Journal of Magnetism and Magnetic Materials 104-107 (1992) 575-576 North-Holland Al lm

N o r m a l - s t a t e s u s c e p t i b i l i t y a n i s o t r o p y o f m e t a l l i c c o p p e r o x i d e s

I. Kos, M. Miljak and V. Zlati6 Institute of Physics of the University of Zagreb, PO Box 304, 41001 Zagreb, Yugoslavia

Normal-phase anisotropy of Lal.9Sro.iCu204, YBazCu3OT_y and Bi2.2SrL75CaiCu2Os.i5 single crystals has been mea- sured. Below some characteristic temperature, T d i a , a n anomalous temperature-dependent diamagnetic contribution devel- ops in all the metallic samples. AXdia(T) increases until, at some lower temperature, the superconducting phase starts to influence the response. The total change, I Ax(Tdi~)-AX(Zc)l, is significant and can exceed the room temperature anisotropy quite substantially. AXdia(T) is of a similar form in all the metallic copper oxides. We find, AXdia(T)=

La __ 1.62× 10 -5 emu/mol) and for YBazCu3OT(T c - - C d i a / ( T / O ) d i a - - 1) for Lal.9Sr0.iCu204 (T c = 16.7 K, Odi . = 15.89 K, C d i a - -

= 87.6 K, ~gai a = 72.17 K, CdV~ = 2.12× 10 -5 emu/mol). The torque data seem to indicate that significant temperature-de- pendent diamagnetism precedes the onset of superconductivity and that AXaia(T) exhibits a universal form.

The normal-phase anisotropy of the ' magnetic sus- ceptibility Ax(T) of Lal.gSroACu204, Y B a z C u 3 0 7 y and Bi2.2Srl.75CalCUzOs.15 single crystals is discussed. The anisotropy is defined as Ax(T) = g 1 (T) - XlI(T), where g . (T) and XII(T) denote the susceptibility along the axes perpendicular and parallel to copper-oxygen planes. At a given temperature and in a given field H, the anisotropy follows directly from the measured torque F(T, H)as A x ( T ) ~ F(T, H ) / H z. Susceptibil- ities x ± ( T ) and XII(T) have also been measured di- rectly by a Faraday balance [1,2] or S Q U I D [3] magne- tometer. Combining the data the intrinsic response can be found.

The anisotropy of Bi, La and Y single crystals is shown in fig. 1. The overall features seem to be rather similar except that the temperature dependence of the additional diamagnetic term in Bi samples is somewhat faster than in La and Y samples. The geometry of the measurement and the relative orientation of the sam-

2.0 . . . . . . . . . . .

S 1.5 ooooo~o o om

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o ,~

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i i i i i i -1° ° 5b lOO' t00' z60 z;o ao0 T e m p e r a t u r e (K)

Fig. 1. Susceptibility anisotropy Ax(T) is plotted for Lal.9SroACuzO 4, YBa2Cu30 7 and Bie2Srl.75CalCuzOs.15 single crystals as a function of temperature below 300 K. The symbols a , [] and 0 correspond to La, Bi and Y samples,

respectively.

pie with respect to the applied field is such that at room temperature, F(T, H) is "posi t ive", i.e. the re- sponse is most paramagnetic along the axis perpendicu- lar to the C u - O planes. In all the samples an addi- tional rapidly varying tempera ture-dependent diamag- netic component to Ax(T) starts to develop below some characteristic temperature T~i a. For T << Tdia, the samples shown in fig. 1 become superconducting. We have T c=16 .7 , 85.5 and 87.6 K for La, Bi and Y samples, respectively. For T > T c but T << Tdi a we find a temperature interval in which the magnetization F(T, H) /H , is a nonlinear function of the applied field. Here, we consider only the temperatures for which the magnetization is strictly a linear function of the field. In Bi samples the nonlinear region is rather broad which makes the data analysis somewhat diffi- cult.

We assume A x ( T ) = Axdia(T) + Axe(T) + AXvv, in the normal phase of copper oxides. Here, A g v v is the Van Vleck response of copper 3d states, estimated as AxvL~, = AX(300 K) for La and AxYv = aX(800 K) for the Y sample, agg(T)=( (g 2 -gf~)/(ge))Xspin(T) is the g factor anisotropy of electron spins in the C u - O plane. At highest temperatures, where AXdia(T)~ 0, the observed behaviour, A x ( T ) ~ T, is consistent with Xspin(T) ~ T.

Anamalous diamagnetism, AXdia(T) , appears for T < Tdi a. Here, we point out that for Lal.9Sr0ACueO 4 samples, the measured Ax(T) actually changes from being "posi t ive" to "negat ive" , while the system is still well above the superconducting transition and Ax(T) is field independent. Such a behaviour cannot be ob- tained from a decrease of the spin susceptibility which, in a system without long-range order, influences the anisotropy only through AXg(T)~Xspin(T). The sum, Axg(T) + AXv v, should have the same sign at all tem- peratures. Hence, most of the observed temperature variation should be associated with an increase of "d iamagnet ism" that reduces the high-temperature

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576 L Kos et al. / Anisotropy of metallie Cu oxides

1.6

1.4

T 1.2

v t .O

o ° 0 . 8

0.6 I

~ 0 . 4

0.z

0 0

1.0

2 0 4 0 60 8 0 1 0 0

Temperature (K)

Fig. 2. Curie-Weiss diamagnetism; AXdia(T) is plotted as a function of temperature for Lal.gSro.iCueO 4 and YBa2Cu30 7 (inset). The data are corrected for the spin anisotropy (see

text). Full line is the "Curie-Weiss" curve.

"paramagnet ic" component and can lead to the total anisotropy of either sign.

The functional form of the diamagnetism in Lal.,~Sro.jCu204 and YBa2Cu30 7 is displayed in fig. 2 by plotting the relative change in the anisotropy with respect to the high-temperature values, corrected for the spin contribution. For all the points shown F(T, H ) / H 2 is field independent. We plot AXdia(T) =

- AXv v 5 . 1 × 10 5 A x ( T ) - AXvv AXg(T), where La = e m u / m o l , AXWv = 1.62 × 10 -4 e m u / m o l and the slope of the spin anisotropy is taken as Ac~ = 1.59 x 10 - s e m u / m o l K. The same AXg(T) has been used to correct the data for Lal.gSr0.1Cu204 and YBa2Cu30 7. The data seem to follow a "diamagnet ic Cur ie -Weiss" form [4], Axdia(T)= --Cdia/(T/Odi~- 1), shown as a full line. For Lal.gSr0.1Cu204, with T~ L"= 16.7 K, we have La __ La __ C d i a - - Odi ~ -- 15.89 K and 1.62 X 10 5 e m u / m o l . For YBa2Cu30 7, with T~ v = 87.6 K, we h a v e OdYa : 72.17 K and CdVa = 2.12 × 10 5 e m u / m o l . Thus, on the T / O scale, the temperature dependence of AXdia(T) for both systems follows the same "diamagnet ic Cur ie -Weiss" law. The ratio Tc/Odi a for both samples is surprisingly close. Unfortunately, the full develop- ment of the diamagnetic component could be seen in the best quality samples only. In samples of a lesser quality the nonlinear response due to the traces of superconductivity in disconnected grains inhibits the measurements of AXdia(T). The normal-phase dia- magnetic response of Bi2.2Srl.75Ca1Cu2OsA 5 and La2_xSrxCu204 samples for x_<0.05 could not be followed to low enough temperatures to justify the Cur ie -Weiss fit.

At present, the explanation of the "diamagnetic Cur ie -Weiss response" is lacking. The usual Fermi- liquid picture could lead to the diamagnetism in the normal state through the fluctuations above the super- conducting groundstate. However, we find it difficult to accept such an explanation because T~i a >> T c for all the samples and the reduction of T c, induced in Y samples by small changes of oxygen concentration [1] and in La samples by small changes in strontium con- centration [3], does not correlate with the correspond- ing changes in Tdi a. The band-structure effects (Landau-Pei re ls diamagnetism) are also difficult to invoke because that requires quasi-particle bands of the order of a few meV in the vicinity of the Fermi level.

The "spin liquid" theories [5] lead to the tempera- ture-dependent diamagnetism at small doping. The hole propagation, in the external field, is not indepen- dent from the distortion of the magnetic background which gives rise to a fictitious gauge field and enhances diamagnetism. However, present calculations along these lines [6] are valid for T>> Odi a only and give a Curie-like rather than Cur ie -Weiss diamagnetism.

Another possibility [1] to explain the data is to assume that the single-particle excitations in cuprates are overdamped and that the Landau current is carried by Bose-like excitations, e.g. pairs of real-space elec- trons in copper-oxygen plain. At very high tempera-

pair tures that leads to a typical Bose response, Agdia (T) ~ 1/T . The interaction between dilute Bose-like exci- tation would lead, within the mean-field approxima- tion, to the result Xdia(T ) ~ x~iair(T)/[1_ VXdi apair(T)]. Thus, the Cur ie -Weiss diamagnetism could be under- stood as a precursor to the 2D Bose condensation that would take place, in zero field, at T = Odi ~.

To conclude, A x ( T ) measurements indicate that (i) significant tempera ture-dependent diamagnetism pre- cedes thc onset of superconductivity, (ii) susceptibility anisotropy in high-To oxides exhibits universal features. The explanation of these unusual effects remains to be given.

R e f e r e n c e s

[l] M. Miljak et al., Europhys. Lett. 9 (1989) 723. [2] M. Miljak et al., Phys. Rev. B 42 (1990) 10742. [3] M. Miljak et al., (1991) unpublished. [4] P.W. Anderson, private communication. [5] P.W. Anderson, Science 235 (1987) 1196. [6] N. Nagaosa and P. Lee, Phys. Rev. 43 (1991) 1233.