Temperature and Emission Current Dependence on Spin Polarization of Field-Emitted Electrons from ⟨110⟩-Oriented Magnetite Whisker∗

We investigated the Verwey transition in field-emitted electrons from ⟨110⟩-oriented magnetite whisker through the measurements of spin polarization. On temperature dependences varying tip voltage as a parameter from 850 V to 950 V, a rapid increase of spin polarization around 100 K due to the Verwey transition was observed more clearly with increase of applied voltage. This results indicates that t2g band of Fe3O4 at surface becomes narrower and possesses lower energy than an ideal bulk state. [DOI: 10.1380/ejssnt.2010.321]


I. INTRODUCTION
In 1970's, spin polarization of field-emitted electrons from transition and rate-earth metals was actively investigated both experimentally [1,2] and theoretically [3].At that time, theoretical calculations were carried out analytically.By contrast, recent first principle calculations have an ability of depicting a physical phenomenon more precisely.As the result, it is predicted that the spin polarization of field emitted electrons from Ni(001) depends on applied electric field, which results from the contribution of a surface state to emission current [4].However, there are no experimental reports so far on field-dependence of spin polarization of field-emitted electrons.
Magnetite is a magnetic material which mankind acquired for the first time and has been investigated by many researchers from a long time ago.Nowadays, magnetite has theoretically been predicted to have perfect spin polarization at Fermi level [5,6], i.e. half metallic property, and its spintronic applications are expected.The Verwey transition has been known as a phenomenon, which conductivity and magnetization of magnetite increase rapidly above transition temperature, i.e., the Verwey point (T v ∼ 120 K) [7,8] 4 , and has inversed spinel structure in which Fe 3+ ion is located at the center of a tetrahedron with vertex of O 2− ions, i.e., A-site, while mixed valence Fe 2+ and Fe 3+ ions are located at the center of an octahedron, i.e., B-site [9].Verwey interpreted that transition is caused by a charge disordering between Fe 2+ and Fe 3+ ions located at the B site.He proposed a model that an extra electron included in Fe 2+ ion behaves as free electron within the B site, and the electron is localized at below Verwey point, and itinerates at above it.It had been conceived that Fe 2+ and Fe 3+ ions order alternately, but the model was disclaimed by experimental results of nuclear magnetic resonance and neutron diffraction method [10].An unifying model for an array of charge and an electronic structure has not yet been determined though it has become possible recently to directly show their detail by using spin-resolved scanning tunneling microscopy [11] and photoemission spectroscopy [12][13][14].
In our previous study [15] we observed the Verwey transition in spin polarization of field-emitted electrons from ⟨110⟩-oriented magnetite whisker.For clarifying the origin of the transition, in this paper, a tip temperature and a voltage dependence of spin polarization were investigated.

II. EXPERIMENT
Magnetite whiskers were produced by thermal oxidation of a stainless steel (SUS 304) substrate with a premixed flame of oxygen and propane on the other side of the substrate [16].By using transmission electron diffraction method, we have confirmed that the magnetite whiskers were of single crystal extending in ⟨110⟩ direction.By micro-sampling method using of a focused ion beam apparatus (FB-2000A, Hitachi Ltd.), single mag- netite whisker was picked up and fixed on a tip of electrochemically etched tungsten wire.Appearance of the emitter is shown in Fig. 1.The etched tungsten wire was spot-welded to the tip of tungsten hairpin filament (0.2 mm dia.), which enables us to thermally clean the emitter surface by directly following current through the filament whose temperature was measured by optical micro pyrometer (PD01 KELLEY).
Measurements were carried out by means of a field emission microscope (FEM) equipped with a Mott polarization analyzer [17] shown in Fig. 2 The prepared emitter was attached to the cold finger of a He cryostat and the emitter temperature was adjusted to 40-300 K by a ceramic heater attached to the finger.The emitter temperature was measured by chromel-gold/iron thermocouple.FEM images reflecting surface conditions of the emitter tip were projected onto a fluorescent screen, and a desired emission area for the measurement of spin polarization was adjusted toward a probe hole by using an X-Y-Z stages and a gimbal system.Field emitted electrons through the probe hole enter the Mott analyzer and accelerated up to 25 keV toward a scattering target.Electrons scattered by a gold target with thickness of 100 nm are detected by 4-channel electron multipliers (CEMs) arranged in 4fold symmetry.Retarding grids placed in front of the each CEM blocked inelastic electrons that lost the kinetic energy higher than 600 eV Asymmetry A m in the number of electrons detected by a pair of CEM's is defined by [18,19] where N R and N L are number of electrons detected by the right and the left CEM's respectively.Actually measured asymmetry A m is summation of spin dependent and instrumental asymmetries, A s and A i , respectively.Instrumental asymmetry A i is caused by efficiency of the detector, irregularity of the target surface, incident angle of the beam axis etc.We defined A i as asymmetry measured with respect to non-polarized electron from tungsten field emitter.Spin polarization P and spin dependent asymmetry A s are related by using an effective Sherman function S eff as In this experiment, we used S eff of 0.15 reported by K.
Iori under the same experimental conditions [20] as we employed.Magnitude of spin polarization |P | and polarization direction within the target plane is estimated by where P X and P Y are polarization of X and Y components respectively.All measurements were carried out under UHV condition whose pressure of 3×10 −8 Pa.

III. RESULTS AND DISCUSSION
Before the measurement of spin polarization, a surface of the magnetite whisker was cleaned by heating at 1200 K for 60 seconds.Subsequently, a field desorption treatment was performed by applying a positive voltage of 6 kV for one hour at the tip temperature of 40 K. Figure 3 shows an FEM image obtained from the sample whisker after the field desorption treatment.Although symmetry originated from the crystal structure is not clear, a fine structure with some blurred bright spots can be seen.The spin polarization was measured for an electron emission site encircled in FEM image in Fig. 3.The measurements were performed within a range from 40 K to 300 K under conditions of tip voltage at 850, 900 and 950 V, and then the respective total emission current which was current flowing into the fluorescent screen was 1.6, 3.9 and 12.2 nA as shown in Fig. respectively.In previous study performed at room temperature [15], it had been confirmed that the spin polarization was stable over 3 hours which was longer time than present data acquisition time of 2.6 hours.Figure 4 show temperature dependences on the spin polarization under conditions of tip voltage.Compared with spin polarization between low and high temperature, relative changes of the spin polarization became higher value with the tip voltage.Especially, at tip voltage of 950 V, a rapid increase of spin polarization at 100 K was clearly observed, which resemble to temperature dependences of magneti- zation.In contrast, the directions of spin polarization at each tip voltage were about the same angle of −120 • counterclockwise with respect to right direction on the fluorescent screen in Fig. 3.That is, it was indicated that emission current was dominated by one of spin band regardless the tip voltage.However, the detail discussions about slight monotonic decrease and rapid decrease of the angle of the polarization in Figs.4(a) and 4(c) are difficult.Although it is considered that magnetic easy axis and crystal structure transform below and above transition temperature, the present measurements were carried out with only two components of spin polarization.The spin polarization at low temperature was noticeably difference to applied field.Figure 5 shows applied field dependences of spin polarization at 40 K for two samples having a tip radius of 47 and 55 nm.These spin polarizations decreased with applied field.It is considered that these results was attributed to the highest energy level of up and down spin bands were same level due to freezing of t 2g electrons among B site.
For understanding these results, the magnetic property and the band structure of magnetite should be taken into account.The magnetic property of magnetite is explained by that antiferromagnetic coupling between A and B sites are caused by super exchange interaction via O 2− ions.Thus spin moments of Fe ions of A and B sites are antiparallel each other.5-fold degeneracy of the 3d orbit of Fe 2+ and Fe 3+ is split into t 2g and e g orbits owing to the crystal field yielded by octahedrally coordinated O 2− Above the Verwey point T v , Fe 2+ is composed of Fe 3+ and an electron, and this electron shows only down spin due to double exchange interaction with ionic core (Fe 3+ ).Below T v , the down spin electrons are localized at B sites, resulting in that energy level of down spin electrons is slightly high or comparable to up spin electrons.Thus, both up and down spin electrons contribute to emission current, namely spin polarization is low value.Above T v on the other hand, down spin electrons included in t 2g orbital are excited thermally to become energetically high.As a result, the spin polarization increases with the tip temperature.
The most stable surface structure of Fe predicted to have antiferromagnetic property by first principle calculation [22].By contrast, the expected structure does not agree with low energy electron diffraction [23] and scanning tunneling microscopy [24], because surface structure of Fe 3 O 4 (110) is influenced by both annealing temperature and partial pressure of oxygen.In addition, by an FEM observation, it is difficult to identify the surface structure due to lack of resolution.However, at least, excitation of t 2g orbit due to Verwey transition is reduced by which a three-dimensional periodical structure is broken for any surface, therefore it is considered that energy differences between down spin t 2g band and up spin band are small above T v .Since tunneling probability in field emission increases exponentially with the electron energy, excited down spin electrons in t 2g orbit are emitted preferentially.Our experimental results support that the energy level of t 2g band is slightly higher than that of up spin band at low temperature, thus namely tunneling probabilities of up and down spin electrons are same order.Because the spin polarization was sensitive to applied field, spin polarization decrease with applied field, as shown Fig. 5.In contrast, with increase in temperature, spin polarization increased due to thermal excitation of t 2g band, which attribute to high tunneling probability.

IV. CONCLUSION
In this study, we measured temperature and emission current dependences of spin polarization of field-emitted electrons from ⟨110⟩-oriented magnetite whisker.On the temperature dependences, the rapid increase of spin polarization at 100 K due to Verwey transition was observed more clearly with increase of applied field.At low temperature, spin polarization decrease with emission current, it is suggested that t 2g band of Fe 3 O 4 at surface becomes narrower and possesses lower energy than an ideal bulky condition.

FIG. 3 :
FIG.3: FEM image obtained from single magnetite whisker.Spin polarization measurements were carried out with an encircled emission area.An inserted arrow indicates reference direction for the spin polarization.