Superconducting phase transitions in ErcY1−cRh4B4

Solid State Communications, Vol. 32, pp. 185—188. Pergamon Press Ltd. 1979. Printed in Great Britain. SUPERCONDUCTING PHASE TRANSITIONS IN Er~Y1..~Rh4B4 K. Okuda, Y. Nakakura and K. Kadowaki Department of Physics, Faculty of Science, Osaka University, Toyonaka, Osaka 560, Japan (Received 26Apr11 1979 by W. Sasaki) The superconducting transition temperature Tel and the reentering temperature T~to the normal ferromagnetically ordered state in the system Er~Y1 , Rh4 B4 were determined as a function of the concentration of Er. Comparing our results with the recent theory of Maekawa et al., the exchange interactions J’ among local spins and I between local 2N(0) spins and ~ superconducting 0.046K, where N(0) electrons is the were density estimated of states. as A sudden ~ 0.30 decrease K and 1 of H~ 2at T~2was observed in a high concentration region suggesting the first order transition. —

THERE HAS BEEN a growing interest in the superconductivity and magnetic properties of ErRh4 B4 which becomes superconducting at T~1= 8.7 K and returns to the normal state at T~2= 0.9 K [1, 2]. Neutron diffraction experiments have shown that the destruction of superconductivity at 7~2is accompanied with the development of long-range ferromagnetic ordering of Er sublattice [3]. Recently, the theoretical formulas of superconducting and magnetic transition temperatures in the rare-earth (R) ternary compounds,RRh4B4,were represented by Maekawa and Tachiki [4] as functions of the intra- and inter-atomic exchange interactions and the concentration of local spins. To verify their theory, it is desired to observe the dependence of T~and TM on the concentration of local spins. In this Letter, we report the concentration dependence of T~1and T~2, and the temperature dependence of upper critical field H~2in the system Er~Y1_~Rh4B4. Samples of Er~Y1 Rh4 B4 were synthesized on three steps to get a good stoichiometry. The first step is the synthesis of binary compounds MB4, where M means Er or Y, by induction heating of the pressed mixture ofM2 03 and boron powders. In this step, the chemical reaction M2O3 + lOB -÷ 2MB4 + B2O3 occurs, where B2O3 are pumped off as gas. This method was better than that of direct arc-melting for getting a single phase ofMB4 As the second procedure, the ternary compounds, MRh4 B4, were prepared by induction- or arc-melting of two constituents, MB4 and Rh. The final compounds, Er~ Y1 Rh4 B4, were obtained from the appropriate mixture of ErRh4B4 and YRh4B4 as in the second step. In each step, the crystal structure was checked by the X-ray diffraction. The heat treatments were done at 1050°Cfor one week. The concentration of Er was determined by the X-ray flourescence method, Superconducting transition temperature 7~and its ,

,

—

-

-

destructing temperature T~2were determined by conventional four-probe dc electrical resistance measurements down to 0.08 K by using an adiabatic-demagnetization refrigerator. The measurements below 1 K were taken in the refrigerator with increasing temperature. The current used in our resistance measurements was 1 mA for all cases. The flux-flow resistance which usually appears in large current measurements was negligible in the present small current. The magnetoresistance curves were taken in the temperature range from 0.08 K up to T~for the whole concentration region of Er in Er~Y1 ~Rh4 B4. Typical examples at 0.08 K are shown for c = 1,0.44 and 0.17 in Fig. 1. The virgin curve for c = 0.44 rises abruptly at a threshold field H8 of about 2 KOe, and reaches a normal resistance at 4 KOe. By decreasing magnetic field, the curve does not follow the virgin increasing curve but gives a finite resistance value at zero field. After then, the magnetoresistance curve follows the initial decreasing curve with field-up and -down as shown by double arrows in Fig. 1. Similar virgin behavior was observed in a concentration region c = 0.44— 0.65, where the threshold field H8 decreased as the concentration increased. No such virgin curve was observed in high(c = 0.7 —1) and low (c = 0—0.4) concentration regions, instead, the magnetoresistance was observed to follow the same curve for field-up and -down as is shown in Fig. 1. The cause of the peculiar virgin behavior in the region c = 0A4—0.65 might be that below TM an inhomogeneous superconducting phase remains in specimens, because of the closeness to the critical concentration, C~,= 0.43, for long-range magnetic ordering as is shown below. This inhomogeneous superconducting phase disappears after the initial application of the field. The temperature dependence of the magnetoresistance curve was taken for all

185

-

186

SUPERCONDUCTING PHASE TRANSITIONS IN Er~Y1~Rh4B4 I

Vol. 32, No.2

I

I

I

I

10.5 1.0 ~ ~ 10.0

-

29.5 I

I

4

I

I

I

8

H(KOe)

Fig. 1. Magnetoresistance curves of Er~Y1 0.08 K. -

I

—

I

12

Rh4 B4 at

-I

~8.5 LU I-

Ic2

L0

°6K

0.5’

3i

______________

~

00

0:2

--S.-

O~ 0.6 concentration c

0~

‘

1.0

9.2k

wi-

Fig. 3. Concentration dependence of 7~and T~ 2in Er~Y1_~Rh4B4. Open and black circles denote T~1and T~2,respectively. I

I

I

I

0

4

H ( KOe)

I

I

I

8

12

___________________

_____________

-

O~8

~ 2

0

p.11k

I

I

I

H (KOe)

8

I I

L

12

Fig. 2. Magnetoresistance curves of Er0 ~Y0 56Rh4B4 as a parameter of temperature. concentrations and an example for c = 0.44 is shown in zero-field fallsuptotozero at Fig. 0_li 2. K The and resistance a hysteresisvalue curveat was observed 0.5 K. Hereafter, we define the temperature at which the zero-field resistance in non-virgin state falls to zero as the lower critical temperature T~ 2,and the temperature at which it returns to the normal value at high temperature, as T~1 The hysteresis curves were observed in a narrow temperature region above 7~,2for the concentrations c = 0.44—1. The obtained concentration dependences of T~1 and T~2are shown in Fig. 3. Open and black circles -

denote 7~and T~2,respectively. Our results of T~= 8.7 K and T~2= 0.87 K in ErRh4B4 are in agreement with the results of Matth.ias eta!. [1, 2] They showed with their specific heat and ac-susceptibility measurements that the transition at T~2in ErRh4B4 is coincident with the onset of long-range magnetic ordering of Er sublattice. So, in this letter we assume that the temperature ~,2 coincides with the magnetic ordering temperature TM in a whole concentration region in Er~Y1_~Rh4B4. Then, the concentration dependence of TM in the present system is given by Oguchi’s theory [5] in a magnetically diluted system as [4] TM/f’

=

2/In [z’/(z’ —4)],

(1)

where J’ is the nearest neighbor exchange interaction among Er spins and z’ is the reduced 8] concentration By best-fitting defined by = I + —(1 ~c) equation (1)z’ with the7c[1 observed concentration dependence in ~ the value of J’ was estimated as J’ 0.30 K, and the theoretical line was calculated as shown -

by the dashed line in Fig. 3. The observed T~2show good agreement with the theoretical line of TM and yield a critical concentration C~ 0.43 for long-range magnetic ordering. The concentration dependence of T~1divided by the superconducting transition temperature T~of the system without magnetic spins is given by Maekawa and Tachiki [4] as

Vol. 32, No.2

SUPERCONDUCTING PHASE TRANSITIONS IN Er~Y1~~Rh4B4

25

I

I

I

I

decreased from c = 1. By best-fitting equation (2) with our results a high concentration the paravalue of 2N(0) wasindetermined as 0.046 K.region, The other 1meters were taken as T~o= 10K and g 3~sN(O)= 0.3 [41 The theoretical line for T~1is represented by the solid line in Fig. 3. In this letter we define the upper critical field H~2

I

\ 20

\

-

-

-

\ 15

as the field at which the resistance begins to rise from zero on the magnetoresistance curve with increasing

\ \

-

magnetic field. The anisotropy of H~2[71is expected in the present crystal which has a tetragonal symmetry, and the anisotropy may induce a broad transition at the upper critical field in the polycrystalline specimen as seen in Figs. I and 2. Thus, our defined H~2may correspond to a minimum value in the anisotropic H~2. The temperature dependence ofH~2was measured for the whole concentration region and the results are

-

\ 10

\

-

~

5

.

...2P

/ 1~~~N\\ / 1,~’ /~ 2 ~-.-

-~

LI

\ \ “~\\ \ ~\

\\‘~“\\

C~O88

2I

shown in Fig. 4. H~2in the Er doped compounds with c ~ I has a broad peak near 4K and decreases with decreasing temperature. The decrease in H~2at low temperatures is explained as follows [81: in the mixed state the persistent current of vortices induces a magnetic field, and this field polarizes the spins of Er ions. A.long with the vortex theflux spin—magnetization of Er contributes to thecurrent, magnetic in the magnetic superconductor Er~Yi...~Rh4B4 (c * 0). The total flux

\

~N~~\\

c~i.oo 00

-

~N

—.“..

-

,./

4 6I 8I TEMPERATURE(K)

10

12

Fig, 4. Temperature dependence of H~2in Er~Y1 ~Rh4 B4 as a parameter of concentration. -

T~/7~= exp 1 /g~csN(0)

—

I/ gBCSN(0)

I

—

187

6I2N(0)C~ ~

T~1

fz

~ ‘

where ~BCs and I are the BCS interaction parameter

and the exchange interaction between local spins and superconducting electrons, respectively. N(0) is the density of state and C~is the reduced 8 I ~S(S concentration + 1). f defined by C~= c[ 1 —(1 c) 1 and f2 are functions of T01 ,J’, and concentration c as given in [4] Since, in their theory, the inelastic scattering of electrons due to the interacting magnetic spin system are taken into account, but the effects of isolated spins, which act on electrons as pair-breakers as studied by Abrikosov and Gorkov [6] are neglected, their theory gives a good approximation in highly concentrated regions and has only qualitative meaning at very low concentrations. So, we tried a quantitative comparison of equation (2) with our experimental results 2N(0) in high concentration parameter equation (2) is regions. the mostThe decisive factor1 in deciding the rate of increase of T~when the concentration c is —

-

,

attractive force between the vortices. As a result, when the spin—magnetization increases at low temperatures, the superconducting state becomes unstable and H~2

ln (1 + f2 /f

1)

which is the sum of the spin and current contributions is quantized. Then, this flux quantization leads to the following situations; the vortex current is drastically affected from the spin—magnetization of Er at low temperatures and the current inversion occurs in some portion of the vortex. The current inversion causes the

/

decreases,

The samples with low concentrations of Er ions (c = 0.3—0.17) showed a finite minimum ofH~2near 0.2 K as is shown in Fig. 4. It was noted in Fig. 4 that H~2,in high concentration specimens with c = 1 —0.8, decreases suddenly at T~2.This sudden decrease in H~2 suggests the first order transition at T~2[9]. It was also noted that the zero-field resistance below T~2is about 60% of the normal values and the positive magnetoresistance was observed as shown in Fig. 1. The origin of the reduced resistance below T~,2may be that traces of the superconducting phase partially remained below T~2in polycrystalline samples but disappeared with the application of magnetic field. Precise measurements in a single crystal should be needed to check these points. Acknowledgements This work was supported by the Grant in Aid for Scientific Research from the Ministry of Education in Japan. The authors are grateful to —

188

SUPERCONDUCTING PHASE TRANSITIONS IN Er~Yi..~Rh4B4

Professor M. Date for his continued encouragement and useful advices. Thanks are also due to Professor M. Tachiki for valuable discussions and suggestions. The authors are much indebted to Dr. G. Adachi for useful directions of synthesizing the rare-earth compounds.

3. 4. 5.

REFERENCES 1. 2.

W.A. Fertig, D.C. Johnston, L.E. DeLong, R.W. McCallum, M.B. Maple & B.T. Matthias, Phys. Rev. Letters 38,987 (1977). H.R. Ott, W.A. Fertig, D.C. Johnston, M.B. Maple & B.T. Matthias,J. Low Temp. Phys. 33, 159 (1978).

6. 7. 8. 9.

Vol. 32, No.2

D.E. Moncton, D.B. McWhan, J. Eckert, G. Shirane & W. Thomlinson, Phys. Rev. Lett. 39, 1164 (1977). 5. Maekawa & M. Tachiki, Phys. Rev. B18, 4688 (1978). T, Oguchi & 1. Obotaka,J. Phys. Soc. Japan 27, 1111 (1969). A.A. Abrikosov & LP. Gorkov, Soy. Phys. JETP 12, 1234 (1961). M. Decroux,4. Fischer, R. Flukiger, B. Seeber, R. Delesclefs & M. Sergent, Solid State Commun. 25, 393 (1978). M. Tachiki, H. Matsumoto & H. Umezawa (to be published). M. Tachiki (private communication). —