BaHfO 3 PLD GdBa 2 Cu 3 O x 25 2 6

1 1 1.1.................................. 1 1.2....................... 3 1.2.1............................ 3 1.2.2.............................. 5 1.2.3......................... 7 1.2.4.................... 9 1.3 REBa 2 Cu 3 O 7 δ......................... 10 1.4.................................. 10 1.4.1................................. 10 1.4.2................................. 11 1.5................................ 12 1.5.1 Ginzburg-Lanau B c2.................. 12 1.5.2 Pippard............................ 13 1.5.3 B c2..................... 14 1.6......................... 15 1.7................................. 16 1.8................................ 17 2 18 2.1..................................... 18 2.1.1........................... 18 2.1.2 IBAD............................... 19 2.1.3 PLD............................... 20 2.1.4............................... 20 2.2............................. 21 i

2.2.1............................... 21 2.2.2............................... 21 2.3............................. 26 3 27 3.1 TEM........................... 27 3.2 J c -B.................................. 28 3.2.1.......................... 28 3.2.2........................ 29 3.2.3........................... 31 3.3 B c2 -T................................. 32 3.3.1.......................... 32 3.3.2........................ 32 4 34 4.1 B c2............................... 34 4.2 B c2............................... 35 4.3 B c2............ 37 4.4...................... 39 4.5 B c2................. 43 4.6 BHO........................ 45 4.7 BHO BZO....................... 46 5 47 49 ii

2.1 ISTEC-SRL...................... 20 3.1............................. 27 4.1 B c2 -T............. 35 4.2................. 36 4.3 77.3 K............. 37 4.4............................ 41 4.5 BHO BZO............. 46 iii

1.1.......... 3 1.2.......... 6 1.3 L d..... 8 1.4 (a) (b) (b) 12 1.5 C MgB 2 J c -B B c2 J c [8]........................ 14 1.6 B c2.......... 16 2.1....................... 19 2.2 IBAD [12].............. 19 2.3 dx................................... 22 2.4 c..................... 24 2.5 M-T B c2 -T.......... 25 2.6 GdBCO TEM [13] (i-iii) (a-c)........................ 26 3.1 c TEM (a)#2 (BHO) (b)#3 (BZO).................................. 28 3.2 77.3 K #1 #3 J c -B (a)0 6 T (b)0 0.5 T......... 29 3.3 (a)77.3 K #2, #4, #5 J c -B BHO (b) J c (0 T) 77.3 K #2, #4, #5 J c -B.......................... 30 iv

3.4 77.3 K #3, #6 J c -B BZO...... 30 3.5 77.3 K #2, #3, #7, #8 J c -B...... 31 3.6 #1 #3 B c2 -T.............. 32 3.7 #2, #4, #5 B c2 -T BHO......... 33 3.8 #3, #6 B c2 -T BZO........... 33 4.1 #1 #3 B c2 -T.. 35 4.2 #4 #6 B c2 -T.. 35 4.3 π ˆN p D B c2 BHO, BZO.......... 36 4.4 g 2 g 2......................... 38 4.5 #2 E-J.......................... 38 4.6 #1 #3 J c -B........................ 38 4.7 #4 #6 J c -B........................ 38 4.8 #2 J s0 (B) A s B γ 1 K = 0.94, B = 1.7 T B.................... 41 4.9 #3 J s0 (B) A s B γ 1 K = 0.72, B = 1.0 T B.................... 41 4.10 #4 J s0 (B) A s B γ 1 K = 0.39, B = 1.5 T B.................... 42 4.11 #5 J s0 (B) A s B γ 1 K = 0.25, B = 2.4 T B.................... 42 4.12 #6 J s0 (B) A s B γ 1 K = 0.78, B = 1.4 T B.................. 42 4.13 K T c BHO, BZO...................... 43 4.14 #1, #2, #6 J c -B B c2 #2, #6 BHO, BZO 5mol 44 v

4.15 #1, #2, #6 F p -B B c2 #2, #6 BHO, BZO 5mol..................................... 44 4.16 #1, #2, #5 J c -B K = 0.94 #5 BHO 5mol-improved........ 45 4.17 #1, #2, #5 F p -B K = 0.94 #5 BHO 5mol-improved........ 46 vi

1 1.1 1908 Leiden Kamerlingh Onnes 1911 4.2 K 1957 Bardeen, Cooper, Schrieffer BCS T c 30 K Johames G. Bednorz Karl Alex Müller T c 30 K (LaBaCuO) 77 K T c YBa 2 Cu 3 O x Bi 2 Sr 2 CaCu 2 O 8 T c T c Meissner Meissner B c T c B c1 Meissner B c2 1

B c B c2 B c1 B c2 Lorentz F L F L J B F L = J B F L v E = B v F L F p JB = J B JB F p J c J c = F p /B T c B c2 J c NbTi Nb 3 Sn T c 10 20 K T c (CuO 2 ) c ab 2 ab c J c c J c J c c F p c J c 2

1.2 1.2.1 [1] 1.1 Lorentz Lorentz B D U U A T k B T k B Boltzmann U Arrhenius 1.1 3

exp( U/k B T ) a f a f a f ν 0 Lorentz v + ( v + = a f ν 0 exp U ) k B T (1.1) Lorentz v v = a f ν 0 [exp ( U ) exp ( U )] k B T k B T (1.2) E = B v ( E = Ba f ν 0 [exp U ) exp ( U )] k B T k B T (1.3) E ν 0 ν 0 = ζρ fj c0 2πa f B (1.4) ζ ζ 2π a f ζ = 4 ρ f J c0 J c0 ) m ( J c0 = A (1 TTc B γ 1 1 B ) 2 (1.5) B c2 A m γ x 1.1 F (x) = U 0 2 sin(kx) fx (1.6) f V Lorentz f = JBV U 0 /2 k = 2π/a f x = x 0 x = x 0 4

0 F (x) = 0 x 0 = a ( ) f faf 2π cos 1 U 0 π (1.7) U U = F (x 0 ) F ( x 0 ) [ ( )] U = U 0 sin cos 1 faf fa ( ) f faf U 0 π π cos 1 U 0 π { ( ) } 1 2 2 = U 0 2f 1 2f ( ) 2f U 0 k U 0 k cos 1 (1.8) U 0 k sin(cos 1 x) = 1 x 2 U = 0 2f/U 0 k = 2J c0 BV/U 0 k = 1 J = J c0 2f U 0 k = J J c0 j (1.9) j (1.8) k = 2π/a f (1.9) U(j) = U 0 [(1 j 2 ) 1 2 j cos 1 j] (1.10) U (j) U + fa f = U + πu 0 j (1.11) (1.3) ( E = Ba f ν 0 exp U(j) ) [ ( 1 exp πu )] 0j k B T k B T (1.12) 1.2.2 Lorentz 1.2 Lorentz 5

Lorentz J B Lorentz Lorentz δ = v/ v J B δf p0 = 0 (1.13) F p0 J c0 J = F p0 /B = J c0 J > J c0 (1.13) J B δf p0 B ηv = 0 (1.14) ϕ 0 ϕ 0 η (1.14) J c0 = F p /B E = B v J J = J c0 + E (1.15) ρ f ρ f = Bϕ 0 /η (1.15) E E = ρ f (J J c0 ) (1.16) 1.2 6

1.2.3 U 0 Û0 V U 0 = Û0V (1.17) Û0 Labusch α L d i Û 0 = 1 2 α Ld 2 i (1.18) F p F p = J c0 B = α L d i (1.19) d i ζ a f d i = a f ζ (1.20) (1.18) 1.28) U 0 = 1 2ζ J c0ba f V (1.21) [2] (1.21) U 0 a f ϕ 0 a f = (2ϕ 0 / 3B) 1/2 R L R L (1.21) U 0 1.3 R a f R = ga f (1.22) 7

g 2 J c g 2 = g 2 e [ 5kB T 2U e ( Baf ν 0 log E c )] 4 3 (1.23) [3] g 2 e g2 U e g 2 = g 2 e U 0 g 2 e g 2 e = C 0 66 2πJ c0 Ba f (1.24) C 0 66 C66 0 = B c 2 ( B 1 B ) 4µB 2 c2 B c2 (1.25) [3] B c L L = ( C44 α L ) 1 2 = ( Baf ζµ 0 J c0 ) 1 2 (1.26) C 44 = B 2 /µ 0 L d L < d L > d L > d 3 1.3 L d 8

1.3 L V V = R 2 L U 0 U 0 = 0.835g2 k B J 1/2 c0 (1.27) ζ 3/2 B 1/4 L > d 2 d V = R 2 d U 0 U 0 = 4.23g2 k B J c0 d ζb 1/2 (1.28) (1/2)(2/ 3) 7/4 (ϕ 7 0/µ 2 0) 1/4 0.835k B (1/2)(2/ 3) 3/2 ϕ 3/2 0 4.23k B U 0 k B T 1.2.4 1.2.1 1.2.2 E cp E ff j 1 ( E cr = Ba f ν 0 exp U(j) ) [ ( 1 exp πu )] 0j k B T k B T (1.29) E ff = 0 (1.30) j > 1 ( E cr = Ba f ν 0 [1 exp πu )] 0 k B T (1.31) E ff = ρ f (J J c0 ) (1.32) E E = (E 2 cr + E 2 ff) 1/2 (1.33) (1.5) A f(a) = K exp [ (log A log A m) 2 ] 2σ 2 (1.34) 9

K σ 2 A m A A E(J) = 0 E f(a)da (1.35) (1.35) E-J [4] 1.3 REBa 2 Cu 3 O 7 δ REBa 2 Cu 3 O x (REBCO) RE=Rare Earth: x = 7 δ δ: J c RE Y, Ne, Sm, Gd, Dy, Ho RE T c RE Gd GdBa 2 Cu 3 O 7 δ (GdBCO) GdBCO YBa 2 Cu 3 O 7 δ T c J c 1.4 1.4.1 1.1 REBCO Y 2 BaCuO 3 Y 2 O 3 BaZrO 3 (BZO) 2.1.3 PLD(Pulsed Laser Deposition) REBCO BZO c c c (B c) B c J c 10

1.4.2 1.4 J c B 2 c /2µ 0 B c D D/2 D/2 ξ ξ > D/2 Û p = B2 c 2µ 0 π ( ) 2 D 2 = πb2 c D 2 8µ 0 (1.36) Ûp D ˆf p = Ûp D = πb2 c D 8µ 0 (1.37) ˆN p F p = ˆN p ˆfp (1.38) F p F p J c = F p /B J c 11

1.4 (a) (b) (b) 1.5 1.5.1 Ginzburg-Lanau B c2 B c2 B c2 B c2 Ginzburg-Lanau [5] Ψ Ginzburg-Landau 1 2m ( i + 2eA)2 Ψ + αψ + β Ψ 2 Ψ = 0 (1.39) m = h/2π h e A α, β Ψ 2 H e z H = B/µ 0 B H B µ 0 H e A = µ 0 H e xi y i y y B c2 (1.39) β Ψ 2 Ψ A x 12

Ψ x (1.39) λ 2 2m d2 Ψ dx 2 + 2e2 µ 2 0 m (H2 e x 2 2H 2 c λ 2 )Ψ = 0 (1.40) ( m ) 1/2 λ = 4µ 0 e 2 Ψ 2 (1.41) (1.40) Schrödinger n ( n + 1 ) H e = 2eµ 0 Hc 2 λ 2 (1.42) 2 H e n = 0 H e = H c2 λ ξ H c2 = 4eµ 0H 2 c λ 2 (1.43) λ = 2 2eµ 0 H c ξ (1.44) e ϕ 0 e = h 2ϕ 0 (1.45) (1.44) (1.45) (1.43) H c2 = ϕ 0 2πµ 0 ξ 2 (1.46) B c2 = ϕ 0 2πξ 2 (1.47) B c2 1.5.2 Pippard B c2 ξ Pippard ξ l 1 ξ = 1 ξ 0 + 1 l (1.48) 13

ξ 0 BCS Fermi v F Boltzmann k B ξ 0 = v F 5.53k B T c (1.49) l ξ ξ 0 ξ 0 l ξ l l ξ B c2 [6] 1.5.3 B c2 B c2 [7] REBCO B c2 J c ) J c (B) = J c (0) (1 BBc2 (1.50) B c2 J c B c2 J c 1.5 B c2 J c B c2 B = 6 T J c 100 B c2 REBCO B c2 1.5 C MgB 2 J c -B B c2 J c [8] 14

1.6 1.1 CuO 2 CuO 2 B c2 ab ξ c ξ ab c B c2 B c2 = ϕ 0 2πξ ξ, B c2 = ϕ 0 2πξ 2 (1.51) B c2 /B c2 = ξ /ξ m a = m b = m m c = m ξ a = ξ b = ξ = ξ (m /m ) 1/2, ξ c = ξ = ξ (m /m ) 1/2 (1.52) ξ m ξ 2 ξ = ξ 3 m am b m c = m 3 λ a = λ b = λ = ( m )1/2 ( ) m 1/2 m λ, λ c = λ = m λ (1.53) λ λ a λ b λ c = λ 3 θ c B c2 (θ) = B c2 ( cos 2 θ + m = B c2 (cos 2 θ + sin 2 θ m ( Bc2 B c2 ) 1/2 ) 2 sin 2 θ ) 1/2 (1.54) [9] (1.54) B c2 θ = 0 c B c J c 15

1.7 1.1 Lorentz B c2 1.6 B c2 J c 0 J c = 0 J c 0 B i B i (T ) 1.6 J c 0 B i 1.6 B c2 16

1.8 GdBa 2 Cu 3 O 7 δ (GdBCO) c J c J c BaZrO 3 BZO BZO BZO J c BaHfO 3 (BHO) BHO BHO J c BZO [10] BHO BHO BZO GdBCO B c2 BHO 17

2 2.1 ISTEC-SRL PLD(Pulsed Laser Deposition) GdBa 2 Cu 3 O 7 δ (GdBCO) [10] BaHfO 3 (BHO) BaZrO 3 (BZO) 3 2.1.1 1.1 REBCO RE: Hastelloy IBAD(Ion Beam Assisted Deposition) MgO PLD CeO 2 PLD GdBa 2 Cu 3 O 7 δ BaHfO 3 BaZrO 3 Sputter Ag Ag/GdBa 2 C 3 O 7 δ (+BaHfO 3 or BaZrO 3 )/CeO 2 /MgO/Hastelloy 2.1 18

2.1 2.1.2 IBAD IBAD [11] 2.2 Ar + 3 IBAD MgO CeO 2 IBAD 2.2 IBAD [12] 19

2.1.3 PLD PLD(Pulsed Laser Deposition) PLD 2 PLD J c 2.1.4 PLD GdBCO #1 #3 #4 #6 J c #7 #8 8 2.1 SQUID T c 2.1 2.1 ISTEC-SRL Sample Material Amount of addition d [µm] T c [K] #1 (Pure) GdBa 2 C 3 O 7 δ 1.1 90.7 #2 (BHO) GdBa 2 C 3 O 7 δ + BaHfO 3 3.5 mol% 1.0 90.5 #3 (BZO) GdBa 2 C 3 O 7 δ + BaZrO 3 3.5 mol% 1.1 89.2 #4 (BHO 2.5mol) GdBa 2 C 3 O 7 δ + BaHfO 3 2.5 mol% 1.2 89.6 #5 (BHO 5.0mol) GdBa 2 C 3 O 7 δ + BaHfO 3 5.0 mol% 1.0 89.2 #6 (BZO 5.0mol) GdBa 2 C 3 O 7 δ + BaZrO 3 5.0 mol% 1.2 89.3 #7 (BHO Thick) GdBa 2 C 3 O 7 δ + BaHfO 3 3.5 mol% 2.5 89.7 #8 (BZO Thick) GdBa 2 C 3 O 7 δ + BaZrO 3 3.5 mol% 2.4 89.8 20

2.2 SQUID c B c J c J c -B - E-J 77.3 K 0 7 T M-T B c2 B c2 -T 2.2.1 SQUID 2 mm 2 mm 1cm 3cm 4 2 mm 2 mm 2.2.2 J c -B c 0 T J c -B l w d l > w x y z J c Bean 2.3 dx dz A di c di c = J c dxdz A B 21

S x ( S = 4x x + l w ) 2 = 4x 2 + 2x(l w) (2.1) B di c dm = SdI c m m = dm = S(x)dI c = S(x)J c dxdz = J c d S(x)dx (2.2) m = J cw 2 (3l w)d (2.3) 12 M m lwd M = J cw (3l w) (2.4) 12l 2.3 dx 22

M (2.4) 2 J c M = J cw (3l w) (2.5) 6l J c = 6l M (2.6) w(3l w) (2.6) M J c SQUID cgs [emu] SI m [A m 2 ] = m [emu] 10 3 (2.7) E-J E-J Maxwell Faraday E-J 1.0 10 8 V/m J (2.3) J c J m = Jw2 (3l w)d (2.8) 12 J = 12l w(3l w) m (2.9) m 2.3 Φ Φ = wlb e + µ 0m d (2.10) 23

B 0 Be 2.4 c Faraday d l d E 1 E = 2(l + w) dφ (2.11) dt (2.10) (2.11) µ 0 E = 2d(l + w) dm dt (2.12) (2.12) E G E = µ 0G 2d(l + w) dm (2.13) dt G d l L 1 = (µ 0 l/2) log(8l/d) d, l L 2 = πµ 0 l 2 /4d G = L 1 /L 2 E (2.9) (2.13) SQUID E-J M-T B c2 -T Zero Field Cool(ZFC) Field Cool(FC) 24

B c2 B i T c T (B c2 ) B c2 T (B i ) B i 2.5 B = 3 T ZFC B = 3 T 78 K T c 90 K 90 K 80 K FC ZFC FC M-T 2.5 2, B i (T ) ZFC FC B c2 (T ) B i (82.0 K) = 3 T, B c2 (83.7 K) = 3 T M-T B c2 -T 0.005 GdBCO+BHO B = 3 T B i exp. fit m [emu] 0.004 B c2 0.003 75 80 85 90 T [K] 2.5 M-T B c2 -T 25

2.3 Transmission Electron Microscope(TEM) TEM TEM TEM 100 nm TEM Japan Fine Ceramics Center(JFCC) TEM TEM 2.6 2.6 GdBCO TEM [13] (i-iii) (a-c) 26

3 3.1 TEM 3.1(a), (b) BHO BZO c TEM c D d p ˆN p = 1 d 2 p (3.1) B = ˆN p ϕ 0 (3.2) 3.1(a), (b) D, d p, ˆNp, B 3.1 GdBCO/BHO or BZO 3.1 BHO BHO BZO 3.1 Sample D [nm] d p [nm] ˆNp [m 2 ] B [T] Lattice mismatch #2 (BHO) 4.4 37.5 0.71 10 15 1.7 5.9 % #3 (BZO) 5.6 46.7 0.46 10 15 1.0 6.5 % 27

3.1 c TEM (a)#2 (BHO) (b)#3 (BZO) 3.2 J c -B 3.2.1 3.2(a), (b) 77.3 K #1 #3 J c (a)b = 0 6 T (b)b = 0 0.5 T 3.2(a) J c 3.5 mol% #2 (BHO) J c BZO BHO 3.2(b) #3 (BZO) B = 0 T J c #2 (BHO) B = 0 T J c 2.1 T c BHO B = 0.3 T #1 (Pure) #2 (BHO), #3 (BZO) J c B = 0.3 T 28

J c [A/m 2 ] 10 11 10 10 T=77.3 K #1 (Pure) #2 (BHO) #3 (BZO) J c [GA/m 2 ] 40 20 10 8 T=77.3 K #1 (Pure) #2 (BHO) #3 (BZO) 10 9 6 4 10 8 0 1 2 3 4 5 6 B [T] (a) 2 0 0.1 0.2 0.3 0.4 0.5 B [T] (b) 3.2 77.3 K #1 #3 J c -B (a)0 6 T (b)0 0.5 T 3.2.2 3.3(a), (b) 3.4 77.3 K #2, #4, #5 #3, #6 J c 3.3(a) J c #4 J c J c B = 0 T J c J c (0 T) J c -B 3.3(b) J c 3.4 J c BZO 5 mol% J c 3.1 BHO, BZO J c BHO 3.5 mol% BZO 5 mol% J c BHO 29

10 11 T=77.3 K 10 0 T=77.3 K J c [A/m 2 ] 10 10 #2 (BHO) #4 (BHO 2.5mol) #5 (BHO 5.0mol) J c / J c (0 T) 10 1 #2 (BHO) #4 (BHO 2.5mol) #5 (BHO 5.0mol) 10 9 10 2 10 8 0 1 2 3 4 5 6 B [T] (a) 0 1 2 3 4 5 6 B [T] (b) 3.3 (a)77.3 K #2, #4, #5 J c -B BHO (b) J c (0 T) 77.3 K #2, #4, #5 J c -B 10 11 T=77.3 K J c [A/m 2 ] 10 10 #3 (BZO) #6 (BZO 5.0mol) 10 9 10 8 0 1 2 3 4 5 6 B [T] 3.4 77.3 K #3, #6 J c -B BZO 30

3.2.3 3.5 77.3 K #2, #3, #7, #8 J c BHO J c BZO J c BHO, BZO J c (0 T) 63% J c [14] #7, #8 J c (0 T) 1.3 BHO, BZO J c BZO fire-works [15] BZO B c BHO c [16] BHO c J c BHO BZO J c 10 11 T=77.3 K J c [A/m 2 ] 10 10 #2 (BHO) #3 (BZO) #7 (BHO Thick) #8 (BZO Thick) 10 9 10 8 0 1 2 3 4 5 6 B [T] 3.5 77.3 K #2, #3, #7, #8 J c -B 31

3.3 B c2 -T 3.3.1 3.6 #1 #3 B c2 -T B c2 1.5.2 B c2 l B c2 l #3 (BZO) #2 (BHO) B c2 #2 (BHO) J c B c2 BHO 6 #1 (Pure) #2 (BHO) #3 (BZO) B c2 [T] 4 2 0 75 80 85 90 95 T [K] 3.6 #1 #3 B c2 -T 3.3.2 3.7 3.8 #2, #4, #5 #3, #6 B c2 -T BHO, BZO 5 mol% T c T c B c2 B c2 BHO, BZO B c2 32

6 #2 (BHO) #4 (BHO 2.5mol) #5 (BHO 5.0mol) B c2 [T] 4 2 0 75 80 85 90 T [K] 3.7 #2, #4, #5 B c2 -T BHO 6 #3 (BZO) #6 (BZO 5mol) B c2 [T] 4 2 0 75 80 85 90 T [K] 3.8 #3, #6 B c2 -T BZO 33

4 3 J c B c2 J c BZO BHO B c2 B c2 2 4.1 B c2 B c2 B c2 -T T c 95% 4.1 4.2 #1 #3, #4 #6 B c2 4.1 db c2 /dt T/T c = 0.95 B c2 -T B c2 BHO 5 mol% B c2 (77.3 K), db c2 /dt B c2 (77.3 K) Pure 1.5 34

6 #1 (Pure) #2 (BHO) #3 (BZO) exp. fit 6 exp. fit #4 (BHO 2.5mol) #5 (BHO 5.0mol) #6 (BZO 5.0mol) B c2 [T] 4 B c2 [T] 4 2 2 0 75 80 85 90 95 T [K] 0 75 80 85 90 T [K] 4.1 #1 #3 B c2 -T 4.2 #4 #6 B c2 -T 4.1 B c2 -T Sample T c [K] B c2 (77.3 K) [T] db c2 /dt [TK 1 ] #1 (Pure) 90.7 5.13 0.455 #2 (BHO) 90.5 7.21 0.626 #3 (BZO) 89.2 6.46 0.549 #4 (BHO 2.5mol) 89.6 6.87 0.589 #5 (BHO 5.0mol) 89.2 7.96 0.787 #6 (BZO 5.0mol) 89.3 6.62 0.624 4.2 B c2 B c2 1.5.2 l B c2 D 2 ˆN p 2 3.1 35

ˆN p (3.1) d p 1 d p = (... d p > 0) (4.1) ˆN p (3.2) d p, B 3.1 4.2 D, ˆNp 77.3 K π ˆN p D B c2 4.3 B c2 B c2 BHO BZO B c2 BHO BZO BHO 1.4 4.2 Sample D [nm] ˆNp [m 2 ] d p [nm] B [T] #2 (BHO) 4.4 0.71 10 15 37.5 1.7 #3 (BZO) 5.6 0.46 10 15 46.7 1.0 #4 (BHO 2.5mol) 4.4 0.51 10 15 44.3 1.5 #5 (BHO 5.0mol) 4.4 1.02 10 15 31.3 2.4 #6 (BZO 5.0mol) 5.6 0.66 10 15 38.9 1.4 10 8 B c2 [T] 6 4 2 exp. fit Pure BHO BZO T = 77.3 K 0 0 0.5 1 πn p D [ 10 7 m 1 ] 1.5 4.3 π ˆN p D B c2 BHO, BZO 36

4.3 B c2 T = 77.3 K B c2 4.3 m = 2 g 2 4.4 [17] ζ #1 (Pure) 2π 4 J c 4.5 E-J E c = 1.0 10 9 V/m J c -B 4.6 4.7 #1 #3 #1 (Pure) #2 (BHO), #3 (BZO) A m, B c2, γ B c2 #2, #3 A m, B c2 A m B c2 BHO BZO A m ( ) B c2 2 2 #4 #6 A m, B c2 2 4.3 77.3 K Sample A m [Am 2 T 1 γ ] B c2 [T] γ σ 2 ζ #1 (Pure) 2.55 10 10 5.13 0.52 1.75 10 2 2π #2 (BHO) 3.83 10 10 7.21 0.70 1.75 10 2 4 #3 (BZO) 2.97 10 10 6.46 0.70 1.75 10 2 4 #4 (BHO 2.5mol) 1.38 10 10 6.87 0.70 1.75 10 2 4 #5 (BHO 5.0mol) 0.96 10 10 7.96 0.70 1.75 10 2 4 #6 (BZO 5.0mol) 3.67 10 10 6.62 0.70 2.10 10 2 4 37

g 2 7 6 5 4 3 #1 (Pure) #2 (BHO) #3 (BZO) #4 (BHO 2.5mol) #5 (BHO 5.0mol) #6 (BZO 5.0mol) T = 77.3 K E [V/m] 10 8 10 10 #2 (BHO) T = 77.3 K exp. theo. 1 T 2 T 3 T 2 1 0 1 2 3 4 B [T] 4.4 g 2 g 2 10 12 10 8 10 9 10 10 4.5 J [A/m 2 ] #2 E-J 10 11 T=77.3 K 10 11 T=77.3 K exp. theo. exp. theo. J c [A/m 2 ] 10 10 #1 (Pure) #2 (BHO) #3 (BZO) J c [A/m 2 ] 10 10 #4 (BHO 2.5mol) #5 (BHO 5.0mol) #6 (BHO 5.0mol) 10 9 10 9 10 8 0 1 2 3 4 5 B [T] 4.6 #1 #3 J c -B 10 8 0 1 2 3 4 5 B [T] 4.7 #4 #6 J c -B 38

4.4 Pure BHO, BZO BHO BZO K c ξ 77.3 K 4.8 nm D/2 B c (1.37) ˆf p = πb2 c D 8µ 0 (4.2) B c B c (0) = 2 T ) B c (T ) = B c (0) (1 TTc (4.3) [18, 19] F p = η ˆN p ˆfp (4.4) η η = 1/2 (4.4) B B B B (4.2) (4.4) B J p = F p B = πη ˆN p B 2 c D 8µ 0 B (4.5) B B c2 39

A m σ A m A s A s = exp( 2σ)A m = A m 1.21 (4.6) A s B γ 1 A s B γ 1 Pure, BHO, BZO Pure A s A s0 A s0 B γ 1 A s0 B γ 1 J p J s0 (B) = K[(A s0 B γ 1 ) 2 + Jp] 2 1/2 (4.7) K J s0 (B) A s B γ 1 B 0.2 T #2 (BHO) 3.1 D = 4.4 nm, ˆNp = 0.71 10 15, B = 1.7 T (4.2) (4.3) (4.4) ˆf p = 1.20 10 4 N/m, F p = 4.25 10 10 N/m 3 BHO (4.5) J p = 2.50 10 10 A/m 2 B #1 (Pure) A m = 2.55 10 10 AT 1 γ /m 2, γ = 0.52 A s0 B γ 1 = 1.63 10 10 A/m 2 K = 0.94 B #2 (BHO) (4.7) J s0 (B ) = 2.81 10 10 A/m 2 A m (4.6) A s B γ 1 = 2.70 10 10 A/m 2 J s0 (B ) B =0.2 T J s0 (0.2 T) = 4.89 10 10 A/m 2, A s (0.2) γ 1 = 5.13 10 10 A/m 2 #3 #6 4.4 J s0 (B) A s B γ 1 4.8 4.12 B J p BZO BHO BZO #2 (BHO) #6 (BZO 5mol) #6 J p #2 1.3 K #2 #6 Pure #2 40

BZO #2 J c K 4.4 Sample A s0 B γ 1 J p J s0 (B ) A s B γ 1 K [A/m 2 ] [A/m 2 ] [A/m 2 ] [A/m 2 ] #1 (Pure) 1.00 #2 (BHO) 1.63 10 10 2.50 10 10 2.81 10 10 2.70 10 10 0.94 #3 (BZO) 2.11 10 10 2.86 10 10 2.56 10 10 2.46 10 10 0.72 #4 (BHO 2.5mol) 1.73 10 10 1.81 10 10 0.98 10 10 1.01 10 10 0.39 #5 (BHO 5.0mol) 1.38 10 10 2.11 10 10 0.63 10 10 0.61 10 10 0.25 #6 (BZO 5.0mol) 1.79 10 10 3.33 10 10 2.95 10 10 2.70 10 10 0.78 10 #2 (BHO) T = 77.3 K 10 #3 (BZO) T = 77.3 K J [ 10 10 A/m 2 ] 5 A s B γ 1 J s0 J [ 10 10 A/m 2 ] 5 A s B γ 1 J s0 0 0 1 B* 2 B [T] 4.8 #2 J s0 (B) A s B γ 1 K = 0.94, B = 1.7 T B 0 0 1 (B*) 2 B [T] 4.9 #3 J s0 (B) A s B γ 1 K = 0.72, B = 1.0 T B 41

J [ 10 10 A/m 2 ] 5 4 3 2 #4 (BHO 2.5mol) T = 77.3 K A s B γ 1 J s0 J [ 10 10 A/m 2 ] 4 3 2 #5 (BHO 5.0mol) T = 77.3 K A s B γ 1 J s0 1 1 0 0 1 B* 2 B [T] 4.10 #4 J s0 (B) A s B γ 1 K = 0.39, B = 1.5 T B 0 0 1 2 B* 3 B [T] 4.11 #5 J s0 (B) A s B γ 1 K = 0.25, B = 2.4 T B J [ 10 10 A/m 2 ] 10 5 #6 (BZO 5.0mol) T = 77.3 K A s B γ 1 J s0 0 0 1 B* 2 B [T] 4.12 #6 J s0 (B) A s B γ 1 K = 0.78, B = 1.4 T B 42

K 4.4 K T c K T c K 4.13 T c K BHO, BZO K K J c T c 1.2 1 0.8 K 0.6 0.4 0.2 Pure BHO BZO 0 89 90 91 T c [K] 4.13 K T c BHO, BZO 4.5 B c2 4.4 B c2 B c2 J c -B J c 4.14 #2 (BHO) #6 (BZO 5mol) J c -B B c2 #2, #6 BHO, BZO 5mol 4.15 F p -B BHO, BZO 5mol J c J c J c 43

J c 1.0 10 8 A/m 2 B i #2, #6, BHO, BZO 5mol B i 4.4, 4.3, 3.2, 3.0 B i J c B c2 10 11 10 10 T=77.3 K #1 (Pure) #2 (BHO) BHO* #6 (BZO 5.0mol) BZO 5.0mol * exp. theo. J c [A/m 2 ] 10 9 4.14 10 8 0 1 2 3 4 5 B [T] #1, #2, #6 J c -B B c2 #2, #6 BHO, BZO 5mol 4 T=77.3 K #1 (Pure) #2 (BHO) BHO * #6 (BZO 5mol) exp. theo. F p [GN/m 3 ] 2 BZO 5mol* 4.15 0 0 1 2 3 4 5 6 B [T] #1, #2, #6 F p -B B c2 #2, #6 BHO, BZO 5mol 44

4.6 BHO J c B c2 B c2 B c2 BZO BHO J c #5 (BHO 5mol) #5 K #2 (BHO) BHO 4.16 4.17 K = 0.94 #5 J c -B F p -B BHO 5mol-improved BHO 5mol-improved B i 5 T F p BHO BHO J c [A/m 2 ] 10 11 10 10 #1 (Pure) #2 (BHO) T=77.3 K #5 (BHO 5mol) exp. BHO 5.0mol improved theo. 10 9 4.16 10 8 0 1 2 3 4 5 6 B [T] #1, #2, #5 J c -B K = 0.94 #5 BHO 5mol-improved 45

F p [GN/m 3 ] 4 2 T=77.3 K exp. theo. #1 (Pure) #2 (BHO) #5 (BHO 5.0mol) BHO 5.0mol improved 4.17 0 0 1 2 3 4 5 6 7 B [T] #1, #2, #5 F p -B K = 0.94 #5 BHO 5mol-improved 4.7 BHO BZO BHO BZO #2, #6 B c2 (77.3 K) 7.96 T, 6.62 T BHO db c2 /dt 0.626, 0.624 B 1.7 T, 1.4 T BHO J p #2, #6 2.50 10 10 A/m 2, 3.33 10 10 A/m 2 BZO BHO BZO 4.5 BHO BZO 4.5 BHO BZO BHO BZO B c2 46

5 GdBa 2 Cu 3 O 7 δ (GdBCO) BaHfO 3 BHO BaZrO 3 BZO J c J c BHO B c2 B c2 BHO B c2 B c2 J c GdBCO J c B c2 BHO BZO BHO BHO 47

ISTEC-SRL NEDO ISTEC-SRL JFCC 48

[1] K. Yamafuji, T. Fujiyoshi, K. Toko, and T. Matsushita: P hysica C 159 (1989) 743. [2] : [ 1998]. [3] T. Matsushita: P hysica C 217 (1993) 461. [4] M. Kiuchi, K. Noguchi, T. Matsushita, T. Kato, T. Hikata, and K. Sato: P hysica C 278 (1997) 62. [5] V. L. Ginzburg and L. D. Landau: Zh. Eksperim. i T eor. F iz. 20 (1950) 1064. [6],,, :, (2004) p. 27. [7] M. Kiuchi, A. Yamamoto, and S. Awaji: Flux pinning properties in MgB 2 bulk. [8] S.X. Dou, S. Soltanian, J. Horvat, X.L. Wang, S.H. Zhou, et al.: Appl. P hys. Lett. 81 (2002) 3419. [9] :, (1994) p. 341. [10] H. Tobita, K. Notoh, K. Higashikawa, M. Inoue, T. Kiss, T. Kato, T. Hirayama, M. Yoshizumi, T. Izumi, and Y. Shiohara: Supercond. Sci. T echnol. 25 (2012) 062002 (4pp). [11],,,,,,,,, : RE123, 115, p. 46 54, 2008. [12] D.P. Norton, C. Park, C. Prouteau, D.K. Christen, M.F. Chisholm, J.D. Budai, S.J. Pennycook, A. Goyal, E.Y. Sun, D.F. Lee, D.M. Kroeger, E. Specht, M. Paranthaman, and N.D. Browning: M aterials Science and Engineering B 56 (1998) 86 94. [13] T. Kato, R. Yoshida, N. Chikumoto, S. Lee, K. Tanabe, T. Izumi, T. Hirayama, and Y. Shiohara: P hysica C 471 (2011) 1012 1016. 49

[14] Y. Takahashi, M. Kiuchi, E.S. Otabe, T. Matsushita, K. Shikimachi, T. Watanabe, N. Kashima, and S. Nagaya: P hysica C 470 (2010) 1284 1287. [15] A. Ichinose, P. Mele, T. Horide, K. Matsumoto, G. Goto, M. Mukaida, R. Kita, Y. Yoshida, and S. Horii: P hysica C 468 (2008) 1627 1630. [16] D. Yokoe, T. Kato, H. Tobita, A. Ibi, M. Yoshizumi, T. Izumi, T. Hirayama, and Y. Shiohara: J. Mater. Sci. 48 (2013) 125 131. [17] K. Himeki, M. Kiuchi, E.S. Otabe, T. Matsushita, K. Shikimachi, T. Watanabe, N. Kashima, S. Nagaya, Y. Yamada, Y. Shiohara: P hysica C 469 (2009) 1457 1461. [18] T. Matsushita, M. Kiuchi, T. Haraguchi, T. Imada, K. Okamura, S. Okayasu, S. Uchida, J. Shimoyama, K. Kishio: Supercond. Sci. T echnol. 19 (2006) 200 205. [19] T. Matsushita: P hysica C 205 (1993) 289 295. 50