PHYSICAL REVIEW LETTERS 126, 186401 (2021)

Spin-Polarized Positronium Time-of-Flight Spectroscopy for Probing Spin-Polarized
Surface Electronic States
M. Maekawa , A. Miyashita , S. Sakai , S. Li , S. Entani , and A. Kawasuso*

National Institutes for Quantum and Radiological Science and Technology, 1233 Watanuki, Takasaki, Gunma 370-1292, Japan

Y. Sakuraba
National Institute for Materials Science (NIMS), 1-2-1, Sengen, Tsukuba-city, Ibaraki 305-0047, Japan(Received 5 November 2020; accepted 25 March 2021; published 4 May 2021)
The energy spectrum of positronium atoms generated at a solid surface reflects the electron density ofstates (DOS) associated solely with the first surface layer. Using spin-polarized positrons, the spindependent surface DOS can be studied. For this purpose, we have developed a spin-polarized positronium
time-of-flight spectroscopy apparatus based on a 22Na positron source and an electrostatic beamtransportation system, which enables the sampling of topmost surface electrons around the Γ point
and near the Fermi level. We applied this technique to nonmagnetic Pt(111) and W(001), ferromagnetic Ni(111), Co(0001) and graphene on them, Co2 FeGa0.5 Ge0.5 (CFGG) and Co2 MnSi (CMS). The results
showed that the electrons of Ni(111) and Co(0001) surfaces have characteristic negative spin polarizations,while these spin polarizations vanished upon graphene deposition, suggesting that the spin polarizations ofgraphene on Ni(111) and Co(0001) were mainly induced at the Dirac points that were out of range in thepresent measurement. The CFGG and CMS surfaces also exhibited only weak spin polarizations
suggesting that the half-metallicity expected for these bulk states was not maintained at the surfaces.
DOI: 10.1103/PhysRevLett.126.186401

Slow positrons injected into the subsurface region of ametal diffuse back to the surface/vacuum interface and are
emitted as positronium (Ps) atoms by picking up theoutermost surface electrons when the Ps formation potential is negative. Because of the energy gain of the formation
potential, electrons below the Fermi level with the width offormation potential can participate in Ps formation. Hence,
Ps energy spectroscopy can provide information regarding
the surface electron density of states (DOS) [1]. AlthoughPs spectroscopy is analogous to photoemission spectroscopy, a critical difference is its extremely high surface
sensitivity [2,3]. This owes to the fact that Ps atom isformed only at the top surface of metal [4,5], while thephotoemission spectroscopy includes electrons fromseveral surface layers. Recently, the angle-resolved Ps
spectroscopy with a milli-electron-volt energy resolution
has been demonstrated in a laboratory scale [6].
When the positron and electron spins are parallel, only
spin-triplet Ps atoms are formed. On the other hand, when
the spins are antiparallel, both spin-triplet and spin-singlet
Ps atoms are formed. Therefore, by observing the change inthe fraction of spin-triplet Ps or spin-singlet Ps upon spinreversal using spin-polarized positrons, information about
the spin-polarized surface DOS may be obtained. Positrons
emitted from radioisotopes are longitudinally spin polarized due to the parity nonconservation in the weakinteraction. Hence, spin-polarized positron beams can beeasily generated. Spin-polarized Ps spectroscopy may
0031-9007=21=126(18)=186401(6)elucidate the nature of the spin polarization of the topsurface electronic states and play a valuable role in the fieldof spintronics.
Spin-polarized Ps spectroscopy was first demonstrated
by the Michigan group in 1982 [7]. In their study, the spinpolarization of a ferromagnetic Ni surface was determinedfrom the field reversal asymmetry of the spin-triplet Ps
fraction deduced from lifetime measurements. We demonstrated the feasibility of a similar experiment based on theenergy spectra of annihilation γ rays of spin-triplet Ps [8].
However, these existing methods cannot resolve the Ps
kinetic energy, and hence the obtained spin polarization is
only an average of all electrons below the Fermi level
picked up by positrons. For more detailed analysis of thesurface electronic states, determination of the electron spinpolarization depending on the energy level, i.e., the spinpolarized DOS, is essential [9]. Spin-polarized and angleresolved Ps spectroscopy with a submicron beam would bean ultimate surface spin probe that is applicable to devicescale samples.
In this work, we report on the development of a spinpolarized Ps time-of-flight (SP PsTOF) apparatus for theenergy-resolved Ps spectroscopy. Using this apparatus, thePs formation potentials for Pt, W, Ni, Co, Co2 FeGa0.5 Ge0.5(CFGG), and Co2 MnSi (CMS) were successfully determined. Through the SP PsTOF experiments, we further
examined the spin polarizations of the above ferromagnetic
surfaces.

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PHYSICAL REVIEW LETTERS 126, 186401 (2021)
LD ∓ dðD=2 þ RÞ
t1;2 ¼ pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ;
EPs =mðD cos θ  d sin θÞ

FIG. 1. Schematic diagram of the positronium time-of-flightapparatus developed in this work.

Figure 1 presents a schematic diagram of the SP PsTOF
apparatus developed in this work. The 22Na source(162 MBq) was deposited on a graphite tray, which wasinserted into a copper capsule equipped with a titanium
window (5 μm thick) and a cone-shaped exit. The source
capsule was mounted on a cold finger and cooled down to
4 K. A solid Kr moderator [10] was deposited on the surface
of source exit. A slow positron beam was generated by amodified Soa gun [11] and transported using einzel lenses. A
90° electrostatic bending section was installed after the firsteinzel lens. Thereby, a transversely spin-polarized positron
beam was obtained. The nominal beam energy was 6 keV.
The beam diameter, flux, and spin polarization wereapproximately 5 mm, 104 eþ = sec, and 30%, respectively.
The positron beam was injected into the sample perpendicularly. The secondary electrons emitted upon positron impact were detected using a channeltron multiplieradjacent to the sample. This provided the start signal for thePsTOF measurement. The Ps atoms generated at the sample
surface were ejected through an aperture of 20 mm
diameter, which restricted the maximum emission angle
to 22° with respect to the surface normal, and underwent
annihilation during flight. The annihilation γ rays weredetected using three NaI scintillation detectors through leadslits. As spin-singlet Ps atoms promptly annihilate in thevicinity of the sample surface, this configuration permits
detection of the annihilation events involving spin-triplet Ps
atoms. In this way, PsTOF spectra were acquired.
The horizontal distance between the sample and the slit
center was L ¼ 107.5 mm. The slit width and length wered ¼ 15 mm and D ¼ 50 mm, respectively. The beam pipe
radius was R ¼ 55 mm, and hence the Ps atoms did notcollide with the inner wall of the pipe prior to passing theslit section. Assuming that the Ps kinetic energy (EPs ) is
monochromatic and Ps atoms are ejected with an angle of θwith respect to the surface normal, then the PsTOF
spectrum has a distribution from time t1 to t2 given byð1Þ

where m denotes the electron rest mass. Practically, t1
represents the threshold time of the PsTOF spectrum,
which is earlier than the ideal threshold time given byd ¼ 0. The Ps atoms should also have a certain angular
distribution reflecting the electron band dispersion relationship due to the momentum conservation law. Ps atoms
emitted with larger θ values afford earlier t1 values for thesame EPs . For the largest θ value of 22° using the present
apparatus and the typical EPs value of 3 eV, t1 ¼ 80 ns,
which is only 3 ns earlier than that for θ ¼ 0°. This was
confirmed by a Monte Carlo simulation of the PsTOF
spectrum considering the detection efficiency and time
resolution of the electrical system, as depicted in Fig. 2(a).
Figure 2(b) shows PsTOF spectra for various EPs values at
θ ¼ 0°. These provide the total time resolution functions
depending on EPs . By converting the timescale to theenergy scale, the energy resolution can be obtained (e.g.,
approximately 1 eV for EPs ¼ 3 eV). Practically, theenergy resolution could be raised to 0.2–0.5 eV by
optimizing the slit geometry.
Thus, even if we use the energy scale converted from thetimescale with EPs ¼ mðL0 =tÞ2 and the effective length
given by L0 ¼ L − dðD=2 þ RÞ=D for θ ¼ 0°, the error in
the determination of the maximum Ps energy would besmall. Ps atoms formed from electrons with wave vectors
around the Γ point and within θ ≤ 22° are detected. The
maximum transverse wave numberpof
electrons picked up
ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
by positrons is given by kmax ¼ 2 mð−ΦPs þ EÞ sin θ=ℏ,
where ΦPs is the Ps formation potential and E is the electron
(a)

(b)

FIG. 2. Positronium time-of-flight spectra obtained via
Monte Carlo simulations (a) for a positronium energy of 3 eVwith various emission angles and (b) for an emission angleof 0° with positronium energies ranging from 0.5 to 5 eV in
0.5 eV steps.

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PHYSICAL REVIEW LETTERS 126, 186401 (2021)
energy (relative to the Fermi level EF : ΦPs ≤ E ≤ 0). For
instance, for ΦPs ¼ −3 eV, kmax ∼ 0.5 Å−1 at EF .
In the described apparatus, ferromagnetic samples could
be in-plane magnetized using an electromagnet (50 mT)
positioned in the sample preparation chamber. By rotating
the sample around the beam center axis, the relative
direction of positron spin polarization and magnetization
could be varied from parallel to antiparallel. Different
spectra under the parallel and antiparallel conditions would
indicate the occurrence of polarization effects. The spinpolarization of electrons depending on E is given by
PTOF− ðEPs Þ ¼

1 2ϵð1Þ þ ϵð0Þ F∦ ðEPs Þ − Fk ðEPs Þ;Pþ 2ϵð1Þ − ϵð0Þ F∦ ðEPs Þ þ Fk ðEPs Þð2Þwhere Fk;∦ ðEPs Þ denotes the PsTOF spectra obtained under
the parallel-antiparallel spin conditions by converting thescale from time to energy with EPs ¼ −ΦPs þ E, andϵð1Þ ¼ 0.3 and ϵð0Þ ¼ 0.4 denote the detection efficiencies
for annihilation γ rays from Ps atoms with magnetic
quantum numbers of 1 and 0, respectively [12].
The samples used in this study were a mirror-polished
W(001) bulk crystal, a Pt(111) film of 100 nm thickness
grown on Al2 O3 ð0001Þ by magnetron sputtering deposition, Ni(111) and Co(0001) films of 30 nm thickness grownusing an electron beam evaporator, and those covered withmonolayer graphene grown via ultrahigh-vacuum chemical
vapor deposition [13–15], CFGG(001) and CMS(001)films of 30 nm thickness grown on MgO(001) by magnetron sputtering deposition [16,17]. The samples were transferred through air into the sample chamber (base pressure:10−8 Pa). The surfaces of the metal samples were cleaned
via 1 keV Ar sputtering and subsequent heat treatment at
appropriate temperatures. (The heat treatment temperatures
for the CFGG and CMS samples were 800 and 400 °C, thatmaintain the L21 structure.) The surfaces of the graphenecovered Ni(111) and Co(0001) samples were cleaned bysimply heating at 600 °C for 20 min.
To interpret the experimental data, density functional
theory calculations were conducted using the ABINIT code[18] with the projector augmented wave method [19] within
the generalized gradient approximation (GGA) [20]. The
electron-positron correlation energy functional was basedon the GGA method [21]. The initial valence electron
configurations were assumed to be 5s2 5p6 5d4 6s2 (W),5s2 5p6 5d9 6s1 (Pt), 3s2 3p6 3d6 4s1 (Mn), 3s2 3p6 3d7 4s1(Fe),
3s2 3p6 3d8 4s1(Co),
3s2 3p6 3d8 4s2
(Ni),
10 2
1
10 2
2
3d 4s 4p (Ga), 3d 4s 4p (Ge), 3s2 3p2 (Si), and2s2 2p2 (C). For W and Pt, the spin-orbit interaction was
also taken into consideration. The Ps formation potentials
given by ΦPs ¼ −Aþ − 6.8 eV, where Aþ is the positron
affinity, were calculated using the bulk systems withprimitive cells under full structural optimization. The kpoint sampling was 10 × 10 × 10. The spin-polarized surface electronic states of Co, Ni, CFGG, and CMS were

calculated using film systems composed of seven monolayers stacked in the surface normal direction. For Co andNi, the primitive cells were aligned parallel to the surfaces,
while for CFGG and CMS, a conventional cell and two
primitive cells, respectively, were aligned. In the calculation of graphene, C atoms were distributed on top of the Ni
and Co surfaces. The van der Waals potential was also
considered [22]. The vacuum layer was initially assumed to
be 20 Å. Full structural optimization was also performed.
The k-point sampling was 9 × 9 × 1 for Fe, Co, and Ni,
5 × 5 × 1 for CFGG and 12 × 12 × 1 for CMS.
The surface DOS in the vacuum region, where Ps
atoms may be formed, was computed from the ABINIT
outputs. The
region of k-point sampling was assumed
pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
to be k ≤ 2 mð−ΦPs þ EÞ sin θ=ℏ. The electron-positron
DOS (DEP ) was obtained by weighting the surface DOS
with the positron density. Subsequently, the surface electron spin polarization depending on E in the vacuum region
was estimated asPcal− ðEÞ ¼

D↑EP ðEÞ − D↓EP ðEÞ

D↑EP ðEÞ þ D↓EP ðEÞ;

ð3Þ

where ↑ð↓Þ denotes the majority (minority) spin channel.
The details of the above calculations have been described
elsewhere [8,23].
Figure 3 presents the PsTOF spectra obtained for the
metal sample surfaces before and after subtracting the
lifetime background of spin-triplet Ps ½∝ expð−t=142 nsÞ,as indicated by the broken curves. Approximately 5 × 104
annihilation events were accumulated for each spectrum.
The peaks at t ¼ 0 are attributable to prompt annihilation
events, namely, the free annihilation of positrons in thesamples and/or annihilation of spin-singlet Ps. The full
width of the prompt peaks was approximately 70 ns. Upon
closing the lead slits, these prompt peaks disappeared,
which indicates that scattered γ rays from the inner wall of
the beam pipe were responsible for the prompt peaks.
The spectrum threshold times were determined to be 35 ns
later than the zero-cross points by considering the width ofthe prompt peaks mentioned above. From the maximumPs kinetic energies given by the threshold times, the Ps
formation potentials were determined to be −2.5 eV (Pt),−4.9 eV (W), −3.3 eV (Co), −2.7 eV (Ni), −3.9 eV(CFGG), and −4.8 eV (CMS). These values are in good
agreement with the calculated Ps formation potentials(−2.8 eV (Pt), −5.2 eV (W), −3.6 eV (Co), −3.1 eV(Ni), −4.9 eV (CFGG) and −4.6 eV (CMS).
Figure 4 presents the spin polarizations [PTOF− ðEPs Þ] as afunction of Ps energy relative to the maximum value(EPs þ ΦPs ) obtained from the SP PsTOF measurements
and Eq. (2) for all the samples. In the cases of nonmagnetic
Pt and W surfaces, only random and small fluctuations
around zero are seen. For the Ni(111) and Co(0001)
surfaces, the spin polarizations were negative from 0 eV186401-3

PHYSICAL REVIEW LETTERS 126, 186401 (2021)

FIG. 3. Positronium time-of-flight spectra obtained for
the Pt(111), W(001), Ni(111), Co,(0001), CFGG(001), andCMS(001) samples before and after subtracting the lifetime
spectrum component of spin-triplet positronium (broken curves),i.e., ∝ expð−t=142 nsÞ. The chained lines indicate the positionsof maximum positronium energies considering the time resolution of the measurement system.

to −1.5 ∼ −2 eV. In contrast, for the graphene-covered
Ni(111) and Co(0001) surfaces, the spin polarizations were
sufficiently lost. The spin polarizations observed for the
CFGG(001) and CMS(001) surfaces are also very small.
Figure 5 shows DEP calculated for the Ni(111),
Co(0001),
graphene=Nið111Þ,graphene=Coð0001Þ,
CFGG(001), and CMS(001) surfaces. The surface of
CFGG or CMS includes Co face and FeGaGe face or
MnSi face equally. As seen from these plots, the spinpolarization of the Ni(111) and Co(0001) surfaces in thevicinity of the Fermi level were negative. Whereas, the spinpolarizations of the graphene-covered Ni(111) andCo(0001) surfaces were significantly lost near the Fermi
level. The spin polarizations for the CFGG(001) andCMS(001) surfaces are also rather suppressed. (We discussthese details in the next paragraph.) For a direct comparison
between the experimental and calculation results, Fig. 4

FIG. 4. Spin polarizations obtained from SP PsTOF measurements, PTOF
− , as a function of positronium energy relative to its
maximum energy for the Pt(111), W(001), Ni(111), Co(0001),
graphene=Nið111Þ, graphene=Coð0001Þ, CFGG(001) andCMS(001) samples. The red broken curves represent the simulated spin polarization from the spin-polarized DOS (DEP ) shownin Fig. 5 and the energy resolution function of PsTOF system.

shows the SP PsTOF spectra simulated by convoluting DEP
with the system energy resolution function depending on
the Ps energy (broken lines). These well reproduced theexperimental data. This means that the experimental
SP PsTOF spectrum shows the spin polarization below
the Fermi level in an extended energy scale. For instance,
the negative spin polarization of Ni down to ∼ − 0.5 eV in
Fig. 5 is reflected down to ∼ − 1.5 eV in Fig. 4. Thus, theSP PsTOF measurement provides the spin polarization of
topmost surface electrons around the Γ point and near the
Fermi level.
The spin polarizations of the Ni(111) and Co(0001)
surfaces in the vicinity of the Fermi level are known to be
negative owing to the sd-hybridized upper majority spinband with fewer states and the d-like upper minority spinband with more states [9,24]. In contrast, at thegraphene=Nið111Þ surface, the spin polarization has beenreported to be positive on the basis of spin-polarized

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PHYSICAL REVIEW LETTERS 126, 186401 (2021)
spectroscopy with a sufficient energy resolution has alreadybeen in use [6]. By extending this method to the spinpolarized version and furthermore by employing a submicron beam, the device-scale topological materials [29] inthe ballistic conduction regime will also be attractive
systems.
This work was financially supported by JSPS KAKENHI
under Grants No. 17K19061 and No. 20K05454.

*

FIG. 5. Spin polarizations of electron-positron DOSs (DEP )around the Γ point as a function of electron energy relative to the
Fermi level calculated for Ni(111), Co(0001), graphene=Nið111Þ,graphene=Coð0001Þ, CFGG(001) and CMS(001) surfaces.
Broken lines represent the results including the K point where
the Dirac point of graphene is located.

metastable deexcitation spectroscopy results [25]. This has
been explained via the polarization of the graphene DOS
due to the strong hybridization of the graphene π orbitals
with the dz2 and dx2 − y2 orbitals [26]. Hence, such a spinpolarization should be induced near the K point where theDirac point of graphene is located. Actually, as shown in
Fig. 5, the positive spin polarizations appear at around−0.5 eV in the calculation including K points (brokenlines). It is known that CFGG and CMS have half-metallic
bulk characteristics. However, at the surfaces, the halfmetallicity is not necessarily maintained. The present
calculation indicates that the half-metallicity is lost eventhough important k points related to the half-metallicity
such as X and W points are sampled within the angle
restriction. The reason for the absence of half-metallicity is
explained as the formation of new surface bands in the gapof minority spin channel [27].
In this work, we demonstrated that the SP PsTOF
spectroscopy provides the spin polarization of topmost
surface electrons around the Γ point and near the Fermi
level. There might be many potential applications of thecurrent apparatus. For instance, the surface ferromagnetism
predicted recently for narrow-gap semiconductors based on
the quaternary Heusler alloys [28] is an intriguing target
considering the fact that such a feature is absent in
the conventional Heusler alloys. The angle-resolved Ps

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