Damian Józefiak

Anna Sip

Mateusz Rawski

Andrzej Rutkowski

Sebastian Andrzej Kaczmarek

Bent Ole Højberg

Borg Jensen

Ricarda Margarete Engberg

D Jozefiak

Dietary divercin modifies gastrointestinal microbiota and improves growth performance of broiler chickens

Keywords: broiler chicken, bacteriocin, salinomycin, digestibility, microflora

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.

Abstract 1. The aim of the present study was to investigate the effects of dietary 21 administration of a divercin AS7 liquid preparation on broiler chicken performance, 22 nutrient digestibility, counts of lactic acid bacteria (LAB) and coliform bacteria, as 23 well as on the microbial activity in the gastrointestinal tract (GIT) as expressed by 24 digesta pH and concentrations of short-chain fatty acids and lactic acid. 25 2. A total of 450 1-d-old male Ross 308 chickens were randomly distributed to three 26 dietary treatments, with 15 pens per treatment and 10 birds per pen. The dietary 27 treatments consisted of a positive control (PC) supplemented with 60 mg/kg 28 salinomycin, a negative control (NC) without any additives, and the divercin (DIV) 29 supplemented diet containing 0.2 ml/kg of the liquid divercin AS7 preparation. 30 3. The dietary divercin AS7 supplementation significantly increased body weight gain 31 at 35 d compared to the NC group. Moreover, the pH of crop contents was higher and 32 that of caecal contents lower in birds fed on the divercin supplemented diets. 33 4. Significantly lower counts of LAB were observed in the crops and caeca of the birds 34 treated with divercin. Further, the divercin supplementation decreased lactic and 35 succinic acid concentrations in the crop and ileum. 36 5. The present study demonstrates that the use of divercin supplemented diets can 37 influence composition and activity of the microbiota in the broiler chicken GIT even in 38 the lower parts that should otherwise not be targeted due to the peptide structure of the 39 In recent years, a number of studies have demonstrated a close relationship between 42 broiler performance, health and the gastrointestinal tract (GIT) microbiota (Engberg et 43 al., 2002;[START_REF] Maisonnier | 399 Effects of microflora status, dietary bile salts and guar gum on lipid digestibility, 400 intestinal bile salts, and histomorphology in broiler chickens[END_REF][START_REF] Engberg | Influence of 354 whole wheat and xylanase on broiler performance and microbial composition and 355 activity in the digestive tract[END_REF][START_REF] Choct | Managing gut health through nutrition[END_REF]. Taking the 44 complexity and biodiversity of the GIT micro-ecosystem into consideration, a 45 manipulation of the GIT microbiota in a way that is profitable for the host-bird and for 46 the farmer, however, seems a difficult goal to achieve. Several studies have 47 demonstrated that the protective potential of the native commensal microbiota may 48 easily be disrupted by different nutritional factors [START_REF] Dahiya | Potential strategies for 343 controlling necrotic enteritis in broiler chickens in post-antibiotic era[END_REF][START_REF] Choct | Managing gut health through nutrition[END_REF], 49 thereby compromising one of the suggested ways for the commensal microbiota to 50 support performance and health of broilers; namely elimination of pathogenic bacteria 51 from the GIT. On the other hand, it is also well recognised that the commensal 52 microbiota, no matter how protective it may be, does impose a burden upon the host 53 that goes beyond simply competing for feed components [START_REF] Engberg | Effect of 348 zinc bacitracin and salinomycin on intestinal microflora and performance of broilers[END_REF], via 54 more specific mechanisms such as compromising fat digestibility (Knarreborg et al. 55 2002). A mere reduction in the commensal microbial load of the GIT may therefore, in 56 a short term perspective, represent a growth promoting factor for the host, though 57 admittedly, it may at the same time render the host more susceptible to pathogen 58

invasion. 59

Probiotics with potentially beneficial effects on broiler growth and health have 60 gained considerable interest [START_REF] Choct | Managing gut health through nutrition[END_REF] and have been shown to stimulate the 61 immune system and to reduce the growth and intestinal colonisation of pathogenic 62 bacteria by competitive exclusion (Rijkers et al. 2010) [START_REF] Joerger | Alternatives to antibiotics: bacteriocins, antimicrobial peptides 368 and bacteriophages[END_REF]. Even though bacteriocins have been used in human nutrition for 65 decades [START_REF] Cleveland | Bacteriocins: 336 safe, natural antimicrobials for food preservation[END_REF][START_REF] Joerger | Alternatives to antibiotics: bacteriocins, antimicrobial peptides 368 and bacteriophages[END_REF][START_REF] Leisner | 388 Carnobacterium: positive and negative effects in the environment and in foods[END_REF], only limited 66 information is available regarding the effects of directly fed bacteriocins on broiler 67 chickens. A few recent publications do however indicate that different bacteriocins 68 administered with the feed may inhibit GIT colonisation by Campylobacter jejuni and 69 Salmonella enteritidis [START_REF] Stern | 444 Paenibacillus polymyxa purified bacteriocin to control Campylobacter jejuni in 445 chickens[END_REF][START_REF] Line | Isolation and purification of enterocin E-760 with broad 393 antimicrobial activity against gram-positive and gram-negative bacteria[END_REF]. 70

Among bacteria capable of producing bacteriocins, much attention has been 71

paid to the lactic acid bacteria, LAB [START_REF] Stern | Isolation of a Lactobacillus salivarius strain and purification of its bacteriocin, 449 which is inhibitory to Campylobacter jejuni in the chicken gastrointestinal system[END_REF][START_REF] Svetoch | 453 Inactivating methicillin-resistant Staphylococcus aureus and other pathogens by use of 454 bacteriocins OR-7 and E 50-52[END_REF]. 72

Carnobacterium is a genus of LAB that can be isolated from various sources such as 73 the GIT of fish, dairy products and alpine permafrost [START_REF] Leisner | 388 Carnobacterium: positive and negative effects in the environment and in foods[END_REF]). The 74 Carnobacterium genus comprises nine described species, of which Carnobacterium 75 divergens and Carnobacterium maltaromaticum have been most widely studied, due to 76 their role in the inhibition of many pathogenic and food spoilage bacteria such as 77 Clostridium, Bacillus,Brochothrix,Streptococcus,Staphylococcus and Micrococcus. 78 They do, however, also possess antimicrobial activity against fellow LAB of the genera 79 Lactobacillus, Leuconostoc, Carnobacterium, Pediococcus and Enterococcus (Sip et 80 al., 1998;[START_REF] Leisner | 388 Carnobacterium: positive and negative effects in the environment and in foods[END_REF]; a feature potentially related to Carnobacterium 81 bacteriocin production. 82

Carnobacterium divergens produces the subclass IIa bacteriocins consisting of 83 30 to 60 amino acids [START_REF] Leisner | 388 Carnobacterium: positive and negative effects in the environment and in foods[END_REF]) and so far, three major bacteriocins produced 84 by this species have been identified; divercin V41 [START_REF] Rihakova | Insights into Structure-Activity Relationships in the C-Terminal Region of 419 Divercin V41, a Class IIa Bacteriocin with High-Level Antilisterial Activity[END_REF] [START_REF] Sip | Enhancement of bacteriocin production 435 by Carnobacterium divergens AS7 in the presence of a bacteriocin-sensitive strain 436 Carnobacterium piscicola[END_REF]) and divergicin M35 (Tahiri et al. 2004). Apart from the data from our 86 preliminary study [START_REF] Józefiak | The effects of 378 Carnobacterium divergens AS7 bacteriocin on gastrointestinal microflora in vitro and 379 on nutrient retention in broiler chickens[END_REF], no information is so far available on the use 87 of bacteriocins produced by Carnobacterium divergens as feed additives for broiler 88 chickens. The aim of the present study was therefore to investigate the effects of a 89 divercin AS7 preparation on broiler chicken performance, nutrient digestibility, counts 90 of coliform bacteria (indicator of potential pathogens) and LAB (representative 91 commensals) as well as on the microbial activity in the GIT expressed by the levels of 92 pH and short-chain fatty acids. 93

MATERIALS AND METHODS 94

Birds and housing 95

The effect of the divercin AS7 supplementation was evaluated in a growth performance 96 experiment with broiler chickens kept in floor pens (1.58 × 1.16 m) over an 97 experimental period of 35 d. A total of 450 1-d-old male ROSS 308 chicks were 98 randomly distributed to three dietary treatments using 15 replicate pens per treatment 99 and 10 birds per pen. The birds were given 23 h light and 1 h dark during the first 100 week, and then 19 h light and 5 h dark from d 7 to 21. From 22 to 42 d of age, there 101 was 23 h light and 1 h dark. The positive control (PC) diet was supplemented with an 102 ionophore coccidiostat (salinomycin, 60 mg/kg), the negative control diet (NC) did not 103 contain any additive and the divercin diet (DIV) was supplemented with 200 AU 104 divercin/ml (0.2ml/ kg). 105

Diets and feeding programme 106

The compositions of the experimental diets are presented in activity was quantified by two-fold dilutions, and expressed in activity units (AU) per 108 millilitre as previously described by [START_REF] Ennahar | 357 Biochemical and genetic evidence for production of enterocins A and B by 358 Enterococcus faecium WHE 81[END_REF]. The divercin AS7 preparation 109 was produced according to the technology elaborated by [START_REF] Sip | Production of bacteriocin by 438 Carnobacterium divergens in batch and continuous culture[END_REF] and was 110 provided in liquid form. In the last 5 d of the experiment, 0.2% of the wheat was 111 replaced by titanium oxide as an internal marker for digestibility analyses. 112

Data collection 113

The feed intake and body weight of the chickens were measured on d 14 and 35. 114

Mortality was registered throughout the entire experiment. At the end of the trial (35 d) 115 from each experimental group, 21 randomly picked chickens (three chickens from 7 116 pens) were killed by cervical dislocation. For analyses of gastrointestinal contents 117 (enumeration of bacteria, pH and organic acid concentrations), the contents of crop, 118 ileum and caecum from three birds per pen were pooled (7 replicate digesta samples of 119 approximately 10 g). Approximately 5 g of the sample were used freshly for the 120 culturing of intestinal bacteria and for pH analyses. The rest of the samples were 121 immediately frozen and stored at -20ºC for the analysis of organic acids by gas 122

chromatography. 123

For the evaluation of apparent metabolisable energy (AME N ) and nutrient 124 digestibility, a further 15 randomly chosen birds per treatment (one bird per pen) were 125 killed on d 35 and ileal contents were collected. The ileum was removed and digesta 126 were flushed from the terminal ileum (15 cm adjacent to the ileo-caecal junction). To 127 provide sufficient material for chemical analysis, the fresh ileal samples were pooled 128 into 5 replicates of approximately 60 g. From the same pens excreta samples of approx. 129

Chemical analyses 132

Feed samples were analysed in duplicate for crude protein, crude fat, and crude fibre 133 using AOAC (2005) methods 976.05, 920.39 and 2002.04, respectively. For all 134 chemical analysis, samples were ground to pass through a 0.5 mm sieve. Titanium 135 dioxide was determined according to the method described by [START_REF] Short | Determination of 432 titanium dioxide added as an inert marker in chicken digestibility studies[END_REF], and 136 samples were prepared according to the procedure proposed by [START_REF] Myers | Technical 412 Note: A procedure for the preparation and quantitative analysis of samples for titanium 413 dioxide[END_REF]. 137

Gross energy was determined using an adiabatic bomb calorimeter (KL 12Mn,138 Precyzja-Bit PPHU, Poland) standardised with benzoic acid. Nitrogen content was 139 analysed by the Kjel Foss Automatic 16210 (A/S N. Foss Electric, Denmark) and the 140 crude protein content was calculated using a multiplication factor of 6.25. Fat content 141 was determined using Soxtex System HT 1043, Extraction Unit (Foss Tecator 142

Denmark). 143

Microbiological analyses 144

The pH of pooled digesta from the crop, ileum and caecum was measured immediately 145 after slaughter using a combined glass and reference electrode. The rest of the sample 146

(2.5 g), was diluted in 30 ml of sterile pre-reduced salt medium (Miller and Wolin 147 1974). For enumeration of bacteria, the suspension was homogenised for two minutes 148 in CO 2 -flushed plastic bags using a stomacher homogeniser (Interscience, France). 149 Subsequently, the samples were serially diluted in 10-fold steps using pre-reduced salt 150 medium according to the technique of [START_REF] Miller | A serum bottle modification of the Hungate 403 technique for cultivating obligate anaerobes[END_REF]. Lactic acid bacteria 151 The concentration of short-chain fatty acids and lactic acid in the contents of 156 the different gastrointestinal segments was determined by gas chromatography as 157 described earlier [START_REF] Canibe | Effect of feeding 331 fermented liquid feed and fermented grain on gastrointestinal ecology and growth 332 performance in piglets[END_REF] using a Hewlett Packard gas chromatograph 158 (Model 6890, Hewlett Packard, Agilent Technologies, Naerum, Denmark) equipped 159 with a flame-ionisation detector and a 30-m ZB-5 column with an internal diameter of 160 0.32 mm and coated with 5%-phenyl 95%-dimethylpolysiloxane with a film thickness 161 of 0.25 µm. Total concentration of organic acids is expressed as the sum of acetic, 162 propionic, butyric, isobutyric, valeric, succinic and lactic acids. 163

Digestibility calculations 164

The following equations were used to calculate the apparent digestibility of the protein, 165 fat (using titanium dioxide and fat digestibility (dig.) calculation as an example) and 166 Where GE is gross energy, N is nitrogen, TiO 2 is titanium oxide, and 34.39 is the 175 energy equivalent of uric acid nitrogen (i.e., 34.39 kJ/kg uric acid nitrogen). 176

AME N content of experimental diets: 167 168 Fat dig. (%) = {1 -[(TiO 2 % diet /TiO 2 % digesta/excreta ) × (fat% digesta/excreta /fat% diet )]} 169 ×100 170 171 AME N (kJ/kg)=GE kJ/kg diet -[GE kJ/kg excreta •(TiO 2 % diet /TiO 2 % excreta )]-34.39•{N% diet 172 -[N% excreta •(TiO 2 % diet /TiO 2 % excreta )}] 173

Statistical analysis 177

The study was set up as a completely randomised design, and data were tested using 178 the GLM procedure of SAS (SAS 1990). Means were separated using a Duncan's 179 multiple range test. All statements of significance are based on P<0.05. 180

RESULTS 181

Throughout the trial, the mortality was below 2% without any signs of viral or bacterial 182 infections. Birds fed on diets supplemented with salinomycin showed the best 183 performance results (Table 2). Compared with the non-supplemented control, the 184 divercin supplementation increased the body weight gain in the starter period 185 (P=0.006) and at the end of the trial (P<0.001), and tended to improve total feed 186 conversion ratio as well as feed intake in each growth stage. 187

The levels of apparent metabolisable energy (AME N ) and ileal digestible 188 energy (Table 3) increased after salinomycin supplementation (P<0.001 and P=0.016, 189 respectively). However, there was no difference between PC and DIV treatments with 190 respect to the estimated ileal digestible energy. Although the ileal crude fat digestibility 191 of birds fed the PC diet was approximately 24 percentage points higher than that of the 192 other groups (0.92 vs. 0.68), no statistical significant difference was found (P=0.118). 193

Total tract fat digestibility was significantly higher (P=0.013) in the PC group (Table 194 Tables 2 & 3 near here 3). The lowest ileal crude protein digestibility, as well as total nitrogen retention, was 195 observed in the birds fed the NC diet. 196

In the present trial, the dietary supplementation with salinomycin numerically 197 increased the counts of LAB bacteria (Table 4), but only significantly in the caecum 198 (P=0.015). Divercin tended to reduce the LAB population in the contents of the crop 199 (P=0.14). However in the ileum (P=0.015) and caecum (P=0.006) the reduction was 200 significant. The counts of coliform bacteria in the different intestinal segments were 201 not influenced by the dietary treatments (P>0.05). 202

Compared with the non-supplemented controls, the digesta pH in crop and 203 ileum was higher when birds were fed salinomycin and divercin (P=0.011 and 204 P=0.001, respectively). In the caecum, the pH was highest in the non-supplemented 205 control (P=0.043). 206

In crop contents, the dominant organic acids were lactic acid and acetic acid 207 (Table 5), while succinic acid and butyric acid were detected in small concentrations. 208

Compared with the non-supplemented diet, the addition of salinomycin and divercin 209 reduced lactic acid, acetic acid and succinic acid concentrations by approximately 50% 210 (P>0.001) in crop contents. Also in ileal content, the most abundant organic acids were 211 lactic and acetic acid, whereas succinic acid was detected only in low concentrations 212 (Table 5). The concentration of lactic acid was influenced by the dietary treatment 213 (P<0.001) and was lowest in ileal contents of birds supplemented with salinomycin 214 (34.5 µg/g), as compared with divercin (72.4 µg/g) and the non-supplemented control 215 diet (114.0 µg/g). The concentration of acetic acid in ileal contents was not influenced 216 by the dietary treatment (P>0.05). In caecal contents, the organic acid profile was 217 much more diverse with acetic acid, butyric acid and propionic acid being the 218 dominant organic acids (Table 5). Low concentrations of isobutyric, isovaleric and 219 valeric acids were detected in caecal contents, whereas lactic acid was not detected at 220 this location. In general, divercin reduced the microbial fermentation to the same extent 221 as salinomycin (Table 5). There was no difference between groups with respect to the 222 production of organic acids in the caecum (P>0.05).

DISCUSSION 224

The observed growth promoting effect of salinomycin is in good agreement with 225 earlier studies on broiler chickens [START_REF] Engberg | Effect of 348 zinc bacitracin and salinomycin on intestinal microflora and performance of broilers[END_REF], ruminants (Spears 1990) and 226 pigs [START_REF] Moore | Effect of salinomycin on nutrient 405 absorption and retention by growing pigs fed corn-soybean meal diets with or without 406 oat hulls or wheat bran[END_REF]. In poultry, many of the applied ionophore coccidiostats do 227 not only target Eimeria species but also certain Gram-positive GIT bacteria. These 228 substances have been observed to reduce the numbers of, for example, Clostridium 229 perfringens [START_REF] Bjerrum | The influence of whole 328 wheat feeding on Salmonella infection and gut flora composition in broilers[END_REF] and LAB, including species like Lactobacillus 230 salivarius, previously reported to be dominating in the broiler GIT (Engberg et al., 231 2000). The improvement of bird growth and feed utilisation imposed by salinomycin 232 may be explained by a limitation of microbial growth and activity per se, alleviating 233 the direct competition with the host for nutrients. More specifically, by targeting 234 bacteria responsible for deconjugation of bile salts [START_REF] Knarreborg | 382 Quantitative determination of bile salt hydrolase activity in bacteria isolated from the 383 small intestine of chickens[END_REF]Guban et 235 al. 2006), salinomycin treatment may also improve fat digestibility (Knarreborg et al. 236 2004). In accordance with this, the present study demonstrated an increased fat 237 digestibility and AME N content after dietary salinomycin supplementation. The AME N 238 a chicken showed protective effects on chickens infected with Salmonella pullorum 252 [START_REF] Audisio | Antagonistic effect of 325 Enterococcus faecium J96 against human and poultry pathogenic Salmonella spp[END_REF]. Mountzouris et al. (2010) Lactobacillus salivarius DSM 16351) of healthy adult chickens. These bacteria are all 257 capable of producing bacteriocins [START_REF] Cleveland | Bacteriocins: 336 safe, natural antimicrobials for food preservation[END_REF][START_REF] Joerger | Alternatives to antibiotics: bacteriocins, antimicrobial peptides 368 and bacteriophages[END_REF]Diez-258 Gonzalez, 2007;[START_REF] Nazef | 415 Identification of lactic acid bacteria from poultry feces: evidence on anti-416 Campylobacter and anti-Listeria activities[END_REF], and it has thus been concluded that some of the 259 growth promoting effects were linked to antimicrobial activity of those peptides. 260 However, the highest ileal apparent digestibility coefficients of crude protein and ether 261 extract were observed in avilamycin supplemented treatment, followed by the 262 probiotic-supplemented group (Mountzouris et al., 2010). 263 [START_REF] Grilli | 361 Pediocin A improves growth performance of broilers challenged with Clostridium 362 perfringens[END_REF] showed that pediocin A from Pediococcus pentosaceus 264 FBB61, belonging to the class III bacteriocins, significantly improved growth 265 performance of broiler chickens challenged with Clostridium perfringens. In the 266 present study, we did not enumerate specific pathogens. However, the experimental 267 diets provided animal fat sources (lard and tallow) known to stimulate the intestinal 268 growth of Clostridium perfringens [START_REF] Knarreborg | Dietary 385 antibiotic growth promoters enhance the bioavailability of alpha-tocopheryl acetate in 386 broilers by altering lipid absorption[END_REF]. It cannot be excluded 269 therefore, that some of the observed salinomycin and divercin effects may be linked to 270 a suppression of C. perfringens; a very active player in bile acid de-conjugation 271 [START_REF] Knarreborg | 382 Quantitative determination of bile salt hydrolase activity in bacteria isolated from the 383 small intestine of chickens[END_REF]. 272

Lactobacilli are among the most abundant bacteria in the chicken GIT and 273 typically dominate in the upper GIT segments (crop, gizzard and ileum). Lu et al. 274 (2003) thus reported approx. 70% of the sequences in an ileum-derived 16S rRNA 275 gene library to be allocated to the Lactobacillus genus. In the caecum, on the other 276 hand, where strict anaerobes proliferate readily, lactobacilli only accounted for approx. 277 8% of the library sequences [START_REF] Lu | 396 Diversity and succession of the intestinal bacterial community of the maturing broiler 397 chicken[END_REF]. Lactic acid bacteria are usually 278 considered beneficial for the host bird due to their production of, for example, lactic 279 and acetic acids, leading to pH reduction [START_REF] Engberg | Influence of 354 whole wheat and xylanase on broiler performance and microbial composition and 355 activity in the digestive tract[END_REF], as well as their 280 production of certain bacteriocins [START_REF] Nazef | 415 Identification of lactic acid bacteria from poultry feces: evidence on anti-416 Campylobacter and anti-Listeria activities[END_REF]. On the other hand, there is also 281 certain evidence that some small intestine LAB, e.g. Lactobacillus salivarius and 282 Enterococcus faecium might have negative effects on broiler performance (Engberg et 283 al. 2000;[START_REF] Guban | Relationship of 364 Dietary Antimicrobial Drug Administration with Broiler Performance, Decreased 365 Population Levels of Lactobacillus salivarius, and Reduced Bile Salt Deconjugation in 366 the Ileum of Broiler Chickens[END_REF]. 284

In general, the observations of the present study suggest salinomycin as well as 285 divercin can suppress the overall microbial activity of the broiler GIT; the 286 concentration of organic acids was thus highest in the non-supplemented control group 287 in each GIT segment (Table 5), though not significant for the caecum, and the observed 288 levels of total and individual organic acids were in good agreement with our earlier 289 studies [START_REF] Józefiak | The effect of 370 β-glucanase supplementation of barley-and oat-based diets on growth performance and 371 fermentation in broiler chicken gastrointestinal tract[END_REF][START_REF] Józefiak | Effects of 374 dietary inclusion of triticale, rye and wheat and xylanase supplementation on growth 375 performance of broiler chickens and fermentation in the gastrointestinal tract[END_REF]. The suppression of the microbial 290 activity by salinomycin and divercin is clearly reflected in the pH levels of the upper 291 GIT segments, but not in the caecum; an apparent discrepancy also observed earlier 292 [START_REF] Engberg | Effect of 348 zinc bacitracin and salinomycin on intestinal microflora and performance of broilers[END_REF]. More specifically, the LAB activity also seemed to be 293 suppressed by salinomycin and divercin, as indicated by the lower lactic acid 294 concentrations and higher pH in the upper parts of the GIT (crop and ileum), compared 295 with the control group. Surprisingly, however, significant reduction of the LAB (MRS) 296 counts was only observed in the ileum of the divercin treated broilers, whereas 297 salinomycin actually increased caecal LAB counts; a discrepancy that cannot be readily 298 explained, but similar trends have been observed before [START_REF] Engberg | Effect of 348 zinc bacitracin and salinomycin on intestinal microflora and performance of broilers[END_REF] and it 299 emphasises the complexity of the mechanisms involved. In particular, the question of 300 which species of broiler GIT lactic acid bacteria may be targeted by divercin and 301 salinomycin remains unanswered, as no detailed identification of the involved LAB has 302 been conducted. 303

A recent study by [START_REF] Shin | Isolation and 429 characterization of bacteriocin-producing bacteria from the gastrointestinal tract of 430 broiler chickens for probiotic use[END_REF] showed that the broiler chicken GIT is inhabited 304 Even though carnobacteria are relatively widespread in nature, however, there is so far 306 no evidence that they are present in the GIT of broiler chickens [START_REF] Leisner | 388 Carnobacterium: positive and negative effects in the environment and in foods[END_REF]; a 307 fact that may explain the strong effects of divercin AS7 introduction on bacterial 308 fermentative activity. The fact that divercin AS7 in the present study tended to 309 suppress LAB even in the caecum indicates that this bacteriocin, even in an 310 unprotected form, may continue to be active in the lower segments of the broiler GIT, 311 although, as a protein, it is prone to hydrolysis in the upper intestine. 312

To our knowledge, the present study is the first attempt to use a 313

Carnobacterium divergens bacteriocin as a feed supplement and to demonstrate 314 positive growth promoting and antibacterial effects of divercin in broiler chickens. 315 Although consistent with our preliminary studies [START_REF] Józefiak | The effects of 378 Carnobacterium divergens AS7 bacteriocin on gastrointestinal microflora in vitro and 379 on nutrient retention in broiler chickens[END_REF], the results 316 presented here should be followed up by further investigations in order to provide 317 more detailed information on broiler growth performance, for example, in response to 318 different divercin doses; as well as the specific bacteria being targeted by the 319 bacteriocin. Finally, it could be attempted to increase the effectiveness of divercin in 320 the broiler GIT by protective encapsulation of the peptide. 321

F

  spread-plating on de Man, Rogosa and Sharp (MRS) agar (Merck 152 1.10660) incubated for 48 h at 38ºC in anaerobic jars (Anaerocult® A, Merck 153 1.13829). Coliform bacteria were enumerated by spread-plating on MacConkey agar 154 (Merck 1.05465) incubated aerobically for 24 h at 38ºC. 155

  higher than the calculated energy value of the diets (13.6 vs. 13.0 239 MJ/kg). Compared with the NC diet, the ileal digestible energy increased after 240 divercin supplementation (10.3 vs. 11.6 MJ/kg), being in between the NC and the PC 241 diet. Both additives also improved ileal crude protein digestibility as well as nitrogen 242 retention. The present results thus suggest that the divercin-medicated improvement in 243 broiler growth performance (P=0.001) and feed utilisation (P=0.059) may be directly 244 linked to an improved nutrient digestibility, due to a reduction of the GIT microbial 245 load and activity.. 246 Dietary supplementation with different bacteriocins has been shown to suppress 247 different pathogenic bacteria. Cole et al. (2006) demonstrated significant reduction of 248 Campylobacter jejuni in turkey poults after dietary addition of bacteriocin B602 from 249 Paenibacillus polymyxa (NRRL B-30509), and bacteriocin OR7 from Lactobacillus 250 salivarius (NRRL B-35014). Enterococcus faecium strain J96 isolated from the crop of 251

  examined avilamicin and a probiotic 253 product based on 5 bacterial species isolated from the crop (Lactobacillus reuteri DSM 254 16350), jejunum (Enterococcus faecium DSM 16211), ileum (Bifidobacterium 255 animalis DSM 16284), and caecum (Pediococcus acidilactici DSM 16210, and 256

  -producing bacteria with antibacterial activity against pathogens. 305

a

  The positive control (PC) diet contained 60 mg/kg of salinomycin 512 b The negative control (NC) diet did not contain any additives 513 c The divercin supplemented diet contained 200 AU of divercin/ml (0.2 ml/kg) 514 d SEM -standard error of the mean 515 e P -probability 516 x, y, z Within rows, mean values without a common superscript differ significantly.

Table 1

 1

	. The divercin

Table 1

 1 100 g were collected at 35 d. The digesta and excreta samples were immediately 130 frozen, freeze-dried and ground before further analyses. 131

	near here

Table 4

 4

	near here

Table 1 .

 1 Composition of the basal diets and their calculated nutritive value

	o
	r
	P
	e e r
	R e v i e w
	O n
	l y

D-biotin, 0.18 mg; pyridoxine, 4.0 mg; ethoxyquin, 0.09 mg; Mn (MnO 2 ), 73 mg; Zn (ZnO), 55 mg; Fe 473 (FeSO 4 ), 45 mg; Cu (CuSO 4 ), 20 mg; I (CaI 2 O 6 ), 0.62 mg; Se (Na 2 SeO 3 ), 0.3 mg. 474 b Replaced corresponding amount of the wheat in each diet, from 30-35 d of broiler growth 475 Page 22 of 25 E-mail: br.poultsci@bbsrc.ac.uk URL: http://mc.manuscriptcentral.com/cbps

Table 2 .

 2 Performance results477

	Item	PC a	Treatment NC b	DIV c	SEM d	P e
		Feed conversion ratio (g feed/g gain)
	1 -14 d	1.48 y	1.54 x	1.49 y	0.01	0.001
	14 -35 d	1.60	1.67	1.67	0.02	0.140
	1 -35 d	1.58	1.65	1.61	0.01	0.059
			Body weight gain (g/bird)
	1 -14 d	328 x	304 y	320 x	3.37	0.006
	14 -35 d	1474 x	1360 y	1413 xy	14.25	0.003
	1 -35 d	1801 x	1664 z	1733 y	15.83	<0.001
			Feed intake (g/bird)
	1 -14 d	484	469	476	3.77	0.236
	14 -35 d	2357	2274	2349	18.99	0.138
	1 -35 d	2838	2737	2790	18.21	0.074

a The positive control (PC) diet contained 60 mg/kg of salinomycin 478 b The negative control (NC) diet did not contain any additives 479 c The divercin supplemented diet contained 200 AU of divercin/ml (0.2 ml/kg)

Table 3 .

 3 Ileal digestibility of nutrients and energy, nitrogen retention and AME N

	483
	484
	485
	486
	487

480 d SEM -standard error of the mean 481 e P -probability 482 x, y, z Within rows, mean values without a common superscript differ significantly. e P -probability 496 x, y, z Within rows, mean values without a common superscript differ significantly.

Table 4 .

 4 Counts of coliform and lactic acid bacteria (log cfu•/g digesta) and pH in 510crop, ileal and caecal digesta 511

Table 5 .

 5 Concentrations of organic acids (µmol/g digesta) in the contents of crop, 524ileum and caecum of broiler chickens. The divercin supplemented diet contained 200 AU of divercin/ml (0.2m/kg) Within rows, mean values without a common superscript differ significantly.

	Item	PC a	Treatment NC b	DIV c	SEM d	P e
			Crop
	Coliforms	6.98	7.08	6.55	0.110	0.112
	Lactic acid bacteria	7.92	7.93	7.41	0.124	0.140
	pH	4.33 x	3.94 y	4.31 x	0.189	0.011
			Ileum
	Coliforms	6.47	6.29	6.24	0.144	0.785
	Lactic acid bacteria	7.90 y	7.72 y	7.03 x	0.142	0.015
	pH	6.28 x	5.14 y	5.55 x	0.376	0.001
			Caecum
	Coliforms	7.88	7.71	7.13	0.191	0.253
	Lactic acid bacteria	9.24 x	8.53 y	8.00 y	0.180	0.006
	pH	5.49 y	5.78 x	5.52 y	0.181	0.043

a The positive control (PC) diet contained 60 mg/kg of salinomycin 526 b The negative control (NC) diet did not contain any additives 527 c

E-mail: br.poultsci@bbsrc.ac.uk URL: http://mc.manuscriptcentral.com/cbps British Poultry Science

Ruminants. Journal of Nutrition, 120: 632-638.


Camille Perrot

F Chevillotte

R Panneton

HAL is

Introduction MOTIVATION

Need to increase or adapt the sound absorption spectrum of commonly used sound absorbing materials

• Inefficient materials in the low frequency range • Need to adapt the absorption spectrum to the emission spectrum

A variety of performance demands are increasingly being placed on sound absorbing material systems.

A bottom-up approach for microstructure optimization of long-wavelength sound absorbing materials was recently presented using hybrid estimates based on direct numerical evaluation of macroscopic parameters and analytical models [1].

Results of this paper tend to demonstrate the existence of a microstructural configuration maximizing the area under the sound absorption spectrum, together with the optimal range of local characteristic lengths.

This is a crucial conclusion, notably for foam and fibrous materials manufacturers, which need to be confirmed with a more general formulation proposed by Lafarge (see [2]). This section reports and quantifies differences obtained with the simplified and refined models, see Fig. 4.

The optimal microstructural configuration is correctly estimated from a simplified model with only 3% of uncertainty on the global performances.

However, for very diluted (large porosities) porous structures, the simplified model underestimates significantly the material performances with uncertainties reaching up to 30%. Moreover, in this limit, where the best absorbing structure may lie, the physics have to be reconsidered (because both the nonslip conditions for velocity and temperature loose their physical justifications).

More sophisticated computational methods such as molecular dynamics will be considered to tackle physical acoustics of nano-porous materials as a future work.

Fig 1 .

 1 Fig 1. Linking micro-structure and acoustical macro-behaviour

Fig 4 .

 4 Fig 4. Response surface of the performance index I representing the area under the sound absorption curve in the frequency range 0 -10 000 Hz for varying (w-throat size, r-fiber radius) couples (top-left); and associated 2D practical chart (bottom-left). Response surfaces of the error E made on I when using the simplified model instead of the refined one (top-right); and corresponding practical chart (bottom-right).

1Fig 3 .

 3 Fig 3. Throat size (left), fiber radius (center), and cross-section shape (right) effects.


Cornelis Jacominus Van Der Beek

Marcin Konczykowski

Ruslan Prozorov

C J Van Der Beek

Anisotropy of strong pinning in multi-band superconductors

Keywords: numbers: 74.25-q, 74.25.N-, 74.25.Sv, 74.25.Wx

published or not. The documents may come

Introduction

The multi-band nature of superconductivity in iron-based superconductors has now been well established [1,2]. While direct measurement of the magnitude of the superconducting gap on the different Fermi-surface sheets has been and is the most convincing method in this respect, it is not the easiest. Therefore, many researchers have resorted to the measurement of the anisotropy of the superconducting parameters such as the coherence length and the penetration depth [3,4,5,6,7,8,9] to prove the multi-band nature of superconductivity of these layered materials. This manifests itself through the inequality of the anisotropy factors ε ξ ≡ ξ c /ξ ab and ε λ ≡ λ ab /λ c , which are the respective ratios of the coherence lengths ξ c and ξ ab parallel and perpendicular to the anisotropy (c)-axis, and of the penetration depths λ ab and λ c for supercurrents running in the ab-plane and along the c-axis respectively. The anisotropy of the coherence length is usually obtained from that of the upper critical fields B ⊥ c2 and B c2 for field oriented parallel to, and perpendicularly to the c-axis [3,4,5,6,8,10,11]. The anisotropy of the penetration depth is most often extracted from the anisotropy of the lower critical fields B ⊥ c1 = (Φ 0 /4πλ 2 ab ) ln κ ab and B c1 = (Φ 0 /4πλ ab λ c ) ln κ c parallel and perpendicular to the c-axis [6,7,12], or from direct measurements using microwave techniques [13,14,15] (here κ ab ≡ λ ab /ξ ab while κ c ≡ λ ab λ c /ξ ab ξ c ) [16]. The inequality of ε ξ and ε λ was first observed [17,18,19,20], and theoretically described [21] in the archetypical twoband superconductor MgB 2 . It was shown that in the case of weakly coupled twoband superconductors such as MgB 2 , Ginzburg-Landau theory, which, for single-band superconductors, introduces the anisotropy ratio ε = ε ξ = ε λ as the square-root of the ratio of the effective masses m ab and m c perpendicular and parallel to the c-axis, is inappropriate [22].

More recently, critical current density measurements have been used to address the anisotropy of superconducting parameters in the iron-based superconductors. In particular, Kidzun et al. [23] and Hänisch et al. [24] applied the anisotropic Ginzburg-Landau scaling procedure of Ref. [32], developed for single band superconductors, to the critical current density of epitaxial LaFeAsO and Ba(Fe 1-x Co x ) 2 As 2 films. They found that the extracted temperature dependence of the anisotropy parameter, ε(T ), matches that of the anisotropy parameter determined from scaling of the upper critical field [24]. This appears to validate the use of critical current density measurements for obtaining reliable values of the anisotropy parameters. This approach was taken further by Moll et al. [25], who specifically fashioned micrometer-sized SmFeAsO bridges to measure the three independent critical current densities, j c ab for current running in the ab-plane and field oriented along the c-axis, and j ab ab and j ab c for current in the ab-plane and along the c-axis, respectively, and field in the ab-plane (see the definitions in Fig. 1). The three critical currents were also measured independently in single crystalline LiFeAs by using a Hall-probe array magnetometry technique [26]. These measurements allowed the direct extraction of the coherence length anisotropy.

However, the interpretation of the critical current anisotropy is, a priori , not so

L ⊥ = L ε 2 λ ε 1/2 b (B ab; u ⊥ ab) (18)
by a factor ε λ . Note that the pinning length shows the same behavior as L c only if abstraction is made of the difference between ε λ and ε ξ . The critical current density follows trivially,

j c ab = f Φ 0 L = ε 2 λ ε 3/2 b j c s (B ab; j c) (19)
j ab ab = f ⊥ Φ 0 L = ε 2 λ ε 3/2 b ε ξ j c s , (B ab; j ab; j ⊥ B) (20)
expressions that are valid for B < (ε b /ε 2 λ )B * (see below).The dependence of the critical current densities for motion parallel and perpendicular to the c-axis does not follow the same relation as in the weak pinning limit of section (II B), and the ratio

j ab c j ab ab = ε ξ (21)
is entirely determined by the coherence length anisotropy. Turning to higher fields, our task is to determine the trapping area u 2 0 and u ⊥2 0 for in-plane and out-ofplane vortex displacements, respectively. These are determined by the shear-and tilt moduli for vortex lattice deformations within the ab plane, c 66 = ε 3 λ c 66 and c 44 ∼ ε 2 λ /ε ϑ c44 , and out-of-plane vortex deformations, c ⊥ 66 = c 66 /ε λ and c ⊥ 44 ∼ c44 , respectively. 14,15 Taking into account that the for B ab the vortex lattice is distorted, with in-plane and out-of-plane vortex spacings given by a 0 = a 0 /ε λ and a 0 = ε λ a 0 respectively, we have

u 2 = ε u 2 (22) L ⊥ = L ε 2 λ ε 1/2 b
by a factor ε λ . Note that same behavior as L c only difference between ε λ and follows trivially,

j ab c = f Φ 0 L = ε 2 λ ε 3/2 b j ab ab = f ⊥ Φ 0 L = ε 2 λ ε 3
te that the pinning length shows the L c only if abstraction is made of the ε λ and ε ξ . The critical current density

ε 2 λ ε 3/2 b j c s (B ab; j c) (19)
ε 2 λ ε 3/2 b ε ξ j c s , (B ab; j ab; j ⊥ B) (20)
re valid for B < (ε b /ε 2 λ )B * (see bece of the critical current densities for perpendicular to the c-axis does not lation as in the weak pinning limit of the ratio j ab c total pinning force and the critical curre

j ab c = f Φ 0 n i u 2 0 = ε 2 b ε λ j c s (B ab j ab ab = f ⊥ Φ 0 n i u 2 0 = ε 2 b ε λ ε ξ j c s ; (B a
The crossover field B(ε b /ε 2 λ )B * delimiti validity of Eqs. (19,20) and Eqs. (24,25 by comparing the high-and low field v spective critical current densities. The ra of the in-plane and out-of-plane critical c is again determined by the coherence len Note that where, in the weak pinning reg current density for B ab, j ab, is l in for B c, j ab, in the strong pinn smaller.

These expressions correspond to what w obtained from the full non-local tilt modu at the deformation vectors (k x = 2πn i u 2 0

III. EXPERIMENTAL DET

Single crystals of LiFeAs were grown as described in detail elsewhere 9 and w for measurements in sealed ampoules. Im opening, 0.16 × 0.22 × 0.80 mm 3 samp a wire saw, washed and protected in m sample was then repeatedly measured a showing no degradation as long as a con ture and oxigen was eliminated. Addit were extensively characterized by transp straightforward. In principle, the critical current depends in a non-trivial manner on the specific nature of the pinning potential, that is, on the kind of defects and impurities that are present in the superconducting material. It also depends non-trivially on the details of vortex elasticity. A supplementary complication comes from the fact that vortex pinning in the iron-based superconductors is, certainly at the low magnetic fields, dominated by the so-called strong pinning [27,28] by nm-sized impurities [29,30,31]. In this regime, the anisotropy of the critical current may be influenced by the size and shape of the strongly pinning defects. Therefore, it is important to understand why the measurements of Refs. [23,24], as well as those of Konczykowski et al. [26], yield the coherence length anisotropy with such precision, even though the authors [23,24] applied a single-band approach to analyze their results.

In the following, we explore the effect of different anisotropies on the critical current in the strong pinning regime in single-band and multi-band superconductors. Our goal will be limited to the identification of the main origin of the anisotropy of the critical current. This justifies a purely phenomenological approach, in which we will suppose that, in a single-band superconductor, the angular dependence of the properties of the superconducting state enter through the angular dependence of the penetration depth, λ(ϑ) = λ ab /ε ϑ for supercurrents running at an angle ϑ with respect to the ab-plane, while the angle-dependent coherence length ξ(ϑ) = ξ ab ε ϑ . Here ϑ is the angle between the orientation of interest and the ab-plane. The scaling function

ε ϑ = ε 2 cos 2 ϑ + sin 2 ϑ < 1 (1)
can be found in Refs. [32,33]. For multi-band superconductors, we will assume that the angular dependence of vortex-related quantities in the mixed state can be described by two different anisotropy ratios ε λ (ϑ) and ε ξ (ϑ) for the penetration depth and the coherence length, and that the angular dependence of these ratios is the same as Eq. ( 1). In all cases, ε ξ ξ will be assumed to be larger than the distance between the structural layers, so that the material can be described as "continuously anisotropic". Josephson tunneling between layers is beyond our consideration. In section 2.2 we first derive anew the results for the critical current density of Ref. [33], for the case of weak collective pinning of individual vortices, keeping track of the anisotropies introduced by the coherence length and the penetration depth, respectively. In section 2.3, we then apply the same procedure to the formulae of Ref. [28] for strong pinning by large point defects, which is more appropriate in iron-based superconductors at low fields. Here, the effect of a non-spherical shape of the pinning defects is also taken into account.

The procedure has the merit of demonstrating that the field-orientation-dependence of the ab-plane critical current density j ab (ϑ) is, in all cases, determined by the competition of two factors. The coherence length anisotropy is responsible for the increase of the j ab (ϑ) as the magnetic field is aligned towards the ab-plane, mainly because of the larger elementary pinning force experience by the vortex lines as these are turned towards the ab-plane. For large defects, this effect is counteracted by the penetration-depth anisotropy, which result in a larger line energy and therefore larger pinning energies when the vortices are aligned parallel to the c-axis. In most situations, the latter effect is much weaker than the first, so that the anisotropy extracted from field-angular dependent measurements of the critical current yields ε ξ .

The latter is also true for the anisotropy of the critical current density itself. On very general grounds, it is shown that the ratio j ab c /j ab ab is, in all cases, equal to the coherence length anisotropy ratio ε ξ . This fact was recently exploited to extract the fielddependence of ε ξ in single crystalline LiFeAs [26]. We note that the results below are relevant not only for iron-based superconductors, but also for high T c superconducting cuprate thin films, tapes, and composite conductors.

Critical current anisotropy in uniaxial anisotropic superconductors

Weak collective pinning in single-band superconductors

The anisotropy of the critical current density may, in principle, depend on the underlying pinning mechanism in the material. A flagrant example is the presence of anisotropic pinning centers such as heavy-ion irradiation-induced amorphous columnar defects [34,35,36], which introduce a preferential orientation for the vortex lines supplementary to that imposed by the anisotropic material. However, in the case of weak collective pinning by dense atomic-scale point defects, the anisotropy of the critical current density ought not to depend on the details of the defect landscape, but only on the material properties. It can thus be straightforwardly obtained using the scaling formalism introduced by Blatter et al. [32,33].

In the so-called single-vortex pinning regime, in which the critical current is not limited by intervortex interactions, the critical current density j ab in the (ab) plane, perpendicular to the symmetry (c)-axis, is expected to be field-angle independent,

j c ab = n d f 2 p ξ 2 ab Φ 0 L c 1/2 = j ab ab = n d f ⊥2 p ξ ab ξ c Φ 0 L ab c 1/2 ≡ j SV . (2)
Here, f p is the elementary pinning force of a single point defect for a vortex directed along the c-axis, n d ξ -3 is the point defect density, and the factors ξ 2 ab and ξ ab ξ c derive from the statistical averaging of the pinning forces over the vortex core. The brackets . . . denote averaging over the vortex core. For field aligned along ab, one is faced with a larger pinning force f ⊥ p for "out-of-plane" vortex motion along c, since the pinning range [38] r f ∼ ξ c = εξ ab is shorter in this direction. However, this is compensated by the larger longitudinal correlation length L ab c = L c /ε for field oriented along the ab-plane as compared to L c for field c [33]. In this specific situation, L ab c does not depend on the direction of the vortex displacement u in the pin potential. The anisotropic vortex line tensions, ε ⊥ 1 = ε 1 /ε 3 and ε 1 = ε 1 /ε for out-of-plane and in-plane vortex displacements respectively, compensate for the anisotropies of the elementary pinning force and the pinning range, i.e.

L ab c = ε ⊥ 1 n 1/2 d f p /ε 2/3 ε 1/3 (u ⊥ ab) (3)
= ε 1 n 1/2 d f p 2/3 1 ε 1/3 (u ab) (4) = L c /ε. (5)
Here ε 1 ∼ ε 2 ε 0 and ε 0 = Φ 0 /4πµ 0 λ 2 ab are the vortex line tension and the vortex line energy for magnetic induction B c, and Φ 0 is the flux quantum. Hence, the critical current density j c ab for field along the c-axis is equal to the critical current density j ab ab (with B ⊥ j) for field along the ab-plane.

The c-axis critical current density j ab c for B ab on the other hand involves "inplane" vortex motion, and is reduced by the anisotropy factor ε, such that j ab c = εj c ab . These relations do not hold in the so-called "bundle regime", in which vortex interactions reduce the magnitude of the critical current density. Then, j ab (Bε ϑ ) follows the wellknown field-angular scaling relation in ε ϑ = (ε 2 cos 2 ϑ +sin 2 ϑ) 1/2 as detailed in Ref. [33].

Here ϑ is the angle between the direction of the magnetic induction and the ab-plane.

Weak collective pinning in multi-band materials

We now turn our attention to the situation in the multi-band iron-based superconductors. In what follows, the multi-band nature of superconductivity will be taken into account phenomenogically, by simply introducing different anisotropies ε ξ and ε λ of ξ and λ, respectively. Then we can rederive the results or Ref. [33], but keeping track of these different factors. We shall restrict ourselves to the single vortex regime of pinning, in which the critical current density is constant as function of magnetic field. In iron-based superconductors, this is thought to be relevant in a range of intermediate field strengths, sufficiently high for the critical current not be dominated by the strong pinning contribution due to nanometer-sized point-like pins (section 2.3), but below the onset of the so-called "second magnetization peak" regime, which is not described by the collective pinning theory [29,30]. Typically, this corresponds to a field range of several tenths of Tesla, to a few Tesla at most.

Elementary pinning force

The elementary pinning force f p can, within factors, be written as the product of the condensation energy B 2 c /2µ 0 = ε 0 /2πξ 2 ab , the defect volume 4 3 πD 3 v , and the inverse range of the pinning potential, r -1 f . In the case of pinning by mean-free path variations [29,30,33,37], a scattering factor proportional to g(ρ D )(ξ 0 /D v ) should be introduced, with g(ρ D ) the Gor'kov function, ρ D = v F /2πT c l ∼ ξ 0 /l the disorder parameter, v F the Fermi velocity, l the mean free path, and ξ 0 = 1.35ξ(0) the temperature-independent BCS coherence length. Disregarding the possibility of anisotropic scattering, the elementary pinning force for magnetic fields not aligned with the c-axis is modified because of the anisotropy of the vortex line energy ε 0 , which involves the kinetic energy of current components flowing both parallel to c and ab as well as the anisotropy of the vortex core radius, and because of the anisotropic range of the pinning potential. When B is aligned along the ab-plane, the first effect introduces a factor ε λ and the second a factor ε -1 ξ . As for the pinning range, this also depends on the orientation of the supercurrent. For j ab, j ⊥ B, vortex motion is parallel to the symmetry axis and, in the low-field limit (B < 0.2B c2 ), r ⊥ f = ξ c , while for j c, r f = ξ ab . Therefore,

f p = ε λ ε ξ f p (B ab; j c; |B| < 0.2B c2 ) (6)
f ⊥ p = ε λ ε 2 ξ f p (B ab; j ab; j ⊥ B; |B| < 0.2B c2 ). (7)
For higher fields, the pinning range is given by the intervortex distance:

r ⊥ f = ε 1/2 ξ a 0 , while r f = a 0 /ε 1/2 ξ [with a 0 = (2Φ 0 / √ 3B) 1/2 the vortex spacing for B c ] [38]. Therefore f p = ε λ ε 1/2 ξ f p , (B ab; j c; |B| > 0.2B c2 ) (8)
while

f ⊥ p = ε λ ε 3/2 ξ f p (B ab; j ab; j ⊥ B; |B| > 0.2B c2 ). (9)

Pinning correlation length

The isotropy of the pinning correlation length for B ab in Eqs. (3,4) is nominally lifted, because the anisotropy of the vortex line tension,

ε ⊥ 1 = ε 1 /ε 3 λ and ε 1 = ε 1 /ε λ ,
bears mainly to that of λ, while the range r f is determined by the value of the coherence length in the direction of the vortex displacement. As a result, the pinning length L c = (ε

1/3 ξ /ε 4/3 λ )L c
of a vortex confined to the ab-plane will no longer be equal to L ⊥ c = (ε

5/3 ξ /ε 8/3 λ )L c = (ε ξ /ε λ ) 4/2
L c for a vortex confined to a plane containing the c-axis.

However, in a three-dimensional superconductor, both in-plane and out-of-plane random displacements are allowed, and both determine the metastable vortex position and the critical current density. Taking into account Eqs. (6,7) and the difference of the line tensions for in-plane and out-of-plane vortex displacements, and minimizing the sum of elastic and pinning energy ε

1 (ξ ab /L c ) 2 + ε ⊥ 1 (ξ c /L c ) 2 -(n d f 2 p /L c ) 1/2 ξ 3/2 ab ξ 1/2 c - (n d f ⊥2 p /L c ) 1/2 ξ 3/2 c ξ 1/2
ab , we obtain

L c = 2 2/3 ε 1/3 ξ ε 2 λ + ε 2 ξ 2/3 L c . (10)
If the coherence length anisotropy dominates the penetration depth anisotropy, the vortex excursions will be mainly confined to the ab-plane, the large pinning force in the c-direction prohibiting out-of-plane excursions.

Critical current density

As in Eq. ( 2), the critical current density is determined from the equality of the Lorentz force on a correlated pinned vortex segment and the total pinning force on that segment,

Φ 0 j c L c = n d f 2 p L c 1/2 L c ξ ≡ F p ( 11
)
where ξ is the square-root of the vortex core area. For the two different directions of motion of vortices parallel to the ab-plane, we find

j ab c = ε λ ε 2 λ + ε 2 ξ 1/3 2 1/3 ε 2/3 ξ j SV (B ab; j c) (12)
j ab ab = ε λ ε 2 λ + ε 2 ξ 1/3 2 1/3 ε 5/3 ξ j SV (B ab; j ab; j ⊥ B). ( 13
)
Note that for ε λ → ε ξ , j ab c → εj SV and j ab ab → j SV , in agreement with the results outlined in Section 2.1. More importantly, the critical current density is independent of the range r f of the pin potential. Since the core area and the pinning length are the same, irrespective of the direction in which the vortices are driven, the difference between these expressions is entirely due to the different elementary pinning forces for in-plane and out-of-plane vortex motion. As a result, the anisotropy

j ab c j ab ab = ε ξ ( 14
)
is uniquely determined by the anisotropy of the vortex core (i.e. of the coherence length). Therefore, the measurement of the j ab c /j ab ab -anisotropy directly yields the coherence length (B c2 -) anisotropy.

The above conclusion, a consequence of the fact that the critical current density in the single vortex regime can be written as j c = F p /Φ 0 L c , can be extended to all field and temperature ranges. In particular, in the bundle pinning regime [33], Eq. ( 11) is replaced by

j c BV c = n d f 2 p V c 1/2 (15)
where the correlation volume V c = R 2 c L c is the product of the square of the transverse correlation length R c and the longitudinal correlation length L c . Since, for a given magnetic field orientation, the correlation volume is the same regardless of the direction in which the vortices are being driven, the anisotropy of the critical currents for different driving directions is always given by the anisotropy of the elementary pinning force.

Strong pinning in anisotropic superconductors

We now investigate the case of so-called strong pinning [27,28,39], i.e., the situation in which a type-II superconductor contains point-like defects or heterogeneities with typical dimensions b z , b x parallel and perpendicular to the field direction larger the coherence length, and density n i much smaller than ξ -3 . Then, the (first moment of the) pinning force from different defects does not average out as in the weak pinning case. The critical current density is now determined by the direct sum of the forces exerted by each pin a vortex line is able to take advantage of [27]. This situation is encountered in cuprate superconductor thin films [28,40] and coated conductors [41], in which second-phase nanoparticles are responsible for pinning, as well as in most iron-based superconductors at low fields [29,30,31]. In the latter materials, the presence of nm-scale heterogeneity of the superconducting properties is thought to play the role of the strong pins, thereby determining both the highly inhomogeneous vortex distributions, as well as the low-field critical current density [31].

At low fields, the number of pins a vortex line can benefit from is solely determined by the vortex line tension. The mean characteristic length L = π -1/2 (ε 1 /n i U p ) 1/2 of free vortex between two effective pins is determined by the balance of the tilt deformation energy ε 1 (u/L) 2 of the line, and the pinning energy gain per pin, U p . At magnetic inductions exceeding B * = πΦ 0 n i (U p /ε 0 ), the intervortex repulsion rather than the line tension limits the number of defects any given flux line can take advantage of. The pinning length is then given by L = n i u 2 0 , where the trapping area u 2 0 = U p /(c 66 c44 ) 1/2 a 0 is determined by the balance between the pinning energy gain and the energy of the lattice deformation. For B c, the shear modulus is given by c 66 ≈ ε 0 /4a 2 0 , and the non-local tilt modulus is evaluated as c44 ≈ ε 2 ε 0 /a 2 0 . For field along the c-axis, the critical current density is [28]

j s = f Φ 0 L = n 1/2 i f Φ 0 πU p ε 1 1/2 (B < B * ) (16) = n i f Φ 0 2U p ε 0 Φ 0 B 1/2 (B > B * ) (17)
where the maximum force that a single strong pin can exert on a vortex line (for B c)

f = B 2 c 2µ 0 1 r f πb z ξ 2 ab ln 1 + b 2 x 2ξ 2 ab = 1 4 ε 0 b z r f ln 1 + b 2 x 2ξ 2 ab ( 18
)
is the product of the condensation energy over the range of the pinning potential, the core volume occupied by the defect, and a logarithmic factor taking into account the modification of the supercurrent distribution around the defect [28,42]. Here we have assumed that the pinning defects are insulating, and of ellipsoidal shape with halfaxes b x ab and b z c. Eq. (18) interpolates between the logarithmic dependence on dimensions expected for large defects with b x , b z ξ ab , and the simple factor (b x /ξ ab ) 2 proportional to the defect cross-sectional area that one has for small defects.

Elementary pinning force

In order to evaluate the anisotropy in the limit of strong pinning, both with respect to the field orientation and the driving direction, we again start by evaluating the change of the elementary force f with field orientation. Contrary to the case of weak pinning, f is reduced by a factor ε λ for B ab, due to the decrease of the vortex line energy. A supplementary complication enters in that the smaller core cross-section for field not aligned with c, as well as the geometrical anisotropy of the defects, affect the factor under the logarithm. For B ab and j c, i.e. in-plane vortex motion, the pinning range r f = ξ ab is the same as for vortices parallel to the c-axis, while for the motion along c of vortices parallel to the ab, it is the smaller c-axis coherence length that enters. One thus has

f = ε λ ε b (0) f (B ab; j c) (19)
f ⊥ = ε λ ε ξ ε b (0) f ; (B ab; j ab; j ⊥ B) (20)
for arbitrary orientation ϑ of the field with respect to the c-axis,

f = ε λ (ϑ) ε b (ϑ) f (j c) (21)
f ⊥ = ε λ (ϑ) ε b (ϑ)ε ξ (ϑ) f. (j ab; j ⊥ B) (22)
where we have introduced the geometrical anisotropy

ε b (ϑ) = 1 sin 2 ϑ + b 2 x b 2 z cos 2 ϑ ln (1 + b 2 x /2ξ 2 ab ) ln 1 + b x b 2 x sin 2 ϑ + b 2 z cos 2 ϑ/2ξ 2 ab ε ξ (ϑ) (23)
for model ellipsoidal defects. For spherical defects of size ∼ ξ ab , this reduces to a simple factor ε ξ (ϑ). The pinning energy for B ab is

U ab p = [ε λ /ε b (0)]U p , while for arbitrary orientation it is U p (ϑ) = [ε λ (ϑ)/ε b (ϑ)]U p .
2.3.2. Single vortex limit of strong pinning We first examine the limit of low fields. The pinning length L for arbitrary field orientation takes on different values depending on the direction of the deformation: it is larger for out-of-plane deformations, due to the larger line tension ε ⊥ 1 ∼ ε 1 /ε 3 λ (ϑ) in this direction [33]. At equilibrium, the most favourable pinned configuration will be determined by

L = ε 1/2 b (ϑ) ε λ (ϑ) L, (u ab) ( 24
)
since this is smaller than

L ⊥ = ε 1/2 b (ϑ) ε 2 λ (ϑ) L (B ab; u ⊥ ab) (25)
by a factor ε λ (ϑ) ≡ ε 2 λ cos 2 ϑ + sin 2 ϑ. Thus, the vortex adapts to the pin potential by deformations parallel to the ab plane rather than perpendicularly to the field direction. Note that in all cases, except that of extremely oblate defects (ε b < ε 2 λ ), the typical length of a pinned segment ab exceeds that for B c, and thus, each vortex ought to be, on average, pinned by a smaller number of defects. If one assumes that the vortices can seek out the most favorable pinned configuration at each stage of their motion, the ab-plane critical current density simply follows as

j ab (ϑ) = f ⊥ Φ 0 L = ε 2 λ (ϑ) ε 3/2 b (ϑ)ε ξ (ϑ) j s ; (j ab; j ⊥ B; B < B * ) (26)
valid for B < B * (see below). If the relevant pinning centers are relatively small (radius of the order of ξ ab ) and isotropic, the critical current density scales as ε 2 λ (ϑ)ε -5/2 ξ (ϑ). In the case of single-band superconductors, where ε λ (ϑ) = ε ξ (ϑ) = ε ϑ , this reduces to the scaling law j ab (ϑ) ∝ ε -1/2 ϑ . For B ab, the critical current densities parallel and perpendicular to the c-axis depend on the anisotropies of the penetration depth and the coherence length in a different combination than in the weak pinning limit of section (2.2): However, the generality of expression ( 16) together with a L that does not depend on driving direction signifies that their ratio only depends on the coherence length anisotropy. In particular, for B ab, the ratio of critical currents for in-plane and out-of-plane motion of vortices

j ab c = f Φ 0 L = ε 2 λ (0) ε 3/2 b (0) j s (j c; B < B * ) ( 27
)
j ab ab = f ⊥ Φ 0 L = ε 2 λ (0) ε 3/2 b (ϑ)ε ξ (0)
j ab c j ab ab = ε ξ ( 29
)
again directly yields the coherence length anisotropy. The case in which vortices cannot equilibrate during driven motion was explored in Ref. [42]. Then, vortices can only take advantage of those pins that are located within a distance u t of the plane of motion. The "dynamic" critical current density j tr = f /Φ 0 L for driven motion depends on the vortex length L trapped between adjacent pins. Analysis yields, for the critical current density for field along c, [42] The ab-plane critical current density for arbitrary field direction is obtained as using the parameters corresponding to (hard) motion, perpendicular to the field direction.

j tr = n 4/9 p f U p ε 1 5/9 ξ -2/9 . ( 30
)
Inserting relevant parameters, we obtain

j ab,tr (ϑ) = n 4/9 p f ⊥ U p (ϑ)ε λ (ϑ) ε b (ϑ)ε ⊥ 1 5/9 1 [ε ξ (ϑ)ξ] 2/9 (31) = ε 29/9 λ (ϑ) ε 14/9 b (ϑ)ε 11/9 ξ (ϑ) j tr . (32)
In the case of small spherical defects and similar anisotropies for the coherence length and the penetration depth, j ab,tr (ϑ) ∼ ε 4/9 ϑ j tr .

For field along the ab-plane, the critical current densities along c and ab are determined by hard and easy motion respectively, so that

Unlike the above results, the ratio of the "dynamic critical currents" j ab c,tr /j ab ab,tr = ε ξ /ε 10/9 λ does not uniquely depend on the coherence length anisotropy. Surprisingly, the derived dynamic critical current densities for vortex motion along the hard-and the easy direction are nearly equal in single band materials, because the anisotropy of the elementary pinning force cancels that of the vortex line tension.

2.3.3.

Three-dimensional strong pinning Turning to higher fields, our task is to determine the trapping radii u 0 and u ⊥ 0 for in-plane and out-of-plane vortex displacements, respectively. These are determined by the shear-and tilt moduli for vortex lattice deformations within the ab plane, c 66 = ε 3 λ (ϑ)c 66 and c 44 ∼ c44 , and out-of-plane vortex deformations, c ⊥ 66 = c 66 /ε λ (ϑ) and c ⊥ 44 ∼ (ε λ (θ)/ε λ ) 2 c44 , respectively [43,44]. Here θ = π 2ϑ is the angle with respect to the c-axis, and ε λ (θ) ≡ ε 2 λ sin 2 θ + cos 2 θ [33]. Taking into account the distortion of the vortex lattice into account, with in-plane and out-of-plane vortex spacings given by a 0 = a 0 /ε 1/2 λ (ϑ), and a ⊥ 0 = ε 1/2 λ (ϑ)a 0 respectively, we have

u 2 0 = u 2 0 ε b (0) (35)
u ⊥2 0 = ε λ ε λ (ϑ) ε b (0)ε λ (θ) u 2 0 , (36)
so that for B ab,

u 2 0 = u 2 0 ε b (0) (37)
u ⊥2 0 = ε 2 λ ε b (0) u 2 0 . (38)
Thus, compared to the orientation c, a vortex in the ab-plane can wander a similar distance in the plane, but a much smaller distance perpendicular to it. The trapping area u 0 u ⊥ 0 = [ε λ /ε b (0)]u 2 0 , so that the length of a pinned vortex segment L = 1/n i u 0 u ⊥ 0 exceeds L for B c by a factor ε b (0)/ε λ . The critical currents for vortex motion within the ab plane and perpendicular to it are

j ab c = f Φ 0 n i u 0 u ⊥ 0 = ε 2 λ ε 2 b (0) j c s (B ab; j c; B > B * ) (39)
j ab ab = f ⊥ Φ 0 n i u 0 u ⊥ 0 = ε 2 λ ε 2 b (0)ε ξ j c s ; (B ab; j ab.j ⊥ B; B > B * ) (40)
The crossover field B * = B * /ε b (0) delimiting the range of validity of Eqs. (39,40) with respect to Eqs. (27,28) is determined by comparing the high-and low field values of the respective critical current densities. It depends only on the specific details of the pinning centers.

The ratio j ab c /j ab ab = ε ξ of the in-plane and out-of-plane critical current densities is once again determined by the coherence length anisotropy. Note that where, in the weak pinning regime, the critical current density for B ab, j ab, is the same as (or comparable to) that for B c, j ab, in the strong pinning regime it may be noticeably smaller.

Finally, we give the expression for the field-dependent ab-plane critical current density as function of field orientation,

j ab (ϑ) = ε 2 λ (ϑ) ε 2 b (ϑ)ε ξ (ϑ) j c s (j ab; j ⊥ B; B > B * ) (41) ∝ j ab ab (B = 0) 1 [ε b (ϑ)B] 1/2 , ( 42
)
valid for fields lower than the angle-dependent crossover field B * (ϑ) = B * /ε b (ϑ). For small spherical defects in a single-band superconductor, this yields the well-known scaling law in ε ϑ B [32,33].

Discussion

The following salient features emerge from the above derivations. First is the fieldangular dependence of the critical current density in the ab-plane. Eqs. ( 26) and (41) for the strong pinning critical current both involve the ratio of powers of the penetration depth anisotropy and the coherence length anisotropy. The penetration depth anisotropy in the denominator mainly comes from the line energy term appearing in the elementary pinning force. The coherence length anisotropy appears mainly due to the varying core size for different orientations, which determines the order parameter gradient and therefore, also, the magnitude of the pinning force.

As a result, for small defects of size comparable to the coherence length, only the latter contribution matters. Fig. 2(a,c) shows the field-angular dependence of the abplane critical current density for such small defects, for two values of the penetration depth anisotropy, and different ε ξ . Such a plot mimics the temperature dependence of pinning in the iron-based superconductors, in which ε ξ ε λ increases with temperature, the two reaching near equality near T c . At low temperature ε ξ ε λ and the coherence length anisotropy completely dominates the behaviour. This is why thin films and crystals of the 1111-family of iron-based superconductors seem to behave as single-band anisotropic superconductors, and scaling of j ab with the product of the magnetic field and Eq. ( 1) yields the B c2 -anisotropy [23]. Note that the change of apparent anisotropy with changing ε ξ may be very difficult to observe; for example, as the temperature is increased, the absolute value of the coherence length also increases, so that defects that are to be considered "large" at low temperature become "small" close to T c .

For larger defects, see Fig. 2(b,d), the scaling is disrupted, since now, the role of the angular-dependent vortex line energy becomes important. This results in a local maximum of the critical current for field aligned with the c-axis. For sufficiently large or strongly-pinning defects, this effect can result in the inversion of the apparent material anisotropy. As summarized in Fig. 3, this effect is not peculiar to multi-band superconductors, but is a property of strong flux pinning, as opposed to weak pinning.

The effect of large defects on the field-angular dependence of the critical current density is particularly pronounced in the case of oblate and prolate defects, see Fig. 4. Note that this effect is different in nature from that of extended columnar [34,35,36], planar defects [45,46] or intrinsic pinning [47,48,49,50], for which depinning takes place by half- [35,47] or quarter-loop [51] nucleation rather than by pin-breaking. The nucleation-type depinning leads to a sharp maximum of the critical current density for field aligned with the defect direction, while the depinning from oriented ellipsoidal defects leads to a much broader maximum. In Fig. 4, the broad maxima of the critical current density as function of field angle correspond to the effect of the ellipsoidal defects, while the sharp structure, for field ab is due to the material anisotropy. On top of that comes the possible effect of intrinsic pinning by the layered structure of the material, such as this may have been revealed by deviations from field angular-dependent scaling in Ref. [23]. The above analysis shows that in presence of strong pinning, the breakdown of simple scaling with ε ϑ [23] can arise because of several reasons, among which, the presence of point-like defects of dimensions larger than the coherence length, and the presence of defects of distinctly different dimensions and aspect ratios.

A final and general conclusion is that the measurement of the critical current density anisotropy for field parallel to the ab-plane (perpendicular to the anisotropy axis of the material) is a useful tool for the direct determination of the coherence length anisotropy ε ξ . It was shown above, on very general grounds, for both the weak-and strong pinning scenarios, that the j ab c /j ab ab ratio is always equal to ε ξ . This is because the relative pinned volume, i.e. the collective pinning length L c in the case of single vortex collective pinning, the correlation volume V c in the case of bundle pinning, and the pinned length L in the case of strong pinning, only depends on the field orientation and not on the direction in which the vortices are being driven. Moreover, the critical current density does not depend on the range of the pinning potential. Therefore, only the anisotropy of the pinning force determines, in the end, the anisotropy of the critical current density. Since this is given by the anisotropy of the vortex core in a given field orientation, we may expect that it directly yields the coherence length anisotropy.

The latter fact was recently exemplified by measurement of the three critical currents j ab c , j ab ab , and j c ab on single crystalline LiFeAs [26]. Figure 5 shows the temperature dependence of the three critical currents, as determined by Hall array magnetometry of the flux density gradient on different crystal faces under different modes of field application. From this, one may determine, directly, the ratio j ab c /j ab ab to yield the temperature-and field-dependent coherence length anisotropy factor ε ξ (T, B). Fig. 6 shows that the result is in excellent agreement with the same quantity, determined from the upper critical field measurements of Refs. [10,11,52]. Note that the anisotropy factor ε ξ has a non-trivial behaviour, in which it increases as function of field, but decreases as function of temperature. It can therefore not be simply explained in terms of the reduced field B/B c2 at which the measurements were performed, in conjunction with the temperature dependence B c2 (T ).

Conclusion

The field-angular dependence and anisotropy of the weak and strong pinning critical current density in uniaxial anisotropic single-band and multi-band superconductors was considered, using a simple phenomenological approach introducing distinct anisotropy factors ε λ and ε ξ for the penetration depth and the coherence length respectively. Expressions for the field-angular dependent and anisotropic critical current density are derived. It turns out that the field-angular dependence of the ab-plane critical current density is determined by the competition between two effects. These are the angular variation of the vortex line energy, and therefore the pinning energy, which is maximum for field parallel to the c-(anisotropy) axis, and the angular variation of the vortex core size (coherence length), which yields larger elementary pinning forces for field parallel to ab. As a result, the field-angular dependence of the critical current density in materials with a relatively large coherence length anisotropy (small ε ξ ) and/or relatively small point-like pinning centers is indistinguishable from that in a single-band superconductor. Analysis of this angular dependence then yields the coherence length (upper critical field) anisotropy. On the other hand, in (single-band and multi-band) superconductors with modest anisotropy and large point-like pinning centers, strong pinning for field oriented along the c-axis can lead to an apparent inversion of the anisotropy. Furthermore, we have shown, on very general grounds, that the ratio of the c-axis and ab-plane critical current densities for field along the ab-plane always yields the coherence length anisotropy ε ξ . This can therefore be extracted as function of temperature and field, at magnetic inductions far below the upper critical field B c2 . , measured in single crystalline LiFeAs using a Hall probe array magnetometry technique [26], for applied magnetic fields of 0.5 T ( ), 1 T (2), and 2 T (•). Filled symbols show the anisotropy ratio ε -1 ξ determined from the anisotropy of the upper critical field B c2 in Refs. [10], [11], and [52] .

Acknowledgments

Research Initiative (2010-0018300). The work of R. Prozorov in Palaiseau was funded by the St. Gobain chair of the Ecole Polytechnique. C.J. van der Beek and M. Konczykowski acknowledge the hospitality of Ames Lab and Iowa State University during the preparation of this work.

  / b ε ξ expressions that are valid low).The dependence of t motion parallel and perpe follow the same relation a section (II B), and the rat ϑ c44 , and out c ⊥ 66 = c 66 /ε λ and c ⊥ 44 ∼ c44 account that the for B a with in-plane and out-of-p a 0 = a 0 /ε λ and a 0 = ε λ a 0 of low fields. The pinning on different values depending on the formation: it is larger for out-of-plane to the larger line tension ε ⊥ in this st favorable pinned configuration, as current, is determined by /2 , (B ab; u ab) ; u ⊥ ab)

Figure 1 .

 1 Figure 1. Sketch defining the three independent critical current densities in an anisotropic superconductor. (a) j c ab is the (most commonly measured) critical current density for current in the ab-plane, field along the c-axis. (b) the ab-plane critical current density j ab ab for field in the ab-plane. This configuration involves the hard motion of vortex lines along the c-axis. (c) the c-axis critical current density j ab c for field parallel to the ab-plane. This involves the easy motion of vortices along the ab-plane.

  j s ; (j ab; j ⊥ B; B < B * )

Figure 2 .

 2 Figure 2. (Color online) Angular dependence of the critical current density in the single vortex limit of strong pinning, for anisotropies representative of (a,b) the (Ba,K)Fe 2 As 2 system and (c,d) the NdFeAsO and SmFeAsO systems, containing spherical insulating defects. The different values of ε ξ are introduced to mimic the temperature dependence of the anisotropy. The graphs (a,c) depict the expected behaviour for small defect sizes, b x = b z = ξ, while panels (b,d) are for large defects with b x = b z = 10ξ. ϑ is the angle with respect to the ab-plane.

Figure 3 .

 3 Figure 3. (Color online) Angular dependence of the critical current density in the single vortex limit of strong pinning, for anisotropies representative of (a) the (Ba,K)Fe 2 As 2 system and (b) the NdFeAsO and SmFeAsO systems, for different radii b x = b z of spherical insulating defects. ϑ is the angle with respect to the ab-plane.

Figure 4 .

 4 Figure 4. (Color online) Angular dependence of the critical current density in the single vortex limit of strong pinning, for anisotropies representative of (a,b) the (Ba,K)Fe 2 As 2 system and (c,d) the NdFeAsO and SmFeAsO systems, for ellipsoidal oblate and prolate insulating defects with half axes b x = 5ξ, b z = ξ, and b x = ξ, b z = 5ξ, respectively. ϑ is the angle with respect to the abplane.

Figure 5 .

 5 Figure 5. (Color online) Temperature dependence of the three independent critical current densities along the main crystalline axes of single crystalline LiFeAs, at an applied field of 1 T. The data depict j ab c (•, current density along c, field along ab), j ab ab ( , current in the ab-plane, perpendicular to the magnetic field, also aligned in the ab-plane), and j c ab ( , current in the ab-plane, field along the c-axis). The relevant magnitude of j ab ab and j c ab suggest pinning either by insulating point defects of typical size ∼ ξ -2ξ, or by areas larger than 2ξ showing weaker superconductivity than the surrounding matrix.

  Work at Ames Laboratory was supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under contract No. DE-AC02-07CH11358. Work at SNU was supported by National Creative

Figure 6 .

 6 Figure 6. (Color online) Temperature dependence of the ratio j ab ab /j ab c , measured in single crystalline LiFeAs using a Hall probe array magnetometry technique[26], for applied magnetic fields of 0.5 T ( ), 1 T (2), and 2 T (•). Filled symbols show the anisotropy ratio ε -1