ESR intensity and the Dzyaloshinsky-Moriya interaction of the nanoscale molecular magnet V15

Abstract

The intensity of electron spin resonance (ESR) of the nanoscale molecular magnet V 15 is studied. We calculate the temperature dependence of the intensity at temperatures from high to low. In particular, we find that the low-temperature ESR intensity is significantly affected by the Dzyaloshinsky-Moriya interaction. I. INTRODUCTIONThe V 15 molecule has been one of promising nanometer-scale molecular magnets since it was first synthesized. Different experiments on the magnetization process have shown that the magnetization changed adiabatically in a fast sweeping field, and a magnetic plateau appeared in a slow sweeping field due to thermal bath attached to the molecule. are not yet fully understood.In this paper, first we numerically calculate the temperature dependence of the ESR intensity of V 15 using a new numerical method (the double Chebyshev polynomial method) of calculating the Kubo formula. We find that the model Hamiltonian for V 15 including the DMI successfully reproduces the experimental temperature dependence of the ESR intensity.Second we investigate the ESR at very low temperatures. We find that the intensity ratio (the intensity of V 15 divided by that of a spin 1/2) is affected by the DMI at small fields.We propose that experimental observation of the intensity ratio enables us to estimate the DMI in V 15 . Finally, we analyze the ESR at low temperatures using a triangle model whose 2 energy levels model the low-lying levels of V 15 . Figure 1 shows the structure of vanadium ions in V 15 . We consider the following spin II. MODEL AND FORMULATIONHamiltonian for V 15 . 17-19The first term on the right-hand side of Eq. (1) describes the Heisenberg interaction. Coefficients J ij take three values J, J 1 , and J 2 (|J| > |J 2 | > |J 1 |) depending on the bonds on the upper and lower hexagons. Three spins between two hexagons interact with the hexagons by J 1 and J 2 . There is no interaction among these three spins 3 . We set J = −800K, J 2 = −350K, and J 1 = −225K. 20 The second term describes the DMI. We assume the existence of DM vectors {D ij } at the bonds of J. In the third term, H denotes the static magnetic field applied to the molecule. We will ignore other effects such as dipolar fields, hyperfine interactions, and the crystal field, which are considered to be negligibly small.Indeed, the dipolar and hyperfine fields are estimated as 1 mK and 50 mK, respectively 7 .

Computation of ESR spectra from the time evolution of the magnetization: Comparison of autocorrelation and Wiener-Khinchin-relation-based methods

“…It is one of the fundamental pieces of information obtained in ESR experiments. Its temperature dependence has been calculated for the single molecular magnet V 15 [17]. In this subsection, we demonstrate that I x obtained by the WK method correctly reproduces the exact ED results.…”

“…This requires of the order D 2 = 2 2N operations, which becomes prohibitively large if N is of the order of 20 or larger. Fortunately, for larger systems, we can obtain accurate estimates of thermal equilibrium averages by making use of the so-called thermal typical state |Φ β = e −β H /2 |Φ [16,17,22,24], also called "a Boltzmann-weighted random vector" [16,17] or "a canonical thermal pure quantum state" [24], where |Φ denotes a random state on the D-dimensional hypershere. In essence, we have [22]…”

“…By making use of the symmetries of the system we may reduce the dimensions of the block diagonalized Hamiltonian. Even with these efforts, in practice, the system size is still limited to about 20 spins.The restriction imposed by the exact diagonalization approach can be alleviated by computing the autocorrelation function (AC) from the time evolution of a pure state [15][16][17].The ESR spectrum is obtained by Fourier transformation of the autocorrelation function of the transverse magnetization. In the AC method, a pure state evolves in time according to the time-evolution operator e −iH t the action of which can be computed efficiently by means the Chebyshev polynomial [18][19][20][21] or the Suzuki-Trotter-product-formula method [15,22].…”

From Linear to Nonlinear Responses of Thermal Pure Quantum States

“…Unfortunately, it is hard to calculate or predict NLR in many-body quantum systems except for very limited cases, such as in an off-resonant field whose effects can be renormalized into the system parameters [14,15]. This situation stands in contrast to the LR, with many elaborate methods developed, such as DMRG [16][17][18], quantum Monte Carlo simulations [19,20], kernel polynomial method [21], time correlation in pure quantum states [22][23][24][25][26][27][28][29][30][31], and matrix-product state [32]. Some of them were applied to NLR [24,30] but only in a limited situation such as infinite temperature.…”

Controllable magnetic thermal rectification in a SMM dimmer with the Dzyaloshinskii–Moriya interaction

“…Due to the DMI broken spin and spatial symmetry, the characteristic electron transport signatures have been studied, for example, a specific magnetic field dependence of the transport, nonlinear transport signatures, the violation of spin selection rules [17][18][19][20][21] . In experiment, DMI has been found in the Mn6, Mn12 and V3 22 ,V15-based molecular 23,24 . Therefore, looking for the role of the DMI under the nonequilibrium conditions is crucial to modulating magnet thermal transfer.…”