Annual Report

Materials Science with Muon Spin Rotation

Virginia State University

Petersburg, VA 23803

Supported by NASA Grant NAG- 1-4 16

Report Period: 3/1/87 - 2/29/88

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OU271 5
Annual Report

Materials Science with Muon Spin Rotation

Virginia State University

Petersburg, VA 23803

Supported by NASA Grant NAG-1-416

Report Period: 3/1/87 - 2/29/88

During the twelve-month period March 1, 1987 through

February 29, 1988 the focus of activity in the MSMSR program was

muon spin rotation studies of superconducting materials, in

particular the new high-Tc materials and the heavy-fermion

materials CeCu2.iSi2.

A set of MuSR experiments was done at the Alternating

Gradient Synchrotron of Brookhaven National Laboratory in May

1987. Three materials were studied: (1) the high-Tc

superconductor YBa2Cu30?, (2) an oxygen-depleted variant on the

"parent" compound to Lai. 8 sSro. i sCu04 , La2Cu04-y, and (3) the

heavy-fermion superconductor CeCu2.iSi2.

The data obtained on YBa2Cus07 were combined with data

obtained on Lai. 85Sro. 15Cu04 in February 1987 in a paper,

"Systematic Variation of Magnetic-field Penetration Depth in

High-Tc Superconductors Studied by Muon Spin Relaxation", which

has been submitted to Physics Review B for publication. It is

included as Appendix A to this report.

The data obtained on La2Cu04-y are presented in a paper

which was published in Physical Review Letters on August 31,

1987. This is included as Appendix B to this report. A further

comparison of these data with neutron scattering results was

reported by our colleague Y. J. Uemura at the Interlachen HTSCM2S Conference in February 1988. This paper, which will appear

in the conference proceedings, is also included in this report as

Appendix C.

The director spent the period August 1-6, 1987 at the TRIUMF

laboratory in Vancouver, B.C., working on a MuSR study of

YBa2Cus07-y, which was found to be antiferromagnetic below about

220K, similar to LazCuCM-y. These results were published in the

March 14, 1988 issue of Physical Review Letters and are included

in this report as Appendix D.

The May 1987 study of CeCu2.iSi2 indicated the simultaneous

presence of superconductivity and static magnetic ordering in

this material below about 0.8K. Further MuSR studies with a

helium-dilution refrigerator were clearly needed, so the

director, along with two colleagues from the College of William

and Mary (W. J. Kossler and X. H. Yu) and Y. J. Uemura of BNL

went to the Swiss Institute for Nuclear Research in November 1987

to study CeCu2.iSi2 in the MuSR low-temperature facility there.
The phenomenon observed at BNL was confirmed and the magnetic

ordering appears to be a spin glass. These results are detailed

in a paper which has been submitted to Physical Review Letters

and is included here as Appendix E. A shortened and revised

version of this paper was presented at the Interlaken HTSC-M2S

meeting by Y. J. Uemura. It is included here as Appendix F. The

travel to Switzerland was supported by the National Science

Foundation.

Apart from superconductors, we also continued to analyze

data taken during earlier experimental runs on metal hydrides. A

paper on "Muon Motion in Titanium Hydride" is being submitted to

Physical Review B and is included here as Appendix G.

The director spent the periods July 11-August 1 and August

12-September 3, 1987 at the Los Alamos Meson Physics Facility

(LAMPF) working on two nuclear physics experiments, a search for

eta-mesic nuclei, and a study of nuclear pion charge-exchange

reactions at rest. His travel was supported by a National

Science Foundation grant administered by the College of William

and Mary. VSU graduate student Norman Fuqua (since graduated)

participated in the July run.

A paper based upon a December 1986 search for eta-mesic

nuclei done at the Brookhaven AGS has been accepted for

publication in Physical Review Letters. It is included in this

report as Appendix H.

A long set of MuSR experiments at BNL began in February 1988

and continued into May 1988 (which explains the lateness of this

annual report). A variety of high-Tc materials were studied,

including YBa2Cua-KCox 0?. These data will be described in the

next six-month report.

Lucian R. Goode, Jr., who did his thesis research on MuSR

studies of iron alloyed with gold, dysprosium and tantalum,

received the M. S. degree in physics in May 1987. Norman Fuqua

wrote his thesis on inelastic scattering of polarized protons

from i2C (done at Los Alamos) and received the M. S. degree in

July 1987. Li-Tai Song has passed the orals on his thesis, "The

Surface Muon Beam at Brookhaven National Laboratory" and should

receive the M. S. degree in July 1988. Nana Adu has passed the

orals on his thesis, "A Muon Spin Rotation Study of Zirconium

Hydride", and should also receive the M. S. degree in July 1988.

A senior physics major, Michael R. Davis, who worked extensively

on this research program, graduated magna cum laude from VSU in

July 1987.

The director gave four talks on the studies of

superconducting materials done at BNL, TRIUMF, and SIN during

this reporting period. They were presented at the Virginia

Academy of Science meeting in Norfolk in May 1987, at a MuSR

colloquium held at the Los Alamos Meson Physics Facility in

August 1987, at a NASA workshop held at the NASA Langley Research
Center in January 1988, and at a meeting of the VSU Society of

Physics Students, also held in January 1988. A presentation was

planned for the Virginia Academy of Science meeting to be held in

Charlottesville in May 1988.

The director continues to serve on the board of trustees of

the Southeastern Universities Research Association, which is

building the Continuous Electron Beam Accelerator Facility in

Newport News, VA, and which operates the SURANet computer

network. In December 1987 he was appointed to the board of

directors of the Virginia Research Network, and in May 1987 he

was appointed to the Governor's Ad Hoc Committee on the

Superconducting Super Collider.

A temperature controller and a CAMAC crate controller, both

ordered during the SSPRI grant period, arrived during the summer

of 1987 and have been installed in the MuSR rig at BNL. An 8-MHz

80287 math chip for the IBM PC/XT has been installed and is

operating.

Dr. Robert I. Grynszpan, the co-investigator of this

research program, was in residence at VSU between October 28 and

November 14, 1987. He worked with Dr. Min Namkung of NASA

Langley on magnetoacoustic measurements of fatigue in metals

during his visit. These results will be included in the next

report. A student of Dr. Grynszpan from the University of Paris,

Patrick Langlois, is expected to visit VSU as an exchange student

during the summer of 1988. He will work with Dr. Namkung at NASA

Langley on further magnetoacoustic measurements of fatigue in

metals.

The report period of March 1, 1987 to February 29, 1988 saw

the development of muon spin rotation into perhaps the best

technique for measuring the microscopic properties of high-Tc and

heavy-fermion superconductors. The coming year is full of

promise for continued studies in these areas, as well as the more

traditional areas which utilize the muon probe, such as metal

hydrides and magnetism.

We appreciate the support of NASA, and the collaboration of

scientists from William and Mary, Brookhaven National Laboratory,

George Mason University, and NASA Langley, all of which have been

vital to the success of this program.

Carey E. Stronach

Director

June 3, 1988
r

APPENDIX A
N88-2424 3

Systematic Variation of Magnetic-field Penetration Depth

in High-Tc Superconductors Studied by Muon Spin Relaxation

Y.J. Uemura

 l), V.J. Emery *), A.R. Moodenbaugh *), M.Suenaga *), D.C. Johnston 2)-a

)

A.J. Jacobson

 2>, J.T. Lewandowski 2>, J.H. Brewer 3), R.F. Kiefl 3>, S.R. Kreitzman 3) /

G.M. Luke

 3), T. Riseman 3>, C.E. Stronach 4>, W.J. Kossler 5), J.R. Kempton5

)-6)

X.H. Yu

 5), D. Opie s), H.E. Schone 5)

1) Brookhaven National Laboratory, Upton, New York 11973

2) Corporate Research Laboratories, Exxon Research and Engineering Co., Annandale,

i

New Jersey 08801

3) TRIUMF and Department of Physics, University of British Columbia, Vancouver,

British Columbia, V6T 2AS, Canada

4) Virginia State University, Petersburg, Virginia 23803

5) College of William and Mary, Williamsburg, Virginia 23185

ABSTRACT

The muon spin relaxation rate a has been measured in the high-Tc superconductors

YBaiCuzOx for x = 6.66, 6.95, 7.0, and Lai.8sSro.isCruO4 in transverse external magnetic fields 1 ~ 4&G. We find a simple relation which connects the transition temperature

TC, the magnetic-field penetration depth XL, the carrier concentration na, and the effective

mass m* as TC oc a a 1/A^,2 a n3/m*. The linear dependence TC <x na/m* suggests a

'high energy scale for the coupling between superconducting carriers.
The discovery

 l

 -

2

 of the layered Oxide high-Tc superconductor systems La2_ySryCu04

and YBa-iCuzOr has triggered extensive experimental activity

 3 and renewed theoretical interest

 4>s

 in the search for a novel mechanism for superconductivity. Muon .Spin

Relaxation (/xSR) is a direct method6 for measuring magnetic-field penetration depth

in superconductors7. (J.SR has been applied to the high-Tc oxide superconductors8"

11

and related antiferromagnets12'

13

. Because of recent technological development in sample preparation, it has now become possible14

 to study single-phase specimens with the

oxygen concentration controlled to within ± 0.02 per formula unit (/f-u.). In this paper,

•»

we present fj.SH measurements on YBaiCu$Ox superconductors with averaged oxygen

concentrations x = 7.0, 6.95, and 6.66 /f.u.. We combine these results with the earlier

work9 on Lai^^SrQ^^CuO^, and focus on the systematic dependence of the observed

muon relaxation rate a and the derived penetration depth A£. The results indicate that

the superconducting transition temperature TC is approximately proportional to the superconducting carrier concentration ns

 divided by the effective mass m*. We discuss the

implication of this relation on energy scales of the coupling between the carriers.

The sintered pellet specimen of YBaiCuzOi was prepared using a method described

in ref. 15. The powder specimens of YBa2Cu2O6.g5 and YBazCusOe.BG were prepared by

-using another method described in ref. 14. which reports Meisner effect and susceptibility

measurements on a series ofYBaiCu^Ox specimens ranging from x = 6.0 to 7.0. The specimens with x > 6.5 show superconductivity. The ^*SR experiments on YBa-zCusO? were

performed at the ACS muon channel of Brookhaven National Laboratory with a transIverse external magnetic field Hext of 1 kG applied perpendicular to the initial direction'of

muon spin polarization. The measurements on YBaiCuzO§.$s and YBaiCuzO$.§§ were
carried out at the M15 muon channel of TRIUMF (Vancouver) with Hext = 4kG. In both

cases, the data were taken by cooling the specimen in external field from T > TC to lower

temperatures.

In the transverse- field fj,+SR experiments, one observes the decay time histogram of

positive muons stopped in the specimen

N(t) oc «p(-t/rM)[l + <AGx(*)c0s(W;t*)I, (l)

where rM is the muon lifetime 2.2 ^sec, A is the initial precession asymmetry, CJM is the muon

precession frequency, and the relaxation function Gz (t} represents the time evolution of the

muon spin polarization. At all measuring temperatures (5.0K < T < 300 K], the observed

precession amplitude A indicates that within experimental error all the muons stopped in

the specimen contribute to the precession signal. The frequency u/M was approximately

equal to ^^H^t (-y^ = 2;r x 1.355 x 104/Oe is the gyromagnetic ratio of /i+) above TCUP decreased slightly with decreasing temperature below TC, due to the partial exclusion

of the external field Hext in. the type II superconductors at Hext > Hc\. For simplicity,

here we assume a Gaussian shape for Gx(t}:

G,(t)=«rp(-^), - (2)

where a is the muon spin relaxation rate.

Figure 1 shows the temperature dependence of a obtained for the present YBa^Cu^Ox

compounds together with the earlier results9 on Lai.8s5r0.isCuO4. The very small values

of a observed in all the specimens above TC can be accounted for by nuclear dipolar

broadening. Combining this feature with the full amplitude for A and the reduction
of Up below TC, one can conclude that there is no static magnetic ordering in these

superconducting specimens either above or below TC- This aspect was comfirmed in the

zero-field /zSR measurements on YBa-zCusO-r . Below TC, the value of c increases rapidly

with decreasing temperature. This is due to the inhomogeneity of the static local field at

the muon site in the type-II superconducting state where Hext penetrates as a lattice of

flux vortices. We notice here that the four different specimens in Fig. 1 have reasonably

similar shapes for the curvature of the temperature dependences cr(T}. This implies that

TC is approximately proportional to a(T —» 0), as demonstrated in Fig. 2 for the four

different specimens.

Pincus et al.16 used the London equation to calculate the distribution of magnetic

fields in the vortex state, and obtained the second moment

(3)

with the flux quanta 0o, for the square lattice of the vortex when the second moment

becomes independent of the external field Hext, i.e., when A£ is comparable to or greater

than the distance between adjacent vortices. The present condition with Hext — 1 *~ 4kG

satisfies this criterion. For a triangular lattice, one needs to multiply10 a factor of 0.93

to the right hand side of eq. (3). Then, one can deduce the value of the penetration

depth A£ directly from the observed relaxation rate a which corresponds to 7

Figure 3 shows the temperature dependence of XL thus obtained for the triangular vortex

lattice. The values for Ai(T —»• 0) are listed in Table 1. In the field-cooled measurements,

the density of the magnetic flux is kept almost constant above and below TC- If one

changes the external field in the superconducting state, in contrast, the flux vortices have
to move within the sample to change the spatial flux density, and thus the experimental

results become sensitive to the flux pinning17. Therefore, it is important to measure the

penetration depth in the field-cooled condition, as in the present experiment.

In actual systems, we noticed that the functional form of Gx(t] is somewhat in between

Gaussian and exponential. This is due to the complicated distribution of magnetic fields

for the vortex lattice as well as to the effect of anisotropy on the penetration depth A£,.

Correcting for the former effect would reduce the resulting values of XL by about 30 %. For

the case of maximum anisotropy where the penetration depth A in the soft direction (Hext

applied parallel to the CuO plane) is infinite, Celio et a/.18 find that the value of A for

Hext ± {CuO plane} to be about half the powder averaged value. These corrections make

it difficult to deduce the absolute values of XL accurately. However, we stress here that

the relation a ex 1/A^2 holds for any of the above calculations. Therefore, the systematic

and temperature variations of XL can be discussed based on Figs. 1 and 3.

The London penetration depth XL is given as a function of effective mass m* and the

carrier density na as

/ m*v2

(4)

m*c2

Combining this with the relation a = ^y^AJI2), eq.(3), and the approximate experimental result <7 oc Zc, we obtain a simple relation

Tig

Thus, the transition temperatures TC of the four different samples are simply proportional to the carrier concentration na divided by the effective mass m* regardless of the

crystallographic differences of the samples.
The relation TC oc n (n: normal-state carrier density) has been found by Hall constant and related measurements for La^-ySr^CuO^ between y'= 0 ~ 0.15 (ref. 19) and

YBa-2CuzOx between z = 6.5 ~ 7.0 (ref. 20). This linear relation can also be obtained

in a calculation of the number of holes for a formula unit, assuming charge neutrality for

La-iCuO* and YBa.iCuzO§.± and adding 1 hole for the substitution of Sr to La and 2

holes for additional oxygen per formula unit. These results suggest that the carrier concentration ns

, rather than the effective mass m* , plays a major role in changing TC in eq.

5. Indeed, the Pauli susceptibility at T > TC or the Sommerfeld constant -7 of the low

temperature specific heat, which are proportional to m'n1/

3

, do not depend much on the

>

differences in material21, supporting the above view point. The present work has shown

that the linear relation holds for the superconducting carrier concentration na.

We now discuss the implications of the relation TC oc n,/m*. In the BCS theory22

with the phonon-mediated coupling of electrons, TC is given in the so-called weak coupling

limit as

where kg is the Boltzmann constant, UD is the Debye frequency, V represents the effective

attractive interaction, and.J9(e/) is the density of states at the Fermi energy e/. To obtain

this equation, one assumes e/ >• hup and solves the secular equation by integrating the

energy range of the coupling interaction 0 — > hu^, which results in the pre-exponential

factor hup. It is difficult to reconcile the relation TC °c na/m* with eq. (6), because

|.D(e/) does not depend on n in the 2-dimensional non-interacting electron gas. Recent

single-crystal measurements23 on Hcz and on the transport properties suggest a highly

6
2-dimensional character for the electron system. Moreover, the magnitude of the electronphonon interaction V, inferred from the temperature dependence of linear resistivity in

the normal state24, is too small to explain the high transition temperature in the standard

phonon-mediated mechanism.

In contrast, when the energy scale of the attractive interaction which couples the

carriers is larger than that of 6f, the energy integration in the secular equation runs over

the range 0 to e/. This would, put, roughly speaking, e/ in the pre-exponential factor

of eq. (6) instead of hup. In a two-dimensional. non-interacting electron gas, the Fermi

energy €/ is proportional to the quantity n/m*. Then one could expect the simple relation

^

TC oc na/m*. This argument works without essential change also for three dimensional

systems where ep cc n2/

3

/m*. Thus, the relation TC <x n3/m* suggests a high energy

scale of the interaction which mediates the coupling between superconducting carriers in

high-Tc superconductors. Such a high energy scale may be found in models based on the

large transfer integral of a carrier between the oxygen and neighboring copper atoms5.

The linear relation TC oc na is also expected in a resonating- valence-bond picture25.

We study the temperature dependence of XL with examples of Y Ba^CuzO^^e, and

YBa^Cu^Or.o. The sharp changes of a(T] near TC observed for these samples suggest a

good homogeneity in the oxygen concentration. As shown by the solid lines in Fig. 3, the

experimental data agree well with the empirical formula22

AL(T) = . (7)

LV j

This result is consistent with earlier /iSR works

 8>l°, but disagrees with a recent bulk

measurement26. Equation (7) is calculated for A£ much smaller than the coherence length

7
£ by assuming an isotropic energy gap at the Fermi surface. For XL > £, the BCS theory22

predicts that A£,(T) increases more rapidly than eq. (7) with increasing temperature at

T < Q,7Tc- The anomalous zeros of the energy gap at some point or line of the Fermi

surface would change the theoretical curves for \L (T) to increase faster with increasing

temperature in the low temperature region. Therefore, the present results suggest that

the energy gap is predominantly finite.

In summary, based on the muon spin relaxation experiments, we have shown that the

approximate proportionality TC cc na/m* holds universally for different high-PC oxide superconductor systems. This feature suggests the high energy scale of the coupling between

*

superconducting carriers.

This work is supported by the Division of Materials Sciences, US Department of

Energy under contract 76-AC02-CH00016, the US National Science Foundation under

DMR 8503223, NASA under NAG-1-416, and by the NSERC of Canada.
REFERENCES

a) present address: Department of Physics and AMES Laboratory (USDOE), Iowa State

University, Ames, Iowa 50011.

b) present address: TRIUMF, UBC, Vancouver, B.C., V6T 2A3, Canada.

1. G.J. Bednorz and K.A. Muller, Z. Phys. B64, 189 (1986).

2. S. Uchida et a/., Jap. J. Appl. Phys. Lett., 26, Ll (1987); C.W. Chu et al., Phys.

Rev. Lett. 58, 405 (1987); R.J. Cava et al., ibid. 408; M.K. Wu et al., ibid 908 (1987)

3. see, for example, papers published in Phys. Rev. Lett. 58,59 (1987), Phys. Rev.

B35,B36 (1987), and Jap. J. Appl. Phys. Lett. 26 (1987).

4. P.W. Anderson, Science 235, 1196 (1987).

5. V.J. Emery, Phys. Rev. Lett. 58, 2794 (1987).

6. For general aspects of muon spin rotation, see proceedings of the four previous international conferences, Hyperfine Interact. 6, (1979); 8, (1981),17 - 19, (1984); 31,

(1986).

7. A.T. Fiory et al. Phys. Rev. Lett. 33, 969 (1974); F.N. Gygax et al. Hyperfine

Interact. 8, 623 (1981).

8. G. Aeppli et al. Phys. Rev. B35, 7129 (1987).

9. W.J. Kossler et ai, ibid. 7133 (1987).

10. F.N. Gygax et al. Europhys. Lett. 4, 473 (1987).

• 11. D.R. Harshman et al., Phys. Rev. B36, 2386 (1987).

12. Y.J. Uemura et al., Phys. Rev. Lett. 59, 1045 (1987).

9
13. N. Nishida et al., Jap. J. Appl. Phys. 26, L1856 (1987).

14. B.C. Johnston et al., Chemistry of High-Tc Superconductors, ACS Symposium Series

Vol. 351, Chap. 14, ed. by D.L. Nelson, M.S. Whittingham and T.F. George, Am.

Chem. Society, Washington DC. (1987), pp 136-151; A.J. Jacobson et al., Phys. Rev.

B (submitted).

15. R.J. Cava et al., Phys. Rev. Lett. 58, 1676 (1987); D.E. Cox et al., J. Phys. Chem.

Solids, in press.

16. P.Pincus et al., Phys. Lett. 13, 21 (1964).

17. some examples of the flux pinning effect can be seen in refs. 8 and 10. According to

a private communication with-A. Schenck, /iSR data taken in the zero-field cooling

procedure are significantly different from specimen to specimen, -even for the same

nominal chemical formula.

18. M. Celio, T.M. Riseman, J.H. Brewer, R.F. Kiefl and W.J. Kossler, unpublished.

19. M.W. Shafer et al., Phys. Rev. 536, 4047 (1987).

20. H. Takagi, K. Kitazawa et al., un published.

i

i

21. K. Kitazawa et al., Jap. J. Appl. Phys. Lett. 26, L748, L751 (1987).

22. J. Bardeen, L.N. Cooper and J.R. Schrieffer, Phys. Rev. 108, 1175 (1957).

23. Y. Hidaka et al. , Jap. J. Appl. Phys. Lett. 26, L377; L726 (1987); T.R. Dinger et

al., Phys. Rev. Lett. 58, 2687 (1987); T.K. Worthington et al., Phys. REv. Lett. 59,

1160 (1987).

24. M. Gurevitch and A.T. Fiory, Phys. Rev. Lett. 59, 1337 (1987).

10
25. G. Baskaran et a/., Solid State Commun. 63, 973 (1987); P.W. Anderson et a/., Phys.

Rev. Lett. 58, 2793 (1987).

26. J.R. Cooper et al., Phys. Rev. B37, 638 (1988).

11
FIGURE CAPTIONS

Fig. 1.

Temperature dependence of the relaxation rate a of the muon spin polarization, as

defined in eq. (2), observed in four different specimens of high-TC superconductors. Data

on £ai.85Sro.i5(7u04 and YBa^CuzO-r were obtained in a transverse external magnetic

field of 1 kG, while the measurements on the other two specimens were performed with a

field of 4 kG.

Fig. 2

Superconducting transition temperature TC, as determined by the /zSR measurement,

plotted versus the values of the muon relaxation rate a at T —» 0 for the four different

specimens of high-Tc superconductors.

Fig. 3

Temperature dependence of the magnetic field penetration depth XL derived from the

muon spin relaxation rate shown in Fig. 1. \L was calculated using a simple approximation

for the triangular vortex lattice as described in the text. The solid lines represent fits of

the data to eq. 7, with XL(T = 0) = 1656 A and Tc = 89.9 K for YBa2Cu2O6.95, and

\L(T = 0) = 1472 A and Tc = 91.1 K for YBa^Cu3O7,Q.

12.
YBa

b

LU

1i —

o:

z:-

o

i

hX

i

1

UJ

rv

O

CD

^

^

3.0

2.0

1.0

r\

°6.95

* °6.66

» La|>8#rQ|5Cu04

h » O Q 1 * 1* * »

°> 0

O o

o

o 4

0 O^o * °

0 * . o

* o

, o ,*« » | 8 on o.

0 25 50 75 100

TEMPERATURE (K)
100

LU

o:

~)

h-

<

tr

LU

CL

o

H

00

o:

i—

50

0

0 I 2 :3

RELAXATION RATE <j(T-0)
5000

0<

4000

3000

Q_

UJ

Q

9. 2000

<

o:

hLU

~Z-

^ 1000

0

I

o .

\ V .

0 LaL85SrQI5Cu

 °4

* YBa2Cu306.66

°6.95

°7.0

I I I

0 20 40 • 60 80

TEMPERATURE (K) .
APPENDIX C
8

- 2424

Comparison between Muon Spin Rotation and Neutron Scattering Studies

on the 3-Dixnensional Magnetic Ordering of La2CuO4_y

Y.J. Uemura1, W.J. Kossler2, J.R. Kempton2'

4

, X.H. Yu2, H.B. Schone2, D. Opie2

C.E. Stronach3, J.H. Brewer4, R.F. Kiefl4, .S.R. Kreitzman4,'G.M. Luke4, T. Riseman4

D.LI. Williams4, E.J. Ansaldo5, Y. Endoh6, E. Kudo6, K. Yamada6, D.C. Johnston7'

0

M. Alvarez7, D.P. Goshorn7, Y. Hidaka8, M. Oda8, Y. Enomoto8, M. Suzuki8, T. Murakami8

1 Brookhaven National Laboratory, Upton, New York 11973, USA

2 College of William and Mary, Williamsburg, Virginia 23185, USA

3 Virginia State University, Petersburg, Virginia 23803, USA

4 TRIUMF and University of British Columbia, Vancover, British Columbia, V6T 2AS,

Canada

5 University of Saskatchewan, Saskatoon, Saskatchewan, S7N 0 WO, Canada

6 Tohoku University, Sendai 980, Japan

7 Corporate Research Laboratories, Exxon Research and Engineering Co., Annandale,

New Jersey 08801, USA

8 NTT Electrical Communications Laboratories, Tokai, Ibaraki 319-11, Japan

ABSTRACT

Muon spin rotation and neutron scattering studies on powder and single- crystal specimens

of La^CuO^-y are compared. The apparent difference between the muon and neutron

results for the ordered moment in the antiferromagnetic state is interpreted as the signature

of increasingly short-ranged spatial spin correlations with increasing oxygen content.

(submitted to the Interlaken HTSC-M?S Conference, February, 1988)
It has been known

 l that the magnetic properties of the antiferromagnetic compound

-y depend sensitively on small differences in the oxygen content y = 0 ~ 0.03.

The input of O2~, equivalent to the substitution of 5r2+ for ia34", removes electrons and

creates holes in the system, and suppresses the 3-dimensional antiferromagnetic ordering.

To study this phenomenon with direct microscopic magnetic probes, experiments were

performed using the muon spin rotation (/iSR) (ref. 2) and neutron scattering3 techniques.

In this paper we present new fiSR data obtained at TRIUMF on a single-crystal and several

powder specimens, compare the muon and neutron results, and discuss their implications.

Figure 1 shows the muon spin p'recession frequency v^ observed in zero field for four

different powder specimens of La-^CuO^-y. i/M is proportional to the static internal magnetic field at the muon site from nearby ordered magnetic moments. Therefore, Fig. 1

represents the temperature and y variation of the ordered Cu moment 5. It is remarkable

that Vp(T —»• 0) (x S(T —»• 0) changes only within about 15 % for the four specimens

despite the large difference in the ordering temperatures TN (from 300 K to 15 K). The

ordered moment has also been measured by neutron scattering by Yamada et al. (ref. 3)

on a few single crystal specimens of jDa2CuO4_y. Figure 2 shows the temperature variation of the sublattice magnetization Ma derived from the intensity of the 3-dimensional

magnetic Bragg reflection. In contrast to the jxSR results, Ma(T —»• 0) decreases by more

than a factor of 3 for the decreasing Neel temperatures of the specimens. In this respect,

;zSR and neutron measurements look inconsistent.

To study further details, we performed /zSR measurements on a single-crystal specimen

of LazCuOi—y (NTT No. 3 specimen in ref. 4, grown simultaneously in the same batch

as sample No. 3 in Fig. 2 and in ref. 2). The neutron magnetic Bragg intensity was

2
measured on this crystal by Endoh et a/.4

, and the temperature variation was very close

to the results shown for sample No. 3' in Fig. 2. The ordered moment estimated from

the neutron study was about Ms(T —»• 0) ~ 0.15/is. Figure 3-(a) shows the muon spin

precession frequency t/M measured on this specimen. ^(T —»• 0) is approximately equal to

the values observed for the other powder specimens (Fig. 1), thus indicating that S(T —»• 0)

is not much different from the value 0.5 ~ 0.6 JJ,B determined by the neutron experiment

(Fig. 2) on the specimens with Z> ~ 300.ff.

We also performed ;*SR measurements in a weak transverse magnetic field of about

100G, and determined the volume fraction of the magnetically ordered part of the specimen

V

as shown in Fig. 3-(b). The magnetic ordering takes place gradually between 200JC and

100J?, below which almost the entire volume of the specimen becomes antiferromagnetic.

Lack of a sharp magnetic ordering is assumed to be due to the inhomogeneous spread of

the oxygen concentration in the large single crystal specimen. Similarly, it is confirmed

that the predominant volume fraction of the powder specimens orders magnetically below

Tff. This rules out the explanation that the difference between muon and neutron results

may be due to a non-ordered volume fraction of the specimens.

The difference between /iSR and neutron results can be understood in the following

way. The /i+ is a point-like probe in real space, and the local field at a muon site is

due mostly to its neighbouring Cu moments. Therefore, once the antiferromagnetic spin

configuration becomes static (t > 1/zsec), even if the spatial correlation may be short

ranged, the /x+ sees the specimen to be almost perfectly antiferromagnetic. In contrast,

the elastic magnetic scattering intensity of neutrons forms a peak in reciprocal space at the

Bragg point only when the spatial 3-dimensional ordering is long ranged. Therefore, the
present results suggest that the magnetic ordering becomes more and more short-ranged

with increasing oxygen content (i.e., with increasing number of holes), resulting in the

decreasing Neel temperatures.

The closed-shell electron configuration of O2~ mediates the super-exchange antiferromagnetic coupling between adjacent Cu moments. When the introduction of a hole makes

the oxygen to be Ol~ (ref 5), the unpaired spin at the oxygen would mediate the effectively ferromagnetic coupling between neighbouring Cu moments. Therefore, the input of

oxygen would create frustrated bonds6 in the Cu — O plane, and thus help to destroy the

long-ranged spin correlation. This picture provides a possible explanation for the present

results. There are two possiblities for the short-ranged correlation: a) the randomness

introduced within the Cu — O plane; and b) the cut-off of the spin correlation between

different Cu. — O planes. It is not possible to determine from the present work whether

either or both of them take place. The neutron study of ref. 4 gives support to b) for the

particular case of the specimen shown ha Fig. 3.

By combining neutron and muon experiments, one can estimate the microscopic static

moment to be S = 0.5 ~ 0.6/*B/Cu. This value is significantly smaller than the integer

moment for spin 1/2, but it can be explained by the quantum spin reduction for the spin

1/2 2-d Heisenberg system obtained from the statistical-mechanics calculations7. A spindensity-wave state is another possibility to create the non-integer moment. From the

present work alone, it is not posssible to tell which is the case.

We axe grateful for useful discussions with R.J. Birgeneau, V.J. Emery, G. Shirane

and S.K. Sinha. This work is supported by the USDOE (DE-AC02-76CH00016), the US
NSP (DMR 8503223), NASA (NAG-1-416), the Canadian NSERC, and by the Japanese

Ministry of Education, Culture and Science (Grant-in-Aid for Scientific Research).
REFERENCES

a) present address: Ames Laboratory (USDOE) and Department of Physics, Iowa State

University, Ames, Iowa 50011, USA.

1 D.C. Johnston et al., Phys. Rev. JB36, 4007.(1987).

2 Y.J. Uemura et al., Phys. Rev. Lett. 59, 1045 (1987).

3 K. Yamada et al., Solid State Commun. 64, 753 (1987).

4 Y. Endoh et al., Phys. Rev. B, submitted (1988).

5 V.J. Emery, Phys. Rev. Lett. 58, 2794 (1987), and references therein.

6 A. Aharony et al., preprint.

7 see, for example, J. Oitmaa and D.D. Betts, "Can. J. Phys. 56, 897 (1978), and

references therein.

6
Figure Captions

Fig. 1 Muon spin precession frequency v^ observed in zero external field on various sinteredpowder specimens of

Fig. 2 Sublattice magnetization Ma derived from the magnetic Bragg-peak intensity of

neutrons on single-crystal specimens of La^CuOi-y by Yamada et al. (after ref. 3).

Fig. 3 (a) Muon spin precession frequency i/M measured in zero external field on the NTT

No. 3 single-crystal of LaiCuO^—y. (b) Volume fraction of the paramagnetic region

of the specimen measured by muon spin rotation experiments in a weak transverse

external magnetic field. It is shown that almost the entire volume of the sample orders

magnetically below about T ~ 100 K.
FREQUENCY (MHz)

o

H

•(0

^J

H__

<! 9

^

rn

30

H

cr\j

rno

—

0

o

b • •*

O 0

-•0

0 _^

b

f-1 •

~ ° 1^

* +

* Z5

0 * ,

s o° - ET 0

 ^ ^

^ ^ 0

^ o ^ • "n -Di

* — i

«d ^ CD_ ^

^ ^ CL

— O -•-

b

CO
MS(/JLB/CU) X fm

HC

(D

NJ

O

O

no

O

O

04

O

O

7\

Q

no

O

- O

i

Oo

- 9 -
n Single Crystal

(a)

(b)

-L O

O

•5?

LU 4

Z>

0

u

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o:

u_

^

^__

 2

o

1 1

0

^ 100

0

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•

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• •

i i i t i

i i i i • i w

.

.

t

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3"

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TEMPERATURE (K)

Figure 3.

- 10 -
APPENDIX E
N88-

Coexisting Static Magnetic Ordering and Superconductivity /) /</

in CeCu2.iSi2 Found by Muon Spin Relaxation

Y.J. Uemura1), W.J. Kossler2), X.H. Yu2), H.E. Schone2>, J.R. Kemp ton2)'0)

C.E. Stronach3), S. Earth4), P.N. Gygax4), B. Hitti4)'2), A. Schenck4* /

C. Baines5), W.F. Lankford6), Y. Onuki7), T. Komatsubara7)

1) Brookhaven National Laboratory, Upton, New York 11978

2) Department of Physics, College of William and Mary, Williamsburg, Virginia 23185

3) Department of Physics, Virginia State University, Petersburg, Virginia 2S80S

4) Institute for Intermediate Energy Physics, ETH Zurich, c/o PSI (formerly SIN), CHi

52S4, Villigen, Switzerland

5) PSI (formerly SIN), CH-52S4, Villigen, Switzerland

6) Physics Department, George Mason University, Fairfax, Virginia 22050

7) Institute of Materials Science, University of Tsukuba, Sakura-mura, Ibaraki SOS, Japan

(January, 1988)

ABSTRACT

Zero- and longitudinal-field muon spin relaxation measurements on a heavy-fermion system.

CeCu<2.iSi<2 have revealed an onset of static magnetic ordering below TM ~ 0.8JC, which

coexists with superconductivity below TC = Q.7K. The line shapes of the observed muon

spin depolarization functions suggest an ordering in either spin glass or incommensurate

spin-density-wave state, with a small averaged static moment of the order of Q.IVB per

formula unit at T -* 0. ' (PACS Nos. 75.20.H, 76.75, 74.70.H)
ij, belongs to a group of Cerium or Uranium intermetallic compounds, called

heavy-fermion systems1, which are characterized by the extremely large T-linear term

C = ^T with 7 ~ 1 Joule/mole deg2 of the electronic specific heat C at low temperatures

inferring very large effective mass m*. In 1979, Steglich et al.2 found a superconducting

transition in CeCu^Sii at T ~ Q.5K, as the first example of the superconducting ground

state of a heavy-fermion system. This discovery triggered extensive study of superconductivity and its possible relation with magnetism in the highly correlated heavy electron

systems

 1)3

. Although there are some susceptibility measurements

 4>5

 which suggest mag-'

netic ordering of non-superconducting systems C&i-yLayCuzSii with y > 0.2 (ref. 5)

and CeCuxSiz with x = 1.9 (ref. 4), so far it has been common to assume1 a purely

superconducting ground state without magnetic ordering for the superconducting compounds CeCuxSi^ with 2.0 < x < 2.2 (ref. 6). In this paper, we present the first direct

evidence from zero-field muon spin relaxation measurements that superconductivity and

static magnetic ordering coexist in CeCu-i.iSii. Muon Spin Relaxation (ptSR)7 is a very

powerful tool to detect static magnetic ordering8'

9

. Previous applications of ^SR to heavyfermion systems led to discoveries of magnetic ordering with quite small ordered moments

(0.001 ~ 0.05 P,B] in superconducting UPt$ (ref. 10) and non-superconducting CeAlz (ref.

11). With the present results on CeCu^.iSi-^, we now have three heavy-fermion superconductors, CeCuz.iSi-2,UPt3, and URu^Si^ (ref. 12), which show co-existing magnetic

orderings.

Superconductivity of the stoichiometric CeCu-z.oSi-2, is known to be somewhat unstable5.

A small amount of additional Cu helps to stabilize the superconductivity of CeCuxSi?

with x = 2.1 ~ 2.2 whose superconducting transition temperature TC is around 0.7 K
(ref. 6). We therefore prepared a poly-crystalline sample of CeCu^.iSi^ by the method

described hi ref. 6. Figure 1 shows resistivity measured on a piece cut off from the sample

of CeCu^.iSiz used in the present /iSR measurement. Reference 6 describes detailed resistivity and specific-heat measurements on a few poly-crystalline samples of CeCuxSi-2 with

x = 1.9 ~ 2.2 made with the same method. The present specimen has TC at around 0.7 K,

and the temperature dependence of resistivity shows the same curvature as reported in ref.

6. To further characterize the present sample, we made a neutron scattering measurement

of the crystal structure, and confirmed that it is a single phase material without any minor

phase within the experimental accuracy of a few volume percent.

We started zero-field /iSR measurements on the present sample of CeCu-^.iSi-z at the

AGS muon channel of Brookhaven National Laboratory by using a 3fTe-cryostat. A rapid

0-^

increase of the muon spin relaxtion rate was found with decreasing temperature below

T ~ Q.SK. We then continued the measurement at SIN, Switzerland, by using a surface

muon beam and a dilution refrigerator. The facility at SIN allowed full access to a wide

temperature region with high-statistics data as we report in this paper. A positive muon

beam was stopped at the sample of CeCu^.iSi^ (2cm x 1cm x 0.5cm) mounted on a cold

finger of the dilution cryostat, and the muon-decay positrons were recorded mainly with a

counter placed in the forward direction with respect to the beam direction. The counting

rate I(t) of this counter is given as ;

1(0 « expH/rM)[l-AG,(0], (1)

where rM is the muon lifetime 2.2 fj.sec, A is the initial decay asymmetry (A ~ 0.25- at

the present condition), and the relaxation function Gz(i) represents the time evolution of

muon spin polarization.
•>

Figure 2-(a) shows the relaxation function Gz(t] thus observed in zero field. "The

relaxation rate increased rapidly below T ~ 0.8K with decreasing temperature. In general,

the depolarization of muon spins in zero field can be due either to randomness of the static

internal local field Hint or to the fluctuating dynamic local fields. One can distinguish

between these two cases by making measurements in the longitudinal external magnetic

field Hezt applied parallel to the initial muon spin direction (i.e., the direction of muon

beam, denoted as z direction hereafter). When the internal field is static and Hezt is

larger than Hint, Hext can align the local field HIOC = Hint + Hext to be nearly parallel

to the muon spin polarization, thus keeping Gz(t] finite. In contrast, the dynamic spin

fluctuations are usually much faster than the corresponding Zeeman frequency u; = 7^ffezt

("yM = 2?r x 13.554M.H'z/A:G) of p.+ , so that there is almost no effect of Hext on Gz(t] for

the dynamic case. We have performed such measurements in Hext = 250G and IfcG at

T = O.IK as shown in Fig. 2-(b). The longitudinal fields suppress the depolarization

and change Gz(t) remarkably. This indicates that the depolarization observed in zero

field is due mainly to the static random local fields of the order of 100 ~ 200G. Similar

measurments with Hext confirmed that the depolarization at T = 0.8K is also due to the

static fields.

The line shapes of G2(t) in zero field shown in Fig. 2-(a) resemble those observed

in the dilute-alloy spin glasses CuMn or AuFe (ref. 8). The lack of coherent oscillation

indicates that the magnitude of the static internal field | Hint \ has a wide distribution.

For a uniform | Hint |? one should have seen a muon spin precession as reported in refs. 9

and 11. Gg(t] in Fig. 2-(a) at T — 0.05K starts with a Gaussian-like shape at t —* 0. This

is somewhat different from the case in the dilute-alloy spin glasses where Gz(t —> 0) decays
with an exponential-like shape when the temperature is well below the susceptibility-cusp

temperature Tg. In this paper, we do not develop a complicated theory to account for this

line shape, but rather adopt a phenomenological relaxation function

G,(«) = ^exp(-l-a^} + ^ezp(-Ai) (2)

to fit the observed data. The first term corresponds to the quick initial decay caused by

the x- and y- components of the static random local fields. The second term represents

the tail arising from the component of H{nt parallel to the initial muon spin direction

(i.e., the z-direction). Reasonably good fits to the data at all different temperatures

0.05JC < T < l.OK were obtained when we assumed Ai/A = 2/3, A2/A = 1/3, with

1

A = 0.25. The present counter configuration without the backward counter, however,

made it difficult to determine the second term of eq. (2) accurately. Therefore, the decay

rate A of the tail, ranging around A ~ l.O/zsec"1, may be subject to a large systematic

error. In contrast, the first term of eq. (2) can be determined with reasonable precision.

From the fit to eq. (2) represented by the solid lines in Fig. 2-(a), we thus obtained the

muon spin relaxation rate a as shown in Fig. 3.

The relaxation rate a in Fig. 3 increases rapidly with decreasing temperature below

I

T ~ 0.8K. This indicates the onset of a random but static magnetic order at the magnetic

ordering temeprature TM ~ 0.8JC. Because of the limited accuracy of the temperature

measurements and control with the cold-finger cryostat, as represented by the horizontal

error-bars in Fig. 3, we can not identify whether the magnetic and superconducting orderings occur simultaneously or whether TM and TC are somewhat different. It is evident

from Figs. 1-3, however, that the superconductivity and magnetic ordering coexist below
T ~ Q.7K in CeCua.iSt'a- The present results indicate that more than 90 volume percent

of the specimen undergoes the magnetic ordering. The relaxation rate a in Fig. 3 represents a measure of the width of the static internal fields as a ~ 1n^< (A-fft-nt)2

 >. The

observed value of a ~ I0fj,sec~l at T -+ 0 corresponds to the static random local fields

of the order of 0/in ~ 120G. In most magnetic materials, local fields at muon sites are

due mainly to the dipolar field from the surrounding moments. Since fj,+ is a point-like

probe in real space, and since information on the muon stopping site is lacking, it is not

easy to accurately estimate the spatial spin structure of the magnetically ordered state of

CeCuz.iSiy. It is, however, possible to note the following.

Spin glass ordering is one of the most likely spin structures which produce a large

distribution of Hint as observed in the present experiment (see ref. 8). This picture is

consistent with the observation of a strong effect of external fields on the susceptibility

measurements of CeCu-i.gSi-i (ref. 4). If one assumes that the majority of Ce (or Cu]

atoms participate in the magnetic ordering, the observed width ~ 120C? of Hint corresponds

to the dipolar field from the ordered moment of the order of 0.1 /ZB- If instead the small

population of Ce3+ ions forms a spin glass with an ordered moment of S^B , like dilutealloy spin glasses, then the observed value of a corresponds to an ordering of about a

i

few percent of the Ce atoms. The latter picture is advocated in ref. 4 for the case of

CeCui.gSiz. The Gaussian-like decay of Gz(t -+ 0) may favor the former type of spin

glass, but then one faces the difficult question as to the origin of the frustration of the

exchange interactions. An incommensurate spin-density-wave state, like that observed in

CePbz (ref. 13), is another possible spin structure which gives the local field at the muon

6
site a wide distribution. Unfortunately, the present experiment alone can not distinguish

the above mentioned three possible spin structures.

A neutron scattering experiment on CeCu^.iSi^ is underway14 to study spatial spin

correlation. For such a small averaged moment as ~ 0.1/iB) however, the magnetic scattering intensity of neutrons is very small. Neutron measurements become even more difficult

when the spin glass ordering makes the scattering diffusive in reciprocal space. In this

respect, the present experiment demonstrates the unique capability of zero-field /iSR to

detect magnetic orderings with small averaged moments. In the previous /iSR study on the

same specimen of CeCu^.iSi-i performed in the transverse external magnetic field15, the

depolarization of muon spins observed below T ~ 0.8K was tentatively attributed to the

inhomogeneous penetration of the transverse external field in the type- II superconducting

state. Zero-field fj.SH can detect the magnetic ordering without the complication of the

field penetration. The present results indicate that a major part of the depolarization

observed in the transverse field was due to the static magnetic ordering. In order to find

out whether the superconductivity and magnetic ordering occur at the same tempeature

or at different temperatures, we are planning to perform additional fj.SH measurements on

specimens with different Cu stoichiometry which may have different TM (see ref. 4).

Recently, a heavy-fermion superconductor UPtz (Tc ~ 0.5JC) was found10 to order

magnetically below T ~ 5K with an extremely small averaged moment of ~ 0.001//BURuiSi-z is another superconducting heavy-fermion system (Tc ~ l.QK] which orders

antiferromagnetically below TN ~ ^K with an ordered moment of O.OS^B per Uranium

atom12. UBeiz is so far the only remaining heavy-fermion superconductor without an
identified magnetic ground state, yet there is a report16

 which suggests a possible antiferromagnetic ordering in UBei3 doped with a small amount of Th. Together with the present

results on CeCu2.\Si-i, these features indicate that the magnetic ordering with extremely

small averaged moment may be a common feature of heavy-fermion superconductors.

In summary, zero-field /iSR measurements on CeCui.iSiz have shown clear evidence

of static magnetic ordering below TM ~ Q.8K with a very small averaged moment of

~ O.l^B in either a spin glass or an incommensurate spin-density-wavestate. This ordering

coexists with superconductivity below TC = 0.7K. Further experimental and theoretical

studies are clearly needed for the full understanding of the role of such magnetic orderings

on the superconductivity of heavy-fermion systems.

We would like to acknowledge useful discusions with P.B. Allen, K. Kakurai, M. Steiner

and E. Recknagel. We thank W. Schonig for help on the measurements at Brookhaven.

This work is supported by the Division of Materials Sciences, US Department of Energy

under contract 76-AC02-CH00016, the National Science Foundation under DMR 8503223

and INT 8413978, NASA under NAG-1-416, and by the Japanese Ministry of Education,

Science and Culture under the Grant-In-Aid for Scientific Research.
REFERENCES

a) present address: TRIUMF, UBG, Vancouver, B.C., V6T 2A3, Canada.

1. for a review of heavy-fermion systems, see, for example, G.R. Stewart, Rev. Mod.

Phys. 56, 755 (1984).

2. F. Steglich et al., Phys. Rev. Lett. 43, 1892 (1979).

3. see, for example, papers presented in the sessions of heavy-fermion systems in recent

conferences, in J. Magn. Magn Matrs. 31 - 34 (1983); 47 - 48 (1985); 54 - 57 (1986);

63 - 64 (1987); and J. Appl. Phys. 55 (1984); 57 (1985); 61 (1987).

4. U. Rauchschwalbe et al., J. Magn. Magn. Matrs. 47 — 48, 33 (1985).

5. F.G. Aliev et al., J. Low Temp. Phys. 57, 61 (1984); N.B. Brandt and V.V.

Moshchalkov, Adv. Phys. 33, 373 (1984).

6. Y. Onuki et al., J. Phys. Soc. Japan 56, 1454 (1987).

7. for general aspects of muon spin relaxation, see proceedings of four previous international conferences, Hyperfine Interact. 6 (1979); 8 (1981); 17-19 (1984); 31 (1986).

8. Y.J. Uemura et al., Phys. Rev. B31, 546 (1985).

9. Y.J. Uemura et al., Phys. Rev. Lett. 59, 1045 (1987).

10. D.W. Cooke et al., Hyperfine Interact. 31, 425 (1986).

11. S. Earth et al., Phys. Rev. Lett. 59, 2991 (1987).

12. T.T.M. Palstra et al., Phys. Rev. Lett. 55, 2727 (1985); M.B. Maple et al., ibid. 56,

185 (1986); C. Broholm et al., ibid. 58, 1467 (1987).

13. C. Vettier et al., Phys. Rev. Lett. 56, 1980 (1986).

9
Y

-

J

-

10
- FIGURE CAPTIONS

Fig. 1. Resistivity measured on a piece of CeCu^.iSi^ cut off from the present specimen used

in the /zSR measurements. Superconducting transition occurs at TC — 0.7JC.

'Fig. 2. (a) Muon spin relaxation function Gz(t) in zero field observed in CeCuy.iSiz- Solid

lines represent fits to eq. (2). (b) Muon spin relaxation function in CeCui.\Sii

observed at T = O.lK in longitudinal external magnetic fields LF of OG, 250G, and

IkG. Solid lines are guides to the eye.

Fig. 3. Muon spin depolarization rate a, as defined in eq. (2), derived from the relaxation

functions observed in CeCuz.iSiz in zero field. The onset of magnetic ordering is seen

\

around TM ~ 0.8K.

11
-200

o

G

S

^

~ 100

en

LU

(T

Pi

2.1 2

•

..•••

~

..•"

.*'**

•• i •^

*

•*

. • w f*

• *

>•

X'

/""

j

%

f

1 '. I | | I |

0.0 .0 2.0 3.0

TEMPERATURE (K)

Figure 1

- 12 -
(a)

CeCu2JSi2

1.0

Gz(t)

0.5

r\r\

A

•Tv-A

TOSi_ 0.91

\X * »*T*i»*

\ C>n

£ XD

"• \ V75 K

x

« "^0

o o^^Sflrf'

K

^^"^^^im-rr^A-^i A A

 A^i^A

I^A

rAA_

i-2__ 0 n no 0 O.Ob K r ^V^TO^saafc^

0. 0.5 1.0 ' * U$ 2D

TIME (/^sec)

T=O.I K

(b)

1.0

GZ(T)

0.5

0.0

V

D

LF= l^kG

250 G

'-o^^o^-a oo

_

0 G

yT T

0. 0.5 1.0 L5T

 2.0

TIME (/^sec)

Figure 2

- 13 -
1

0

<D

O

LJ

hor

z: 5

o

h-

<

X

<

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LU n

o:

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•j-

- , HeXT

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^

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"*-*

-•

. -p

1 ^^^ I

^^^ 1

T

! — • •!

0. 0.5 1.0

TEMPERATURE (K)

Figure 3

- 14 —
APPENDIX F
Static Magnetic Ordering of

Found by Muon Spin Relaxation

Y.J. Uemura1), W.J. Kossler2), X.H. Yu2), H.E. Schone2), J.R. Kempton2)-")

C.E. Stronach3), S. Earth4), F.N. Gygax4), B. Eitti4)-2), A. Schenck4) /

C. Baines3), W.F. Lankford6), Y. Omiki7), T. Komatsubara7)

1) Brookhaven National Laboratory, Upton, New York 11973

2) Department of Physics, College of William and Mary, Williamsburg, Virginia 23185

3) .Department of Physics, Virginia State University, Petersburg, Virginia 2S80S

4) Institute, for Intermediate Energy Physics, ETH Zurich, c/o PSI (formerly SIN), CH.-

5234, Villigen, Svritzerland

5) PSI (formerly SIN), CH-5234, Villigen, Switzerland

6) Physics Department, George Mason University, Fairfax, Virginia 22030

7) Institute of Materials Science, University of Tsukuba, Sakura-mura, Ibaraki 305, Japan

(submitted to the Interlaken HTSC-M?S meeting, February, 1988)

ABSTRACT

Zero- and longitudinal-field muon spin relaxation measurements on a poly-crystal sample

of a heavy-fermion superconductor CeCu^.iSi^ (Tc = 0.7JJC) have revealed an onset of

static magnetic ordering below T ~ Q.8K. The line shapes of the observed spectra in zero

field indicate a wide distribution of static random local fields at muon sites, suggesting

that the ordering is either spin glass or incommensurate spin-density-wave state. The

observed width of the random local field at T = Q.OSJiC corresponds to a small averaged

static moment of the order of 0.1/i.g per formula unit.
tj is the first heavy-fennion system which was found to become superconducting at TC ~ Q.5K (ref. 1). Although there were signatures suggesting possible magnetic

orderings in non-superconducting CeCui.gSi^ (ref. 2) and Cei-yLdyCuzSiz with y > 0.2

(ref. 3), superconducting specimens CeCuzSi2 with x = 2.0 ~ 2.2 have so far been believed to have purely superconducting ground states without magnetic ordering. In this

paper, we present direct evidence from- muon spin relaxation (/*SR) measurements that

superconducting CeCu-z.iSi^ (Tc = 0.7-K") undergoes a random static magnetic ordering

below T ~ Q.8K.

It is known that a small amount of off-stoichiometric excess Cu helps to stabilize

*

the superconductivity of CeCu^Si^- Therefore, we prepared a polycrystal specimen of

CeCu2.i-Si2 with the method described in ref. 4. The superconducting transition temperature TC = Q.7K was determined by a resistivity measurement on a small piece cut out

from the present specimen. A neutron scattering measurement on the crystal structure

confirmed that there is no minor phase within the accuracy of a few volume percent.

Zero- and longitudinal-field /*SR measurements were performed using polarized positive muon beams at AGS/BNL and SIN (Zurich) muon channels. In the zero-field measurements, very small depolarization of muon spins was observed above T = 0.9J5C, while

the depolarization rate increased rapidly with decreasing temperature below 0.8JC. The

zero-field muon spin relaxtion functions Gz(t) (ref. 5) observed at different temperatures

show no precession signal but have line shapes similar to those observed in dilute-alloy

t spin glasses5

. This indicates that the magnitude of local fields at muon sites varies widely,

in contrast to the cases for uniform ferro- or antiferromagnets.
A phenomenological form for t'he muon spin relaxation function

(1)

with Ai/A ~ 2/3 and A^/A ~ 1/3, gives good fits to all the data observed in zero-field.

The first (second) term of eq. (1) corresponds to the depolarization of muon spins by the

components of internal fields perpenducular (parallel) to the initial polarization direction

of the muon spins. Figure 1 shows the temperature dependence of the relaxation rate a.

In order to distinguish whether this depolarization is due to static or fluctuating

local fields, we have also performed /zSR measurements by applying longitudinal external

magnetic fields HL = 250C? and IkG parallel to the initial muon spin direction. The muon

spin polarization had a finite value Gz(t] ~ 0.45 with EL = 250G, and Gz(t) ~ 0.95

with HL = IkG, almost independent on time between 0.5/zsec <t< 2fisec at T = Q.IK.

A similar decoupling of the random field was observed around T = Q.8K. These results

indicate that the depolarization shown in Fig. 1 is due predominantly to the static random

local fields. The rapid increase of a below T ~ 0.8J5C then corresponds to the sharp onset of

static magnetic ordering around the ordering temperature TM = Q.SK. Due to the limited

accuracy of the temperature measurements with the cold-finger dilution cryostat used in

the present experiment, it is not clear whether the magnetic and superconducting orderings

occur simultaneously at the same temperature or independently at different temperatures.

It is, however, evident that the superconductivity and magnetic ordering coexist below

Tc = 0.7 K.

The wide distribution of the static random local fields, as observed in the present

experiment, can be expected either for spin glass (SG) or incommensurate spin-density3
wave (ISDW) systems. The spin glass ordering is consistent with a large field dependence

of the susceptibility observed in the non-superconducting system CeCui.gStj (ref.2). If

one assumes that a majority of Ce (or Cu) moments participate in the spin-glass freezing,

the zero-field relaxation rate a ~ lQ(j.sec~l (the width tf'/'V ~ 120G of the local field)

observed at T = Q.Q5K corresponds to the dipolar field from a static moment of the order

of 0.1 Bohr magneton per formula unit. If the small population of the Ce3+ ions with an

ordered moment of 5 tig forms a spin glass, this value of a is expected for the freezing

moments on a few percent of the entire Ce atoms. From the present work alone, it is not

possible to distinguish among the above-mentioned three possible spin structures (the two

types of SG states and the ISDW state) of CeCu2.i5t2 below TMRecently, a heavy-fennion superconductor UPtz (Tc ~ Q.5K) was found10

 to order magnetically below T ~ 5K with an extremely small averaged moment of 0.001 ~ -

0.02;ijg/Z7 (refs 6,7). URu^Si^ is another superconducting heavy-fennion system (Tc ~

l.OK) which orders antiferromagnetically below Tff ~ 17K with an ordered moment of

0.03/jfl per Uranium atom8. With the present results on CeCu2.i5t2, we now have three

heavy-fermion superconductors which show coexisting magnetic ordering with extremely

small ordered moments (0.001 ~ O.l^a)- This may then be a common feature of the

superconductivity in heavy-fermion systems.

This work is supported by the Division of Materials Sciences, US Department of

Energy under contract 76-AC02-CH00016, the National Science Foundation under DMR

8503223 and INT 8413978, NASA under NAG-1-416, and by the Japanese Ministry of

Education, Science and Culture under the Grant-In-Aid for Scientific Research.
REFERENCES

a) present address: TRIUMF, UBC, Vancouver, B.C., V6T 2A3, Canada.

1. F. Steglich et al., Phys. Rev. Lett. 43, 1892 (1979).

2. U. Rauchschwalbe et al., J. Magn. Magn. Matrs. 47 -48, 33 (1985).

3. F.G. Aliev et d., J. Low Temp. Phys. 57, 61 (1984); N.B. Brandt and V.V.

Moshchalkov, Adv. Phys. 33, 373 (1984).

4. Y. Onuki et al., J. Phys. Soc. Japan 56, 1454 (1987).

5. Y.J. TJemura et al., Phys. Rev. B31, 546 (1985).

6. D.W. Cooke et al., Kyperfine Interact. 31, 425 (1986).

7. G. Aeppli et al., Phys. Rev. Lett. 60, 615 (1988).

8. T.T.M. Palstra et al., Phys. Rev. Lett. 55, 2727 (1985); M.'B. Maple et al., ibid. 56,

185 (1986); C. Broholm et al., ibid. 58, 1467 (1987).
FIGURE CAPTIONS

Fig. 1. Muon spin depolarization rate <r, as denned in eq. (l), derived from the relaxation

functions observed in CeCu2.iSt2 in zero field. The onset of magnetic ordering is seen

around TM ~ O.SK. The superconducting transition temperature TC, determined by

' a resistivity measurement on a piece cut off from the present specimen, is indicated

by the arrow.

6
r

o

CD

jg.

 I0

b

LU

h01

2*^TMB» 5

O

hX

-J

UJ n

/^ in CeCup iSU

*

1 -v Hpy^ A 1t = 0

f^-4

— 4 j»

4

-4

-4,

-4

-•

T

° T

1 — • •!

TEMPERATURE (K)

Figure 1.

- 7 -
APPENDIX G
N88-24247

, *

Muon Motion in Titanium Hydride

J. R. Kempton*, K. G. Petzinger, W.'J. Kossler,

H. E. Schone, and B. S. Hitti*

College of William and Mary, Williamsburg, Virginia 23185

C. E. Stronach and N. Adu

Virginia State University, Petersburg, Virginia 23803

W. F. Lankford#

George Mason University, Fairfax, Virginia 22030

J. J. Reilly

Brookhaven National Laboratory, Upton, New York 11973

E. F. W. Seymour/

University of Warwick, Coventry, England CV4 7AL

Current address: c/o TRIUMF, 4004 Wesbrook Mall, Vancouver,

B. C., Canada V6T 2 A3 .

s

Current address: Institut fur Mittelenergiephysik, ETH

Zurich, c/o SIN, CH-5234 Villigen, Switzerland.

Current address: Autonomous University of Nicaragua,

Managua, Nicaragua.

Motional narrowing of the transverse-field muon spin rotation signal has been observed in -y-TiHx for x=1.83, 1.97, and

1.99. An analysis of the data for TiHi.gg near room temperature

indicates that the mechanism responsible for the motion of the

muon out of the octahedral site is thermally activated diffusion

with an attempt freguency comparable to the optical vibrations

of the lattice. Monte Carlo calculations to simulate the effect

of muon and proton motion upon the muon field-correlation time

have been used to interpret the motional narrowing in TiHli97

near 500 K. The interpretation is dependent upon whether Bloembergen, Purcell, and Pound (BPP) theory or an independent spin-
pair relaxation model is used to obtain the vacancy jump rate

from proton NMR T]_ measurements. Use of BPP theory shows that the

field-correlation time can be obtained if the rate of motion of

the muon with respect to the rate of motion for the protons is

decreased. An independent spin-pair relaxation model indicates

that the field-correlation time can be obtained if the rate of

motion for the nearest-neighbor protons is decreased.
I. Introduction

This paper presents an interpretation of the motional narrowing of the ^SR signal in TiHx near room temperature for x =

1.99 and near 500 K for x = 1.83. We report further analysis of

the data of Kossler et al.1.

The high mobility of the hydrogen nuclei in metals has attracted the attention of scientists for over 100 years.2 During

the past 35 years, the technique of NMR has been used to determine the rate at which these hydrogen nuclei diffuse through

metals and the mechanism responsible for this motion.

 3 To accompany this, theorists have developed models for diffusion of light

interstitials4. The development of these models has not only been

s

helpful in the study of diffusion of hydrogen nuclei, but also

other light particles such as the muon, which is often considered

a light isotope of hydrogen (m^ « mp/9) due to similarities in

charge and spin.

Fukai et al.5 studied the isotopes of hydrogen in a-NbHxDy.

They found that the diffusion coefficient of protons decreased

and that the proton activation energy approaches that of deuterons as more protons are replaced by deuterons. The muon extends

markedly the range of masses studied. Up to now, the muon spin

rotation (^SR) technique has been used to study ZrHx

6

, VHX

6

,

NbHx

7, NbDx7

, PdHx

8

, TiHx1, and YHX

9

. The results of experiments

on FCC dihydride compounds (TiHx, YHX, and ZrHx) exhibit the

following characteristics: partial occupation of interstitial

(octahedral) sites by the muon at low temperatures, escape from

these sites and transfer to vacant substitutional (tetrahedral)
sites in the hydrogen sublattice as the temperature increases,

and motional narrowing of the pSR frequency spectrum at higher

temperatures due to motion of the protons, muons, or both. The

results of studies on the other hydride compounds indicate that

the muon.occupies the vacant substitutional sites of the hydrogen

sublattice upon entering the sample and that motional narrowing

occurs as the temperature is increased, but it should be mentioned that the vacancy concentration in the hydrogen sublattice

of these compounds was of the order of 30% or higher. Although

there exist differences between the pSR studies of the various

hydrogen-alloy systems, all of the compounds (except VHQ.SOS)

display an activation energy (as determined from the field-correlation time at the site of the muon) lower than that measured

for the proton with NMR (Fig. 1). This is indeed surprising since

one naively expects the motion of the muon to be'impeded by that

of the proton and that the measured activation would be equal to

that of the proton.

In section 2 we present our analysis of the data1 which

fields a mean time of stay for a muon at an 0 site. In section

0

3, we develop and show the results of some Monte Carlo calculations of the field-correlation time for a muon at a substitutional site as a function of vacancy hopping rate. The results of

these Monte Carlo simulations are compared to the TiH]_.g7 data (T

~ 500 K) of Kossler et al.1.
II. Activation of Muons Out of Octahedral Sites

The results of Kossler et al.1 for ^SR studies of TiHx are

shown in Fig. 2. They find that the muon depolarization rate, A,

(

G

x(t)

=exP(~A2<t2) in TIH

X

 for T < 200 K can be parameterized by

A

2

 = A§(1-P) + PA$ (1)

where AO and AJ are the depolarization rates for a muon in octahedral and tetrahedral sites, respectively, P is the probability of occupying a T site, and

P = 8(1 - x/2). (2)

where x is the H/Ti ratio. The term inside the parenthesis is

equal to the fractional vacancy concentration in "the hydrogen

sublattice and the factor of eight arises from assuming that the

muon initially stops in an 0 site and jumps to one of eight

nearest-neighbor T sites if vacant. The probability of a muon to

occupy an 0 site is 1-P, and thus these probabilities are 0.96,

0.88, 0.32 for x=1.99, 1.97, and 1.83, respectively. In order to

understand the mechanism responsible for activation of the muon

out of an octahedral site, let us turn our attention to the

study of the TiHlt99 results since this system has the largest

probability for a muon to occupy an 0 site.

The dip in the depolarization rate for TiH^.gg near room

temperature is similar to that seen in niobium where the depression in A was due to muons activating out of relatively more
abundant shallow traps, and then finding deeper traps of lower

concentration.10 In niobium, the muons in the two traps have the

same depolarization rate; whereas in TiH^.gg, the muons in the

abundant and shallow 0-site traps have a larger depolarization

rate than those in the sparser and deep T site traps, yielding an

asymmetric dip in the depolarization rate.

The data for those temperature points (330 < T < 370 K) in

the dip of the depolarization rate (Fig. 2) have been refit using

a form (Abragamian) for the relaxation function which is better

suited to motional narrowing than the Gaussian form.

Gx(t) = exp[-A2rc{eXp(-t/rc) -1 + t/rc) ] (3)

where A2 is the second moment of the field distribution and TC is

the field-correlation time. Any relaxation function (including

the one above.) can be represented as: Gx(t) = exp[-7(t)], which

allows the definition of an average muon spin decay rate, d^/dt.

When this rate is statistically weighted according to an exponential radioactive decay, we can define a dimensionless depolarization parameter:

a —

\J

exp(-t/O (d7/dt) dt, (4)

where r^ is equal to the mean muon lifetime, 2.2 ^s. For the

relaxation function listed in Eqn. 3,

a = A2r

2

rc/(rc + rj . (5).
'« of Eqn. 4 can be naturally related to many theoretical

descriptions of depolarization. We have found that a is not

strongly dependent on the form chosen for ?(t), and have used

7(t) from Eqn.3 for the purposes of obtaining a through Eqn. 5.

We used a to obtain the mean time of- stay at a particular site.

For jjSR studies of Al(Cu), Kossler et al.11 invoked a

motional-narrowing theory for -y(t) to explain the diffusion and

trapping of muons in terms of correlation functions:

pt p*

•y(t) = Si A|\ dt1 \ dt" Fi(t") Gi(t'-t"). (6)

VQ- JQ

where A|, Fi(t) and Gi(t) are the second moment, probability of

occupation and the autocorrelation function for a given site of

type i, respectively. The summation extends over all interstitial

site types, which for titanium hydride are the O'and T sites. To

define our model we proceed as follows:

i) We assume that the muon initially stops randomly in

octahedral sites and then proceeds immediately to a

near neighbor tetrahedral site if one is vacant, so

that the initial probability of occupying an octahedral

site is equal to the probability that it would have no

near neighbor vacant: (l-8c), where c is the vacancy

concentration.
ii) Since the results reported by Kossler et al.1 indicate

that the muon does not activate out of a T site at room

temperature, then

G2(t) = 1. (7)

The autocorrelation function for an 0 site (the shallow

trap) is

= exp(-t/r) (8)

where T is a mean time of stay at an 0 site.

iii) The transition rate r for a muon to migrate from 0

sites to a T site is SC/T, and there is no back migra

tion to 0 sites. Thus F0(t) = 8ce~rt and FT(t) = (1 -

8ce~rt) .

Using these assumptions, we can solve for the mean time of stay

of the muon at an octahedral site as a function of a by substituting Eqn. 6 into Eqn. 4

r- = 8CrM[-0.5{l + 8C + (l

± [0.25{(1 - 8G)a/(a - A§r2)}2 +

(1 - 8c)8CAfr2/(a - A^r2.) } ] V2 ] "1 (9)

and using the experimental a calculated from Eqn. 5. The ± arises

because the same a will occur for either slow 0 - O hops and weak

migration to T sites, or for more rapid hops and greater migration.
We have used the fact that a(T) is single valued at its

experimental minimum and theoretically when the ± bracket is zero

to determine the effective vacancy concentration, c. Upon substituting in 0.059(3) Ais'1, 0.127(3) ps'1

, 0.185(3) A*S and 2.2 MS

for A2,, Af, a and r , we find c to be 0.015(6) which corresponds

to x=1.97(l) and agrees with the known concentration of 1.99(2).

Using the calculated value for the effective vacancy concentration,' we calculated rs(T) and show it in Fig. 3. The line

is a least squares fit to an Arrhenius form,

r = r06Xp(Ea/kT) (10)

where ro = io~13(

1

) s and Ea = 0.48(8) eV. The activation energy

is a measure of the amount of energy necessary for the muon to

activate out of an octahedral site and diffuse between O sites.

The optical vibration frequency i/p for protons in the tetrahedral

sites of TiH2 is 3.3 x 10-1-

3 s~^. ^2 The muon's oscillation frequency in the octahedral sites should be close to this value. The

vibration frequencies for the titanium atoms are about an order

of magnitude slower. An attempt frequency for hopping should be

multiplied by a factor representing the number of paths available

for hopping, a number of order 6. We can therefore only conclude that the mechanism responsible for the activation of the

muon out of the octahedral site is associated with the vibrations

of the muon or hydride lattice atoms.
III. Monte Carlo Simulations

The disagreement between activation energies measured by

and NMR has persisted for almost ten years with the one exception

being the study of VH0.503-6 Richter et al.7 proposed that the

motion of the muon was limited by the availability of vacancies"

near the muon in NbHx and NbDx and that the field-correlation

time, rc, was a measure of the length of time for the field to

change due to the motion of the muon in the dipolar fields

generated by the niobium nuclei. The motion of the protons in

this system primarily has the effect of providing vacancies near

the site of the muon and will not contribute significantly to the

field correlation for the muon in this system. However, this is

not true for the /*SR studies of ZrHx

6

, PdHx

8

, TiHx1, and YHX

9

since the dominant contribution to the dipolar field at the site

of the muon is the sublattice of protons. This means that the

motion of the protons changes the field at the site of the muon.

In other words, the motion of the protons alone will produce a

finite field-correlation time for a stationary muon. Since the

muon is much lighter, and should be able to jump at a higher rate

than a proton, the motion of the muon should be impeded by the

motion of the hydrogen nuclei yielding an activation energy for

the muon field-correlation time of the same order as that for

protons. However, since the activation energies and prefactors

were different for proton- and muon-field-correlation times,1 we

implemented Monte Carlo simulations to describe the effects of

motion of the muon and the protons upon the muon field-correlation time.
Since the path for motion of vacancies (hydrogen atoms) in

TiHx is known to be between nearest-neighbor T sites (as determined by NMR),1-

3 we developed a model with four adjustable parameters: p, p», Pin, and pout/

 to describe the field-correlation

time for the muon with the restriction that the motion of the

muon be limited to nearest-neighbor jumping. The motion of the

vacancies in the unperturbed lattice, i.e. not near a muon,

occurs with some rate p. When the vacancy is next to the muon,

the rate for the muon to move or the rate for the vacancy to move

to the site of the muon is p1. This allows the muon jump rate to

differ from the proton jump rate. Two other rates, pj_n and pOut»

have been added to account for the attraction or repulsion of

vacancies due to the presence of the muon. These reflect a change

in vacancy jump rate as the vacancy approaches the muon. Pin is

the rate at which a second-nearest-neighbor vacancy to the muon

will become a nearest neighbor. pout is the rate at which a

nearest-neighbor vacancy to the muon will become a second-nearest

neighbor.

The 9x9x 9 lattice used for the simulations had periodic

boundary conditions which allowed particles to diffuse from one

edge to the opposite edge. Initially, the muon was placed at the

center of the lattice with seven (= 1%) vacancies randomly distributed. The direction of the external magnetic field was picked

randomly with respect to the coordinate system of the lattice.

The spins on the remaining lattice locations (excluding the

positions of the vacancies) were randomly given orientations

parallel or antiparallel to the field. After this was done, the
dipolar magnetic field due to the protons in the lattice at the

site of the muon was calculated. Having done this, the vacancies

were allowed to move. After each time step, the dipolar magnetic

field at the site of the muon was computed. The total number of

time steps was usually 3000-4000, which was large enough to

determine the field-correlation time at the site of the muon.

Each simulation produced the dot product of the dipolar magnetic

field as a function of time with a unit vector in the direction

A

of the external field

B(t) = §di(t) • Bext (11)

The results of each simulation were then multiplied by the

dot product of the dipolar magnetic field at time t=0 dotted with

a unit vector in the direction of the external magnetic field

A A

(B(0) ^B^ipfO) « Bext) • <B(t)B(0)> , which is used to calculate

G(t) , was obtained by averaging B(t)B(0) over all simulations

with the same values for the four parameters: p, p1, Pin, and

Poutf

G(t) = expC-72 (t-t')<B(t')B(0)>dt'] ' (12)

y

A field-correlation time, rc, is defined such that

<B(rc)B(0)>/<B(0)B(0)> = 1/e.

In order to make the results independent of p, rc was multiplied by p. The results of the simulations are shown in Table I.

The statistical error in these results is estimated to be of the

order of five percent or less.
IV. High Temperature Motional Narrowing of the /iSR Signal

The results of the Monte Carlo simulations were given in

terms of a prc product where p is the vacancy jump rate in an

unperturbed lattice and rc is the field-correlation time. In

order to compare the data to the results of the simulations, we

must multiply the muon field-correlation time by the vacancy jump

rate.

The vacancy jump rate can be determined from the proton NMR

data on 7-TiHx of Korn and Zamir12 and of Bustard et al.13 Korn

and Zamir^-2, using Bloembergen, Purcell and Pound (BPP) theory,

found that the proton field-correlation time is:

'C = (r0)/((2-X)/2)exp[Ea/kT] S. (13)

Where r0 = 2.8(5) * 10"14, and Ea = 0. 507 (10) eV. -

For proton-proton dipolar interactions, the mean dwell time at a

site, Tr (also known as the autocorrelation time) is approximately equal to 2rc. Since 4prc (where c is the vacancy concentration

which is equal to (2-x)/2 ) is of the order of 1 for an SCC lattice, then

P = (SrQ^expC-Ea/kT] s'i. (14)

Bustard et al.13 state that BPP theory may not yield the correct

values for the field-correlation time, because it is not dependent upon the type of lattice and does not provide for correlation effects between diffusing atoms. Instead of using BPP
theory, they used an independent spin-pair relaxation model to

interpret their spin-lattice relaxation times, T]_. Their Monte

Carlo model monitored the time evolution of a large number of

spin pairs. Using the results of their simulations, they determined the mean dwell time for a proton at a site, r, from their

T! data and also from the T^ data of Korn and Zamir12 and found

r = (9.3(6) * 10~15)/(l/2(2-x))exp[0.555(7)eV/kT] s (15)

This yields a vacancy jump rate of

p= (2.7(2) * 1013)exp[-0.555(7)eV/kT] s"1. (16)

Multiplying the vacancy jump rates obtained from both references

by the muon field-correlation times for TiH1>97,-we obtain the

prc product values shown in Table II. The proton hopping rates

obtained by the later and more sophisticated work of Bustard et

al.13 are roughly half those of Korn and Zamir14.

The prc products obtained using either set of proton hopping

rates are only constant below 500 K and rise to about twice their

lower temperature values by 563 K. Naively, one would expect the

vacancy hopping rates near the muon to be about equal to the rate

further away: pout "Pin

 = P; anc* the muon to hop to a nearest

neighbor vacancy at least as fast as a proton: p1 > p. We see

from a comparison of the tables this does not work for T > 500K

for either set of proton hopping rates^and for those of Bustard

et al. (Table II, column 2) at any temperature. An increase of
prc, but with p1 > p can be achieved by a reduction of the rate

at which a vacancy hops to a nearest neighbor site, simulation 8

or 10, p^n = p/10, otherwise one must also reduce p1, simulation

7. A very dramatic increase in the rate of vacancy hopping away

from a nearest neighbor site can increase prc moderately, simulation 5. However, if the results of Bustard et al. are used, we

see that reducing the muon's motion alone (p1 = 0, simulation 7)

is not sufficient and the approach of a vacancy must be

restricted, pj_n < p, see simulations 7-12. The treatment by

Bustard et al. was developed specifically for motion of the

hydrogen nuclear spins on an SC lattice and would appear to be

better suited for extraction of a proton autocorrelation time

from T]_ data compared to BPP theory. However, using an independent spin-pair relaxation model to obtain the vacancy jump rate

requires that the muon affect the motion of the nearest-neighbor

protons.

A vacancy to muon-site hopping rate less than that for a

proton implies the involvement of some other mechanism. This may

also be related to the requirement that pj_n be reduced relative

to p. If the nearest-neighbor hydrogens are bound to the muon by

an excess of 0.1 eV this would reduce Pin sufficiently and possibly force muon hopping to next-nearest-neighbor sites, which

are further apart and would hence reduce the prefactor by an

order of magnitude.
V. Conclusions

We have reanalyzed the TiH1<99 data taken near room temperature by Kossler et al.1

 and have shown that they can be fit to a

model with many shallow traps and a low concentration of deeper

traps for the muon. We find that the mechanism responsible for

the activation of the muon out of the shallow trap (O site) is

associated with the vibration of the -hydrogen sublattice. Secondly/ a method of simulating the effect of the motion of protons

and the muon on the field-correlation time is presented and

applied to the motional narrowing of the /*SR signal in TiH1<97

for temperatures near 500 K. The conclusions from the comparison

of the PTC obtained from the data and from the simulations are

dependent on the method of analysis to obtain an autocorrelation

time for the proton from proton NMR data for 7-TiHx. Using the

results of Korn and Zamir12, we find that the motion of the muon

decreases with respect to the motion of the proton as the temperature increases. Using the results of Bustard et al.13

, we find

that a stationary muon does not explain the results of Kossler et

al.1 and that the presence of the muon inhibits the motion of the

nearest-neighbor protons. It would seem that the method used by

Bustard et al.13 is better suited for analysis of proton T^ data

for -y-TiHx, but the model needed to describe the results of /iSR

experiments is more complicated than the model developed using

BPP theory employed by Korn and Zamir12 to derive the vacancy

jump rate. We believe that the conclusions reached for TiH^^gj

are also valid for TiHi.33, since the proton and muon correlation

times scale inversely with the vacancy concentration. We -also
believe that these conclusions are valid for other FCC metal

hydrides, i.e., ZrHx and Y.HX.

Acknowledgements

The present work is supported by the National Science Foundation under-Grant No. DMR-8503223, by NASA under Grant NAG-1-

416, and by the Division of Materials Science of the U. S.

Department of Energy under Contract No. AC02CH00016.
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A. J. Van der Wai, J. H. Brewer, F. Stucki and L. Schlapbach, Hyp. Int. 17-19. 267 (1984).

9. W. J. Kossler, H. E. Schone, J. R. Kempton, B. Hitti, C. E.

Stronach, G. A. Styles and E. F. W. Seymour, J. Less-Common

Met. 129. 327 (1987).

10. C. Boekema, R. H. Heffner, R. L. Hutson, M. Leon, M. Schillaci, W. J. Kossler, M. Numan and S. A. Dodds, Phys. Rev. B

26., 2341 (1982) .

11. W. J. Kossler, A. T. Fiory, W. F. Lankford, J. Lindemuth, K.

G. Lynn, S. Mahajan, R. P. Minnich, K. G. Petzinger and C.

E. Stronach, Phys. Rev. Let. 11, 1558 (1978).

12. C. Korn and D. Zamir, J. Phys. Chem. Solids 31. 489 (1970).

13. L. D. Bustard, R. M. Cotts, and E. F. W. Seymour, Z. Phys.

Chem. 115. 247 (1979).

14. K. G. Petzinger, Phys. Rev. B 26., 6530(1982).
TABLE I PTC products from Monte Carlo simulations, p is the

vacancy hopping rate far from the muon, p1 is the rate at which

the muon moves to a nearest-neighbor vacancy, Pin is the vacancy

rate for next-nearest-neighbor to nearest-neighbor jumps, Pout ^

the rate for the converse process of Pin, and rc is the field

correlation time for the muon.

Simulation^

01

02

03

04

05

06

07

08

09

10

11

12

Probabilities

P'^Pout^P/ Pin=1°P

Pin=Pout=P' P'-lOp

P'=Pin=P' Pout=P/l°°

P

l=Pin=:Pout=P

P'=Pin=P' Pout=l°P

Pin^Pout3?' P'=P/100

Pin=Pout=P» Pl=0

Pout=P/ Pin=P/l°' P'=10p

Pin=P' Pout=P/l°°/ P'=°

Pout=P'=P' Pin~P/l°

Pout=Pl=P' Pin'P/l00

Pout=P/ Pin=P/l°°/ P'°0

PJLC

6

12

13

23

32

49

52

61

61

98

450

452
TABLE II. prc products for TiH1>97 data.

•rm

432

458

477

493

508

523

543

563

583

rc(us)

4.3(7)

- 2.1(3)

1.3(2)

0.9(1)

0.8(1)

0.8(1)

0.49(9)

0.35(7)

0.04(6)

DfK&Z)rc

24(9)

25(9)

26(9)

26(9)

34(11)

45(14)

43(15)

45(16)

7(11)

DfBlr

39(10)

44(11)

49(11)

50(11)

68(15)

93(20)

93(22)

101(26)

16(26)

K&Z indicates that the vacancy hopping rate has been taken from

Korn and Zamir12.

B indicates that the rate is from Bustard et al.13.
10.0 _-

en

ha

o.i

ctf

»—»

o

oO.Ol p.

0.001

1.5

Y //

V/

xX=1.83

aX=1.97

X=1.80

-— X=1.90

-I

2.0 2.5 3.0

1000/T(K)
i __________ i 0.0

________ ...j

0 100 200 300 400 500 600

Temperature(K)
APPENDIX H
^88-24248

Search for Bound States of the T)—Meson in Light Nuclei

R. E. Chrien, S. Bart, P. Pile, R. Sutter, N. Tsoupas

Brookhaven National Laboratory, Upton, NY 11973

H. 0. Funsten, J. M. Finn, C. Lyndon, V. Punjabi, C. F. Perdrisat /

College of William and i-fary, Wllliamsburg, VA. 23185

B. J. Lieb

George Mason University, Fairfax, VA 22030

T. Kishimoto*

University of Houston, Houston, TX 77004

L. C. Liu, R. Estep, B. Dropesky

Los Alamos National Laboratory, Los Alamos, NM 87545

C. E. Stronach

Virginia State University, Petersburg, VA 73803

R. L. Stearns

Vassar College, Poughkeepsie, NY 12601

Abstract

A search for nuclear-bound states of the TI meson has been carried out. Targets

of lithium, carbon, oxygen, and aluminum were placed in a TI+ beam at 800 MeV./c.

A predicted.-n bound state in 0* (Ex ~ 540 MeV) with a width of «9 MeV was

not observed. A bound state of a size 1/3 of the predicted cross section would

have been seen in this experiment at a confidence level of 3cr (P>0.9987).

*N'ow at Osaka University, Japan
ORIGINAL; PAGE is

OF POOR QUALITY

This paper describes a search for a novel nuclear excitation involving the

creation of a bound n-meson in the nuclear medium. The concept is similar in

spirit to a number of ideas which have been recently vigorously pursued. Some

familiar examples are A hypernuclear states, /!-hypernucl.ear states, antiprotonic

nuclear states, and various diharyon resonances. In each case an attractive

particle-nucleus potential is required and some mechanism to inhibit the decay

process, such as strangeness conservation in the case of the A.

Several suggestions of the existence of bound states of the r\—meson in a

wide range of nuclei have recently been published ~ . The suggestions of this

novel nuclear excitation are based on bound state formation through the attractive N—r\ channel of the N (1535) , where N (.1535) is the (TIN) resonance with

(I.J11) = (1/2,1/2") and mass 1535 MeV/c2. This resonance dominates n protiuc-

£,

tion near threshold. Bhalerao and Liu have shown, by a coupled-channel analysis, that the low-energy nN interaction is attractive with a scattering length

of (0.28+0.2021) fermi. The attractive interaction Is a consequence of the

threshold being below the "N(1535) resonance.

Liu and his collaborators have examined the consequences of this attractive

interaction in the formation of a bound-n state as a function of mass number.

Their study indicates that nuclear bound states could exist for mass numbers

larger than A~10. At low mass numbers, only s-state bound r)'s are predicted.

i

At Larger mass numbers, p- and d-states could become bound. Both binding

energies and widths increase with A. The optimum case, in their analysis, is

r

i j O, formed from the (^+

,p) reaction on 0 at a momentum near 740 MeV/c."

At an angle near 15°, the momentum transfer is favorable for the transition

involving the conversion of p-shelL neutron to an s-shell r\. For higher mass

numbers, the increase in predicted width would make this excitation more

difficult to see over the continuum (n4",p) background which is present.
An experiment to test these predictions was devised with the positive plon

beam available at the Low-Energy Separated Beam I at the Brookhuven M-ternating

Gradient Synchrotron (AGS), and the_Moby Dick Spectrometer. The experimental

arrangement is virtually identical with that used for the product ton and

measurement of. hypernuclei, and it has been described in detail in a number of

publications (see Ref. 5 and related references). The only differences involve

the selection of pions, rather than kaons, in the incident particle channel, and

protons in the exiting particle channel.

The spectrometer was set at 15° to be near the maximum for bound eta production as predicted in the analysis of Liu and Haider >'J . For example,

reference 3 predicts the production of an r\ excitation of width of 9 MeV (F*WHM)

and a peak cross section of about 30 ub/sr-MeV, for an incident pion momentum of

300 MeV/c on an 0 target. The peak would appear near zero binding energy in

the ( O+TI) missing mass spectrum corresponding to the emission of protons with

248 MeV kinetic energy in the lab frame, and an excitation of 540 MeV in the 0

system.

Four targets were selected for examination; the target parameters are

listed in Table I. The oxygen target was in the form of water. For lithium, no

n-bound states are predicted, while for carbon, the binding is predicted to be

marginal. Oxygen is expected to display th<> largest bound state cross section;

for larger A the cross sections are. smaller, while the. widths gr-.jw larger.

To confirm a cross section scale and to measure a spectrometer momentum

acceptance function, the reaction pCr"1", p)TM"1" --as measured for a ^ momentum of

PAGE IS

POOR QUALITY
525 MeV/c. This reaction has heen measured hy Che Leningrad group of Cordeev ct

al. , and their reported cross sections were in reasonable agreement (-20%) with

our measurements. To establish the acceptance. Function, the nominal momentum

setting of. the proton spectrometer was varied Prom fi20 to 780 MeV/c, anH the

strength of the observed it+ missing mass peak was used to determine the

acceptance. It was desirable to limit the spectrometer acceptance correction to

no more than 30% of the central value over the entire spectrum. With this

criterion, an acceptance range of ~80 MeV/c was obtainable; i.e., the relative

acceptance is .everywhere larger than 0.7 throughout the range. To obtain a

sufficiently broad range in outgoing proton momenta, overlapping runs were taken

for spectrometer central values of 657, 700, and 740 MeV/c.

The spectrometer resolution was measured by analyzing (p,p') events* for

C, recorded simultaneously with the (n:+,p) events. The missing mass resolution was studied in two separate ways: by using TRANSPORT matrix elements to

Q

calculate the particle momenta, and also by using the program RAYTRACE , which

includes, magnetic corrections to all orders. The spectrometer resolution was

measured to be 4 MeV (FWH.M) using the TRANSPORT analysis and 2.5 MeV (FWHM)

using RAYTRACE. For either mode of analysis, the resolution is sufficient to

detect the predicted ri-gtates without serious resolution broadening of the peak.

These (n,p') studies also serve to confirm the energy scale and the energy

losses in the target and beam windows of the experiment.

The results of the experiment on the 4 targets are shown in the composite

diagram of Fig. I. The inclusive proton spectra of this experiment show a

qualitative similarity to recent (p,p) reaction studies on various nuclei by

Garreta et al. We know of no comparable (~ ,p) data at these pion energies.

The data for each target show a smooth (TU' ,p) cross section down to an energy

corresponding to the ri production threshold.. At lower energies, the cross

ORIGINAL PAGE IS.

OF POOR
ORIGINAL PAGE IS

OF POOR QUALITY

525 MeV/c. This reaction lias been measured hy the Leningrad group of Cordeev et

al. , and their reported cross sections were in reasonable agreement (=20%) with

our measurements. To establish the acceptance function, the nomina.l momentum

setting of the proton spectrometer was varied from fi20 to 780 MeV/c, and the

strength of the observed rc+ missing mass peak was used to determine the

acceptance. It was desirable to limit the spectrometer acceptance correction to

no more than 30% of the central value over the entire spectrum. With this

criterion, an acceptance range of ~80 MeV/c was obtainable; i.e., the relative

acceptance is everywhere larger than 0.7 throughout the range. To obtain a

sufficiently broad range in outgoing proton nomenta, overlapping runs were taken

for spectrometer central values of 657, 700, and 740 MeV/c.

The spectrometer resolution was measured by analyzing (p,p') events* for

C, recorded simultaneously with the (ii+,p) events. The missing mass resolution was studied in two separate ways: by using TRANSPORT matrix elements to

Q

calculate the particle momenta, and also by using the program RAYTRACE , which

includes magnetic corrections to all orders. The spectrometer resolution was

measured to be 4 MeV (FWHM) using the TRANSPORT analysis and 2. "5 MeV (FWHM)

using RAYTRACE. For either mode of analysis, the resolution is sufficient to

detect the predicted ri-states without serious resolution broadening of the peak.

These (p,p') studies also serve to confirm the energy scale and the energv

losses in the target and beam windows of the exoeriment.

The results of the experiment on the u targets are shown in the composite

diagram of Fig. I. The inclusive proton snectra of this experiment show a

qualitative similarity to recent (p,p) reaction studies on various nuclei by

A ' ,

Garreta et al. We know of no comparable (- ,p) data at these pion energies.

The data for each target show a smooth (-ti"l",p) cross section down to an energy

corresponding to the r\ production threshold. At lower energies, the cross
PAGE IS

OE POOR QUALITY

section appears to Increase, and It is plausible to attribute this'increase to

the quasi-free n production process. For the aluminum, oxygen, and possibly

carbon cases an eta peak would, he expected to appear near the position of the

arrow.

The sensitivity of this experiment to narrow r\ bound-state peaks is

obviously compromised by the large proton continuum background observed in this

experiment. This background is presumably attributable to nuclear protons

ejected by the incident pions through various processes, including quasi-free

knockout, multiple pion and proton scattering, and pion absorption. To establish the experimental sensitivity quantitatively, a statistical analysis was

carried out in detail. The analysis was made on data that were not corrected

for momentum acceptance, since the correction process increased the spread of

the data points significantly. Fluctuations about a polynomial fit to the

uncorrected data were analyzed with a standard least squares fitting code.

The quantitative statement of the experimental sensitivity, based on the

largest observed fluctuation in the data,, is the following: the detection of a

peak with a full-width at half maximum of 9 Me'v' in the 0 data occurs at a

confidence level of 3o (0,9987) for a peak height of 8.7 ub/sr/MeV. This size

is about one-third of the prediction of Ref. 3. The "o target was predicted in

Ref. 3 to be the most favorable case, i.e., the one displaying the largest cross

section. Similar sensitivities obtain for the Lithium and 'carbon cases, while

for aluminum the size of the fluctuations, due to a poorer statistical accuracy,

preclude any strong statements.

It is interesting to remark on the similarities of the spectra shown in

Fig. 1 with the spectra obtained in the experiment of Garreta —both of which

experiments were designed to search for narrow states located near the. onset of

a quasi-free process. In the latter the search is for p states, while in our
ORIGINAL PAGE IS

OF POOn QUMJTY

work, we are searching for a structure due to bourul r\ states.

The (p,p) process is thought to proceed via the annihilation of. the p with

a target nucleon to produce, on average, 5 pions whicli subsequently interact

with the A-l target nucleons and eject protons. Thus the suhsequent stages of

the process are similar to the (i:"l~,p) reaction. Reference 9 documents the fact

that over a very wide range of proton momenta, the cross section has a

Maxwellian shape:

d

2a/dQdE = C(E)1/2exp{-E/TJ

where E represents proton kinetic energy.

We adopted the same parameterization to characterize the (ii+,p) data. > For

the fitting procedure, it was necessary to exclude the r\ quasi-free region;

hence only data outside the allowed kinematical range of r| production was used.

The resulting fits were then extrapolated into the r\ quasi-free region, these

fits are indicated in Fig. I. We believe that the obvious excess which occurs

near the onset of the n threshold is attributed to o quasi-free processes.

Art expanded region near the n threshold is shown in Fig. 2 for the oxygen

target. ' To indicate the various reaction mechanisms more explicitly, three

curves are shown: Che dashed curve is the Maxwellian fit to the (7i+,p) inclusive process, the solid curve shows an estimate of the auasi-free r\ production

added to the Maxwellian, and the dotted curve shows the p-shell bound eta state

predicted by Liu and Haider »' . It should be clear from the figure that a

peak of the predicted size would be visible in the experiment; it is not seen.

The size of the quasi-free production observed in the °0 data is roughly

in line with the observations of Peng and collaborators at a somewhat lower

beam momentum of 680 MeV/c. An estimate of the magnitude of the expected
ORIGINAL PAGE IS

QB EOOR QUALITY.

quasi-free eta produce ton was based on the elementary cross sections of

Litchfield et al. and of Brown et al. " (the Latter for the charge con j u\;ati>

(TI~ ,n) reaction). The. shape of the onset of the quasi-free process near

threshold was taken from Ref. 3, anil that result was arbitrarily normalized to

our data as shown in Fig. 1. From this normalization, a result for the

effective number of. scatterers, defined as,

., dcr(nnclear)

N

eff =

d(T (elementary)

can be obtained. The preliminary estimate of the quasi-free cross section,

derived from the fit of Fig. 2 and integrated over the spectrum shape presented

by Ref. 3 leads to a value da/dQ (qf) = 150. |ib as compared to a value 191 |ib

derived from Ref. 11. We estimate therefore that Ne pc is of the order of

unity (=0.8). This is quite comparable to the value characteristic of hypermiclear cross sections and an order of magnitude higher than Neff deduced from

(p,p) nuclear interactions.

In summary, the search for a narrow ^-nuclear bound state has produced

negative results. A peak, one-third the size predicted would have been seen in

oxygen at a confidence level of Vj. The conclusion is either that widths for

such excitations are rnucli larger than predicted, or that the production cross

sections are much smaller than predicted, or both.

The authors express their appreciation to the ACS technical staff and to

the RNI, Medium Energy Group support staff consisting: of F.. Meier, A. Minn, and.

J. Rutherford. This research has been performed under the following grants:

r>E-AC02-76CH00016 (USOOE), nE-AS05-76FRO (IJSDOE), PHY-RSO^RSO-OS (N'SF), and

NAG-1-416 (NASA).
ORIGINAL PAGE IS

References OF POOR QUALITY

1. Q. Haider and L. C. Liu, Phys. Lett. 172B. 7.57 ( L986) ; 174B, 465 (E)

(1986).

2. G. L. Li, W. K. Cheng, T. T. S. Kuo , Phys. Lett. 195R. 515 (1987).

3. L. C. Lin and Q. Haider, Phys. Rev. C34 , 1845 (1986).

4. R. S. Bhalerao and L. C. Liu, Phys. Rev. Lett. 54, 865 (1985).

5. E. C. Milner et al., Phys. Rev. Lett. 54, 1237 (1980).

6. V. A. Gordeev et al., Nucl. Phys. A364, 408 (L981).

7. Karl Brown et al., CERN Report 80-04 (1980).

•»

8. S. Kowalski and H. Enge, Proceedings of the International Conference on

Magnet Technology, Hamburg, 366 (1970), unpublished), and H. Enge (private

communication).

9. D. Garreta et al., Phys. Lett. 150B, 95 (1985); D. Garreta et al., Nucl.

Phys. A470, 445 (1987).

10. J. C. Peng in "Hadronic Probes and N'uclear Interactions", AIP Conf. Proc.

133m 255 (1985).

11. P. J. Litchfield, Phys. Re". 183. 1152 (1969).

12. R. M. Brown et al., N'ucl. Phys. HI53, 89 (1979).
Figure Captions ORIGINAL PAGE IS

OE POOR QUALITY

1. The proton kinetic e.ner/;y spectra obtained for Liu: r.arjjets Jtxami.nod i.n this

experiment at 800 MeV/c incident n'1". Tn each r.as«, a Maxwell.i.an Function

was fit to the (TT:+,P) inclusive proton iMir-.r;;;/ above the '-jta [)roduction

threshold. The tirrows indicate that threshold t:or <^ncli target. The error

bar shown indicates the standard deviation for a typical datum no.ar

threshold.

2. The region of the oxygen spectrum in which an n-hound state would appear is

shown in this figure. The dashed curve shows the extrapolated Maxwel,lian

fit to the inclusive (>c,p) background, and the solid curve shows the

quasi-free ^-production added to the (T,D) back-Jround. The dotted durve

indicates a state in which a p|/2 shell neutron has been transformed into

a hound t] , with the s.i^;i, width and bindin>: predicted by ref. '?. The data

are clearly inconsistent with that prediction.
Table I. The target thicknesses and the total dead-t ime-cor rected pion

irradiations for Che spectra obtained in this experiment are indicated.

Dead-Time-Corrected n

Target Thickness (gin/cm" ) Pion Irradiation

Li 2.23 2.92xl01 0

Water 2.15 4.57xl010

Al 2.03 1.66xl010

Polyethylene 2.15 (calibration ) 1.40x10

ORIGINAL

OF POOR

ORIGINAL PAGE IS

OF. POOR QUALITY
>

<D

I

i_

CO

JO

ii

_

CD

LU

-Q

C^

T3

b

CM

ID

150

130

I 10

90

220

180

140

300

260

220tC

t

0

340

300

260

A

220 240 260 280

E (MeV)

300
330.0

.Co

co

iz;

O

C£

O

310.0-

290.0-

270.0 -

EO

C£!

CO

CO

CO

O

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250.0-

230.0

200.0 220.0 240.0 260.0

PROTON KINETIC ENERGY (MEV)

280.0