A quantum sensor for atomic-scale electrical and magnetic fields

Pattern preparation

The Ag(111) floor was ready in ultra-high vacuum by repeated cycles of sputtering with Ar⁺ and heating to 800 Ok, after which transferred to the chilly STM. The person Fe atoms and PTCDA molecules had been deposited in situ on the pattern at roughly 10 Ok. To permit in situ deposition of atoms and molecules on the pattern contained in the STM, the pattern just isn’t aligned with the axis of the magnet²⁷. As a consequence, the 2 perpendicular parts (in-plane and out-of-plane) of the vector magnet are tilted ~7° with respect to the pattern floor airplane (Fig. 1b).

STM and ESR measurements

All experiments had been carried out at 1.4 Ok in a home-built STM with a two-axis vector magnet and ESR functionality with a large frequency vary²⁷. Differential conductance (dI/dV) spectra had been measured utilizing the traditional lock-in approach with the suggestions loop switched off and an a.c. modulation amplitude V_mod. The PtIr tip was handled in situ by managed voltage pulses and indentations into the clear Ag floor, leading to a clear Ag-coated tip. The spectroscopic signature of the Ag(111) floor state was used to substantiate the cleanliness of the tip. The frequency-dependent transmission losses of the cables within the STM had been compensated by adjusting the supply energy of the RF sign generator throughout the sweeps of the RF frequency f to acquire a continuing amplitude V_RF on the tunnel junction for the continuous-wave ESR experiments⁴⁹. All ESR spectra had been measured in constant-current mode with very low suggestions achieve to compensate for sluggish drift and to maintain the tip–pattern distance fixed.

Fabrication of the quantum sensor

The quantum sensor was constructed in two steps. First, a spin-polarized STM tip was fabricated by transferring as much as three Fe atoms from the Ag(111) floor to the Ag-coated non-magnetic tip apex. To switch particular person Fe atoms from the Ag(111) floor to the tip, a voltage pulse of 1.6–1.9 V was utilized whereas the tip was withdrawn from close to level contact with the Fe atom. Second, one of many 4 carboxylic oxygen atoms of an remoted PTCDA molecule on the floor was contacted with the tip, whereupon a covalent bond between the tip apex and the oxygen atom shaped^50,51. Within the subsequent step, the tip with the hooked up molecule was pulled vertically upwards by about 12 Å till the molecule was utterly indifferent from the floor and reached the standing orientation on the tip. This process decouples the PTCDA molecule from the steel and ends in a singly charged radical^{28,29,50,51,52,53}. Affirmation of the standing orientation got here, first, from imaging the thus accomplished quantum sensor by scanning it throughout a single Fe atom on the floor—the Fe atom acts as an efficient tip on the floor to scan the true tip apex, that’s, the standing PTCDA molecule. The ensuing picture in Fig. 1c with its two elliptical options resembles the STM picture of a standing PTCDA molecule on a pedestal of two Ag atoms on the Ag(111) floor^28,29. This proves the presence of a standing PTCDA molecule within the fabricated quantum sensor. Second, after its fabrication, the quantum sensor was used to file an atomically resolved picture of the Ag(111) floor (Prolonged Knowledge Fig. 6). The tip top at which this picture was scanned proves the presence of a standing molecule of roughly 12 Å top above the metallic tip apex.

Construction of the quantum sensor

To find out the construction of the quantum sensor on the base of the standing molecule, that’s, on the interface to the metallic STM tip, we constructed numerous standing molecules on the Ag(111) and measured their dI/dV spectra. Evaluating these with the dI/dV spectra of the quantum sensor, we obtained details about the construction and composition of the quantum sensor. Particularly, we positioned the PTCDA molecule on Ag + Fe and Fe + Fe pedestals on the Ag(111) floor by managed manipulation with the STM tip (Prolonged Knowledge Fig. 7). The process is analogous to fabricating standing PTCDA on Ag + Ag pedestals on Ag(111)²⁸. If the pedestal of standing PTCDA on the Ag(111) floor contained at the least one Fe atom, inelastic spin excitations at increased voltages had been noticed within the dI/dV spectrum (Prolonged Knowledge Fig. 7), much like these on the tip when PTCDA just isn’t ESR energetic (Prolonged Knowledge Fig. 4). Due to this fact, we conclude that the ESR-active PTCDA on the tip, that’s, the PTCDA within the functioning quantum sensor, can’t be instantly sure to an Fe atom, however have to be standing on an Ag + Ag pedestal, which is according to its dI/dV spectrum that’s attribute of a spin-½ system. The Fe atoms on the tip thus solely allow the ESR driving mechanism and supply the spin polarization for the detection of the spin state of the quantum sensor^24,34,35, however usually are not instantly sure to the standing molecule. The Ag + Ag pedestal on the Ag tip donates an electron into the standing PTCDA, thus offering the sensing spin ½.

Magnetic coupling throughout the quantum sensor

A comparatively giant ({vec{B}}_{textual content{tip}}) with a magnitude of ~0.9 T (most important textual content) is generated on account of magnetic interactions between Fe atoms on the tip and the sensing spin. Magnetic couplings giving rise to native ({vec{B}}) fields of this magnitude are sometimes generated by neighbouring atoms at distances of ~2 Å by way of direct change^37,44. At first sight, this means a direct binding of PTCDA to at the least one of many Fe atoms on the tip, however this may be dominated out as mentioned above. Due to this fact, we speculate that the magnetic coupling between the Fe atoms and the sensor spin is mediated by the Ruderman–Kittel–Kasuya–Yosida interplay, which is thought to achieve ample power in related atomic preparations⁵⁴. On this mannequin, the Fe atoms on the tip induce a spin polarization within the conduction electrons of neighbouring Ag atoms of the Ag-coated tip, which, in flip, polarize the sensor spin, thereby producing the massive ({vec{B}}_{textual content{tip}}) on the sensor spin. The polarization of the Ag conduction electrons additionally explains the delicate detection of the quantum spin state by tunnelling magnetoresistance.

Orientation of the quantization axis of the sensing spin

The efficient subject ({vec{B}}_{textual content{eff}}=({B}_{x}+{T}_{x},{B}_{y}+{T}_{y},{B}_{z}+{T}_{z})) skilled by the quantum sensor is a vector sum of the identified exterior subject ({vec{B}}_{textual content{ext}}=({B}_{x},{B}_{y},{B}_{z})) and the initially unknown tip subject ({vec{B}}_{textual content{tip}}=({T}_{x},{T}_{y},{T}_{z})). For the reason that sensor is a spin-½ system (isotropic g issue ≈ 2; most important textual content), the magnetic second ({vec{m}}_{textual content{s}}={vec{e}}_{textual content{s}}{mu }_{textual content{B}}) of the sensing spin is aligned with ({vec{B}}_{textual content{eff}}), that’s,

The orientation and power of ({vec{B}}_{textual content{tip}}) might be deduced from the magnetic subject dependence of the resonance frequency f₀ of the sensor (Fig. second), analogous to earlier STM-based ESR experiments³⁸. It’s typically assumed that Fe-decorated magnetic ideas have giant magnetic anisotropies and {that a} change of the exterior magnetic subject course could trigger the tip subject to flip by 180° alongside a simple axis³⁸.

In response to equation (1), within the absence of electrical and magnetic dipole moments of an area object, the magnetic-field-dependent resonance frequency ({f}_{0}({vec{B}}_{textual content{eff}})) is expounded to (left|{vec{B}}_{textual content{eff}}proper|) by

In our experimental setup, the parts of ({vec{B}}_{textual content{ext}}) are given by B_x = B_|| cos θ + B_⊥ sin θ, B_y = 0 and B_z = −B_|| sin θ + B_⊥ cos θ with θ = 7° (most important textual content and Fig. 1a). To find out the three unknown vector parts T_x, T_y and T_z of ({vec{B}}_{textual content{tip}}), we match equation (5) concurrently to all recorded resonance frequencies f₀ for the completely different out-of-plane (⊥) and in-plane (||) exterior fields (Fig. second), permitting for a 180° flip of the tip subject orientation between the 2 detected resonances for the in-plane course. From the match, we discover that the resonances for out-of-plane (blue dots in Fig. second) and at low frequency for in-plane (orange dots in Fig. second) outcome from the identical orientation of the tip subject. The resonances at excessive frequency for in-plane (orange crosses in Fig. second) outcome from the tip subject orientation being flipped by 180°. Lastly, the orientation of the sensor spin ({vec{e}}_{textual content{s}}) follows from ({vec{B}}_{textual content{eff}}) in accordance with equation (4). The ensuing orientations of ({vec{B}}_{textual content{tip}}), ({vec{B}}_{textual content{eff}}) and ({vec{e}}_{textual content{s}}) for the magnetic subject dependencies of f₀ proven in Fig. second are proven in Prolonged Knowledge Fig. 2.

Word that the orientation of ({vec{B}}_{textual content{tip}}) strongly influences f₀ and its response to the exterior magnetic fields. Due to this fact, it’s not doable to infer the orientation of ({vec{B}}_{textual content{tip}}) with out becoming the mannequin to the info. We have now additionally utilized the above tip mannequin to the 2 quantum sensors proven in Prolonged Knowledge Fig. 3 and obtained a superb settlement between the experimental information and the mannequin. This confirms the final applicability of our mannequin to explain the behaviour of the quantum sensors within the exterior magnetic subject. It is usually doable to rationalize the bistability of ({vec{B}}_{textual content{tip}}) and thus the prevalence of two ESR traces as soon as its orientation has been decided (Supplementary Part 1).

Transduction parameter

To characterize the transduction parameter γ for electrical subject sensing, we assorted the bias voltage V_DC and recorded the response of the resonance frequency f₀ at a set setpoint present of I = 15 pA. Since these measurements had been carried out in constant-current mode, the tip–pattern distance additionally assorted because the bias voltage was modified. Word {that a} change within the tip–pattern distance will end in a unique electrical subject felt by the sensor, since to a primary approximation (plate-capacitor mannequin) the electrical subject E within the STM junction is expounded to the gap z by E = V_DC/z. To disentangle the results of the bias voltage V_DC and the change in distance on the response of f₀, we carried out two extra experiments.

First, we measured the dependence of f₀ on the setpoint present I for a set bias voltage of V_DC = −70 mV in constant-current mode, that’s, with the suggestions on (Prolonged Knowledge Fig. 8a). On this case, the change in f₀ is solely the results of a change within the tip–pattern distance, because the suggestions loop regulates the gap to achieve the setpoint present for the fastened bias voltage. Within the measured vary from 5 pA to 25 pA, we discover a linear dependence of f₀ on I. A linear match to the info in Prolonged Knowledge Fig. 8a yields a slope of 25.8 MHz pA⁻¹. Second, we recorded an I(V) spectrum with the quantum sensor in constant-height mode, that’s, at fastened tip–pattern distance (Prolonged Knowledge Fig. 8b). For this measurement, the tip was initially stabilized at one of many setpoints used for the measurement of the bias dependence of f₀, that’s, V_DC = −70 mV, I = 15 pA (Fig. 2e). These two information units allowed us to right for the impact of the gap change when measuring f₀ as a operate of V_DC in constant-current mode.

As an instance this, we give attention to measurements at damaging bias voltages (Fig. 2e), for the sake of simplicity. Prolonged Knowledge Fig. 8b reveals that altering the bias voltage from −70 mV to −20 mV would change the present from 15 pA to six pA if we had been measuring in constant-height mode. Nevertheless, since throughout the ESR sweep at 15 pA we’re in constant-current mode, the suggestions loop decreases the tip–pattern distance to right for the 9 pA present discount at fixed top between the 2 bias voltages. In response to Prolonged Knowledge Fig. 8a, this 9 pA discount corresponds to an extra resonance frequency shift of ~−230 MHz. The resonance shift from −70 mV to −20 mV is −2.163 GHz at fixed present (Fig. 2e). Corrected for the impact of the gap lower (present improve), the resonance frequency shift is subsequently −2.393 GHz at fixed top.

To acquire the transduction parameter γ, we corrected all f₀ that had been measured as a operate of V_DC at fixed present for the impact of the gap/present change, as described above, and fitted the ensuing information with a linear match, yielding −0.047 GHz mV⁻¹ (Fig. 2e). Notably, the linearity of the f₀ versus V_DC curve in Fig. 2e is actually preserved when information are plotted at fixed top, as a result of the I(V) dependence is near linear for the low bias voltages thought-about right here (cf. Prolonged Knowledge Fig. 8b).

We additionally decided the transduction parameters for the sensors in Prolonged Knowledge Fig. 3a,b, acquiring γ ≈ −0.065 GHz mV⁻¹ and γ ≈ −0.104 GHz mV⁻¹, respectively. Word that these values usually are not corrected for adjustments of the tip–pattern distance.

Electrical dipole moments

In response to the Helmholtz equation

the floor potential ({Phi }_{textual content{s}}) is expounded to the perpendicular dipole density ({Pi }_{perp }). The duty of figuring out the (perpendicular) electrical dipole moments

of the Ag dimer and the Fe atom thus reduces to measuring the floor potential of the pattern (A is the world coated by the dimer or atom, respectively). For the reason that quantum sensor responds to the electrical potential ({Phi }^{* }) on the place (vec{r}) of the sensor spin, that’s, on the place of the PTCDA molecule on the tip, the duty quantities to reconstructing the floor potential ({Phi }_{textual content{s}}left(vec{r}{prime} proper)) within the object floor from the potential ({Phi }^{* }(vec{r})) within the imaging airplane that’s situated a number of Å above the article floor. ({Phi }_{textual content{s}}left(vec{r}{prime} proper)) and ({Phi }^{* }(vec{r})) are associated by an electrostatic boundary worth downside. It was proven that their relation might be expressed as⁵⁵

the place the PSF (xi) might be calculated from the Dirichlet Inexperienced’s operate. If the tip–pattern junction is approximated by parallel plates (pp), equation (8) turns into

with ({vec{r}}=({vec{r}}_,{rm{z}})).

If a degree dipole is positioned at ({vec{r}}_{parallel }^{,prime}) on the planar floor, the floor potential will develop a deformation

the place ({epsilon }_{0}) is the vacuum permittivity, and one obtains from equation (9)

for the potential on the place of the sensor. That is the potential that adjustments the ESR frequency. We calculated ({Phi }^{* }left(vec{r}proper)) by including up the potentials of the unique dipole and an infinite collection of picture dipoles which can be generated by alternately mirroring on the planar tip and pattern surfaces, thus taking the screening of the dipole’s subject by each the metallic pattern and the metallic tip into consideration⁵⁵. This screening will increase the lateral decision of the quantum sensor as a result of it results in an exponential decay of the PSF with lateral distance from the sources (right here level dipole) within the floor airplane.

The sensitivity of the ESR frequency to electrical potentials follows from the experimental transduction relation ({f}_{0}=gamma {V}_{textual content{DC}}+{gmu }_{textual content{B}}left|,{vec{B}}_{textual content{eff}}proper|/h) (Fig. 2e), measured on the naked floor (({Phi }_{{rm{s}}}=0)) at sufficiently giant lateral distance from both the Fe atom or the Ag dimer. On the utilized bias voltage V_DC, the potential on the sensor on this case is ({Phi }_{textual content{sensor}}=alpha {V}_{textual content{DC}}), with (alpha equiv dPhi /d{V}_{{rm{DC}}}). Therefore, when it comes to the appearing potential ({Phi }_{textual content{sensor}}), the transduction relation turns into

It needs to be famous that each α and γ are properties of the sensor itself and thus could range for various sensors.

We now return to the case of the purpose dipole on the floor. On the idea of equations (11) and (12), it causes a frequency shift of the quantum sensor relative to equation (12) of

We be aware that for a common boundary worth downside

holds⁵⁵. Within the current case, this turns into (with equation (11))

If one normalizes the operate (frac{{epsilon }_{0}}{{P}_{perp }}{Phi }^{* }({vec{r}}_{parallel },z)) that was calculated by summing up the infinite collection of picture dipole potentials (see above) to yield 1 after integration over the imaging airplane at every z, a normalized PSF ({xi }_{textual content{pp}}^{,* }left(left|{vec{r}}_{parallel }-{vec{r}}_{parallel }^{prime} proper|,zright){=xi }_{textual content{pp}}left(left|{vec{r}}_{parallel }-{vec{r}}_{parallel }^{prime} proper|,zright)/alpha (z)) is obtained with which equation (13) lastly turns into

The unknown α(z) thus drops out.

We used equation (16) to suit the experimentally measured ({Delta f}_{0}left(vec{r}proper)/gamma) information for the Ag dimer and the Fe atom (Fig. 3d,e). To this finish, ({xi }_{textual content{pp}}^{,* }left(left|{vec{r}}_{parallel }-{vec{r}}_{parallel }^{prime} proper|,zright)) features for every z had been precalculated in steps of 0.5 Å. Then, P_⊥ and z had been used as match parameters, thereby deciding on the pair that yields the smallest χ² error. We be aware that two similar values for the heights, z_Ag = 14.5 ± 1.0 Å for Ag₂ and z_Fe = 14.5 ± 1.0 Å for Fe, had been obtained within the two unbiased suits of the Ag₂ and Fe information that had been recorded on the identical tip heights. This confirms the reliability of the process. Word that z displays the peak of the imaging (sensing) airplane, not the peak of the tip.

Magnetic dipole moments

The magnetic dipole–dipole interplay between the magnetic second ({vec{m}}_{textual content{s}}) of the quantum sensor and the native magnetic second ({vec{m}}_{textual content{Fe}}) of the Fe atom is given by

with β ≈ 3, the place μ₀ is the vacuum permeability, (vec{r}=(x,y,z)) is the gap between the 2 magnetic moments and (hat{r}) is the corresponding unit vector. The vertical distance z between the 2 magnetic moments stems from the peak distinction between the PTCDA molecule (sensor) on the tip and the Fe atom on the floor and thus signifies the place the magnetic sensing happens within the molecule (Supplementary Part 2). We assume that the electrical and magnetic sensing happen on the identical level within the molecule, that’s, we set z = z_Fe = 14.5 Å as obtained from the dedication of the electrical dipole second (Strategies). The orientation of the quantization axis of the quantum sensor and its magnetic second is extracted from the magnetic subject dependence in Fig. second (Strategies). It’s ({vec{m}}_{textual content{s}}approx (-0.1,-0.6,-0.8){mu }_{textual content{B}}) for B_⊥ = −0.5 T in Fig. 3c. Owing to the uniaxial magnetic anisotropy of Fe on Ag(111)⁴⁶, solely the out-of-plane element m_Fe,z of the magnetic second of Fe is taken into account, that’s, m_Fe,x = m_Fe,y = 0. Lastly, to suit the analytical expression ({{{E}}}_{{rm{dd}}}(vec{{{r}}})) (equation (17)) to the info in Fig. 3e, we use m_Fe,z and β as free match parameters. The most effective least-squares match yields m_Fe,z = −3.2 ± 0.4 μ_B and β = 3.1 ± 0.05. The fitted β is in good settlement with the attribute exponent (β ≡ 3) of the magnetic dipole–dipole interplay, confirming the belief that the interplay originates from the dipole–dipole interplay. Furthermore, the wonderful settlement between the magnetic second of Fe decided with the quantum sensor and the literature worth (most important textual content) confirms the belief that the electrical and magnetic sensing happen on the identical location within the sensor (Supplementary Part 2). We be aware that the quantum sensor just isn’t restricted to sensing out-of-plane parts, however can be utilized as a three-dimensional (vec{B})-field sensor, permitting the dedication of magnetic moments with arbitrary orientation.

We be aware that for all fabricated quantum sensors, we noticed a response to the native electrical and magnetic fields of an Fe atom. The resonance frequency response for the sensors offered in Prolonged Knowledge Fig. 3 is proven in Prolonged Knowledge Fig. 9 for various lateral method instructions.