Anomalies in the longitudinal ultrasonic attenuation and the velocity variation in the mixed state of a V3Si single crystal

Solid StateCou~munications,Vol. 18, pp. 505—508, 1976.

Pergamon Press.

Printed in Great Britain

ANOMALT~SIN THE LONGITUDINAL ULTRASONIC ATTENUATION AND THE VELOCITY VARIATION IN THE MIXED STATE OF A V3Si SINGLE CRYSTAL T. Fukase, M. Tachiki, N. Toyota and Y. Muto The Research Institute for Iron, Steel and Other Metals, Tohoku University, Katahira, Sendai, 980 Japan (Received 16 September 1975 by T. Nagamiya) In addition to sharp attenuation peaks of longitudinal sound waves propa. gating along the [001] axis of a V3Si single crystal at the upper critical fields H~2,new large attenuation and broad velocity peaks were observed in the mixed state. The new anomaly is explained by a mechanism related to the anisotropy of flux in the crystal tetragonally deformed by the band Jahn—Teller effect. WE MADE ultrasonic studies on a single crystal of V3Si and observed anomalously large and sharp attenuation peaks at the superconducting transition temperatures in the absence and presence of magnetic fields. Moreover, we found new attenuation peaks in the mixed state. At the points where the attenuation peaks appear, broad peaks of the sound velocity were observed. In the present letter we wish to report on these anomalies and propose a mechanism for explaining the new attenuation peaks. A V3Si single crystal with resistance ratio 17 was 1 The superconducting grown by atemperature floating zone transition ofprocess. this sample was determined to be 16.7 K by resistivity measurements. In the present study we used longitudinal sound waves propagating along the [001] axis of the crystal. The attenuation of a sound wave with 375 MHz was measured by the ordinary pulse method and the velocity change of a sound wave with 15 MHz was measured by the pulse superposition method with the precision of 10 No correction was made for the length change with temperature and magnetic field, Figure 1 shows the temperature dependence of the ultrasonic attenuation in zero magnetic field. Open and solid circles indicate the measured values of the attenuation coefficient when the temperature increases and decrease.~,respectively. As seen in this figure the attenuation coefficient abruptly increases below 24K and has a hump around 18 K. This increase of the attenuation coeffictent may be caused by the occurrence of the tetragonal transformation which has been observed in V 2 A sharp peak of the attenuation coefficient ap3Si. at T~as indicated by an arrow. The difference in pears the value of the attenuation coefficient at T~,and at 9 K is larger by a factor of one hundred than that expected for usual dirty superconductors. In our experiment in magnetic fields, the sample was first cooled down to 4K and then a magnttic field .

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Fig. I. Temperature dependence of the attenuation of the longitudinal wave with 375 MHz in zero field. Open and solid circles indicate the values measured in the processes of temperature increase and decrease, respectively. was applied in the [001] direction of the crystal. Figure 2 shows the temperature dependence of the attenuation coefficient in a field of 0.54 kOe, When the temperature increases, a structuie appears at the temperature mdicated by T* in Fig. 2. The sharp peak indicated by T~ shifts slightly to a lower temperature than T~in zero field. The hump around 18 K still remains even in the presence of the magnetic field. When the temperature decreases, the structure at T* disappears, although the hump around 18K and the peak at T~remain. Figure 3 shows the temperature dependence of the attenuation coefficient in a field of 2.8 kOe. The structure in Fig. 2 grows up to a remarkably large peak in a scan of increasing temperature, and T* shifts to a lower temperature. In a scan of decreasing temperature, no peak was observed at T* similarly to the previous case. Figure 4 shows the temperature dependence of an

506

ANOMALIES IN THE MIXED STATE OF A V3Si SINGLE CRYSTAL VSSi 81 [O0lJ/fq//H L ~ mode 375MHz

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Fig. 4. Temperature dependence of an elastic constant cii obtained from the velocity measurement of the longitudinal wave with 15 MHz propagating along the [001] axis in magnetic fields parallel to the [001]axis. The experimental values measured in the process of temperature increase only are shown in the figure. The temperatures T~are indicated by arrows. l.74~

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Vol. 18, No. 4

1.746

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Fig. 3. Temperature dependence of the attenuation of the longitudinal wave with 375 MHz in 2.8 kOe. Open and solid circles indicate the values measured in the processes of temperature increase and decrease, respect ively. elastic constant c~obtained from the velocity measurements. In the absence of field, the elastic constant varies monotonically and reversibly with regard to the temperature variation. The curve of c~vs4/deg temperature has a lulik above T~ and at T~(l/cii)dci~/dT= 48.5 10 (1/c~i)dc 4/degx below ~ These values 1i/dT= 9.6 x l0 4 hi are in agreement with those obtained Testardi. the presence of magnetic fields, broadby peaks were observed at T* when the temperature increased. The height of the peak increased as the field increased. When the

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Fig. 5. Hysteresis in the temperature variation of an elastic constant cii. The directions of arrows indicate the direction of temperature change. temperature decreased, the elastic constant decreased smoothly without any anomaly similarly to the case of the attenuation. Figure 5 shows hysteresis appearing in the temperature variation of the elastic constant. When temperatures were below T*, the variation was reversible. When temperatures were above T*, the hysteresis shown in Fig. S were observed. Figure 6 shows the upper critical field H~ 2and the field H* at which the new anomaly occurs as functions of temperature. Open and solid circles indicate the values which were ddtermined from the attenuation and velocity measurements, respectively. The values of H~ 2

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ANOMALIES IN THE MIXED STATE OF A V3Si SINGLE CRYSTAL

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electron effective mass along the elongated axis is expected to be much larger than those along the contracted

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Fig. 6. Temperature dependence of H* and H~2.Open and solid circles indicate the values determmed from the attenuation and velocity measurements, respectively, The bars denote the widths of the attenuation and velocity peaks. obtained in the present experiment is inare good agreement 5 which indicated by those by Pulver, awith solid line measured in Fig. 6. The bars in Fig. 6 represent the widths of the attenuation and velocity peaks around T*. The values of.!? determined from the attenuation measurement are in good agreement with those obtained from the velocity measurement. Our experimental results on the anomaly appearing at the field H* are summarized as follows: (1) The field intensity H* converges to zero at T~.This means that the anomaly has connection with the superconductivity in V 3Si. (2) The field intensity I? is stronger than ~ and much weaker than H~2.Accordingly, the anomaly occurs in the region of the mixed state. (3) The anomaly is observed only in the first scan of increasing temperature in a fixed magnetic field. For explaining the anomaly mentioned above, we consider the following mechanism. We assume that the tetragonal transformation occurs in our sample at result, Tm 2’6’7 As the owing to the band Jahn—Teller effect. extremely anisothe conduction electron band becomes tropic below Tm. In the case of V 3Si, one of the cubic axes is elongated and two other axes are contracted. The •

507

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axis. The anisotropy of the effective mass causes the anisotropy of flux in the mixed state. When an external magnetic field is applied along the contracted axis of the crystal, the lower critical field H~iis shown to be smaller than that H~1which one has when the field is applied along the elongated axis. The free energy of the mixed state in the field along the contracted axis is lower than that in the field along the elongated axis. We call the free energy difference the anisotropy energy. Then, owing to the anisotropy energy, the domains elongated in the [100]and [010] directions are more stabilized than the domains elongated in the [001] direction in the field applied in the [0011direction. The anisotropy energy increases as either the field or temperature increases, and overcomes the energy barrier for reorientation from one .

.

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kind of domain to other kinds of domain at certam critical values of the field and temperature. The field H* is considered to be the field at which the anisotropy energy compensates the barrier energy at T*. Batterman and Barrett actually kinds ofhave domain in V observed the existence of 8various The 3Si by X-ray [001]domains may reorient to theexperiments. [1001 or [010] domains under fields exceeding H*. If the strain induced by an impressed sound causes a back and forth motion of domain walls, the sound energy dissipates to the energy of the domain wall motion. The attenuation maxima are expected to occur at H* and T* where the domain walls easily move. This model is consistent with the experimental fact that the anomaly was not observed when the temperature decreases, since the [0011domains have been swept out by an external magnetic field in the process of temperature increase beyond T*. The calculation of the anisotropy energy of the mixed state and the detailed description of the mechanism of domain reorientation will be published elsewhere.

Acknowledgements WeTsuzuki, would like to thank T. Yamada, Professor T. Professor H. Professor Fukuyama and Mr. T. Koyama for many useful discussions. We also wish to thank Mr. T. Ono, Mr. Y. —

Haryu, Mr. T. Miura and Mr. T. Yamada for the prepar~ ation of the sample.

REFERENCES 1.

FUKASE T., UEMA K. & MUTO Y., Phys. Lett.49A, 129 (1974).

2. 3.

WEGER M. & GOLDBERG I.B., Solid State Phys. 28, 1 (1973). TOYOTA N., FUKASE T. & MUTO Y., Proc. 14th mt. Conf Low Temp. Phys. 2,5 (Otaniemi 1975).

4.

TESTARDI L.R., Phys. Rev. B3, 95 (1971).

5.

PULVERM.,Z. Phys. 257,22(1972).

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ANOMALIES IN THE MIXED STATE OF A V3Si SINGLE CRYSTAL

6. 7.

LABBE J. & FRIEDEL J.,J. Phys. (Paris) 27, 153, 303 and 708 (1966). COHEN R.W., CODY G.D. & HALLORAN J.J., Phys. Rev. Lett. 19,840(1967).

8.

BATTERMAN B.W. & BARRETT C.S., Phys. Rev. Lett.

13, 390 (1964).

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