CN112113991B - A non-local resistive nuclear magnetic resonance measurement method - Google Patents
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Abstract
本发明的一种非局域电阻式核磁共振测量方法属于自旋电子学技术领域，主要步骤包括：将非局域测量用二维电子气霍尔条形样品置于带有试样旋转台的低温恒温器中，形成具有磁畴结构的量子霍尔铁磁态；针对量子霍尔铁磁态进行非局域电阻测量、据获得的量子霍尔铁磁态电阻峰与倾角关系图谱对该量子态进行电阻式核磁共振测量、依据所获核磁共振图谱对量子霍尔铁磁态进行核自旋弛豫时间T1和核自旋退相干时间T2测量。本发明通过非局域测量构型的引入，实现了小电流下的动态核极化，从而确保所测量子态始终处于平衡态，所测量子态非局域电阻比正常测量电阻小2个数量级，将电阻式核磁共振测量精度提高了1个数量级。
A non-local resistance nuclear magnetic resonance measurement method of the present invention belongs to the technical field of spintronics, and the main steps include: placing a two-dimensional electron gas Hall strip sample for non-local measurement in a sample rotating table In the cryostat, a quantum Hall ferromagnetic state with a magnetic domain structure is formed; the non-local resistance measurement is performed for the quantum Hall ferromagnetic state, and the relationship between the resistance peak and the dip angle of the quantum Hall ferromagnetic state is obtained. According to the obtained nuclear magnetic resonance spectrum, the quantum Hall ferromagnetic state is measured by nuclear spin relaxation time T 1 and nuclear spin decoherence time T 2 . The invention realizes the dynamic nuclear polarization under small current by introducing the non-local measurement configuration, thereby ensuring that the measured sub-state is always in the equilibrium state, and the non-local resistance of the measured sub-state is 2 orders of magnitude smaller than the normal measurement resistance , which improves the measurement accuracy of resistive NMR by an order of magnitude.
Description
Technical Field
The invention belongs to the technical field of spintronics, and relates to a method for detecting quantum state intrinsic characteristics and novel topological states with ultrahigh sensitivity in a minimally invasive manner.
Background
Nuclear magnetic resonance techniques with ultra-high detection sensitivity, accuracy and resolution are now widely used in many scientific research fields. Generally, high signal-to-noise ratio measurements require that the number of sample nuclei measured by the technique be no less than 1015. Obviously, this requirement is difficult to satisfy in low dimensional materials or devices (e.g., semiconductor single quantum well confined two-dimensional electron gas systems with atomic number less than 108). For this reason, the discoverer of the quantum hall effect, von krey research team of mapplet, germany, created a resistive nuclear magnetic resonance measurement technique in 1988 using electron spin resonance-induced dynamic nuclear polarization and successfully achieved highly sensitive detection of single-layer GaAs/AlGaAs quantum well Ga and As nuclei. From this point on, the resistance-type nuclear magnetic resonance measurement technology is widely used for the research of GaAs two-dimensional electron gas electron spin and nuclear spin dynamics and spin qubit. However, the technology has been limited to GaAs/AlGaAs systems for more than two decades, and the underlying reason is that the dynamic nuclear polarization method relied on is derived from the unique properties of GaAs two-dimensional electron gas: a small lambertian g factor and an ultra-high electron mobility. To expand the application of this NMR measurement technique with ultra-high sensitivity to GaAs, the applicant's topic group developed a completely new dynamic nuclear polarization method (japanese patent No. P5569945 and US patent No. US9310449B2 were obtained in 2014 and 2016, respectively) by using a gradient magnetic field technology, and successfully realized resistive nuclear magnetic resonance measurement of InSb two-dimensional electron gas. The method is expected to be used for resistive nuclear magnetic resonance characterization of a two-dimensional electron gas system with large effective mass or large Lambda factor.
It should be noted that the dynamic nuclear polarization method adopted in the resistive nmr measurement is based on the induction of nuclear spin polarization by a large current flowing through the sample test region. The larger working current can easily generate joule heat inside the sample, thereby affecting the quantum state characteristics and weakening the measurement signal strength. In particular, the current under the magnetic field condition generates a hall bias in the two-dimensional electron gas perpendicular to the magnetic field and the current direction, and the larger the current, the larger the generated hall bias. At this point, the measured quantum state is actually in an unbalanced state, which severely hinders the detection and characterization of its intrinsic properties. The influence of the Hall bias on the quantum state is seriously ignored in the past transport measurement and resistance type nuclear magnetic resonance measurement.
Disclosure of Invention
The invention aims to solve the technical problem of how to realize the dynamic nuclear polarization of a measured quantum state area under the condition of weak current and provide a magnetic resonance technology for detecting the intrinsic characteristic of the quantum state in a minimally invasive manner, which has higher measurement precision than the traditional resistance type nuclear magnetic resonance.
The technical problem is solved by the following technical scheme:
a non-local resistance type nuclear magnetic resonance measurement method comprises the following specific steps:
step S1: placing a two-dimensional electron gas Hall strip-shaped sample for non-local measurement in a cryostat with a sample rotating platform, and precisely adjusting an included angle between a sample normal line and a static magnetic field direction generated by an additional magnet of the cryostat through a stepping motor to enable two Landau energy levels with opposite two-dimensional electron gas spin to be overlapped so as to form a quantum ferromagnetic Hall state with a magnetic domain structure; the length-to-width ratio l/w of the Hall strip sample is greater than 3 so as to ensure that the measured non-local resistance is far greater than the ohmic resistance caused by the diffusion of the applied current;
step S2: the method comprises the steps of firstly, fixing a non-local resistance measurement configuration, researching the dependency relationship between the resistance peak characteristic of the quantum Hall ferromagnetic state and the current magnitude under the configuration, and calculating the Hall bias voltage epsilon generated by the applied current in a sample bodyH＝ρxyI/w in accordance with ∈HObtaining a current threshold value through the relation with the effective temperature, wherein the temperature of the sample is not obviously improved and is still in an equilibrium state when the current threshold value is smaller than the threshold value; under the condition of low current far lower than a threshold value, the inclination angle of the sample is adjusted to change the interaction between electrons at the overlapping part of the Landaus, and a magnetic resistance map of a resistance peak changing along with the inclination angle is drawn; then, changing the non-local resistance measurement configuration to repeat the measurement; because the resistance peak characteristic is derived from the quantum Hall ferromagnetic state magnetic domain structure, the change of the resistance peak characteristic indicates the change of the corresponding quantum state magnetic domain structure;
step S3: performing resistance-type nuclear magnetic resonance measurement on the quantum state according to the relation map of the resistance peak and the inclination angle of the quantum Hall ferromagnetic state obtained in the step S2, and firstly, applying current close to a threshold value in the resistance peak area to polarize nuclear spin; closing the current after the polarization resistance of the nuclear spin resonance peak reaches saturation, simultaneously utilizing a coil wound around the sample to generate a transverse alternating magnetic field to depolarize the nuclear spin, and obtaining the resistance peak caused by depolarization near the nuclear spin resonance frequency as the nuclear magnetic resonance peak; then, drawing a variation map of the nuclear magnetic resonance peak and the inclination angle;
step S4: performing nuclear spin relaxation time T on the quantum Hall ferromagnetic state according to the nuclear magnetic resonance spectrum obtained in the step S31And nuclear spin de-coherence time T2And (6) measuring.
Further, in step S1, the width w of the Hall strip-shaped sample is preferably 20-30 μm, and the length l of the Hall strip-shaped sample is preferably 60-150 μm; the product of the Langdg factor and the effective mass m of the sample to be detected satisfies mg ═ 2cos thetacWherein thetacIs a Landau level coincidence angle of 60-70 DEG, and the two-dimensional electron gas density is 2-3 x 1015m-2Two-dimensional electron gas electronMobility greater than 10m2Vs to ensure that the quantum hall ferromagnetic state formed has a clear resistance peak.
Further, the implementation process of step S4 is as follows: firstly, inducing quantum Hall ferromagnetic state to generate dynamic nuclear polarization through current; after the resistance value caused by polarization tends to be saturated, a continuous alternating magnetic field generated by a single-strand coil wound around the sample is utilized to implement a depolarization process at the resonance frequency point of the measured sub-state atomic nucleus; after the resistance value caused by depolarization tends to be saturated, the alternating magnetic field is closed, so that the atomic nucleus is in the repolarization process; the natural exponential function fitting is carried out on the time variation curve of the repolarization resistance to directly obtain T1And by the formula Tr ═ T1/(1+ω2T1T2) Calculating to obtain T2Wherein Tr is obtained by fitting a natural exponential function of a depolarization resistance time-varying curve, and omega is the ratiometric frequency of the measured atomic nucleus.
Compared with the traditional resistance type nuclear magnetic resonance technology, the invention has the following advantages:
1. by introducing the non-local resistance measurement configuration, the induced current of the measured sub-state area for dynamic nuclear polarization is reduced by nearly 50 times, so that the generation of joule heat is avoided to a great extent, the Hall bias voltage is greatly reduced, the quantum state is ensured to be always in a balanced state in the nuclear magnetic resonance measurement process, and the intrinsic characteristics of the quantum state are favorably detected and characterized;
2. different non-local measurement configurations show different quantum Hall ferromagnetic state characteristics, and the possibility is provided for a system to comprehensively research the quantum state;
3. because the measured sub-state non-local resistance is smaller than the normal measured resistance by about 2 orders of magnitude, the resistance value of the resistance type non-local resistance is more sensitive to the slight change of the sample characteristic, and the resistance type nuclear magnetic resonance measurement precision is further improved by 1 order of magnitude.
Description of the drawings:
FIG. 1 is a schematic diagram of a Hall bar sample in an embodiment of the present invention.
FIG. 2 is comparative data of measured sub-state magnetoresistance before and after improvement of the measurement method in the example of the present invention.
FIG. 3 is comparison data of nuclear magnetic resonance signals before and after improvement of the measurement method in the example of the present invention.
FIG. 4 is nuclear spin relaxation and decoherence time data of measured sub-states in an embodiment of the present invention.
Detailed Description
The technical solution of the present invention will be specifically described below with reference to the accompanying drawings.
The schematic diagram of the InSb/AlInSb two-dimensional electron gas Hall strip-shaped sample is shown in figure 1, wherein the length l of a Hall measurement area 1 is 100 micrometers, and the width w of the Hall measurement area is 30 micrometers. The sample has the Langdg factor of g to-50 and the effective mass of m to 0.015me(meEffective quality of electrons) and the electronic gas density is 2.8 x 1015m-2Electron mobility of 19m2Vs, these parameters ensure that all electrons occupy only the first sub-band of the two-dimensional electron gas energy band and form a quantum hall ferromagnetic state below the laboratory maximum operating magnetic field (15T). The quantum state is formed at an included angle of 64 DEG and 13T of a static magnetic field direction of an additional magnet of the thermostat and a sample normal, and a longitudinal resistance (R) is measured by a Hall67,25＝V25/I67，I67: the current between the electrodes 6 and 7 in fig. 1 is 31.6nA in magnitude; v25: voltage between electrodes 2 and 5 in fig. 1) and the results are shown in fig. 2. By way of comparison, FIG. 2 also shows the quantum state non-local resistance (R)23,45＝V45/I23Current I of2313.6nA flows through the electrodes 2 and 3 away from the measurement voltage V45The electrodes 4 and 5) used exhibit a fine structure, and R23,45And R67,25The resistance magnitudes differ by nearly two orders of magnitude. The basic principle of non-local measurement is to use the hall edge states 8 to transport electrons away from the area of applied current, thereby avoiding the passage of large currents in the measurement area. By systematically researching the dependency relationship between the Hall ferromagnetic state resistance peak characteristic and the current magnitude in the configuration, the current threshold value of the sample in the equilibrium state can be determined to be 3.16 muA. Although I23The 3.16 muA belongs to the large current category for low-dimensional sample low-temperature test, but the body current flowing through the sample measuring area at the moment is obtained through calculationOnly about 10nA, corresponding to a Hall electric field epsilonH＝ρxyI/w is 10V/m, where ρxyAt 26k Ω, the effective temperature is correspondingly changed by about 100mK, thereby ensuring that the measurement region is always in equilibrium. It is noted that the fine structure of the resistance peak and the corresponding current threshold vary as the measurement configuration changes. The measurement was carried out using a Lake Shore AC resistance bridge (Model 370) with a test frequency of 13.7Hz and a current of 31.6 nA; oxford Instrument MX400 dilutes the condenser at a temperature of 1K.
Non-local resistance type nuclear magnetic resonance measurement is carried out near a quantum Hall ferromagnetic state (11T-15T, figure 2): a fixed magnetic field will23Increased to 3.16 muA, the non-local resistance R to be measured23,45After saturation (polarization process) the nuclear spins are depolarized by applying an alternating magnetic field (of the order of μ T) generated by a coil 9 wound around the sample, the frequency of the alternating magnetic field is continuously varied and sought115The resonance resistance peak of the In nucleus (i.e. the resistive nuclear magnetic resonance signal). The sample was found to have a resonance signal (. DELTA.R) at 13T23,45) Strongest, its amplitude variation ratio (Δ R)23,45/R23,45) Is a conventional resistance-type nuclear magnetic resonance measurement (Δ R)67,25/R67,25) 10 times higher (see fig. 3). As mentioned earlier, since the bulk current flowing through the sample is only 10nA, it is ensured that the region where dynamic nuclear polarization occurs is always in equilibrium. This is important for detecting the intrinsic properties of the quantum states and has not been possible with any previous test approach.
Further, inducing the quantum Hall ferromagnetic state to generate dynamic nuclear polarization through current; after the resistance value caused by polarization tends to be saturated, a continuous alternating magnetic field generated by a single-strand coil wound around the sample is utilized to implement a depolarization process at the resonance frequency point of the measured sub-state atomic nucleus; after the resistance value caused by depolarization tends to be saturated, the alternating magnetic field is closed, so that the atomic nucleus is in the repolarization process; the natural exponential function fitting is carried out on the time variation curve of the repolarization resistance to directly obtain T1And by the formula Tr ═ T1/(1+ω2T1T2) Calculating to obtain T2In which Tr is plotted by depolarization resistance versus timeFitting natural exponential function to obtain omega as the ratio frequency of the measured atomic nucleus115The In nucleus, ω, was 10Hz under the continuous alternating magnetic field conditions used In this experiment.
T1And T2The measured data are shown in FIG. 4, and it can be seen from FIG. 4 that the quantum state has a smaller T at 13T1(8s) and 1/T1Decreases linearly with increasing temperature T, while T2Decreases as T increases. Theoretical analysis of these data confirmed that a novel topological particle, domain wall stark, exists in the magnetic domain wall of the quantum hall ferromagnetic state in the wigner lattice form.
It can be seen from the above embodiments that the present invention introduces a non-local resistance measurement configuration into resistive nuclear magnetic resonance measurement, which not only improves the measurement sensitivity, but also provides a method for minimally invasive detection of quantum state intrinsic characteristics and novel topological states. The above-mentioned embodiments are provided to explain the objectives, technical solutions and achievements of the present invention in detail. It should be understood that the above description is only exemplary of the present invention, and is not intended to limit the present invention. Any modification, equivalent replacement, and improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (2)
1. A non-local resistance type nuclear magnetic resonance measurement method comprises the following specific steps:
step S1: placing a two-dimensional electron gas Hall strip-shaped sample for non-local measurement in a cryostat with a sample rotating platform, and precisely adjusting an included angle between a sample normal line and a static magnetic field direction generated by an additional magnet of the cryostat through a stepping motor to enable two Landau energy levels with opposite two-dimensional electron gas spin to be overlapped so as to form a quantum ferromagnetic Hall state with a magnetic domain structure; length to width ratio of the Hall strip samplel/w >3 to ensure that the measured non-local resistance is much greater than the ohmic resistance caused by the spreading of the applied current;
step S2: the method comprises the steps of firstly, fixing a non-local resistance measurement configuration, and researching the configurationThe dependence of the peak resistance characteristic of quantum Hall ferromagnetic state on the current magnitude is calculated, and the Hall bias voltage ℰ generated by the applied current in the sample body is calculated𝐻=𝜌𝑥𝑦𝐼/wAccording to ℰ𝐻Obtaining a current threshold value through the relation with the effective temperature, wherein the temperature of the sample is not obviously improved and is still in an equilibrium state when the current threshold value is smaller than the threshold value; under the condition of low current far lower than a threshold value, the inclination angle of the sample is adjusted to change the interaction between electrons at the overlapping part of the Landaus, and a magnetic resistance map of a resistance peak changing along with the inclination angle is drawn; then, changing the non-local resistance measurement configuration to repeat the measurement; because the resistance peak characteristic is derived from the quantum Hall ferromagnetic state magnetic domain structure, the change of the resistance peak characteristic indicates the change of the corresponding quantum state magnetic domain structure;
step S3: performing resistance-type nuclear magnetic resonance measurement on the quantum state according to the relation map of the resistance peak and the inclination angle of the quantum Hall ferromagnetic state obtained in the step S2, and firstly, applying current close to a threshold value in the resistance peak area to polarize nuclear spin; closing the current after the polarization resistance of the nuclear spin resonance peak reaches saturation, simultaneously utilizing a coil wound around the sample to generate a transverse alternating magnetic field to depolarize the nuclear spin, and obtaining the resistance peak caused by depolarization near the nuclear spin resonance frequency as the nuclear magnetic resonance peak; then, drawing a variation map of the nuclear magnetic resonance peak and the inclination angle;
step S4: performing nuclear spin relaxation time on the quantum Hall ferromagnetic state according to the variation map of the nuclear magnetic resonance peak and the inclination angle drawn in the step S3T 1And nuclear spin detrapping timeT 2The measurement is carried out as follows:
firstly, inducing quantum Hall ferromagnetic state to generate dynamic nuclear polarization through current; after the resistance value caused by polarization tends to be saturated, a continuous alternating magnetic field generated by a single-strand coil wound around the sample is utilized to implement a depolarization process at the resonance frequency point of the measured sub-state atomic nucleus; after the resistance value caused by depolarization tends to be saturated, the alternating magnetic field is closed, so that the atomic nucleus is in the repolarization process; the method is directly obtained by fitting the time-dependent change curve of the repolarization resistance with a natural exponential functionT 1And by the formulaTr = T 1/(1+ω 2 T 1 T 2) Is calculated to obtainT 2WhereinTr is obtained by fitting a natural exponential function of a depolarization resistance time-varying curve,ωis the ratio frequency of the measured nuclei.
2. The non-local-area-resistance-type NMR measurement method according to claim 1, wherein in step S1, the Hall strip-shaped sample has a widthw20 to 30 μm in lengthl60 to 150 μm; land of sample to be testedgFactor and effective massmThe product ofmg= 2cosθ cWhereinθ cThe electron beam is a Landau level coincidence angle, the value of the Landau level coincidence angle is 60-70 degrees, and the two-dimensional electron gas density is 2-3 multiplied by 1015 m-2Two-dimensional electron gas electron mobility is larger than 10m2/Vs。
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| Publication number | Priority date | Publication date | Assignee | Title |
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| US4791368A (en) * | 1986-03-24 | 1988-12-13 | Kabushiki Kaisha Toshiba | Automatic magnetic field measuring apparatus using NMR principles |
| WO2003049197A1 (en) * | 2001-12-06 | 2003-06-12 | Japan Science And Technology Agency | In-solid nuclear spin quantum calculation device |
| CN105242094A (en) * | 2015-11-11 | 2016-01-13 | 电子科技大学 | FM/NM thin-film structure inverse spin hall voltage value measurement method |
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| US9310449B2 (en) * | 2009-12-18 | 2016-04-12 | Japan Science And Technology Agency | Nuclear-spin polarization detection device and nuclear-spin polarization detection method |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| US4791368A (en) * | 1986-03-24 | 1988-12-13 | Kabushiki Kaisha Toshiba | Automatic magnetic field measuring apparatus using NMR principles |
| WO2003049197A1 (en) * | 2001-12-06 | 2003-06-12 | Japan Science And Technology Agency | In-solid nuclear spin quantum calculation device |
| CN105242094A (en) * | 2015-11-11 | 2016-01-13 | 电子科技大学 | FM/NM thin-film structure inverse spin hall voltage value measurement method |
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| Title |
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| Role of chiral quantum Hall edge states in;Kaifeng Yang et al.;《NATURE COMMUNICATIONS》;20170420;1-7 * |
| 电阻式核磁共振测植的最新进展;刘洪武 等;《物理学报》;20120731;第61卷(第4期);147302 * |
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