10 K [START_REF] Naito | Trapped magnetic field and vortex pinning properties of MgB 2 superconducting bulk fabricated by a capsule method[END_REF]. In order to understand this behavior, a more detailed investigation of the magnetic properties is required. The obtained magnetization data were evaluated further and transferred into a pinning force analysis, where the pinning force F p = j c × B is plotted versus a scaling field h = H a /H irr , with H a denoting the applied magnetic field. [Figs. 2 (a,b)]. The resulting curves should scale according to f(h) ~ h p (1-h) q as introduced by Dew-Hughes (DH) [START_REF] Dew-Hughes | Flux pinning mechanisms in type II superconductors[END_REF]. This analysis revealed for the sample prepared at 950 °C a well developed scaling of the normalized pinning force data at low and intermediate temperatures with the scaling parameters p = 0.65, q = 1.35 and a peak located at h 0 = 0.35 (data obtained from fit to all data, indicated by a red line). This would indicate pinning at normal conducting precipitates according to DH [START_REF] Dew-Hughes | Flux pinning mechanisms in type II superconductors[END_REF]. Similar values were obtained in the literature for small, pure MgB 2 samples, see e.g., the review of Ref. [START_REF] Sandu | Pinning force scaling and its limitation in intermediate and high-temperature superconductors[END_REF]. For a dominating flux pinning at the grain boundaries, h 0 ~ 0.22 would be expected, which is not the case here. In contrast to this behavior, the samples prepared at 775 and 800 °C reveal a clear non-scaling. As indicated in Fig. 2 (b), the resulting fit to all data cannot describe the situation. At higher T, the peak position shifts to h 0 = 0.4, and at low T, a peak position h 0 < 0.2 is reached. Peak positions h 0 < 0.2 cannot be explained by the common scaling model, except that the anisotropy γ or the percolation, p c play a dominating role. This effect was discussed previously in Ref. [START_REF] Eisterer | Calculation of the volume pinning force in MgB 2 superconductors[END_REF], where j c was calculated using the parameters γ = 4 and p c = 0.25. This produces a shift of h 0 from 0.33 (isotropic case, point pinning) to about 0.18. This further implies that in order to deduce the acting pinning mechanism from the peak position of the pinning force scaling of MgB 2 samples, the anisotropy and percolation should be known. In Fig. 3, the resulting peak positions h 0 are shown as a function of temperature. Only the data of the sample prepared at 950 °C exhibits a plateau which is a prerequisite for the scaling, whereas the data of the other samples are continuously increasing with increasing temperature. Here, one should note the results of the DH fitting to all data as indicated by the dashed lines, being slightly larger than the individual peak positions. Additionally, the temperature dependence of the anisotropy parameter, γ(T), is plotted here. The anisotropy is changing with temperature according to γ(T) = γ*+k(1-T/T c ), where γ* = 1.87 is the effective mass anisotropy and k = 6 [START_REF] Shi | Out-of-plane and in-plane anisotropy of upper critical field in MgB2[END_REF]. As a result, γ(T) changes from 6 to 2 on increasing T, yielding h 0 = 0.158 to 0.33. In contrast to this, p c is only slightly varying between 0.2 and 0.3 [START_REF] Eisterer | Calculation of the volume pinning force in MgB 2 superconductors[END_REF]. The large variation of h 0 obtained for the samples prepared at 775 and 800°C implies that the grain boundary character (connectivity) must change when processing the samples at higher reaction temperatures [START_REF] Eisterer | Magnetic properties and critical currents of MgB2[END_REF].

In Ref. [START_REF] Eisterer | Calculation of the volume pinning force in MgB 2 superconductors[END_REF], a different scaling procedure was suggested where a field H n is employed instead of H irr . H n is defined as the field where the pinning force F p drops to 50% of its value above the peak position, i.e., all curves should pass the point (0.5,1) in the scaling diagram. The advantage of approach is that an area just below h n = 1 exists which is not so sensitive to the effective values of γ and p c . Figure 4 presents the results of this modified scaling procedure. In (a), a well developed scaling is obtained. The scaling reveals a peak at h n = 0.48 (a) and 0.25-0.43 (b). For (a), this indicates dominating pinning at small precipitates, while in (b) the pinning is changing from grain boundary pinning to pinning at small precipitates. The data of Fig. 3 indicate that grain boundary pinning is significant only at low temperatures, whereas at higher temperatures, flux pinning at normal conducting precipitates plays the dominating role. As this conclusion also holds after applying the modified scaling procedure (see Fig. 4), this finding is an important one for the further development of MgB 2 bulk magnets. In Fig. 4 (b), the temperature dependence of the peak position is still visible. This further implies that p c is changing with increasing reaction temperature, together with the grain size. Furthermore, the arrow points to a shape change of the curves at low T, which is also seen in the inset with the original F p (B) curves; the origin of which is discussed to be a competition of inter-and intragrain contributions to the pinning [START_REF] Jung | Flux pinning mechanism in single-crystalline MgB2 thin films[END_REF]. The change of the grain boundary character depending on the reaction temperature is also manifested in the resistance measurements (measured during field-cooled warming) as presented in Fig. 5. The magnetoresistance data reveal a much sharper superconducting transition for the sample prepared at 775 °C, whereas the transitions broaden up much more on increasing the magnetic field for the sample at 950 °C. This also reflects the non-scaling of the forces, as the R(T,B) curves correspond to the M(T,B) behavior as discussed in Refs. [START_REF] Koblischka | Superconducting transitions of Nd-based 123 superconductors in fields up to 7 T[END_REF][START_REF] Pradhan | Evidence of strong flux pinning in meltprocessed ternary (Nd-Eu-Gd)Ba 2 Cu 3 O y superconductors[END_REF].

Microstructural observations obtained from scanning electron microscopy (SEM) and atomic force microscopy (AFM) indicated that the grain size is the crucial parameter to improve the critical currents as well as the trapped field values. This confirms the results of previous works [START_REF] Muralidhar | Optimization of the fabrication process for high trapped field MgB2 bulks[END_REF][START_REF] Muralidhar | Recent developments in melt processed Gd-123 and MgB 2 materials at RTRI[END_REF][START_REF] Fuchs | High trapped fields in bulk MgB 2 prepared by hot-pressing of ball-milled precursor powder[END_REF]. Figure 6 presents typical AFM topography images of the samples recorded in the tapping mode. The images clearly reveal the polycrystalline nature of the sample. Individual MgB 2 grains show a specific crystallite shape and the dimensions of the grains are up to 400 nm. Obviously, the grain size and grain arrangement of (a) represents an optimal configuration, thus leading to the high trapped field values. The increase of the trapped fields for the sample prepared at 950 °C is attributed to the formation of nano-sized MgB 4 particles at the higher reaction temperature, which can provide additional, strong flux pinning by δT c -pinning [START_REF] Cai | Variation of pinning mechanism and enhancement of critical current density in MgB2 bulk containing self-generated coherent MgB 4 impurity[END_REF], but the worse character of the grain boundaries does not allow to reach the trapped field values of the sample prepared at 775 °C. Another important aspect for the development of bulk, MgB 2 -based supermagnets is the energizing procedure applied. MgB suffers -in contrast to the bulk RE-123 samples -from flux jumps and the specific flux penetration in form of dendrites or avalanches, especially at low temperatures [START_REF] Denisov | Onset of dendritic flux avalanches in superconducting films[END_REF][START_REF] Colauto | Mapping flux avalanches in MgB 2 filmsequivalence between magneto-optical imaging and magnetic measurements[END_REF]. The microstructures shown in Fig. 6 directly confirm that the sample surface is inhomogeneous, formed of stacks of elongated grains with a length of up to 400 nm, and thus, a complicated percolative current flow takes place. The magnetization loops measured at 5 and 10 K with a sweep rate of 10 mT/s indicated the presence of flux jumps. Therefore, for energizing MgB 2 supermagnets, it will be an essential task to develop a suited procedure, which may also include countermeasures like the application of a conductive thin-film cover onto the samples. A first attempt of such a procedure can be found already in Refs. [START_REF] Colauto | Mapping flux avalanches in MgB 2 filmsequivalence between magneto-optical imaging and magnetic measurements[END_REF][START_REF] Stahl | The avalance process in gold covered MgB2 films[END_REF], which indeed helps to reduce the number of flux jumps occurring in MgB 2 thin film samples. Tests are on the way also on bulk MgB 2 samples.

Fig. 1 .

 1 Fig. 1. The irreversibility lines (open symbols) and the measured trapped fields (full symbols) for several selected samples. The inset illustrates the recorded trapped fields at 20 K as a function of the reaction temperature.

  MgB 2 -based bulk supermagnets M. R. Koblischka, A. Wiederhold, M. Muralidhar, K. Inoue, T. Hauet, B. Douine, K. Berger, M.Murakami and

Fig. 2 .

 2 Fig. 2. Pinning force scaling for the sample prepared at 950 °C (a) and 775 °C (b). The shown fits are fits to all data. The dashed lines indicate the peak positions determined. The strong non-scaling of (b) is clearly visible.

Fig. 3 .

 3 Fig. 3. The peak positions, h0, of the Fp(B)-curves as a function of temperature. The values for h 0 as determined by the fits are indicated as dashed lines. Additionally, the temperature dependence of the anisotropy, γ(T), is shown according to Ref. [14].

Fig. 4 .

 4 Fig. 4. Modified scaling procedure according to Ref. [15] using a scaling field, Hn, for the sample prepared at 950 °C (a) and at 775 °C (b). The arrow in (b) indicates the shape change at low temperatures, which is also visible in the Fp(B) diagram (inset).

Fig. 5 .

 5 Fig. 5. Specific resistance as function of temperature for various applied fields for the sample prepared at 775 °C (a) and at 950 °C (b).

Fig. 6 .

 6 Fig. 6. AFM topography images (tapping mode) of the MgB 2 sample prepared at 775 °C (a) and of the sample prepared at 850 °C (b).IV. CONCLUSIONTo summarize, MgB 2 samples of 20 mm in diameter and 7 mm thickness, prepared with optimized processing temperature, exhibited a trapped field of ~1.5 T at 20 K. The characterization of small samples showed a change of flux pinning mechanisms as seen in the pinning force scaling. The current flow in the samples depends strongly on the grain boundary character, which gets worse on increasing the sintering temperature as revealed by the magnetoresistance measurements. 775 °C was found to be the optimum temperature to reach high trapped fields, while the sample prepared at 950 °C exhibits additional flux pinning provided by MgB 4 particles, however, due to the degraded grain boundaries, the trapped field achieved is not as high as of the sample prepared at 775 °C.

ACKNOWLEDGEMENT

The collaboration Saarbücken-Nancy is supported by the INTERREG IVa project GRMN, which is gratefully acknowledged.