Nuclear Zeeman splitting measured through the Mössbauer effect

Loef, J. J. van 1967

NUCLEAR

Physica 33 Zeeman Centennial Conference, Amsterdam 188-194

ZEEMAN

THROUGH

SPLITTING

THE

MEASURED

MOSSBAUER

EFFECT

b y J. J, VAN L O E F Reactor Instituut Delft, Nederland

Synopsis From the Zeeman hyperfine splitting in 57Fe, the effective magnetic field acting on the nucleus can be derived. It is shown that the M6ssbauer technique is particularly suited to study the sublattice magnetization in rather complicated magnetic systemst An important parameter for the observation of the Zeeman splitting is the product of the nuclear Larmor frequency and the electron-spin correlation time. The apparens collapse of the hyperfine splitting observed in a few cases can be interpreted in term. of very rapid relaxation. The nuclear Z e e m a n splitting arises from the interaction of the nuclear magnetic dipole m o m e n t , p, with the magnetic field, H, due to the a t o m s own electrons. The H a m i l t o n i a n of the interaction is Hm

=

-- p.H----

-- gpnI.H

(1)

a n d the nuclear e n e r g y levels which are o b t a i n e d are Em

---- - - p H m d I

---- - - p g n H r n i

mi=I,I--

1 .....

--I

(2)

with ml the magnetic q u a n t u m n u m b e r , I the nuclear spin q u a n t u m n u m b e r , Pn is the nuclear m a g n e t o n a n d g the g y r o m a g n e t i c ratio (g-factor). According to this equation, there are 2 1 + 1 equally spaced levels; the Z e e m a n splitting between a d j a c e n t levels is g p n H a n d the splitting between the lowest and the highest level is 2 g p n H I . This e q u a t i o n applied to the lowest nuclear states in 57Fe leads to the h y p e r f i n e splitting shown in figure 1. It should be p o i n t e d out t h a t in the M6ssbauer effect m e a s u r e m e n t s g a m m a - r a y transitions are observed between two nuclear levels, which in general b o t h exhibit magnetic h y p e r f i n e splitting. T h e e m i t t e d g a m m a r a y s correspond to a transition from a p a r t i c u l a r magnetic sublevel of an excited nuclear state to a sublevel of the g r o u n d state. T h e selection rule depends on the m u l t i p o l a r i t y of the radiation. T h e 14.4-keV transition in 57Fe is a magnetic dipole radiation, which gives rise to six allowed transitions (Am -----

=o,

1). --

188

--

NUCLEAR

ZEEMAN

SPLITTING

AND MOSSBAUER

TABLE

EFFECT

189

I

P r o p e r t i e s of 57Fe Ground state E n e r g y (keV) Spin and parity M a g n e t i c m o m e n t (nm) Quadrupole moment (barn) M e a n life (see)

0 1/2 --

0.0903 0 stable

First excited state 14.36 3/2

--

-- 0.153 0.29 1.4 >( 10 -7

3+ 1+ 3_2

13-

-/1 1¢t

Fig. 1. Magnetic hyperfine splitting of the ground and first excited state of 57Fe. From the measured magnetic hyperfine splitting, a nuclear parameter, the moment p, and an atomic parameter, the field H, can be derived. As the magnetic moment of the nuclear ground state in general is known from conventional microwave resonance and atomic beam experiments, the M6ssbauer hyperfine spectrum determines the moment of the excited state. In this way, nuclear g factors have been determined of the first excited states in the following nuclei: 57Fe, 61Ni, llgSn, 1291, lSlEu, 161Dy, 166Er, 169Tm and 197Au. The excited state moments, especially those of the rare earth isotopes, have been helpful in our understanding of certain nuclear models 1). The hyperfine splitting also yields the effective magnetic field acting on the nucleus. Though there are a number of mechanisms which can give rise to magnetic fields at the nucleus, the most important contribution comes from the so-called Fermi contact interaction, that is the direct coupling between the nucleus and the s-electrons. Differences in spin-up and spindown s-electron charge densities at the nucleus appear if the atom contains a partially filled magnetic shell, e.g. the 3d shell in the case of iron. The exchange interaction between the spin-up polarized d-shell and the spin-up s-electron is attractive, while that between the d-shell and a spin-down s-electron is repulsive. As a result the radial parts of the two s-electron wave functions will be different, one being pushed toward the nucleus, the other pulled outward. The Fermi contact interaction thus causes a local magnetic

190

j . j . VAN LOEF

field at the nucleus which can be of the order of several hundred kilooersted. This field combined with the nuclear moments gives rise to nuclear Zeeman splitting which in iron at room temperature is 50 times as large as the natural line width of the 14.4-keV gamma-ray transition in 57Fe. In order to observe the nuclear Zeeman splitting through the M6ssbauer effect it is necessary to apply Doppler motion to the source or to the absorber. The gamma-ray intensity through the sample measured as a function of the Doppler velocity yields the M6ssbauer spectrum. Our M6ssbauer apparatus uses a 40 cm long lever which is moved to and fro at constant velocity by a motor-driver cam; the motion is imparted to the 57Co source at a point at adjustable distances from the lever hinge• Thus the source velocity can be adjusted between 0 and I0 mm/s. A hydraulic transmission between lever and source, consisting of two cylinders and pistons connected by a tube filled with oil, dampes out parasitic vibrations. The source mounting is such that M6ssbauer spectra of two different absorbers are obtained in two detectors simultaneously 2). Our absorbers are iron compounds, in most cases as a polycristalline powder about 20 to 30 mg in weight and spread out over an area of 1 t o 2 c m 2. The M6ssbauer spectrum in ferrimagnetic crystals provides detailed information about the environment of the iron nuclei. Apart from the hyperfine DOPPLER VELOCITY (rnrn/sec)

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M6ssbauer absorption spectrum of S?Fe in ]3aFel~O19. The hyperfine components of four different effective fields are indicated.

NUCLEAR ZEEMAN SPLITTING AND MOSSBAUEREFFECT

191

field, the spectrum contains information about the interaction between the nuclear quadrupole moment and the electric field gradient (from the quadrupole splitting), and furthermore about the s-electron charge density at the nucleus (from the center or isomer shift). The M6ssbauer technique is particularly suited to study nuclear Zeeman splitting in rather complicated magnetic systems, in which the iron atoms are located at different non-equivalent sites in the crystal lattice. As an example, four different hyperfine fields are found in BaFel2019 (ferroxdure) with a strength ratio which corresponds with the known occupation of the different lattice sites s). Although such a hyperfine spectrum in principle consists of 24 resonance lines a number of lines m a y coincide; nevertheless the analysis shown in figure 2 is rather straight-forward as there are simple relationships between the different components of the various hyperfine spectra. In addition measurements of the M6ssbauer spectrum as a function of temperature give information about the sublattice magnetization of the crystal under study. An interesting compound is antiferromagnetic NazFesOg. The structure, derived from X-ray diffraction, is characterized by different sites of the trivalent iron atom such that four out of five iron atoms in a ¼ unit cell are tetrahedrally coordinated by oxygen atoms (A site) and one out of five octahedrally coordinated (B site). Two equally populated tetrahedral sites are present, which differ with respect to the distances between the iron atom and its surrounding oxygen atoms 4). The M6ssbauer spectrum of Na3FesO9 at room temperature in figure 3 shows the familiar six-line Zeeman pattern and moreover two rather broad lines in the center. Above the N6el temperature (TN ~ 100°C), the spectrum consists of two lines only, which is characteristic for a quadrupole splitting. DOPPLER VELOCITY (mmlsec) -10 420]-

,

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,

~

,

-,

,

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,

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,

D 420

Na3 F¢S09

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i"

x-

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/

I.¢1

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v

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o

W

400

¢J

,

,,

,

,,

,

,

,

•

,

;

,

;

,

' ii

Fig. 3. M6ssbauer absorption spectrum in NaaFesOg.

m0

192

j . j . VAN LOEF

On the bases of the line shape of the resonance lines and the size of the quadrupole splitting, the following analysis is made. In the normal hyperfine spectrum we can distinguish for each hyperfine component two lines of equal strength, each of which belongs to the Zeeman splitting at either one of the A sites. The effective magnetic field at both sites is about 380 kOe (roomtemperature), and the size of the isomer shift in either spectrum is typical for the tetrahedrally coordinated iron atomS). The two hyperfine spectra differ only with respect to the size and the sign of the quadrupole splitting. This result m a y be of interest in order to know which is the preferred direction of the magnetization vector at each of the two lattice sites. The two center lines with an intensity of about 20°//0 of the total resonance absorption should belong to the B-site nuclei. Apparently the hyperfine splitting at these nuclei is strongly reduced. This m a y occur when the electron spin-flip frequency is of the same order of magnitude as the nuclear DOPPLER VELOCITY (mm/sec) ,s ~'u ;. ~Fe~OH

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./.

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~260

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50O

~90

25O

2S0

74O

24O

230

230

220

l

I

I

I

I,

T

t

f

- 220

Fig. 4. M6ssbauer spectrum of ~FeOOH of different particle size.

NUCLEAR ZEEMAN SPLITTING AND MOSSBAUER EFFECT

193

Larmor precession frequency. It is necessary therefore that the electron spin relaxation times in the B and in the A site atoms respectively are very much different. This result is consistent with the weak magnetic coupling of the B site atoms with their neighbours in the crystal lattice. A reduced hyperfine splitting is observed also in studying superparamagnetism by means of the M6ssbauer effect 7). Superparamagnetism occurs in ultrafine pacticles of ferromagnetic materials (about 100 A in size), and it is characterized among others by the absence of magnetic hysteresis because of thermal fluctuations. In figure 4 the M6ssbauer spectra of a. FeOOH (goethite) at room temperature show a very marked progressive asymmetric broadening and decrease of amplitude of the hyperfine lines up to the point of collapse of the hyperfine field in samples with dreceasing particle size 8). The latter has been verified by X-ray line broadening. These phenomena can be explained by the superparamagnetic behaviour of the goethite particles, ill which the electron spins fluctuate in times which are comparable with or shorter than the nuclear Larmor precession time (about 10-s s). Experiments are in progress to measure the M6ssbauer effect as a function of temperature and we hope that these studies m a y furnish information on the distribution of spin relaxation times.

Note added in proo[: Recently some doubt has been cast upon the origin of the two broad central lines in the Na3Fes09 spectrum (fig. 3). It turns out that these lines disappear after heating and annealing of the sample while the magnetic hyperfine spectrum remained unchanged. Moreover in the X-ray diffraction pattern the same crystal structure was identified.

Discussion remark by A. Kastler CParis): X~rhich is t h e r e a s o n t h a t t h e Mt~ssbauer h y p e r f i n e s p e c t r a are n o t s y m m e t r i c a l w i t h r e s p e c t t o zero v e l o c i t y ?

Answer by J. J. van Loe[: T h e a s y m m e t r y is called t h e i s o m e r shift. T h i s s h i f t is d u e t o a difference in e n v i r o n m e n t of t h e i r o n nuclei in source a n d a b s o r b e r respectively.

194

NUCLEAR ZEEMAN SPLITTING AND MOSSBAUER EFFECT REFERENCES

1) W e r t h e i m , G. K., Mtissbauer Effect (Academic Press, New York 1964). 2) S l e g t e n h o r s t , R., Reactor Institute Delft Report 132-65-01. 3) Van Loef, J. J. and F r a n s s e n , P. J. M., Phys. Letters 7 (1963) 225. Van W i e r i n g e n , J. S. and R e n s e n , J. G., First European Congress on Magnetism, Vienna (1965). 4) R o o y m a n s , C. J. M. and R o m e r s , C., J. Phys. Chem. Solids, to be published. 5) W a t s o n , R. E. and F r e e m a n , A. J., Phys. Rev. 123 (1961) 2027. Van Loef, J. J., to be published. 6) Van d e r Woude, F and D e k k e r , A. J., Phys. Status solidi 9 (1965) 775. Blume, M., Phys. Rev. Letters 14 (1965) 506. 7) S c h u e l e , W. J., S h t r i k m a n , S. and T r e v e s , D., J. appl. Phys. 36 (1965) 1010. N a k a m u r a , T., S h i n j o , T., E n d o h , Y., Y a m a m o t o , N., Shiga, M. and N a k a m u r a , Y., Phys. Letters 12 (1964) 178. 8) Van d e r K r a a n , A. M., and Van Loef, J. J., Phys. Letters 2~ /1966) 614.