Download Magnetic resonance force microscopy and a single-spin by Gennady P. Berman, Fausto Borgonovi, Vyacheslav N Gorshkov, PDF
By Gennady P. Berman, Fausto Borgonovi, Vyacheslav N Gorshkov, Vladimir I Tsifrinovich
Magnetic resonance strength microscopy (MRFM) is a speedily evolving box which originated in Nineties and matured lately with the 1st detection of a unmarried electron spin lower than the outside of a non-transparent strong. additional improvement of MRFM recommendations could have a good impression on many components of technological know-how and expertise together with physics, chemistry, biology, or even drugs. Scientists, engineers, and scholars from a number of backgrounds will all have an interest during this promising box. the target of this "multi-level" booklet is to explain the elemental ideas, functions, and the complicated concept of MRFM. targeting the experimental oscillating cantilever-driven adiabatic reversals (OSCAR) detection approach for unmarried electron spin, this publication comprises beneficial examine info for scientists operating within the box of quantum physics or magnetic resonance. Readers strange with quantum mechanics and magnetic resonance should be capable of receive an knowing and appreciation of the elemental rules of MRFM.
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Sample text
Its components along the effective magnetic field in an integral of motion in our system. 21). Using the Heisenberg representation generated by the unitary operator U = exp(—iHt/h), we can prove that the average spin in any magnetic field evolves like a quasiclassical magnetic moment. 38) 24 3. SPIN DYNAMICS — QUANTUM DESCRIPTION does not change, while the operator, 5J = WS'^U, evolves according to the Heisenberg equation of motion: dt S'j j = --[S'j,H}. 11). Then, we obtain jtS'x = -i>yBv[S'x, S'y] - ijBz[S'x, S'z] = -7(S'yBz - S'zBy).
Now we can estimate the value of the static CT displacement, ZQ. The magnetic force F, produced by the spin magnetic moment on CT, points in the negative ^-direction and has a magnitude 3Bd F = ^-g7 ( IIQMQ = 2^B^-T-d[^-rd) Rp \2_onn «390aN. , . 3) The corresponding static displacement of the CT is ZQ = —F/kc, where kc is the CT spring constant. 5 /xN/m reported by Stowe et al. in Ref. [17], we obtain ZQ W —60 pm. This value should be compared with the thermal vibrations of the CT. 7 mK. 5) When estimating zrms we assume that the bandwidth of the measuring device, Wb, is larger than the cantilever frequency, LOC, as the noise spectral density has a maximum at w = uc.
Here zp = zp(x,t) is the cantilever displacement at a point x, S = wctc is the cross-sectional area of the cantilever, p is its density, Y is its Young's modulus, / = wct3c/\2. 25) are: zp(x = 0) = ^ ( s = 0) = S (2 x = lc) = ^ (3 x = lc) = 0. 27) 32 4. MECHANICAL VIBRATIONS OF THE CANTILEVER The eigenfunctions fj (x) are orthogonal to each other and can be normalized to the cantilever length lc: f ° dx fj(x)fm{x) = Sjm lc. 30) The CT amplitude for any mode is twice the amplitude of the mode. As a result, the effective mass m* = mc/4, where mc = plcu>ctc is the cantilever mass.