# Coupled ferroelastic distortion and spin crossover in the Fe(PM-PEA)2(NCS)2 system: a Landau theory approach

Ricardo G. Torres, Francisco Javier Valverde Muñoz, Elzbieta Trzop, Eric

Collet, Guillaume Chastanet

► To cite this version:

Ricardo G. Torres, Francisco Javier Valverde Muñoz, Elzbieta Trzop, Eric Collet, Guillaume Chastanet. Coupled ferroelastic distortion and spin crossover in the Fe(PM-PEA)2(NCS)2 system: a Landau theory approach. Journées Scientifiques de l'Association Française de Magnétisme Moléculaire 2022, Nov 2022, Dourdan, France. hal-03857174

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# Coupled ferroelastic distortion and spin crossover in the Fe(PM-PEA)₂(NCS)₂ system: a Landau theory approach

Ricardo G. TORRES¹, Francisco Javier VALVERDE-MUÑOZ¹,², Elzbieta TRZOP¹,³, Eric COLLET¹,³, Guillaume CHASTANET⁴

¹Univ Rennes, CNRS, IPR (Institute de Physique de Rennes), UMR 6251, F-35000 Rennes, France; ²Instituto de Ciencia Molecular, Departamento de Química Inorgánica, Universidad de Valencia, 46980 Paterna, Valencia, Spain; ³DYNACOM IRL2015 University of Tokyo - CNRS - UR1, Department of Chemistry, 7-3-1 Hongo, Tokyo 113-0033 - Japan; ⁴ICMCB - UMR5026 87, Avenue du Docteur Schweitzer 33608 PESSAC cedex, France.

## Fe(PM-PEA)₂(NCS)₂

* SCO mononuclear complex.

* Spin transition → Unsymmetric hysteresis loop.

**Unusual behavior:**

* Low T, low-spin (LS) phase is high symmetry (hs): Orthorhombic Pccn

* High T, high-spin (HS) phase is low symmetry (ls): Monoclinic P2₁/c

**Motivation:**

* Understand:

* Coupling (symmetry breaking ferroelastic distortion and non symmetry breaking spin transition)

* HS ls and LS hs phases

## Experimental curves

<figure><img src="image_3.png" /><figcaption>HS fraction</figcaption></figure>

$$ \gamma = \frac{N_{HS}}{N_{HS} + N_{LS}} $$

<figure><img src="image_4.png" /><figcaption>Symmetry Breaking</figcaption></figure>

$$ \eta \propto |\epsilon_{13}| $$ $$ |\epsilon_{13}| = \left| 0.5 \frac{c(T)}{c_0(T)} \cos(\beta(T)) \right| $$

Pccn

<figure><img src="image_5.png" /><figcaption>Group-subgroup relationship</figcaption></figure>

<figure><img src="image_6.png" /></figure>

P2₁/c

## Previous Theoretical Model (Collet & Azzolina, 2021)

<figure><img src="image_7.png" /><figcaption>Coupling</figcaption></figure>

$$ \Phi = F_{ST} + F_{SB} + \lambda_{\eta} v_{s} \eta^{2} + \lambda_{q} v_{s} \left(\frac{1-q}{2}\right) + \frac{1}{2} C_{s}^{0} v_{s}^{2} $$ $$ \Phi = Aq + \frac{B}{2}q^2 + \frac{C}{4}q^4 + \frac{a}{2}\eta^2 + \frac{b}{4}\eta^4 + Dq\eta^2 $$

<figure><img src="image_8.png" /><figcaption>Symmetry breaking Ferroelastic distortion</figcaption></figure>

<figure><img src="image_9.png" /></figure>

## Strong coupling limit model

### Simple second order model

**Strong coupling:** $Dq \gg \frac{a}{2}$

$$ \Phi = Aq + \frac{B}{2}q^2 + Dq\eta^2 + \frac{b}{4}\eta^4 $$

$$ \text{Stability conditions:} \qquad \begin{cases} B > 0 \\ D < 0 \\ \frac{d\Phi}{d\eta} = 0, \frac{d\Phi}{dq} = 0 \\ b > 0 \end{cases} $$

$$ \frac{d^2\Phi}{d\eta^2} > 0, \frac{d^2\Phi}{dq^2} > 0, \frac{d^2\Phi}{dq d\eta} > 0 $$

$$ \text{Solutions:} \quad \eta = 0, \eta^2 = -\frac{2Dq}{b} $$

<figure><img src="image_10.png" /></figure>

$$ T_1 = T_2 \text{ when: } B = \frac{D^2}{b} $$

<figure><img src="image_11.png" /></figure>

**Stability limits:**

$$ \frac{d\Phi_{\eta \neq 0}}{dq} \Big|_{q=1} \Rightarrow T_2 = \frac{2}{a_0} \left( \frac{B}{2} - \frac{D^2}{b} \right) + T_{ST} $$

$$ \begin{cases} q = \frac{-a_0(T_{ST} - T)}{B} \\ T_1 = \frac{Bq}{a_0} + T_{ST} \end{cases} \quad \text{Since } q < 0: \quad T_1 < T_{ST} $$

$$ B < \frac{D^2}{b} $$

<figure><img src="image_12.png" /></figure>

### Higher order model

$$ \Phi = Aq + \frac{B}{2}q^2 + \frac{C}{4}q^4 + \frac{b}{4}\eta^4 + Dq\eta^2 $$

<figure><img src="image_13.png" /></figure>

<figure><img src="image_14.png" /></figure>

* Azzolina, G., Bertoni, R., & Collet, E. (2021). *Journal of Applied Physics*, 129(8).

* Collet, E., & Azzolina, G. (2021). *Physical Review Materials*, 5(4), 1–11.

* Azzolina, G., Bertoni, R., Ecolivet, C., Tokoro, H., Ohkoshi, S. I., & Collet, E. (2020). *Physical Review B*, 102(13), 1–13.

* Carpenter, M. A., Salje, E. K. H., & Graeme-Barber, A. (1998). *European Journal of Mineralogy*, 10(4), 621–691.

* Létard, J.-F., Guionneau, P., Codjovi, E., Lavastre, O., Bravic, G., Chasseau, D., & Kahn, O. (1997). *Journal of the American Chemical Society*, 119(44), 10861–10862.