The magnetic resonance force microscope

Ever since the discovery of electron paramagnetic resonance (EPR) [1], nuclear magnetic resonance (NMR) [2], [3], [4], and ferromagnetic resonance (FMR) [5], these magnetic resonance techniques have proved to be extremely powerful and have/had a profound impact on a variety of research areas ranging from medicine and biology to chemistry and physics. The strengths of magnetic resonance techniques are manifold and include the ability to study the local surrounding of atoms and the character of the binding in molecules (NMR), to quantify electrical fields in matter via crystal fields and spin–orbit coupling (EPR) and to measure anisotropy energies in ferromagnets (FMR), to mention just a few. Furthermore, the methods are non-invasive and it is possible to study systems in their natural surrounding, e.g. in a liquid or under extreme conditions, such as high pressure. On the other hand, magnetic resonance techniques suffer notoriously from their rather poor sensitivity, thus excluding these methods very often from research fields in material science where either the structures to be studied are too small, or because single crystals of desired size are not available and thus one has to work with powder samples, limiting the amount of information which can be gained. Different avenues have been tried to improve the sensitivity especially in the field of NMR. One approach is to change the detection part, which was for example tried by using superconducting quantum interference devices (SQUID) to detect the magnetic resonance signal. However, as estimated in Ref. [6], SQUID-NMR only outperforms standard NMR at external fields below B₀<0.6 T. Another way to improve the sensitivity is to try to increase the tiny thermal spin-polarization. Such was demonstrated recently by working with hyperpolarized ¹²⁹Xe. The ¹²⁹Xe is optically pumped, circular polarized light being used to transfer its angular momentum to the electronic and nuclear spins [7]. Hyperpolarized ¹²⁹Xe has been used to study amorphous surfaces [8], and also used in magnetic resonance imaging (MRI) [9]. Even though this approach is very attractive for some particular applications, it cannot be used to study surface near regions close to buried interfaces.

In 1991 Sidles [10] came up with the intriguing idea of detecting the magnetic resonance spin signal not inductively but mechanically via force detection. He coined this approach a magnetic resonance force microscope (MRFM). The motivation for this work originates from developments in the field of scanning probe techniques in the late 1980s, especially the atomic force microscope (AFM). In these devices micro-mechanical resonators are used as force sensing elements which can routinely measure forces as small as 10⁻¹⁴–10⁻¹⁵ N. He showed that this detection scheme has the potential for single spin sensitivity. The basic coupling equation is$\mathbf{F}(\mathbf{r},t)=-\mathrm{\nabla }\mathcal{E}=\mathrm{\nabla }[\mathbf{M}(\mathbf{r},t)\cdot \mathbf{B}]=[\mathbf{M}(\mathbf{r},t)\cdot \mathrm{\nabla }]\mathbf{B}(\mathbf{r}),$where M(r,t) is the resonant magnetization and B(r) the field from a micromagnet mounted on a mechanical resonator. A typical setup is sketched in Fig. 1.

The micromagnet mounted on the mechanical resonator produces an extremely inhomogeneous magnetic field that serves two purposes: (i) it couples the mechanical resonator to the magnetic moments in the sample (Eq. (1)), and (ii) it defines the spatial regions of the sample where the magnetic resonance condition is met. Thus, it is already clear, that such a device can be utilized as an imaging tool. We will not discuss the imaging aspects of the MRFM in this review since these have been extensively reviewed by Nestle et al. [11].

In fact, mechanical detection of magnetic resonance signals was first proposed by Gozzini [12] in the 1960s. Rather than a force coupling (Eq. (1)), an angular momentum coupling was proposed, i.e. resonant absorption of photons from the electromagnetic field which exert a torque on a mechanical resonator. This idea was revived by a group from Pisa [13], [14], who realized a working apparatus where the sample is mounted onto a micro-mechanical resonator driven in the torque mode. This arrangement is gradient free, and hence any complications due to the micromagnet are absent. The disadvantage of this approach is its intrinsic inability for imaging. Another ‘gradient free’ proposal was reported by Leskowitz et al. [15] where the dipole field of resonant spins is coupled to a magnet mounted on a membrane and hence drive it. The membrane magnet is imbedded in an assembly of other magnets in order to homogenize the total magnetic field at the sample position. This proposal was realized recently in a first prototype [16] and was shown to work.

Since our focus of MRFM applications will be on magnetic systems in this review, it is worth briefly examining other methods available, considering their strengths and flaws, and compare them with the MRFM. This list is not comprehensive and only a few, rather different methods will be illustrated, starting with nuclear probe methods. A set of nuclear techniques exists which utilize the fact that the weak decay is not invariant under parity transformation [17]. As a result, the decay products, which can be detected even for a single decay, are preferentially emitted in the direction of the spin of the decaying particle or atom. Furthermore, the initial source can be generated almost 100% spin polarized. These two ingredients give these methods a very high sensitivity compared to standard magnetic resonance. To this class of techniques belong the β-NMR [18], [19], the muon spin rotation technique (μSR) [20] and the recently developed low energy μSR (LE-μSR) method [21]. Bulk μSR is the least applicable method for thin film studies, since muons with high energy (4.2 MeV) are implanted into matter and the resulting stopping distribution is of the order of 0.5 mm, thus preventing studies of thin or buried magnetic layers. LE-μSR has demonstrated recently the ability to study very weak magnetic signals in the magnetic multilayer system Fe/Ag/Fe [22], where the muons were stopped in a 20 nm thick silver layer measuring the oscillating spin polarization of the conducting electrons, induced by the adjacent iron layers. Though, LE-μSR has an impressive depth resolution of about 1 nm with a range of 0–300 nm, the lateral resolution is nonexistent, excluding this method for the moment from studies of magnetic nano-devices such as MRAMs. Mössbauer spectroscopy [23] is another interesting sensitive nuclear method in the field of magnetism. In Mössbauer spectroscopy resonant absorption of nuclear X-rays are used as an extremely sensitive measure of the local environment surrounding the Mössbauer nuclei. The extremely high energy resolution is possible because for some specific sources the emission as well as the absorption of the nuclear X-rays is recoilless, i.e. the recoil is taken by the whole crystal rather than the single emitting or absorbing nucleus and hence there is no Doppler shift involved which would broaden the energy distribution of the X-rays. In the field of magnetism the prominent Mössbauer source is ⁵⁷Co–⁵⁷Fe. For thin films a derivative of standard Mössbauer spectroscopy, the conversion electron Mössbauer spectroscopy (CEMS) [23] has been shown to be very powerful. CEMS takes advantage of the ionization of inner electrons during the X-ray absorption. These conversion electrons have typical escape depths up to 100 nm. By imbedding a monolayer of ⁵⁷Fe at a controlled position within an iron layer, interesting properties, such as the hyperfine field and local charge distributions can be measured via isomer shifts and quadrupole splittings, thus yielding valuable information especially in magnetic multilayers. The big disadvantage of Mössbauer spectroscopy and CEMS is the very limited availability of proper sources, thus restricting these methods to studies of a very narrow class of materials. In the field of optical methods the magneto-optic Kerr effect (MOKE) is extensively used to characterize magnetic films. It directly measures the sample magnetization distribution by determining the rotation of the plane of polarization of light upon reflection. Recently it was also implemented as a near field optical scanning probe [24], thus improving the lateral resolution down to ≲100 nm. Naturally this method is limited to the surface which needs to be magnetic. The wider availability of synchrotron radiation paved the way to new methods such as X-ray spectromicroscopy [25], [26]. Special kinds of photoemission processes [circular-(XMCD) or linear-dichroism (XMLD)] yielding magnetic contrast are utilized. By combing these with an electron microscope for extracting the photoelectrons from the surface a scanning method called photoemission electron microscope (PEEM) has been developed. The lateral resolution of PEEM is of the order of 50 nm. The strength of this approach is that it is chemical specific since one tunes the X-rays to the specific 2p→3d (d band transition metals) or 3d→4f (rare earth elements) transitions, which are specific for each element. A disadvantage is that an insulating sample charge up quickly and hence only studies on conducting samples have been successful. Furthermore the analyzed electrons have an escape depth of roughly <10 nm thus limiting the method to near surface regions. In scanning electron microscopy with polarization analysis (SEMPA) [27] an incident highly focused electron beam scans a magnetic surface. The secondary electrons emitted, originating from the magnetic layers are spin polarized. By collecting these electrons and sending them through a spin analyzer, usually a Mott detector, magnetic contrast is gained. The lateral resolution of this method is roughly 10 nm. Very similar limitations as for PEEM apply. Scanning probe methods such as scanning tunnelling microscopy (STM), atomic force microscopy (AFM) and magnetic force microscopy (MFM) will be discussed in Section 2. Though STM and AFM have proven single atom resolution, they are only sensitive to the topmost layers of a surface. The MFM method does not have the sensitivity of the other two scanning probe methods mentioned and furthermore the spatial origin of the magnetic fields measured by MFM cannot easily be identified. This all too brief overview hopefully shows, that the listed methods all have their limitations, and we hope to convince the reader that the MRFM approach has a potential worthy of exploration since it can yield valuable information not available by other methods.

Before going over to a detailed discussion, we would like to present a short overview of experiments and developments accomplished at present. The first magnetic resonance force signal was detected by Rugar et al. in 1992 who mechanically detected the electron spin resonance signal (eMRFM) from a 30 ng crystal of diphenylpicrylhydrazil [28]. Two years later, Rugar et al. reported the mechanical detection of ¹H nuclear magnetic resonance (nMRFM) in 12 ng of ammonium nitrate [29]. These two pioneering experiments demonstrated that a microfabricated cantilever, similar to those developed for atomic force microscopy, can detect the magnetic moment of a microscopic sample. In the case of NMR [29], the achieved sensitivity of 10¹³ spins at room temperature and in a field of 2.4 T, represents a substantial improvement over the standard coil detection sensitivity. Significant progress has been made in the past few years. In 1996, Zhang et al. mechanically detected the ferromagnetic resonance signals (fMRFM) of yttrium iron garnet [30]. Imaging experiments with eMRFM [31], [32], nMRFM [33], [34] and fMRFM [35] were performed. Improved force sensitivity was demonstrated by operating at low temperature [36], [37], [38]. Force maps of a sample were obtained with the magnetic probe placed on the mechanical resonator in eMRFM [39] and fMRFM [35], [40]. The highest sensitivity reported to date is ∼200 fully polarized electron spins in a 1 Hz bandwidth. This result was obtained by operating an eMRFM at 77 K in a very large magnetic field gradient [41]. In 1996, Wago et al. demonstrated that a combination of pulsed NMR techniques with fast adiabatic passage enabled measurement of the nuclear spin-lattice relaxation rate of ¹⁹F nuclei in calcium fluoride at low temperature [36]. The same method was used to measure the longitudinal spin relaxation rate of ¹H in ammonium sulfate at room temperature [34], [42]. Klein et al. [43] were able to demonstrate two different T₁ values in a microscopic crystallite of ammonium sulfate, one being attributed to spins in the surface layer of the crystal. They also measured the spin–spin relaxation time T₂ of protons. Smith and co-workers [44] also demonstrated nMRFM on ¹⁹F in Nd doped CaF₂ at 20 K. Recent eMRFM work in vitreous silica at 5 K showed that the same principles can also be applied to study electron angular momentum dynamics of slowly relaxing E′ centers [38].

The purpose of this review is to fill in a gap between experts in the field of magnetic resonance and those in the field of scanning probe techniques. The review shall help magnetic resonance experts to see the potential of the MRFM and to understand the technical requirements for the detection part, originating from scanning probe techniques. Scanning probe experts, unfamiliar with the concept of magnetic resonance, might see the review as an introduction, helping them to understand the specific requirements needed for magnetic resonance application. The review will also present results, though some are still preliminary, from MRFM studies related to the field of magnetism.

The review is structured as follows: in Section 2 some principles of scanning probe techniques, relevant to the MRFM, will be presented. Longitudinal spin manipulation, necessary for an efficient coupling between the spin system and the micro-mechanical resonator, will be discussed in Section 3. Section 4 discusses details about the interaction between the spin system and the detection part of MRFM. In order to understand ongoing technical developments, it is important to understand the different sources of noise which might hamper the measurement. This will naturally lead to estimates of the ultimate sensitivity of MRFM and is discussed in Section 5. After this rather technical section, first results of MRFM studies in magnetic systems will be given in Section 6, showing the potential of the method. Section 7 discusses the necessary technical developments for future MRFM setups. The question of whether or not single spin detection is possible at all, even if the necessary force sensitivity of MRFM can be achieved and all noise sources controlled, will be discussed in Section 8.