Anisotropic transferred hyperfine fields acting on 119Sn in gadolinium metal and alloys

Solid State Communications, Vol. 18, pp. 823—825, 1976.

Pergamon Press.

Printed in Great Britain

ANISOTROPIC TRANSFERRED HYPERFINE FIELDS ACTING ON ‘19Sri IN GADOLINIUM METAL AND ALLOYS* A. Balabanov, I. Felner and I. Nowik The Racah Institute of Physics, The Hebrew University, Jerusalem, Isarel (Received 11 August 1975; in revised form 12 October 1975 by W. Low) Mossbauer studies of 0.1% 119Sn in gadolinium alloys at 4.1 K were performed. The spectra were well reproduced by a superposition of hyperfine fields according to the RKKY model with kF = 1.27 ±0.04 A1. In Gd 0 95Tm0~05where the magnetization is along the c-axis, the transferred field per Gd ion is 4 ±1% lower than in Gd0.97Tb0.~where the magnetization is perpendicular to the c axis. 19Sn in WE PRESENT here Mossbauer of dilute in ‘ the Gd metal and alloys from whichstudies the anisotropy transferred field has been established. The analysis of the spectra of ‘19Sn in GdI_XYX confirmed the validity of the RKKY mechanism in the production of transferred fields in 4f metals. The numerical value obtained for kF = 1 .27 A’ is slightly lower than the free electron gas model prediction (1.38 A1), a result which is certainly to be expected considering the band structure of Gd metal.’ Samples of 0.1% “9Sn in Gd metal, Gd 0 97Tb0.03, Gd0~95Tm0.05,Gd0~95Sc0~05 and Gd1XYX (x = 0.15,0.25 and 0.40) were prepared by melting the metals in an induction furnace. Mossbauer studies the 24 keY 119SnThe in these samples (100 of mg/cm2 transition of absorbers) were performed in a vertical geometry where both source (Ba119SnO 3) and absorber were kept at 4.1 K. Some of the spectra obtained are shown in Figs 1 and 2. The well resolved six line patterns observed in these spectra prove that large magnetic hyperfine fields are acting on the U95~nuclei though the Sn ions themselves are diamagnetic. It is believed that the magnetic hyperfine structure observed in a diamagnetic ion in a magnetically ordered metallic system arises from two possible mechanisms. The first is due to local conduction electron polarization by the magnetic ions in the crystal, the second is due to the polarization of the ns closed shells of the diamagnetic ions by either direct overlap or through the conduction electrons. Almost all diamagnetic ions diluted into the magnetic 3d or 4f metals show transferred hyperfine fields. In the 4f metals it is generally accepted that the observed transferred hyperfine fields are mainly generated via the conduction electrons. Within the Rudderman—Kittel—Kasuya—Yosida (RKKY) model of *

indirect exchange in metals’ the spin density of the conduction electrons at a distance R from a magnetic ion with alligned spin S~is given by a closed form formula PRK(R) a (SZ>[(2kFR)

cos (2kFR)

—

sin (2kFR)]/R4.

(1) Since the transferred hyperfine field is proportional to this density and since all magnetic ions contribute to the spin density at a given site, one can express the transferred hyperfine field by a simple lattice sum, which will strongly depend on the value of the Fermi momentum kF. The analysis of the experimental spectra was done by a least square fit assuming that theeach spectra are composed of computer a superposition of subspectra with a hyperfine field given by H({nJ)

=

~

[niS~i

+

(N,

—

n,)SR] A

F(y1)

(2)

where F(y) 4,yis the Rudderman—Kittel function (y cosy sin y)/y 1 = 2kFRI and R. is the distance from the Sn probe to the ith shell surrounding it. n, is the number of Gd ions out of N~ions in the ith shell. SGd = 7/2 and S~is 0, 1 and 3 for Y (or Sc), Tm and Tb, respectively. The relative intensity of such a subspectrum is given within random distribution statistics by a product of binomial expressions:

Supported in part by the United States—Israel Binational Foundation. 823

—

=

(N1) x’~r~i(1 —x)~’~~ \fl.

(3)

Thus in fitting the experimental spectra the theory should require only two adjustable parameters, A and kF. In practice however one cannot consider in an exact manner too many neighbouring shells and thus the actual fitting procedure was performed using:

ANISOTROPIC TRANSFERRED HYPERFINE FIELDS ACTING ON 119Sn

824

Vol. 18, No. 7

1.000 0.999

•

.•

~•:

1.000

~•

•••

0.8

-

1.0 0.6

-

.

—

97Tb03

Ia I—

-

• H~~(x)/H~.~(0) A

I-

0.999 0.4

1 000

-

Tc(x)/Tc(0)

nAM~(x)/AM5(0)

(1-~)

~095Tm005

19Sn hyperfine field, conduction electron 0.2 Gdi_XY,~ 0.c I I I 0.1 0.2 0.3 0.4 0.5 Fig. 3. The ‘ 0

I-, I.-

0.998

Gd

0.996

_____________________________ -3

-2

-1

0

VELOCITY

1

2

contribution to the magnetic moment and Curie point as a function of x in Gd 1.XYX.

3

(cm/sec)

119Sn in gadolinium alloys

Gd 0•75Y0•25 and less than 4% in the GdØ.95R0.05 samples. The best fits obtained the not Gdl_XYX samples yield 1. for It was possible to reproduce kF 1.27 ±0.04 spectra A the =experimental with kF = 1 .38 A1 which is the value of the free electron gas model with three conduction electrons per atom, even when allowing adjust-

Fig. 1. Mossbauer spectra of at 4.1 K. The solid curves were obtained assuming the RKKY model with kF = 1.27 A’.

1.000

The average hyperfine field Hau(X) calculated I~

0.999 0 C-,

directly from the ~9Sn: Gdl_XYX experimental spectra

~

-

•

does not—x), followFig. the3.expected simple formula H(x) = H(0)(1 This observation is consistent with data forshell the contribution mentsimilar of the nearest contribution;of conduction the Curie point tT~(x)J~ as a function ofx, Fig. 3. The electrons to the magnetic moment [z~.M~(x)1 2 and for

,••

—~r:d#•

0.999

1.000

observed similarity of the three quantities Ha~(X), 0.995

M’I~(x),and model, ifJ~

Gdo.isYo.m

-

T~(x)is

well explained within the RKKY

1is assumed to be independent ofx. ln this case all three quantities are proportional to the same I

—3

-2

I

I

-1 0 i VELOCITY (cm/sec)

I

2

3

9Sn in Gdl_XYX at 4.1 K. Fig. 2. Mossbauer spectra of “ The solid curves were obtained 1. assuming the RKKY model with kF = 1.27 A 3

H(n1, n2, n3)

=

~

~

+ (N~— n,)SR]AF(yI)

1=1

+ [(1

—

lattice sum. The spectra of Gd0 97Tb003, Gd095Tm005 and Gd 1. One obtains that were H({N,}) in Gd assuming kF = 1.27 A 0 95Sc005 analyzed 097Tb003, and in pure Gd metal is 328 ±2 kOe whereasGd0~95Sc0~05 in Gd 0~95Tm0~05 it is 315 ±2 kOe. It seems most reasonable that the Gd0 95Tm0~5sample is different from the others (Fig. 1) because in this alloy the magnetization is along the c- 4 axis whereas in the other it is in be thedue basal This anisotropy of 13alloys kOe cannot toplane; dipolar

x)SGd + xSR] ~ N~AF(y

1) (4)

Only thehere. average the morerequired distant shells (i> 3) is considered Thisof procedure the introduction of an additional parameter: the spread in the hyperfine fields due to the fact that only three shells were rigorously considered (even so 243 inequivalent sites were considered). This spread turned out to be about 7% in

fields (—S 5 kOe) and is attributed to anisotropic conduction electron polarization at the Sn probe site. An aniso4 The anisotropy theobserved Gd hyperfine tropic hyperfine field has in been also atfield the isGdof

nucleus. sign to that of Sn, the field is larger along the opposite c-axis.4 However in the case of Gd, in addition to the

transferred field, the hyperfine field also contains a single ion contribution, core polarization and local conduction electron polarization by the Gd ion itself. Ifwe

825 Vol. 18, No. 7 ANISOTROPIC TRANSFERRED HYPERFINE FIELDS ACTING ON 1’9Sn assume that the anisotropy in the transferred field for interpret as being due to anisotropic conduction electron Gd is similar to that for Sn we conclude that the polarization. Our analysis of the 119Sn spectra in Gd observed large anistropy of opposite sign in the Gd total alloys confirms the validity of the RKKY mechanism in hyperfine field is due mainly to the anisotropy in the Gd the formation of transferred fields in 4f metals. The single ion contributions to the hyperfine field, analysis also yields an average value for kF = 1.27 ± To sumarize, we have observed anisotropic trans0.04 K1 in Gd metal. ferred fields acting on dilute Sn in Gd alloys which we

1.

REFERENCES FREEMAN A.J., in Magnetic Properties ofRare Earth Metals, (Edited by ELLIOT R.J.), -Ch. 6. Plenum Press. (1972).

2. 3.

TOHYAMA KOHJI & CHIKAZUMI SOSHIN,J. Phys. Soc. Japan 35,47(1973). CHILD H.R. & CABLE J.W.,J. App!. Phys. 40, 1003 (1966).

4.

BALJMINGER E.R., DIAMANT A., FELNER I., NOWIK I. & OFER S.,Phys. Rev. Lett. 34,962 (1975).