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Electric field gradients near the Fe(110) surface
LETTER TO THE EDITOR
Journal of Magnetism and Magnetic Materials 92 (1990) L11-L13 North-Holland
Lll
Letter to the Editor
Electric field gradients near the Fe(110) surface J. Korecki and W. Karas Solid State Physics Department, Academy of Mining and Metallurgr, 30-059 Cracow, Poland Received 14 December 1989; in revised form 14 June 1990
The electric field gradients measured at the surface of Fe(110) using in situ monolayer probe conversion electron Mrssbauer spectroscopy were interpreted using a simple model. The spatial oscillation of the e!ecwric field gradient near the surface, which is observed experimentally, is also predicted by the calculations.
1. Introduction All the nuclei which have a nuclear spin quantum number I >_ 1 have a non-spherical charge distribution. The interaction of this charge distribution with the surrounding electronic charge produces a measurable effect, provided that the electronic charge has sufficiently low symmetry. The effect is duc to a coupling between the quadrupole moment of the nucleus and the electric field gradient (EFG) of the electronic charge. This situation occurs commonly in non-cubic crystals or near the surface, where the translational symmetry is broken. In this paper we concentrate on the second case. Electric field gradients can be measured via hyperfine interactions. Recently the E F G were measured near the surface of cubic metals using perturbed 7-~' angular correlations (PAC) [1,2] and MiSssbauer spectroscopy [3]. We would like to present a very simple moO,-] ,~,h;,,h A , ~ , - , - ; k , ~ the observed experimental situation at least qualitatively. The reliable calculations of the E F G require the detailed knowledge of the electronic structure. This kind of calculation making use of F L A P W method [41 was performed by Fu and Freeman for Fe(ll0) surface [51.
2. Theoretical approach The electric field gradient tensor is defined as
o-'u~
~%- OxoOx~ ~
AU~Io,
(2.1)
i.e. its components are the second derivatives of the Coulomb potential U~ at the nucleus site. The term with the Laplace operator m,~st be subtracted because only the traceless part couples to the quadrupole moment of the nucleus. In a frame of reference where this tensor is diagonal only two components are independent because of the relation V,.x + Vyy + V.: = O.
(2.2)
The splitting of the nuclear levels caused by the quadrupole interactior, is usually characterized by two parameters: ~/ ~,,n th,~ ~,,,-,-,mm,-,- p._~,-:~rnm,~,= ( V,.,. - 1~.,. ) / V= . with the convention ] V= ] > .
.
IV,,I >--IV,, I. I n the present paper we try to estimate the EFG resulting at the metal surface. We assume that the dominating effect is of the purely electrostatic origin and comes from the broken transla-
0304-8853/90/$03.50 © 1990 - Elsevier Science Publishers B.V. (North-Holland)
J. KoreckL W. Karas / Electric fieM gradients near the Fe(110) surface
L12
tional symmetry of both electronic and nuclear charges. We have neglected details of the electrooic structure. Thus we use a point charge model in which metal is considered as consisting of a lattice of point charges representing nuclei embedded in a homogeneous electron gas of the density #. Consequently, the E F G is given as a sum of nuclear (V,) and electronic (V~j) contributions. The contribution coming from the assembly of discrete nuclear charges q,, (with Cartesian coordinates x,,,~) is given by a semiconvergent sum V ~ c'= E qn n.o
3x2~-rf r~
Vx~= V,,y= -~'rrp,
(2.4)
Table 1 ~ : aad r/ calculated near the surface of a semifinite metal (in units Ze/a3o) Structure
~:
r/
3.9797 - 0.0632 0.0007
0.00
8.6906 - 1.6921 0.1366
0.63 0.52 0.86
bcc(001 ) 1 layer 2 layer 3 layer
3.8607 -0.3156 0.0118
0.00
bcc(110) 1 layer 2 layer 3 layer
0.8588 -0.0056 0.0001
0.75 0.20 -
fcc(001) 1 layer 2 layer 3 layer fcc(ll0) 1 layer 2 layer 3 layer
3. Experimental surfaces
determination
of
EFG
near
(2.3)
2 -]- Xn2 2 "~ Xn3. 2 in the case of the howhere r 2 = Xnl mogeneous semicrystal all q,, are equal to the nuclear charge Ze in the elementary cell with volume 12. We performed the summation using a plane summation method given by De Wette [6] for a semifinite crystal for fcc and bcc ',atUces " with the surface in (001) and (110) plane. Th= contribution coming from the free electron gas yields in the obvious way from a Poisson equation: V=: = --~,rrp;
where p = - Z e / l ' ~ is the density of the electron gas (z-axis is chosen as the surface normal). The EFG values calculated for different structures and orientations are presented in table 1. To obtain EFG for a given crystal one must multiply the results from table 1 by Ze/a3o, where Ze is the nuclear charge and a 0 is the lattice c,.,n~tant for a given crystal.
z axis
x axis
[OOl]
[1001
[]101
[001]
[001]
[100]
[ilO]
[001]
The first study of the electric field gradients at surfaces was performed with PAC for In(111) surface [7]. At the surface EFG value for this tetragonal crystal was drastically enhanced by a factor 4. It was difficult to detect the non-vanishing electric field gradients for cubic metals. In the M~ssbauer experiment for Fe(110) films on Ag [8] the spatial resolution of two or three atomic layers was too small to measure a meaningful value. Beside the spatial resolution, the second factor limiting surface EFG determination is the surface self-diffusion which causes an intermixing of atoms near the surface. Only by careful sample preparation was it possible to detect the surface EFG for Fe(110) films on W(110) using in situ Conversion Electron Mt~ssbaver Spectroscopy (CEMS) [3]. The monolayer spatial resolution was achieved by using a monolayer probe of 57Fe epitaxial Fe(110) films consisting otherwise of non-M/Sssbauer 57Fe. The experiments were performed both for uncoated and Ag-coated surfaces [9]. In this paper we give the more exact analysis of the quadrupole splittings for uncoated samples. A crucial problem of the CEMS measurements was to keep the surface clean during the measurement taking a few hours. It was demonstrated [3] that the hyperfine magnetic field at the surface changes with time due to contamination of the film surface from the residual gases. Fortunately, the changes in hyperfine magnetic field were systematic, so that the clean surface values could be derived by extrapolation to the time just after preparation. The same effect was expected also for the quadrupole splitting. Surprisingly, the quadrupole splitting values remain nearly constant over the time of measure-
LETTER TO THE EDITOR
J. Korecki, IV. Karas / Eiectrzc field gradients near the Fe(110) surface
ment. It is plausible that the adsorbed atoms cau:.e E F G distribution which is difficult to determi~e from magnetically split MiSssbauer spectra. Tt~,: MiSssbauer spectra were fitted neglecting the dcviation from rotational symmetry with respect to the surface normal. If we try to add the asymmetry parameter 71 in the fitting procedure the fit qua!i~ was independent of the ~ value. Consequently the:fitted value of the quadrupole interaction parameter c is connected with the nuclear quadrupole moment Q ( Q = 0 . 2 1 6 × 1 0 -24 c m 2 ) , the angle /3 between the hyperfine magnetic field and EFG axis (z axis) and the E F G component V= by: ,=
eOV.(¢os
Table 2 Comparison of the calculated (present work) and measured values of EFG. The data for Cu(100) are taken from Klas et al. [1], for Cu(110) from Klas et al. [2] and for Fe(110) from Korecki and G r a d m a n [3]
v~: (v/~, 2) exp.
,7 calc,
exp.
calc.
Ca fcc(001) 1 layer 2 layer
_+ 100 5:20 -
35.3 - 0.5
0.00 0.00
0.00 0,00
fcc(110) 1 layer 2 layer
_+80+ 2 + 50 + 10
77.2 - 15.0
0.74 0.50
0.63 0.52
-
0.75 0.20
# - 1).
Because the magnetization for our samples lies i~, the film plane, and we assumed the z axis in the [110] direction (normal to the film plane), fl = 90 ° The similar values of c obtained for two independent sample series (full points and open points) with a slightly different preparation mode confirm the reliability of CEMS analysis. Only for the first two layers did we observe measurable effects. The quadrupole splitting in the first layer corresponds to V= = +(33 + 7) V A*2, whereas in the second layer a small negative value V= = - ( 6 + 4) V A ? is observed. For the third and deeper layers the ~,: already vanishes, as can be expected in metals due to the screening by conduction electrons. The EF(3 was also measured with PAC at the surface o.~ monocrystalline copper films for (100) [1] and (110) [2] orientations using l~lln probe atoms. The obtained values of V= are of the same order of magnitude and also approach zero already for the third layer. In table 2 the experimental data are compared with the calculation described in the previous section. Our naive model gives the correct order of magnitude of the E F G only by assumption of the broken translational symmetry. The 7/ values for fcc(ll0) surfaces agree in the perfect way. The oscillations of EFG near the surface are suggested both experimentally and theoretically. Recently, the FLAPW calculation for Fe(ll0) surface, considering EFG too, was published [5]. The calculated V= values confirm the experimental findings. Similarly as for the hyperfine magnetic field
k 13
Fe bcc(ll0) 1 layer 2 layer
33 + 8 - 6+ 4
13.7 - 0.1
data, the measurements at low temperatures and calculations extended for higher temperatures are necessary for the detailed comparison between theory and experiment.
Acknowledgement This work was supported by CPBP 01.08.
References [1] T. Klas, J. Voigt, W. Keppner, R. Wesche and G. Schatz, Phys. Rev. Lett. 57 (1986) 1068. [2] T. Klas, J. Platzer, R. Wescbe and G. Schatz, to be published. [3] J. Korecki and U. Gradmann, Phys. Rev. Lett. 55 {1985) 2491. [4] E. Wimmer, H. Krakauer, M, Weinert and A.J. Freeman, r~hys. Rev. B 24 (!981) 864. [5] C.L. Fu and A.J. Freeman, J. Magn. Magn. Mat. 69 ~1987) L1. [6] F.W. de Wette, Phys. Rev. 123 (1961) 103. [7] W. Koerner, W. Keppner, B. Lehndorff-Junges and G. Schatz, Phys. Rev. Lett. 49 (1982) 1735. [8] J. Tyson, A.H. Owens, J.C. Walker and G. Bayreuther, J. Appl. Phys. 52 (1981) 2487. [9] J. Korecki and U Gradmann, Hyperfine Interactions 28 (1986) 931.
Journal of Magnetism and Magnetic Materials 92 (1990) L11-L13 North-Holland
Lll
Letter to the Editor
Electric field gradients near the Fe(110) surface J. Korecki and W. Karas Solid State Physics Department, Academy of Mining and Metallurgr, 30-059 Cracow, Poland Received 14 December 1989; in revised form 14 June 1990
The electric field gradients measured at the surface of Fe(110) using in situ monolayer probe conversion electron Mrssbauer spectroscopy were interpreted using a simple model. The spatial oscillation of the e!ecwric field gradient near the surface, which is observed experimentally, is also predicted by the calculations.
1. Introduction All the nuclei which have a nuclear spin quantum number I >_ 1 have a non-spherical charge distribution. The interaction of this charge distribution with the surrounding electronic charge produces a measurable effect, provided that the electronic charge has sufficiently low symmetry. The effect is duc to a coupling between the quadrupole moment of the nucleus and the electric field gradient (EFG) of the electronic charge. This situation occurs commonly in non-cubic crystals or near the surface, where the translational symmetry is broken. In this paper we concentrate on the second case. Electric field gradients can be measured via hyperfine interactions. Recently the E F G were measured near the surface of cubic metals using perturbed 7-~' angular correlations (PAC) [1,2] and MiSssbauer spectroscopy [3]. We would like to present a very simple moO,-] ,~,h;,,h A , ~ , - , - ; k , ~ the observed experimental situation at least qualitatively. The reliable calculations of the E F G require the detailed knowledge of the electronic structure. This kind of calculation making use of F L A P W method [41 was performed by Fu and Freeman for Fe(ll0) surface [51.
2. Theoretical approach The electric field gradient tensor is defined as
o-'u~
~%- OxoOx~ ~
AU~Io,
(2.1)
i.e. its components are the second derivatives of the Coulomb potential U~ at the nucleus site. The term with the Laplace operator m,~st be subtracted because only the traceless part couples to the quadrupole moment of the nucleus. In a frame of reference where this tensor is diagonal only two components are independent because of the relation V,.x + Vyy + V.: = O.
(2.2)
The splitting of the nuclear levels caused by the quadrupole interactior, is usually characterized by two parameters: ~/ ~,,n th,~ ~,,,-,-,mm,-,- p._~,-:~rnm,~,= ( V,.,. - 1~.,. ) / V= . with the convention ] V= ] > .
.
IV,,I >--IV,, I. I n the present paper we try to estimate the EFG resulting at the metal surface. We assume that the dominating effect is of the purely electrostatic origin and comes from the broken transla-
0304-8853/90/$03.50 © 1990 - Elsevier Science Publishers B.V. (North-Holland)
J. KoreckL W. Karas / Electric fieM gradients near the Fe(110) surface
L12
tional symmetry of both electronic and nuclear charges. We have neglected details of the electrooic structure. Thus we use a point charge model in which metal is considered as consisting of a lattice of point charges representing nuclei embedded in a homogeneous electron gas of the density #. Consequently, the E F G is given as a sum of nuclear (V,) and electronic (V~j) contributions. The contribution coming from the assembly of discrete nuclear charges q,, (with Cartesian coordinates x,,,~) is given by a semiconvergent sum V ~ c'= E qn n.o
3x2~-rf r~
Vx~= V,,y= -~'rrp,
(2.4)
Table 1 ~ : aad r/ calculated near the surface of a semifinite metal (in units Ze/a3o) Structure
~:
r/
3.9797 - 0.0632 0.0007
0.00
8.6906 - 1.6921 0.1366
0.63 0.52 0.86
bcc(001 ) 1 layer 2 layer 3 layer
3.8607 -0.3156 0.0118
0.00
bcc(110) 1 layer 2 layer 3 layer
0.8588 -0.0056 0.0001
0.75 0.20 -
fcc(001) 1 layer 2 layer 3 layer fcc(ll0) 1 layer 2 layer 3 layer
3. Experimental surfaces
determination
of
EFG
near
(2.3)
2 -]- Xn2 2 "~ Xn3. 2 in the case of the howhere r 2 = Xnl mogeneous semicrystal all q,, are equal to the nuclear charge Ze in the elementary cell with volume 12. We performed the summation using a plane summation method given by De Wette [6] for a semifinite crystal for fcc and bcc ',atUces " with the surface in (001) and (110) plane. Th= contribution coming from the free electron gas yields in the obvious way from a Poisson equation: V=: = --~,rrp;
where p = - Z e / l ' ~ is the density of the electron gas (z-axis is chosen as the surface normal). The EFG values calculated for different structures and orientations are presented in table 1. To obtain EFG for a given crystal one must multiply the results from table 1 by Ze/a3o, where Ze is the nuclear charge and a 0 is the lattice c,.,n~tant for a given crystal.
z axis
x axis
[OOl]
[1001
[]101
[001]
[001]
[100]
[ilO]
[001]
The first study of the electric field gradients at surfaces was performed with PAC for In(111) surface [7]. At the surface EFG value for this tetragonal crystal was drastically enhanced by a factor 4. It was difficult to detect the non-vanishing electric field gradients for cubic metals. In the M~ssbauer experiment for Fe(110) films on Ag [8] the spatial resolution of two or three atomic layers was too small to measure a meaningful value. Beside the spatial resolution, the second factor limiting surface EFG determination is the surface self-diffusion which causes an intermixing of atoms near the surface. Only by careful sample preparation was it possible to detect the surface EFG for Fe(110) films on W(110) using in situ Conversion Electron Mt~ssbaver Spectroscopy (CEMS) [3]. The monolayer spatial resolution was achieved by using a monolayer probe of 57Fe epitaxial Fe(110) films consisting otherwise of non-M/Sssbauer 57Fe. The experiments were performed both for uncoated and Ag-coated surfaces [9]. In this paper we give the more exact analysis of the quadrupole splittings for uncoated samples. A crucial problem of the CEMS measurements was to keep the surface clean during the measurement taking a few hours. It was demonstrated [3] that the hyperfine magnetic field at the surface changes with time due to contamination of the film surface from the residual gases. Fortunately, the changes in hyperfine magnetic field were systematic, so that the clean surface values could be derived by extrapolation to the time just after preparation. The same effect was expected also for the quadrupole splitting. Surprisingly, the quadrupole splitting values remain nearly constant over the time of measure-
LETTER TO THE EDITOR
J. Korecki, IV. Karas / Eiectrzc field gradients near the Fe(110) surface
ment. It is plausible that the adsorbed atoms cau:.e E F G distribution which is difficult to determi~e from magnetically split MiSssbauer spectra. Tt~,: MiSssbauer spectra were fitted neglecting the dcviation from rotational symmetry with respect to the surface normal. If we try to add the asymmetry parameter 71 in the fitting procedure the fit qua!i~ was independent of the ~ value. Consequently the:fitted value of the quadrupole interaction parameter c is connected with the nuclear quadrupole moment Q ( Q = 0 . 2 1 6 × 1 0 -24 c m 2 ) , the angle /3 between the hyperfine magnetic field and EFG axis (z axis) and the E F G component V= by: ,=
eOV.(¢os
Table 2 Comparison of the calculated (present work) and measured values of EFG. The data for Cu(100) are taken from Klas et al. [1], for Cu(110) from Klas et al. [2] and for Fe(110) from Korecki and G r a d m a n [3]
v~: (v/~, 2) exp.
,7 calc,
exp.
calc.
Ca fcc(001) 1 layer 2 layer
_+ 100 5:20 -
35.3 - 0.5
0.00 0.00
0.00 0,00
fcc(110) 1 layer 2 layer
_+80+ 2 + 50 + 10
77.2 - 15.0
0.74 0.50
0.63 0.52
-
0.75 0.20
# - 1).
Because the magnetization for our samples lies i~, the film plane, and we assumed the z axis in the [110] direction (normal to the film plane), fl = 90 ° The similar values of c obtained for two independent sample series (full points and open points) with a slightly different preparation mode confirm the reliability of CEMS analysis. Only for the first two layers did we observe measurable effects. The quadrupole splitting in the first layer corresponds to V= = +(33 + 7) V A*2, whereas in the second layer a small negative value V= = - ( 6 + 4) V A ? is observed. For the third and deeper layers the ~,: already vanishes, as can be expected in metals due to the screening by conduction electrons. The EF(3 was also measured with PAC at the surface o.~ monocrystalline copper films for (100) [1] and (110) [2] orientations using l~lln probe atoms. The obtained values of V= are of the same order of magnitude and also approach zero already for the third layer. In table 2 the experimental data are compared with the calculation described in the previous section. Our naive model gives the correct order of magnitude of the E F G only by assumption of the broken translational symmetry. The 7/ values for fcc(ll0) surfaces agree in the perfect way. The oscillations of EFG near the surface are suggested both experimentally and theoretically. Recently, the FLAPW calculation for Fe(ll0) surface, considering EFG too, was published [5]. The calculated V= values confirm the experimental findings. Similarly as for the hyperfine magnetic field
k 13
Fe bcc(ll0) 1 layer 2 layer
33 + 8 - 6+ 4
13.7 - 0.1
data, the measurements at low temperatures and calculations extended for higher temperatures are necessary for the detailed comparison between theory and experiment.
Acknowledgement This work was supported by CPBP 01.08.
References [1] T. Klas, J. Voigt, W. Keppner, R. Wesche and G. Schatz, Phys. Rev. Lett. 57 (1986) 1068. [2] T. Klas, J. Platzer, R. Wescbe and G. Schatz, to be published. [3] J. Korecki and U. Gradmann, Phys. Rev. Lett. 55 {1985) 2491. [4] E. Wimmer, H. Krakauer, M, Weinert and A.J. Freeman, r~hys. Rev. B 24 (!981) 864. [5] C.L. Fu and A.J. Freeman, J. Magn. Magn. Mat. 69 ~1987) L1. [6] F.W. de Wette, Phys. Rev. 123 (1961) 103. [7] W. Koerner, W. Keppner, B. Lehndorff-Junges and G. Schatz, Phys. Rev. Lett. 49 (1982) 1735. [8] J. Tyson, A.H. Owens, J.C. Walker and G. Bayreuther, J. Appl. Phys. 52 (1981) 2487. [9] J. Korecki and U Gradmann, Hyperfine Interactions 28 (1986) 931.