# Dynamic response of the spin-crossover solid Co(H-2(fsa)2 en)(py)(2) to a pulsed magnetic field

Azzedine Bousseksou, K. Boukheddaden, Michel Goiran, C. Consejo, M.L.

Boillot, Jean-Pierre Tuchagues

► To cite this version:

Azzedine Bousseksou, K. Boukheddaden, Michel Goiran, C. Consejo, M.L. Boillot, et al. Dynamic response of the spin-crossover solid Co(H-2(fsa)2 en)(py)(2) to a pulsed magnetic field. Physical Review B, 2002, 65, pp.172412. 10.1103/PhysRevB.65.172412. hal-00015706

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Dynamic response of the spin-crossover solid Co(H₂(fsa)₂en)(py)₂ to a pulsed magnetic field

A. Bousseksou,¹,* K. Boukheddaden,²,† M. Goiran,³ C. Consejo,¹,³ M-L. Boillot,⁴ and J-P. Tuchagues¹

¹Laboratoire de Chimie de Coordination, UPR 8241, CNRS, F-31077 Toulouse cedex, France

²Laboratoire de Magnétisme et d'Optique, Université de Versailles, 45 Avenue des Etats-Unis, F-78035 Versailles, France

³Laboratoire National des Champs Magnétiques Pulsés, CNRS/UPS/INSA, Avenue de Rangueil, F-31077 Toulouse Cedex, France

⁴Laboratoire de Chimie Inorganique, UMR 8611, Université Paris-Sud, 91400 Orsay, France

(Received 23 January 2002; published 30 April 2002)

The spin transition between the paramagnetic high-spin (HS) and low-spin (LS) electronic states of Co<sup>II</sup>(H<sub>2</sub>(fsa)<sub>2</sub>en)(py)<sub>2</sub>, [H<sub>2</sub>(fsa)<sub>2</sub>en=N,N'-ethylene bis(3-carboxysalicylaldimine), py=pyridine] under a pulsed and intense magnetic field (32 T) has been probed by optical reflectivity. In the absence of perturbation, a thermal hysteresis loop (ΔT=19.4 K, T<sub>1/2</sub>=126 K) was detected. Applying a magnetic field of 32 T to the solid, the initial state of which belongs to the ascending branch of the hysteresis loop, leads to an irreversible and quasicomplete S=1/2→S=3/2 transition. The experimental evidence of this crossover triggered by a pulsed magnetic field is reported here in conjunction with an adequate Ising-like model. This two-level model, used as a first approach, allows us to reproduce quantitatively the -4.9 K shift in transition temperature under the effect of the 32 T static magnetic field. The dynamic aspects of the previous model are also explored, leading to a description of the main features of the phenomenon. Indeed, an irreversible (reversible) jump of the high-spin fraction is predicted when the pulsed magnetic field is applied in the metastable LS (HS) phase.

DOI: 10.1103/PhysRevB.65.172412

PACS number(s): 75.90.+w, 05.50.+q, 05.70.Ln, 78.20.Ls

Spin-crossover (SC) materials, studied extensively for their thermo-, piezo-, photo-, and magnetochromic properties,¹ seem to have promising potentialities as high-density reinscribable memories. Indeed, the state of such bistable systems can be addressed on the molecular scale. The variety of properties displayed by such systems might be employed in writing or reading processes. From this point of view, a synergy between the elaboration of new materials and the study of mechanisms which govern addressing of information should be tentatively sought. In this respect, the understanding and control of the dynamic processes between the macroscopic metastable and stable states appears to be crucial. This field has a strong connection with the very active and more general theme of the dynamics of phase transitions² and justifies the intense collaboration between the scientific communities of chemists and physicists.

The discovery of the light-induced excited spin-state trapping (LIESST) effect³ in spin-crossover systems has opened a new field of investigation, i.e., the study of out-of-equilibrium properties in such systems. Photoinduced bistability studied from the experimental⁴ and theoretical⁵ points of view affords typical examples. Recently, Ogawa et al.⁶ have reported that the LIESST effect can show nonlinear characteristics such as thresholdlike behavior, incubation time, and phase separation, suggesting the existence of a cooperative photoinduced phase transition in SC solids. Recently, partial triggering of the iron(II) spin crossover in solid Fe(Phen)<sub>2</sub>NCS<sub>2</sub> has also been evidenced upon application of a high magnetic field in the hysteresis loop.⁷

We report here the possibility of a quasicomplete commutation of cobalt(II) between the two states of a SC system by a pulsed magnetic field (PMF). Choosing a cobalt-based SC system follows the idea that cobalt(II) materials as well as iron(III) ones have metal-ligand bonds shorter than those in iron(II) materials, leading to faster relaxation dynamics between the high-spin (HS) and low-spin (LS) states, which

should enhance the PMF addressing of SC. We also report on a theoretical analysis based on a stochastic approach of the dynamic behavior of the high-spin fraction under applied PMF.

For this study, we have thus prepared the SC complex Co<sup>II</sup>(H<sub>2</sub>(fsa)<sub>2</sub>en)(py)<sub>2</sub> [H<sub>2</sub>(fsa)en=N,N'-ethylene bis(3-carboxysalicylaldimine,py)=pyridine] following the method described by Torihara et al.⁸ If the energy barriers in the solid state are thermally accessible, cobalt(II) (d<sup>7</sup>) in the previous molecule may be either in the LS state (t<sub>2g</sub><sup>6</sup>e<sub>2g</sub><sup>1</sup>,S = 1/2) or in the HS state (t<sub>2g</sub><sup>5</sup>e<sub>2g</sub><sup>2</sup>,S = 3/2), both of which are paramagnetic and correspond to strong and weak ligand field energies, respectively. At the macroscopic level, an external perturbation such as temperature, pressure, light, or magnetic field can induce a spin crossover between the two states. The spin transition in Co(H<sub>2</sub>(fsa)<sub>2</sub>en)(py)<sub>2</sub> is also associated with a color change and can thus be probed by reflectivity measurements. Indeed, the color of the sample changes from red in the LS state to orange in the HS state.

Figure 1 shows the temperature dependence of the HS fraction of the sample, which consists in an abrupt thermally induced spin crossover. This first-order transition, evidenced by a 19-K-wide hysteresis loop centered at 126 K, is observed by reflectivity measurements⁹ on a microcrystalline sample (15 mg) of Co(H<sub>2</sub>(fsa)<sub>2</sub>en)py<sub>2</sub>.

To carry out the experiments of magnetoswitching in molecular spin-crossover systems, we have used the experimental facility of the Laboratoire National des Champs Magnétiques Pulsés (LNCMP) which produces high magnetic fields [up to 32 T (Fig. 2) and very recently 60 T] of long duration, by discharge in the resistive coil of a battery of condensers (1.25 MJ, 25000 μF) beforehand charged under a 0–10 kV voltage.

The cobalt(II) HS fraction, denoted n<sub>HS</sub>, can be probed instantaneously with an optical reflectivity setup⁹ utilizing a continuous helium-neon laser (632.8 nm) irradiation with a power of 5 mW.
<figure><img src="image_2.png" /><figcaption>FIG. 1. Thermal hysteresis [high-spin fraction ($n_{HS}$) vs temperature] of Co(H$_2$(fsa)$_2$en)(py)$_2$, obtained by reflectivity measurements.</figcaption></figure>

The PMF shown in Fig. 2 has been applied to various states of the metastable HS and LS phases, corresponding to initial states of equilibrium in the descending and ascending branches of the thermal hysteresis loop shown in Fig. 1, respectively. The results obtained are displayed with the $n_{HS}$ curves (B) in Figs. 3 and 4. Figure 3 shows that application of the high magnetic field is without any effect on the descending branch of the hysteresis loop. Indeed, in this case, the initial state is a metastable HS one, and the effect of the PMF is to increase the free-energy barrier, further stabilizing the HS phase. Therefore, the PMF effect naturally leads to a reversible evolution of the HS fraction.

When the high magnetic field is applied in the ascending branch of the thermal cycle, corresponding to the metastable LS phase (Fig. 4), the latter is destabilized and the HS fraction grows irreversibly according to the nucleation and growth process, which continues beyond the duration of the perturbation. In this region, all metastable LS domains, initially close to an unstable state, switch owing to the magnetic field. Quantitatively, Fig. 4 shows that for an initial $n_{HS}$ fraction ~0.3, the magnetic field induces a quasitotal irreversible triggering of the spin transition with an increase of approximately 60% of the HS fraction. On the time scale of the observation, no delay between the magnetic excitation $B(t)$ and the response $n_{HS}(t)$ of the system is observed. In addition, the final HS state (denoted $n_{HS}^f$) induced by the field is very long lived.

It is also remarkable that the amplitude $\Delta n_{HS} = n_{HS}^f - n_{HS}^0$ of the spin state change strongly depends on the initial state $n_{HS}^0$ (Fig. 5). Indeed, the experimental data represented

<figure><img src="image_3.png" /><figcaption>FIG. 2. Time dependence of the applied magnetic field pulse.</figcaption></figure>

<figure><img src="image_4.png" /><figcaption>FIG. 3. The reversible response of a HS fraction in Co(H$_2$(fsa)$_2$en)(py)$_2$ to an applied PMF in the metastable HS state.</figcaption></figure>

by triangles show that $\Delta n_{HS}$ is maximum when $n_{HS}^0 \approx 0.2$; $\Delta n_{HS}$ decreases quite sharply when the PMF is applied on both sides of this value.

On the other hand, this maximum efficiency in PMF addressing has to be correlated with the thermal evolution of the magnetic susceptibility of the system which also presents a maximum in this temperature range. Such a relation may be obtained using simple considerations in the adiabatic approach.

First, it is straightforward to consider that the magnetic field, which stabilizes more the HS than the LS state, induces a shift $\Delta T_c$ of the transition temperature. In a macroscopic quasistatic approach, this transition temperature shift is given by $\Delta T_c = -\Delta\chi B^2/2\Delta S$, where $\Delta\chi$ is the change in magnetic susceptibility and $\Delta S$ is the entropy variation. Using the experimentally obtained values for $\Delta\chi$ and $\Delta S$,¹⁰ we find that when the magnetic field is increased up to 32 T, both transition temperatures of the thermal hysteresis loop decrease by 4.9 K, which is quite important. This result allows us to determine, in the frame of this adiabatic approximation, the amplitudes $\Delta n_{HS}$ of the changes. The results obtained are plotted as squares in Fig. 5, and they are in quite good agreement with the experimental data. In particular, this first simple approach allows a quite good localization of the $n_{HS}$ region where the response of the system to the magnetic field effect is enhanced.

From the microscopic theoretical point of view, a cooperative spin-crossover solid under a magnetic field **B** can be described by an extended Ising-like model,¹¹ for which the Hamiltonian is written as

<figure><img src="image_5.png" /><figcaption>FIG. 4. Set of isotherms $n_{HS}(B)$ showing the irreversible (and quasitotal) triggering effect on the HS fraction in Co(H$_2$(fsa)$_2$en)(py)$_2$ for an applied PMF in the metastable LS state.</figcaption></figure>
<figure><img src="image_6.png" /><figcaption>FIG. 5. Comparison of the amplitudes of conversion in Co(H₂(fsa)₂en)py₂ obtained experimentally (triangles) and by using the quasistatic approach (squares).</figcaption></figure>

$$ \hat{\mathbf{H}} = \frac{\Delta_0 - kT \ln g_+ / g_-}{2} \sum_i \hat{\sigma}_i - \sum_{i \neq j} J \hat{\sigma}_i \hat{\sigma}_j - g_L \mu B \hat{S}_z^H \sum_i \frac{\hat{\sigma}_i + 1}{2} - g_L \mu \hat{S}_z^L B \sum_i \frac{1 - \hat{\sigma}_i}{2}. \quad (1) $$

In this specific Hamiltonian, the HS and LS states are associated, respectively, with the eigenvalues +1 and -1 of the fictitious spin operator $\sigma$ with their respective different degeneracies $g_+$ and $g_-$. Here $2\Delta_0$ is the energy difference $E(\text{HS}) - E(\text{LS})$ for isolated molecules, and $J$ accounts for ferroelastic interactions between neighboring molecules. The last two terms are the Zeeman contribution in the HS and LS states, respectively, where $\mu$ is the Bohr magneton, $g_L$ the Landé factor, and $S_{H,L}$ is the magnetic spin moment corresponding to the HS and LS states. In absence of a magnetic field, the transition temperature $T_{1/2}$, obtained for equal populations of HS and LS states, is given by $T_{1/2} = \Delta_0 / k_B \ln(g_+ / g_-)$. Under a static magnetic field $B$, such as $g_L \mu B \ll kT_{1/2}$, the shift of the transition temperature $\delta T_{1/2}$ is expected to be given by

$$ \delta T_{1/2} = - \frac{g_L^2 \mu^2 B^2}{24 k_B \Delta_0} [(2S_H + 1)^2 - (2S_L + 1)^2]. $$

In the case of Co(H₂(fsa)₂en)py₂ for which $S_H=3/2$, $S_L = 1/2$, $\Delta_0=700$ K,¹⁰ under a magnetic field of 32 T we obtain $\delta T_{1/2} = -2(\mu_B B)^2 / k_B \Delta_0 \approx -4.9$ K. This negative shift in temperature clearly indicates that the application of the magnetic field stabilizes (destabilizes) the HS (LS) phase.

The dynamic version of this model requires a stochastic description¹² based on the following master equations:

$$ \begin{aligned} \frac{d}{dt} p(\{\sigma\}, t) = & \sum_j W_j(-\sigma_j) p(\{\sigma_j\} - \sigma_j; t) \\ & - \sum_j W_j(\sigma_j) p(\{\sigma_j\} - \sigma_j; t) \end{aligned} \quad (2) $$

$p(\{\sigma\}, t)$ is the probability for observing the system in the configuration $\{\sigma\}=(\sigma_1, \sigma_2, \dots, \sigma_N)$ at time $t$, and $\{\sigma_j\}$ denotes the configuration of all spins except $\sigma_j$. Here $W_j(\sigma_j)$ are the transition rates of the spin flip $\sigma_j \rightarrow -\sigma_j$, induced by

<figure><img src="image_7.png" /><figcaption>FIG. 6. Vibronic intramolecular energy barrier $E_a^0$ for a SC system. $E_H$ and $E_L$ are the energies of the HS and LS states, respectively.</figcaption></figure>

the thermal bath which are constrained to respect the microscopic detailed balance condition.

Due to the existence of a vibronic energy barrier between the HS and LS states at the molecular level, as shown in Fig. 6, the convenient dynamics for the SC problem at high temperature is based on an Arrhenius-like process.¹³ Let us denote by $E_a^0$ the energy barrier between the HS and LS states when they have the same energy, by $E_H$ and $E_L$ their respective energies, and by $W(H \leftrightarrow L)$ the transition rates between the two states. Therefore, $W(H \to L) \propto e^{-\beta(E_a^0 - E_H)}$, and consequently the general form of the rate transition can be written as $W_j(\sigma_j) = (1/2\tau_0)e^{-\beta(E_a^0 + \sigma_j E_j)}$ in which $1/\tau_0$ defines the individual spin-flip rate between the two states and

$$ E_j = -\frac{\Delta_0}{2} + 2 \frac{(\mu B)^2}{kT} + \frac{kT}{2} \ln \frac{g_+}{g_-} + J \sum_i \sigma_i. $$

Inserting this form of transition rates into the master equation (2), we may calculate the temporal evolution of the “magnetization” $m = \langle \sigma_j \rangle$. In the mean-field approximation,¹³ we obtain the following nonlinear differential equation for the HS fraction of molecules, $n_{HS} = (1+m)/2$:

$$ \begin{aligned} \frac{dn_{HS}}{dt} = & -\frac{2}{\tau_0} n_{HS} e^{-\beta \epsilon^+} e^{-2\beta q J n_{HS}} \\ & + \frac{2}{\tau_0} (1 - n_{HS}) e^{-\beta \epsilon^-} e^{2\beta q J n_{HS}}, \end{aligned} \quad (3) $$

with

$$ \epsilon^{\pm} = \pm E_a^{0} \mp \frac{\Delta_0}{2} \mp qJ \pm \frac{kT}{2} \ln 2 \frac{g_{HS}}{g_{LS}} \pm 2 \frac{[\mu B(t)]^2}{kT}. $$

To qualitatively compare the present model with the experimental results, we have resolved Eq. (3) in the ascending and descending branches of the thermal hysteresis loop, for the magnetic pulse represented in Fig. 2. The results obtained in the heating mode, summarized in Fig. 7, lead to the following conclusion: (i) this model is qualitatively in good agreement with the experimental behavior, and (ii) it clearly shows that the nonreversible variation of the high-spin fraction is well reproduced, and the amplitude $\delta n_{HS}$ of the irreversibility depends on the initial state, as found in the experi-
<figure><img src="image_8.png" /><figcaption>FIG. 7. Calculated HS fraction as a function of the pulsed magnetic field **B** in the ascending branch of the hysteresis loop.</figcaption></figure>

ments. In the same way, the reversible character of the evolution of the HS fraction under a pulsed magnetic field is also found when the latter is applied in the descending branch of the hysteresis loop.

In addition, this approach shows that the efficiency of the LS→HS addressing depends on various parameters, including the frequency $1/\tau_0$ of individual spin flip, the strength of the vibronic coupling (from which the energy barrier $E_0^a$ originates), and the transition temperature $T_{1/2}$. Indeed, the same magnetic pulse applied to Fe(Phen)$_2$(NCS)$_2$ (Ref. 7) produces a jump in HS fraction 60% weaker than that obtained with Co(H$_2$(fsa)$_2$en)(py)$_2$. These results are in very

good agreement with the respective shifts in transition temperature, $\delta T_{1/2} = -1.9$ K and $-4.9$ K. Moreover, it is well known from the literature$^{14}$ that relaxation is slower in iron(II) compared to cobalt or iron(III) spin-crossover complexes, due to differences in the strength of the vibronic coupling.

It is also worth mentioning that the nonreversibility of the response is enhanced when the transition temperature is low, and this is definitely in favor of Co(H$_2$(fsa)$_2$en)(py)$_2$ for which $T_{1/2}$=130 K [$T_{1/2}$=180 K for Fe(Phen)$_2$(NCS)$_2$ (Ref. 5)]. It is also interesting to remark that, as an immediate consequence of the fast dynamics, the nonlinear effects of the interactions are hidden in Co(H$_2$(fsa)en)py$_2$, while they are visible in Fe(Phen)$_2$(NCS)$_2$ owing to the appearance of a temporal delay between the excitation (magnetic pulse) and the response (increase in HS fraction).

In conclusion, we have reported here on a quasitotal triggering of spin crossover by a high magnetic field pulse (32 T). This efficiency of the PMF is based on the main idea that the strength of the vibronic coupling governs the relaxation rate (transition rate). This factor appears crucial in realizing an effective control of the LS→HS transition for addressing information with a magnetic field; the addressed information can be read optically. From the theoretical point of view, the static and dynamic effects observed are well reproduced by an extended Ising-like model including the magnetic field effect: they correspond, respectively, to a shift of the transition temperature and a specific nonlinear time-dependent behavior of the HS fraction under a pulsed magnetic field.

<footnote>*Electronic address: boussek@lcc-toulouse.fr</footnote>

<footnote>†Electronic address: kbo@physique.uvsq.fr</footnote>

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<footnote n="2">²N. Nagaosa and T. Ogawa, in *Relaxation of Excited States and Photo-induced Structural Phase Transition*, edited by K. Nasu, Springer Series in Solid-State Science No. 124 (Springer, Berlin, 1997).</footnote>

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