Despite the challenges, neutron resonance spin echo still holds the promise to improve upon neutron spin echo for the measurement of slow dynamics in materials. We present a bootstrap, radio frequency neutron spin flipper using high temperature superconducting technology capable of flipping neutron spin with either nonadiabatic or adiabatic modes. A frequency of 2 MHz has been achieved, which would achieve an effective field integral of 0.35 T m for a meter of separation in a neutron resonance spin echo spectrometer at the current device specifications. In bootstrap mode, the self-cancellation of Larmor phase aberrations can be achieved with the appropriate selection of the polarity of the gradient coils.

Neutron Spin Echo (NSE) as proposed by Mezei1 allows considerably higher resolution of slow dynamics than traditional neutron scattering techniques by using the Larmor precession of a neutron’s spin in a magnetic field to encode the neutron’s velocity into the Larmor phase ϕ = γBdt = γBL/v,2 where γ is the gyromagnetic ratio of the neutron and v is the velocity of the neutron passing through a magnetic field B of length L. A NSE spectrometer is composed of two magnetic field regions of opposite magnetic field directions tuned such that the Larmor phase accumulated in the first magnet is balanced out by the second one, ϕT = ϕ1 + ϕ2 = 0, if the velocity of the neutron is unchanged. Scattering on a sample placed between the two magnets will cause a change in the neutron’s energy ΔE, which results in a change in the total Larmor phase,

Δϕ=ΔEτ/,
(1)
τ=m2γBLλ32πh2=mλ22πhϕ,
(2)

where m denotes the mass of the neutron, λ denotes the neutron wavelength, and h is Planck’s constant. The spin echo time, τ, sets the scale for the polarization change for a shift in energy ΔE. Increased resolution comes from increasing the spin echo time, which can be done by using longer wavelength neutrons or by increasing the field integral ∫BdL in the spectrometer.

Neutron Resonance Spin Echo (NRSE) was proposed as an alternative to NSE which could potentially increase the resolution by replacing the large DC coils with two compact neutron radio frequency (RF) spin flippers separated by length L.3 A RF spin flipper is comprised of a constant field B0 and a transverse RF field with a frequency ω0 = γB0. The equivalent Larmor phase for a NRSE setup of two RF spin flippers separated by zero field is ϕ = 2ω0L/v.3 NRSE has several theoretical advantages over NSE: a NRSE spectrometer arm operated at resonant frequency ω0 = γB0 is equivalent to an NSE spectrometer of the same length operating at magnetic field 2B0; the resolution can be doubled by the “bootstrap” method of replacing a single spin flipper with a pair of flippers that have opposite B0 direction; the stability of the Larmor phase is dependent on the frequency stability of the RF signal generator rather than the stability of the DC field power supply; and utilizing compact coils makes field homogeneity goals easier to achieve while decreasing power requirements.

There are two subtypes of NRSE, in which B0 is either transverse to the beam direction (TNRSE) or longitudinal to the beam direction (LNRSE). TNRSE was first proposed using a linearly oscillating RF field which was mutually transverse to B0 and the beam. An advantage to this method is the relative ease with which the bootstrap configuration can be achieved. Also in this configuration, if the flipper can be made very thin, it can be tilted for use in applications such as Larmor diffraction4 and phonon linewidth measurements.5 However, the confinement of the magnetic fields requires aluminum windings across the beam path, such that each bootstrap spin flipper has 4–8 layers of aluminum wires in the beam path resulting in parasitic scattering and absorption of the neutrons. LNRSE was proposed to take advantage of self-phase cancellation within each flipper.6 LNRSE can also be combined with NSE to increase the dynamic range and utilize the well established NSE techniques for correcting beam divergence effects, i.e., Pythagoras or Fresnel coils, which has recently been demonstrated at the RESEDA beamline at Heinz Maier-Leibnitz Zentrum (MLZ).7 However, the bootstrap method is difficult to implement in the LNRSE configuration without producing zero-field crossings which can depolarize the neutrons.

Modulation of Intensity Emerging from Zero Effort (MIEZE)8 is a variation of NRSE in which only two RF spin flippers are utilized, operating at different frequencies. A polarization analyzer can be placed after the second RF flipper, and an intensity modulation in time and space will persist after the analyzer. The contrast of this modulation can be measured at a detector with adequate timing resolution, and changes in the contrast correlate with neutron energy transfer due to scattering from a sample placed between the analyzer and the detector. This unique placement of the sample allows for samples which are difficult if not impossible to use with traditional NSE or NRSE, i.e., depolarizing samples or sample environments with large magnetic fields.

In this report, we present a transverse neutron resonant bootstrap spin flipper implemented with high-temperature superconducting (HTS) tape and films. HTS tape coil windings allow for increased current density, and consequently, high B0 field and RF frequency can be achieved even with a coil gap for the beam to pass through. Similar to the RF flippers implemented on the Larmor and Offspec9 beamlines at the ISIS Neutron and Muon Source of Rutherford Appleton Laboratory, United Kingdom, the B0 field is transverse to the beam, and the RF field is aligned parallel to the beam direction. The design is similar to the superconducting magnetic Wollaston prisms10 which have been employed in spin echo modulated small angle neutron scattering,11 Larmor diffraction,12 and inelastic neutron spin echo13 and which have very high neutron transmission efficiency.14 Before we discuss the design and characterization of a single spin flipper device, we would like to summarize the NRSE technique and RF spin flipping mechanisms.

The NRSE method as proposed by Golub and Gähler3 is composed of two spectrometer arms, one on either side of the sample, as shown in Fig. 1. Each arm in this case is composed of two RF spin flippers of length d separated by a zero magnetic field region of length L1(2). Incident neutrons are polarized perpendicular to the B0 field of the flipper and beam. After exiting the first spin flipper, the final state has a time, t, and position, x, dependent difference in the up and down spinor components,15 

|ψ(t)=i2αeiΦ(x,t)α+eiΦ(x,t),
(3)
Φ(x,t)=ω0xd/2vt,
(4)

where α±=e±ϕ0/2 is the initial phase of the up (down) component of the spinor and the distance x is relative to the entrance of the device. The time dependence in the polarization follows from the energy difference ΔE = 2ℏω0 between the up and down components of the spin produced by the spin flip.15 The polarization along the initial polarization axis after the spin flipper has a spatial and time dependence15 given by

ψ(t)|σy|ψ(t)=cos2ω0xd/2vt.
(5)
FIG. 1.

A schematic of a two-arm NRSE spectrometer. The neutron beam is along the x^-axis, the B0 field is along the -direction, and the RF fields rotate in the xy plane. Incident neutrons from the left are polarized into the xy plane before traveling through the first pair of RF spin flippers separated by length L1. After scattering from the sample, the neutrons travel through the second pair of RF spin flippers, separated by length L2, and then the spin polarization is analyzed before the neutrons are counted at the detector.

FIG. 1.

A schematic of a two-arm NRSE spectrometer. The neutron beam is along the x^-axis, the B0 field is along the -direction, and the RF fields rotate in the xy plane. Incident neutrons from the left are polarized into the xy plane before traveling through the first pair of RF spin flippers separated by length L1. After scattering from the sample, the neutrons travel through the second pair of RF spin flippers, separated by length L2, and then the spin polarization is analyzed before the neutrons are counted at the detector.

Close modal

Measuring the polarization at a static detector position yields a time dependent oscillation with a frequency of 2ω0. As shown in Fig. 1, the second RF spin flipper in an NRSE spectrometer arm has the same B0 field direction as the first flipper and the RF field phase is synchronized with the first flipper so that the energy splitting between the up and down states is removed, stopping the time modulation. The time dependence of the polarization is similar to the precession of neutron spin in the static field of traditional NSE, which is why the precession in NRSE is often termed zero field precession with a virtual field of 2B0. A second spectrometer arm placed after the sample with the opposite B0 field direction is tuned to have the same effective phase but in the opposite direction as the first arm if the neutron energy is unchanged. Any change in the neutron energy will cause a difference in the transit time and thus relative phase between the spectrometer arms, producing a change in the measured polarization after the second arm. The final phase of a NRSE spectrometer is given by3 

ϕT=1v12ω1(L1+d)+ωG,1L11v22ω2(L2+d)+ωG,2L2,
(6)

where ωG,i is the result of a guide field between the spin flippers if present. The relative phase in each arm can then be tuned for quasielastic or inelastic scattering, in the same manner that NSE is tuned, but varying ω1, ω2 and their respective B0 fields. If present, a guide field in each arm BG = ωG,i/γ may be useful for fine-tuning or increasing the dynamic range of the resolution in NRSE instruments by combining with NSE.16,17 Replacing each individual spin flipper with a bootstrap pair of spin flippers doubles the energy splitting, which has the effect of doubling the frequency in Eq. (5) and the phase in Eq. (6).

Here, we will summarize the MIEZE method; for more detailed derivations, see Refs. 8 and 15. Consider the case in which two RF spin flippers operating at angular frequencies ω1, ω2 separate by distance ΔL and with the second RF flipper located a distance LS from the detector, as shown in Fig. 2.

FIG. 2.

A schematic of a MIEZE spectrometer. The neutron beam is along the x^-axis, the B0 field is along the -direction, and the RF fields rotate in the xy plane. Incident neutrons from the left are polarized into the xy plane before traveling through a pair of RF flippers which are operated at different frequencies. This produces a spatial and time intensity modulation which persists after the polarization analyzer. A guide field can optionally be added between the flippers to increase the dynamic range and instrument flexibility. Please note that the definition of L2 is different from that of the NRSE setup in Fig. 1.

FIG. 2.

A schematic of a MIEZE spectrometer. The neutron beam is along the x^-axis, the B0 field is along the -direction, and the RF fields rotate in the xy plane. Incident neutrons from the left are polarized into the xy plane before traveling through a pair of RF flippers which are operated at different frequencies. This produces a spatial and time intensity modulation which persists after the polarization analyzer. A guide field can optionally be added between the flippers to increase the dynamic range and instrument flexibility. Please note that the definition of L2 is different from that of the NRSE setup in Fig. 1.

Close modal

Following the phase accumulation for each as given in Eq. (5), the phase at the detector can be written as

2ω1ΔLvΔω(L2+d/2)v+ΔωtDγBGLGv,
(7)

where tD is the time measured at the detector, Δω = ω2ω1, and the phase due to a guide field BG is included.

The general MIEZE concept is to create a sinusoidal intensity modulation at the detector, which can be seen by the 2ΔωtD term in Eq. (7). A polarization analyzer can be placed immediately after the second RF flipper, and the intensity modulation persists. Neutrons which scatter will have a different time of flight from the sample to the detector, which will decrease the contrast of the intensity modulation. There is a Fourier time, which is analogous to the spin echo time, that sets the probed scale of energy shift ΔE measured in a MIEZE experiment,

τMIEZE=m2ΔωLSλ3πh2,
(8)

where LS is the sample distance from the detector.

Variance in the incident neutron velocities will also decrease the intensity contrast, and so the setup is tuned to cancel out the velocity dependent terms in the phase. When no guide field is present, the following condition must be satisfied:

Δωω1=ΔLL2+d/2.
(9)

Inclusion of a guide field modifies the condition to remove the velocity dependence on the phase,

BG=2γLGω1ΔLΔωL2+d/2.
(10)

As shown in Eq. (10), it is now possible to select frequencies convenient for the measurement and then tune the guide field to remove the velocity dependence of the phase. This allows for setting ω2ω1 such that Δω and thus τMIEZE may be arbitrarily small. This flexibility is a significant advantage which warrants the inclusion of a guide field between the RF flippers. However, the field integral of the guide field must be sufficiently homogeneous to prevent dephasing of the neutrons. This method of guide field integral subtraction has been recently used to measure a dynamic range of seven orders of magnitude at the RESEDA beamline at FRM II.18 

The contrast of the NRSE signal is dependent on a high spin flipping efficiency to exchange the spin states. Therefore, it is critical to achieve a high spin flipping efficiency, which can be achieved using either adiabatic or nonadiabatic methods. Both utilize a RF field which is transverse to B0 and tuned to oscillate at the resonant frequency ω = ω0 = γB0. The nonadiabatic mode, named to differentiate it from the adiabatic mode, requires an additional tuning of the BRF magnitude for the time neutrons spend inside the RF field and thus is wavelength dependent. The adiabatic mode utilizes a gradient coil to generate an adiabatic rotation of the magnetic field as seen in the frame corotating at ω0. For sufficiently large magnitudes of the RF and gradient fields to satisfy the adiabatic condition, the spin flip efficiency becomes independent of the neutron wavelength, which makes it more favorable in some cases compared to the nonadiabatic mode. Both modes can be achieved with our device, and so we briefly review each spin flip method.

Consider the magnetic field B=B0z^+BRF[cos(ωt)x^+sin(ωt)ŷ] in the coordinate system defined in Fig. 1. The resulting Hamiltonian is

H=γ2B0BRFeiωtBRFeiωtB0.
(11)

Solving the Schrödinger equation for an initially spin up state gives the time evolution of the up and down components of the spinor, from which the probability of a spin flip as a function of time is

P+(t)=ψ|ψ(t)2=γ2BRF  24ωR2sin2ωRt,
(12)

where ωR=(ωγB0)2+γ2BRF  2/2 is the Rabi frequency. When the applied frequency is tuned such that ω=γB0=defω0, the probability reduces to

P+(t)=sin2γBRF2t.
(13)

A complete spin flip is achieved when the magnitude of the RF field and the time during which the field is applied satisfies the condition

γBRFt=π.
(14)

As one can see, classically the spin flip in this case is provided by the precise precession of the polarization vector around the RF field inside the frame which is rotating about the B0 field at frequency ω0.

Adiabatic spin flippers are based on the principle that the polarization vector will follow a field vector which varies “slowly” relative to the spin precession in the magnetic field, as defined by an adiabaticity parameter. Consider the previous set of magnetic fields with the addition of a static gradient coil which produces a gradient dBz/dx. In the frame corotating with the Larmor precession due to the B0 field, the magnetic field is composed of the gradient and RF fields as shown in Fig. 3. With the RF frequency on resonance, the RF field becomes static in this rotating frame. Ideally, the amplitude of the RF field will increase to a maximum at the point where the -component of the gradient field is zero. The polarization of a neutron initially polarized along which is traveling “slowly” through the fields in this rotating frame will adiabatically follow the net field direction, which is shown in Fig. 3, flipping the spin state relative to B0.

FIG. 3.

(a) The fields inside the rotating frame as a function of the position x along a spin flipper of length d and (b) the net field direction in the rotating frame (primed coordinates) as a function of the time of flight through the spin flipper. If the field rotation is slow relative to the spin precession (cones), the spin will adiabatically flip relative to the B0 field in the lab frame.

FIG. 3.

(a) The fields inside the rotating frame as a function of the position x along a spin flipper of length d and (b) the net field direction in the rotating frame (primed coordinates) as a function of the time of flight through the spin flipper. If the field rotation is slow relative to the spin precession (cones), the spin will adiabatically flip relative to the B0 field in the lab frame.

Close modal

An adiabaticity parameter must be set to define “slowly.” Grigoriev et al.19 derived such a parameter by defining the magnetic field of an adiabatic spin flipper as a static field B(x)=(B0+Acos(πx/d))z^ and a rotating field in the transverse plane BRF(x)=Asin(πx/d)(cos(ωt)x^+sin(ωt)ŷ) for a spin flipper of length d. A comparison of the spin precession frequency with the rotation frequency of the magnetic field in the rotating frame yields adiabaticity parameter k,

k=γdAπv1.
(15)

For a given magnitude of the RF and gradient fields, neutrons with velocities slow enough to satisfy the condition of Eq. (15) will undergo an adiabatic, wavelength-independent spin flip. The primary disadvantage of the adiabatic method is that, for the same device size, the RF field and thus power generally must be larger than for the nonadiabatic method in order to satisfy this condition.

There is an addition to the phase of an NRSE spectrometer for an adiabatic spin flipper. Grigoriev et al.19 calculated the polarization of a NRSE arm using single adiabatic spin flippers (not bootstrap) as

Py=σy=Pcos2ω0v(d+L1,2)+sgn(A1)2ϕg1sgn(A2)2ϕg2,
(16)

where L1,2 is denoted in Fig. 1 and sgn(A1,2) indicates the polarity of the first and second spin flipper gradient coils, ϕg1,g2 is an additional phase accumulated in the rotating frame, and the factor P accounts for any loss of polarization.19 This indicates that the additional phase due to the RF and gradient fields can be canceled in identical spin flippers by using the same gradient field orientation, reducing to the phase of a NRSE spectrometer arm with nonadiabatic spin flippers, ϕ = 2ω0(d + L)/v. This should also cancel Larmor phase aberrations due to small inhomogeneities in the RF and gradient fields. Inhomogeneities in the B0 field will contribute to the gradient field in the rotating frame, and consequently, the phase aberrations due to B0 inhomogeneities may also be canceled with this method, for small inhomogeneities which do not adversely affect the spin flipping efficiency. This is a remarkable feature of the adiabatic spin flipping mode.

We set out to build a transverse neutron resonance spin flipper capable of both nonadiabatic and adiabatic spin flipping methods using HTS technology. The TNRSE configuration is geometrically favorable for bootstrap configurations, and the devices can be made very compact with well defined magnetic field regions by using HTS films between the spin flippers. To avoid parasitic neutron scattering, the B0 coil is wound on two iron cores with a gap between them for the beam, as shown in Fig. 4. Using HTS windings allows for higher current densities so that the gap does not limit the maximum B0 field as severely as it would for a non-HTS coil.

FIG. 4.

Schematic of the RF flipper in bootstrap mode. The neutron beam would pass through the hollow cylinder form of the RF coil. Note that this is a simplified geometry, and the top yoke and some structural pieces have been removed for visibility.

FIG. 4.

Schematic of the RF flipper in bootstrap mode. The neutron beam would pass through the hollow cylinder form of the RF coil. Note that this is a simplified geometry, and the top yoke and some structural pieces have been removed for visibility.

Close modal

Cryogenic cooling is provided by a Sumitomo CH-110 cold head supplied with liquid helium from a Sumitomo F-70 compressor, capable of 70 W of cooling power at 30 K. Undesired neutron scattering is further reduced by using single-crystal sapphire windows on the vacuum chamber. There are two separate spin flipper assemblies inside the chamber which can be controlled independently, capable of running in bootstrap configuration with the fields in each spin flipper in opposite directions. As shown in Fig. 4, a gradient coil is used to generate a gradient profile dBz/dx, which is only energized when operated in adiabatic spin flipper mode. The RF field, used in both flipping modes, is linearly oscillating along the beam direction. Most of the structure is made from oxygen free copper due to its high thermal conductivity and for uniform thermal expansion within the device.

As shown in Fig. 4, the B0 coil geometry is a split solenoid with each half of the solenoid comprised of 48 turns of HTS wire, made of yttrium barium copper oxide (YBCO) by SuperPower. A low carbon steel yoke provides a flux return between the top and bottom pole pieces. HTS films separate the magnetic fields in each half of the device and improve the homogeneity of the static fields as a result of the Meissner effect. These films are made of a thin layer of YBCO (350 nm) on a 0.5 mm sapphire substrate and have been measured to have very high neutron transmission efficiency with minimal scattering.14,20 The dimensions of the coil were optimized via finite element analysis simulations using the software MagNet,21 and the optimization of the device has been summerized and presented by Li et al.26Figure 5 shows the variance of the B0 field from the central value based on the simulation. The gradient coil is also wound with HTS wire on a copper plate form. The winding geometry, shown in Fig. 4, is designed to produce dBz/dx = 0.664 GA−1 cm−1. Calibration tests were performed using a pair of Lakeshore HGCT-3020 Hall probes, the results of which are shown in Fig. 6. The B0 coils produce a field of approximately 15 GA−1, and the gradient coils produce a gradient dBz/dx = 0.675 GA−1 cm−1.

FIG. 5.

Variance of the B0 field relative to the central value in the x = 0 plane from simulation.

FIG. 5.

Variance of the B0 field relative to the central value in the x = 0 plane from simulation.

Close modal
FIG. 6.

Measurements of the resultant magnetic field as a function of current for the (a) B0 and (b) gradient coils. Gradient coil measurement is the difference of the field measured at the center and entrance of the spin flipper.

FIG. 6.

Measurements of the resultant magnetic field as a function of current for the (a) B0 and (b) gradient coils. Gradient coil measurement is the difference of the field measured at the center and entrance of the spin flipper.

Close modal

The RF field is provided by a 47-turn 18AWG solid copper magnet wire solenoid wound on a 1.5 in. diameter single-crystal hollow sapphire tube. Sapphire is the perfect material for cooling the RF components as it is an electrical insulator that has a thermal conductivity which is comparable to oxygen-free copper near the operating temperature of 30 K. A pair of copper U-shaped plates is used to shield the generated RF fields from the surrounding components. We calibrated the peak RF field as a function of current by measuring the induced voltage in a pickup loop placed in the center of the RF coil at 1 MHz. The current and measured power for two coils at 20 K as a function of the measured RF amplitude are shown in Fig. 7. Please note that the RF power is measured at the amplifier and thus includes both the RF coil and matching network power dissipation. The cold head has a capacity of 50 W at ≈26 K, which is over twice of the measured power for both the RF coils and matching network at 1 MHz for a field of 30 G. The device has been successfully operated at 2 MHz, and the RF power will increase with the square root of the frequency. Thus, we expect to be able to operate at several megahertz before heat dissipation becomes a limitation. Localized heating could present a problem, e.g., if the solenoid were to heat locally above 50 K; then, increases in the resistivity of the copper would change the load impedance, possibly causing the matching network to fail. Therefore, effective thermal coupling to the sapphire tube is essential.

FIG. 7.

RF coil calibration curve showing current and power as a function of the peak RF magnetic field at 1 MHz. Power is for a pair of RF coils wired in series. Measurements taken at 20 K.

FIG. 7.

RF coil calibration curve showing current and power as a function of the peak RF magnetic field at 1 MHz. Power is for a pair of RF coils wired in series. Measurements taken at 20 K.

Close modal

In order to evaluate the effectiveness of our device as a spin flipper, measurements of the spin flipping efficiency were made for both adiabatic and nonadiabatic configurations. Measurements were conducted at the Missouri University Research Reactor (MURR) beamline 2XC. 4.3 Å neutrons are selected with a graphite monochromator, and λ/2 neutrons are reduced with a beryllium filter cooled by liquid nitrogen. As shown in Fig. 8, a polarized beamline was setup using a V-cavity polarizer and an S-bender analyzer placed immediately before the detector. Permanent magnet guide fields are used to maintain polarization, and nutators, electromagnets which can be rotated, are mounted on each side of the device to control the orientation of the neutron spin at the entrance and exit of the device. Neutron masks of 0.5 in. were placed at the beam shutter and on both sides of the device. Neutrons were counted with a shielded 3He pencil detector. Raw beam polarization was determined to be P0 = 96.9% by using a Mezei flipper at the device position with the same guide field configuration. Please note that the subsequent polarization results are normalized relative to this baseline polarization.

FIG. 8.

Schematic of the polarized beamline with neutron beam incident from the right side of the image. The side iron yoke of the two flippers has been removed for clarity.

FIG. 8.

Schematic of the polarized beamline with neutron beam incident from the right side of the image. The side iron yoke of the two flippers has been removed for clarity.

Close modal

The RF signal is generated by a Keysight 33500B 2-channel function generator and is amplified by an Amplifier Research model 75A250 amplifier. Power is efficiently delivered to the RF coils through a “T” matching network designed with S11 < −20 dB. We use exclusively capacitors for the matching, which is effective when matching in the frequency range f ∈ (200 kHz, 2 MHz). The RF field is determined by measuring the peak current from a Pearson 411C clamp-on current monitor placed between capacitor “3,” as shown in Fig. 9, and the RF coil, readout through an oscilloscope and referencing calibration measurements shown in Fig. 7.

FIG. 9.

Circuit diagram of a “T” matching network used to bridge the RF load impedance to 50 Ω for efficient power transfer.

FIG. 9.

Circuit diagram of a “T” matching network used to bridge the RF load impedance to 50 Ω for efficient power transfer.

Close modal

Lakeshore 625 power supplies are used to supply current to B0, gradient, and nutator coils. Measurement of the spin flip efficiency requires that the nutators are set in the “flipping” mode, i.e., the nutator and B0 fields are parallel. The measured spin state is selected by the polarity of the nutator which is closer to the S-bender analyzer. Reported results are background-subtracted neutron counts which are normalized to counts per 104 beam monitor counts.

Measurements were made at a resonant frequency f0 = 1 MHz, corresponding to magnetic field B0 = 343 G and current I0 ≈ 24 A. The RF magnitude was set using Eq. (14) for λ = 4.3 Å neutrons and using calibration measurements from Fig. 7. Each spin flipper of the bootstrap was fine-tuned separately, with only the B0 coil turned on in the other half as a guide field. B0 was tuned by sweeping the current to find the resonant peak, and then the RF current was fine-tuned for an exact spin flip. Spin flipping efficiency for a single flipper was found to be 94.5% in this mode. After tuning both spin flippers, the device was run with both spin flippers turned on. Figure 10 shows the count of each spin state as a function of the current in flipper No. 2 with flipper No. 1 on tune. Measured polarization in this mode, in which the spin is flipped twice, is 93.6%. It should be noted that, even with perfect magnetic fields, a loss of polarization in each spin flip is expected due to the wavelength dispersion of the beam for the nonadiabatic spin flip method. Inhomogeneities in the B0 and RF coils, as well as cross-talk between the magnetic field components in each half of the device, further decrease the spin flip efficiency.

FIG. 10.

The count of each spin state for the nonadiabatic bootstrap spin flipper, scanning the B0 current in flipper No. 2 with flipper No. 1 tuned for a spin flip. Two spin flips are performed in this configuration when both flippers are on tune.

FIG. 10.

The count of each spin state for the nonadiabatic bootstrap spin flipper, scanning the B0 current in flipper No. 2 with flipper No. 1 tuned for a spin flip. Two spin flips are performed in this configuration when both flippers are on tune.

Close modal

Generally, the RF adiabatic spin flip method is not as sensitive to the RF and gradient coil tuning as the nonadiabatic mode is to the RF field tuning as they only need to be large enough to satisfy the adiabatic condition shown in Eq. (15), whereas the nonadiabatic mode requires fine-tuning of the RF field to the time of flight through the flipper given by Eq. (14). The tuning procedure starts by setting the RF amplitude to approximately 25 G and the gradient coil field to approximately ±25 G at the device entrance using calibration data. The current in B0 was then scanned as in the nongradient test to find the resonant peak. Figure 11 shows the bootstrap mode scan of B0 in flipper No. 2 when flipper No. 1 is on tune. Note that the adiabatic mode has a significantly broader resonant peak than the nonadiabatic mode. This width was observed to increase with the gradient and RF field settings. A single spin flipper efficiency was measured to be 99.2% and bootstrap mode as in Fig. 11 yielded 97.9%. A summary of the measured spin flip efficiencies for each configuration, including for a single adiabatic flip at 2 MHz, is summarized in Table I.

FIG. 11.

The count of each spin state for the adiabatic bootstrap spin flipper, scanning the B0 current in flipper No. 2 with flipper No. 1 tuned to perform a spin flip. Two spin flips are performed in this configuration when both flippers are on tune.

FIG. 11.

The count of each spin state for the adiabatic bootstrap spin flipper, scanning the B0 current in flipper No. 2 with flipper No. 1 tuned to perform a spin flip. Two spin flips are performed in this configuration when both flippers are on tune.

Close modal
TABLE I.

Summary of the spin flip efficiency results.

Polarization normalized
to Mezei flipper (%)
Single non-adiabatic 1 MHz 94.5 
Bootstrap non-adiabatic 1 MHz 93.6 
Single adiabatic 1 MHz 99.2 
Bootstrap adiabatic 1 MHz 97.9 
Single adiabatic 1 MHz low power 98.3 
Single adiabatic 2 MHz 97.6 
Polarization normalized
to Mezei flipper (%)
Single non-adiabatic 1 MHz 94.5 
Bootstrap non-adiabatic 1 MHz 93.6 
Single adiabatic 1 MHz 99.2 
Bootstrap adiabatic 1 MHz 97.9 
Single adiabatic 1 MHz low power 98.3 
Single adiabatic 2 MHz 97.6 

In order to evaluate the sensitivity of the spin flip efficiency to the RF and gradient tunings and thus the adiabaticity parameter, we measured the count rate of one spin state in adiabatic spin flipping mode for a 2-dimensional scan of RF and gradient fields. For the spin state measured in Fig. 12, a low count indicates a high spin flip efficiency. Note that the counts decrease as the gradient and RF fields both increase, which indicates that the efficiency further improves as the adiabaticity parameter increases. This also implies that good efficiency can be obtained even when the adiabaticity parameter is not very large. A single adiabatic spin flip measurement at 1 MHz with RF and gradient fields at 9 G yielded a 98.3% spin flip efficiency. The RF power dissipation is proportional to the square of the RF field current, such that a significant decrease in the RF heating can be achieved with a relatively small trade-off in the spin flip efficiency by maintaining the relative tuning of the gradient and RF fields at a lower magnitude. Also note that when Bgrad ≈ 0, then the spin flipping becomes nonadiabatic and the spin flip efficiency is less than the adiabatic mode due to the wavelength dispersion.

FIG. 12.

An intensity map of one spin state when scanning both the magnitude of the RF field and the gradient field, where Bgrad is the expected field at the entrance of the spin flipper. For the spin state observed, a low count indicates a spin flip.

FIG. 12.

An intensity map of one spin state when scanning both the magnitude of the RF field and the gradient field, where Bgrad is the expected field at the entrance of the spin flipper. For the spin state observed, a low count indicates a spin flip.

Close modal

As shown in Fig. 12, the spin flipping efficiency is best when the RF field is comparable to the gradient field. This relationship between the RF and gradient field for maximum adiabatic spin flip efficiency can be intuitively understood by considering the fields in the rotating frame for the cases shown in Fig. 13, which shows the angle between the net field vector and the initial polarization axis along the length of the spin flipper. If BRF is small compared to Bgrad, then the net field is dominated by the gradient field and the neutron spin will experience an abrupt field change at the zero crossing, which will cause depolarization. If Bgrad is small compared to BRF, within a short distance of entering the device, the net field very quickly rotates from the vertical direction to align with BRF, remaining aligned with BRF until another very quick rotation back to Bgrad at the end of the spin flipper. In both of these cases, the rotation of the net field occurs in very short regions, and the net field direction is quasistatic during most of the spin flipper length. If the field components are comparable in size, then the net field rotates at a constant rate over the full length of the spin flipper, which is ideal for adiabaticity.

FIG. 13.

Plot of the angle of the net field vector in the rotating frame relative to the initial polarization axis for different magnitudes of gradient and RF fields, assuming fields of the form Bgrad=Acos(πx/d), BRF=Asin(πx/d), as in the adiabaticity derivation by Grigoriev et al.19 When the RF field is much smaller than the gradient field, then the spin flip occurs in the very short region where Bgrad ≈ 0. When the gradient field is smaller, then the spin flip occurs in two short half flips when BRF ≈ 0.

FIG. 13.

Plot of the angle of the net field vector in the rotating frame relative to the initial polarization axis for different magnitudes of gradient and RF fields, assuming fields of the form Bgrad=Acos(πx/d), BRF=Asin(πx/d), as in the adiabaticity derivation by Grigoriev et al.19 When the RF field is much smaller than the gradient field, then the spin flip occurs in the very short region where Bgrad ≈ 0. When the gradient field is smaller, then the spin flip occurs in two short half flips when BRF ≈ 0.

Close modal

As discussed in Sec. II, operation of a single RF spin flipper in precession mode, in which the incident polarization is perpendicular to the B0 field, introduces time modulations in the polarization at twice the frequency of the spin flipper. A new Anger camera developed at the Oak Ridge National Laboratory22 was utilized to measure the time modulations and the phase distribution across the beam cross section. It uses a 0.6 mm thick enriched 6Li glass as a scintillator and has internal timing resolution of 100 ns. In principle, it can measure frequencies up to a few megahertz although, in practice, the maximum frequency with measurable contrast is dependent on the neutron wavelength due to the scintillator thickness. Dispersion of the neutrons’ wavelengths reduces the contrast of the time modulation signal at the detector due to variations in the time of flight between the spin flipper and the detector. We used time focusing to minimize this effect by operating the separate spin flippers within the device at different frequencies as in the MIEZE method using the tuning condition of Eq. (9), rather than operating them in the bootstrap configuration. The setup was identical to that of Fig. 8, except using the Anger camera in place of the 3He detector. To maximize the modulation contrast, we use the adiabatic spin flipping method for maximum spin flip efficiency. The phase dependence on the neutron velocities is thus minimized at the detector when the B0 field in each device is in the same direction and the frequencies are tuned according to Eq. (9).

The device first required tuning of the RF, gradient, and B0 currents for each frequency tested as described in Sec. IV. The device was then placed into “precession” mode, in which the nutators were rotated to produce a field which aligns the neutron spins perpendicular to the B0 field produced inside the device. A trigger signal was sent to the detector at a period which is an integer multiple of the expected signal period, which is calculated from the applied RF frequencies. This required a separate Keysight 33600A which sent the trigger to the detector and synchronized the clock of the detector and the RF signal generators.

In bootstrap mode, the frequency of the signal is twice the sum of the frequencies in each half of the device, but in MIEZE, the field directions are the same so that the time modulation is based on twice the difference, which can be seen by the data and fits shown in Fig. 14. As the frequency of modulation increases, the contrast decreases due to the period of the signal approaching the time resolution of the detector.

FIG. 14.

Time modulations measured at the detector with fits for two MIEZE configurations. Fit is to the function p1 + p2 sin(2πp3t + p4) for fitted parameters pi. Fitted frequencies correspond to 2Δω for each. The contrast, p2/p1, is 0.87 at 129 kHz and 0.79 at 400 kHz.

FIG. 14.

Time modulations measured at the detector with fits for two MIEZE configurations. Fit is to the function p1 + p2 sin(2πp3t + p4) for fitted parameters pi. Fitted frequencies correspond to 2Δω for each. The contrast, p2/p1, is 0.87 at 129 kHz and 0.79 at 400 kHz.

Close modal

To characterize and understand the phase generated by the device, we analyzed the relative phase structure across the beam cross section as a way to characterize the magnetic field homogeneity of each component of the device. Performing the time modulation measurement for several hours yields sufficient statistics to fit the time modulation for spatial bins on the detector surface, producing a map of the phase structure. For this test, we used the MIEZE mode running at 200 kHz and 264.8 kHz due to the larger contrast at lower frequencies. As noted in Sec. II, the additional phase due to the RF, gradient, and residual fields can be canceled when using bootstrap adiabatic spin flippers with the correct relative polarity of the gradient coils. As shown in Fig. 15, there is a substantial difference in the phase structure between these configurations. When the gradient coils have the opposite polarity (G+−), there is a distinct structure, whereas when the gradient coils have the same polarity (G++), there is very little structure.

FIG. 15.

Maps of the spatial structure of the phase aberrations for the device with the same (G++) and opposite (G+−) gradient coil polarities, operating in MIEZE mode at frequencies 200 kHz and 264.8 kHz. Measured results are on the left, (a) G+− and (c) G++, and the phase distribution calculated from simulation field integrals are on the right, (b) G+− and (d) G++. The expected phase cancellation is observed for the same gradient coil polarity.

FIG. 15.

Maps of the spatial structure of the phase aberrations for the device with the same (G++) and opposite (G+−) gradient coil polarities, operating in MIEZE mode at frequencies 200 kHz and 264.8 kHz. Measured results are on the left, (a) G+− and (c) G++, and the phase distribution calculated from simulation field integrals are on the right, (b) G+− and (d) G++. The expected phase cancellation is observed for the same gradient coil polarity.

Close modal

The phase at the exit of the device is proportional to the magnetic field integral,

FI=B0+Bgrad+BRFsin(ωt)dt,
(17)

where the integral is performed in time rather than the position in order to include the contributions of the RF field. This was calculated using the simulated magnetic field profiles scaled to the settings used in the experiment and using λ = 4.3 Å neutrons without beam divergence. Please note that the divergence of the neutron beam will cause some averaging of the phase so that the data structure will be smeared out relative to the simulation. The simulation results agree qualitatively with the data. Thus, the additional phase due to the geometry and inhomogeneities can be canceled to the first order by operating the device in bootstrap mode.

We have presented the design and test results for a bootstrap transverse neutron RF spin flipper using high temperature superconducting technology. Spin flipping efficiency and phase aberration measurements show outstanding potential for its application to a NRSE type of spectrometer. We have shown the capability of operating at frequencies up to 2 MHz and using a bootstrap configuration, which would result in an effective field integral of 0.35 T m for a meter of separation between such devices. It is feasible to extend this by another factor of 2 with additional windings on the B0 coil and incremental improvements in the high frequency components to allow a maximum operation frequency of 4 MHz, which would make the field integral comparable to the state-of-the-art NSE instruments.

The maximum beam size for the current design is approximately 2 cm in diameter, which is small compared to existing NSE spectrometers, e.g., the beam cross section of the NSE beamline at the Spallation Neutron Source at Oak Ridge National Laboratory is 4 cm × 8 cm.23 It is feasible to scale the design to double the beam diameter. The primary difficulty with implementing this into a full NRSE spectrometer at this time is the long-standing problem of correcting the beam divergence in the transverse NRSE configuration. Two methods have been studied to overcome this: adiabatically rotating the spin quantization axis to be longitudinal between the spin flippers so that traditional Fresnel coils can be used as in NSE and LNRSE24 and using elliptical supermirrors to focus the beam trajectories.25 In particular, the correction using NSE techniques is desirable as the combination of NRSE with NSE allows for greatly expanded dynamic range and allows easier control of the spin echo time than NRSE by itself.

The presented RF spin flipper would work well in a MIEZE configuration in which all spin manipulation and the polarization analysis is performed prior to the sample. This technique allows for the high resolution measurement of dynamics for samples which are depolarizing or require depolarizing sample environments, e.g., skyrmions, which is challenging for NSE. The measured contrast of a single bootstrap flipper tested in a MIEZE configuration is comparable to the RESEDA MIEZE setup17 although a direct comparison cannot be made at this time due to the limited scope of the present spin flipper test as well as differences in the neutron wavelengths and detectors. A second RF spin flipper is currently being built, which will allow a full characterization of its capability in a MIEZE spectrometer.

The authors thank the research sponsored by the Laboratory Directed Research and Development Program of Oak Ridge National Laboratory, managed by UT-Battelle, LLC, for the U.S. Department of Energy. This material is based on the work supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Contract No. DE-AC05-00OR22725. This research used resources at the Missouri University Research Reactor. The authors would like to thank the operators and support staff, in particular, Peter Norgard, for making accommodations for equipment utilities. The authors would also like to thank Josh Pierce, Todd Sherline, Andre Parizzi, and Mike Hittman for providing equipment, and the authors thank Roger Pynn, Georg Ehlers, Michel Thijs, Jeroen Plomp, and Steven Parnell for helpful discussions.

This manuscript has been authored by UT-Battelle, LLC, under Contract No. DE-AC05-00OR22725, with the U.S. Department of Energy (DOE). The U.S. government retains, and the publisher, by accepting the article for publication, acknowledges that the U.S. government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript or allow others to do so, for U.S. government purposes. DOE will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (http://energy.gov/downloads/doe-public-access-plan).

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