{"type":"doc","content":[{"type":"heading","attrs":{"id":"9a72f351-28ee-4ea6-9043-e900d12692bf","textAlign":"inherit","indent":0,"level":1,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"KKR方法计算磁性体系交换常数"}]},{"type":"heading","attrs":{"id":"6f013a5f-d108-4575-a48c-83c18fe6d27d","textAlign":"center","indent":0,"level":1,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"KKR方法计算磁性体系交换常数"}]},{"type":"heading","attrs":{"id":"315888b9-303a-4e03-9fb4-442b2db9d614","textAlign":"inherit","indent":0,"level":2,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"一、引言"}]},{"type":"paragraph","attrs":{"id":"ca5e551d-b44c-4621-a612-4080598abecb","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"KKR（Korringa-Kohn-Rostoker）方法计算磁性体系交换常数，通常采用Liechtenstein–Katsnelson–Antropov–Gubanov（LKAG）公式。该方法通过自旋向上/向下电子的Green函数，计算体系总能量对两个磁性原子磁矩相对旋转的二阶响应，从而得到交换常数Jij。"}]},{"type":"paragraph","attrs":{"id":"928cf0bf-741d-417c-a79e-106bd59e997f","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"与基于总能量的方法不同，LKAG不需要构建多个磁构型进行能量差计算，而是直接从电子Green函数导出Jij。"}]},{"type":"heading","attrs":{"id":"bb433b49-b91f-4cd3-bdf4-abbca859122c","textAlign":"inherit","indent":0,"level":2,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"二、Heisenberg模型与交换常数定义"}]},{"type":"paragraph","attrs":{"id":"8ba76c6b-252e-4644-a384-09c709b8fe4a","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"磁性体系通常映射为Heisenberg模型："}]},{"type":"image","attrs":{"id":"d4e3bc64-5c30-42d5-b933-71ec953127cb","src":"https://developer.qcloudimg.com/http-save/audit-12559234/a0fb4069d2453880066c40c2deb3e5c7.webp","extension":"","align":"center","alt":"","showAlt":false,"href":"","boxShadow":"","width":"","aspectRatio":0,"status":"success","showText":true,"isPercentage":false,"percentage":0,"isHoverDragHandle":false}},{"type":"paragraph","attrs":{"id":"32a60baa-b308-4c4d-8d35-ecef93ed422a","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"其中i, j表示两个磁性原子，"},{"type":"text","marks":[{"type":"bold"}],"text":"e"},{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"i、"},{"type":"text","marks":[{"type":"bold"}],"text":"e"},{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"j为局域磁矩方向的单位矢量，Jij为交换常数。"}]},{"type":"paragraph","attrs":{"id":"423864c1-4c4a-48d8-b9ce-cacffbf44d75","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"符号约定："}]},{"type":"image","attrs":{"id":"24d68e32-c543-4b19-bfb3-89b0f47dee37","src":"https://developer.qcloudimg.com/http-save/audit-12559234/0a9dcd5b4b934ac256e1c23e3e8ea5ea.webp","extension":"","align":"center","alt":"","showAlt":false,"href":"","boxShadow":"","width":"","aspectRatio":0,"status":"success","showText":true,"isPercentage":false,"percentage":0,"isHoverDragHandle":false}},{"type":"image","attrs":{"id":"3e005eb1-6414-456c-91e5-5197ebe49c2f","src":"https://developer.qcloudimg.com/http-save/audit-12559234/90246bb783c024ef17a4cffad76a9ae2.webp","extension":"","align":"center","alt":"","showAlt":false,"href":"","boxShadow":"","width":"","aspectRatio":0,"status":"success","showText":true,"isPercentage":false,"percentage":0,"isHoverDragHandle":false}},{"type":"paragraph","attrs":{"id":"a82fe1d0-c77b-46b1-b889-6c2dff03dfb2","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"注：不同程序的Hamiltonian符号约定可能存在差异，实际分析时须参照具体软件定义。"}]},{"type":"heading","attrs":{"id":"5db81095-d4b9-43c1-9b2c-dfd9e9c2ffed","textAlign":"inherit","indent":0,"level":2,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"三、LKAG方法核心思想"}]},{"type":"paragraph","attrs":{"id":"764a586f-b1f1-49fa-b31a-f79e230836ac","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"LKAG方法的关键在于考虑两个局域磁矩发生无穷小旋转："}]},{"type":"paragraph","attrs":{"id":"404a1e68-1a42-43e2-b411-d91409b2fe37","textAlign":"center","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"e"},{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"i → "},{"type":"text","marks":[{"type":"bold"}],"text":"e"},{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"i δ"},{"type":"text","marks":[{"type":"bold"}],"text":"e"},{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"i"}]},{"type":"paragraph","attrs":{"id":"79e66c75-f193-4334-8d6b-05a075fd16a6","textAlign":"center","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"bold"}],"text":"e"},{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"j → "},{"type":"text","marks":[{"type":"bold"}],"text":"e"},{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"j δ"},{"type":"text","marks":[{"type":"bold"}],"text":"e"},{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"j"}]},{"type":"paragraph","attrs":{"id":"625c2264-d094-460e-9642-20af17387240","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"体系总能量展开为："}]},{"type":"image","attrs":{"id":"848b338d-0847-4b69-9461-f5a6b2404e07","src":"https://developer.qcloudimg.com/http-save/audit-12559234/9a71011589ccab686a962edbcb582bd9.webp","extension":"","align":"center","alt":"","showAlt":false,"href":"","boxShadow":"","width":"","aspectRatio":0,"status":"success","showText":true,"isPercentage":false,"percentage":0,"isHoverDragHandle":false}},{"type":"paragraph","attrs":{"id":"23c13ad1-0b7b-4ba0-8e8b-c7cbb565926f","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"由此得到："}]},{"type":"image","attrs":{"id":"b3d474da-4aa8-4bee-8f41-8188278af8d1","src":"https://developer.qcloudimg.com/http-save/audit-12559234/ef9875a69771120b94599e7fc7c28101.webp","extension":"","align":"center","alt":"","showAlt":false,"href":"","boxShadow":"","width":"","aspectRatio":0,"status":"success","showText":true,"isPercentage":false,"percentage":0,"isHoverDragHandle":false}},{"type":"paragraph","attrs":{"id":"a75612fa-8788-4504-b254-16cbee5fed69","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"交换常数本质上即为总能量对两个局域磁矩相对旋转的二阶导数。KKR方法的优势在于，该二阶导数可用Green函数直接表达。"}]},{"type":"heading","attrs":{"id":"f0f4ba93-b473-4dff-8fe9-3f63e5ece461","textAlign":"inherit","indent":0,"level":2,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"四、LKAG公式"}]},{"type":"paragraph","attrs":{"id":"877af32b-c4b4-4a45-8de3-817c9e4460fe","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"经典的LKAG公式表达形式为："}]},{"type":"image","attrs":{"id":"458fcbf5-17a9-4d12-b1db-066d30d1c0c8","src":"https://developer.qcloudimg.com/http-save/audit-12559234/e15ee27350f878a6eec100361446ae63.webp","extension":"","align":"center","alt":"","showAlt":false,"href":"","boxShadow":"","width":"","aspectRatio":0,"status":"success","showText":true,"isPercentage":false,"percentage":0,"isHoverDragHandle":false}},{"type":"heading","attrs":{"id":"3a57b7f1-110a-4122-b673-18b57f110566","textAlign":"inherit","indent":0,"level":3,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"4.1 交换分裂 Δi"}]},{"type":"paragraph","attrs":{"id":"8efee9c9-7b21-40d9-80b7-00241ac9d8c6","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"Δi表示第i个原子的交换分裂："}]},{"type":"image","attrs":{"id":"1825d1d5-55c9-4188-a6a5-d848a9e9c7e0","src":"https://developer.qcloudimg.com/http-save/audit-12559234/395fa51706984ed12bc5e03b66882b30.webp","extension":"","align":"center","alt":"","showAlt":false,"href":"","boxShadow":"","width":"","aspectRatio":0,"status":"success","showText":true,"isPercentage":false,"percentage":0,"isHoverDragHandle":false}},{"type":"paragraph","attrs":{"id":"f226e3d6-8c1e-4ade-9f7d-92a838b0f253","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"其中ti↑(E)和ti↓(E)分别为自旋向上和向下的单原子t矩阵。直观上："}]},{"type":"image","attrs":{"id":"4a16d71e-62a0-4df5-a0a8-6a693d7b7aef","src":"https://developer.qcloudimg.com/http-save/audit-12559234/b4eac64b34e2473925ba9fe958044a14.webp","extension":"","align":"center","alt":"","showAlt":false,"href":"","boxShadow":"","width":"","aspectRatio":0,"status":"success","showText":true,"isPercentage":false,"percentage":0,"isHoverDragHandle":false}},{"type":"heading","attrs":{"id":"40632823-a788-4dd0-9ba5-5c0e072382ef","textAlign":"inherit","indent":0,"level":3,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"4.2 Green函数 Gij"}]},{"type":"paragraph","attrs":{"id":"63e61faa-c0a9-4889-bb79-3ebeeaee803e","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"Gij(E)表示从原子i传播到原子j的Green函数："}]},{"type":"image","attrs":{"id":"f51013b7-00cd-490c-89e6-6e1ebbc6dd63","src":"https://developer.qcloudimg.com/http-save/audit-12559234/05f797f8aa19e07b1e31422516f1d74f.webp","extension":"","align":"center","alt":"","showAlt":false,"href":"","boxShadow":"","width":"","aspectRatio":0,"status":"success","showText":true,"isPercentage":false,"percentage":0,"isHoverDragHandle":false}},{"type":"paragraph","attrs":{"id":"efc5e28f-7e1b-425f-858b-ad1da0a64ab7","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"LKAG公式计算的物理过程为：磁性原子i → 电子传播 → 原子j → 再传播回i，这一过程对磁矩耦合的贡献。"}]},{"type":"heading","attrs":{"id":"fa156c9f-5c5b-4a46-92e3-c345bfef9d4a","textAlign":"inherit","indent":0,"level":2,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"五、Green函数与交换作用的物理图像"}]},{"type":"paragraph","attrs":{"id":"cda95e7d-68e9-4bf0-9575-61efb6a70818","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"设体系中有两个磁性原子i和j。以3d电子为例，其具有交换分裂，即自旋向上与向下的电子散射势不同。电子从i传播到j（Gij），受到j的磁性散射（Δj），再传播回来（Gji），产生耦合项："}]},{"type":"image","attrs":{"id":"cd36d9cd-fadd-42b9-8d7b-aa7c03c94982","src":"https://developer.qcloudimg.com/http-save/audit-12559234/e23120dd82f9e47f42624d9bb47a1742.webp","extension":"","align":"center","alt":"","showAlt":false,"href":"","boxShadow":"","width":"","aspectRatio":0,"status":"success","showText":true,"isPercentage":false,"percentage":0,"isHoverDragHandle":false}},{"type":"paragraph","attrs":{"id":"88faa009-9e72-4c68-9a1c-9fc36819604a","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"该量包含了两个磁矩之间的电子介导耦合。因此，KKR-LKAG特别适合研究以下机制："}]},{"type":"bulletList","attrs":{"id":"91e318d1-f280-444e-8c4e-1e4175843413","isHoverDragHandle":false},"content":[{"type":"listItem","attrs":{"id":"d748b1a0-24c8-4748-a784-535b2750d016"},"content":[{"type":"paragraph","attrs":{"id":"92575fd3-a02e-4641-8791-ba488c158002","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"RKKY相互作用"}]}]},{"type":"listItem","attrs":{"id":"762a122f-f1bb-48fa-a9e1-cc8425cd2673"},"content":[{"type":"paragraph","attrs":{"id":"680c49d1-afc0-43b3-9b9b-1a380009a9ac","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"超交换作用"}]}]},{"type":"listItem","attrs":{"id":"54d2a3b5-ad39-4fb8-9b85-d2871c19a7fb"},"content":[{"type":"paragraph","attrs":{"id":"d88a4ead-6b8d-4400-a919-1db7ca8476bb","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"双交换作用"}]}]},{"type":"listItem","attrs":{"id":"d850664a-4d25-4eed-b137-62103bd4d3dd"},"content":[{"type":"paragraph","attrs":{"id":"08c1ab63-3623-4088-964b-fed5a9b3f8ae","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"巡游磁性"}]}]},{"type":"listItem","attrs":{"id":"873ea376-9355-4c35-845f-b231f9bc70c7"},"content":[{"type":"paragraph","attrs":{"id":"ade0883a-a71c-447f-9660-751f31aac2ba","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"长程交换作用"}]}]}]},{"type":"paragraph","attrs":{"id":"5000734a-7edd-4381-bf81-c34b368945bb","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"上述机制本质上均与电子传播相关。"}]},{"type":"heading","attrs":{"id":"04dc7af2-216a-4bda-9bd3-2374e52a3c96","textAlign":"inherit","indent":0,"level":2,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"六、KKR方法的优势"}]},{"type":"paragraph","attrs":{"id":"bf19bbbf-4dd2-4214-bd27-95d12dfab99a","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"KKR基于多重散射理论（Multiple Scattering Theory），将晶体视为电子在各原子间不断散射的过程。KKR直接构造实空间Green函数G("},{"type":"text","marks":[{"type":"bold"}],"text":"r"},{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":", "},{"type":"text","marks":[{"type":"bold"}],"text":"r"},{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"′, E)，天然拥有电子从某一原子传播到另一原子的信息。"}]},{"type":"paragraph","attrs":{"id":"e44d8d6f-6124-4b5c-97d9-40eb3503ec74","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"由于Jij恰好是这种信息的二阶响应，LKAG与KKR的结合具有自然的理论自洽性。"}]},{"type":"heading","attrs":{"id":"a5a2c345-7db0-47e1-a6a5-ea97c9417524","textAlign":"inherit","indent":0,"level":2,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"七、实际计算流程"}]},{"type":"paragraph","attrs":{"id":"a8fa2d12-c7d9-47fe-845c-5c78d7c49900","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"以NiO体系为例，完整计算流程如下："}]},{"type":"orderedList","attrs":{"id":"bedc1528-6d17-402b-91da-d1c890e95f55","start":1,"isHoverDragHandle":false},"content":[{"type":"listItem","attrs":{"id":"1e549be8-8a6b-408b-9adf-e8909e355d48"},"content":[{"type":"paragraph","attrs":{"id":"b6c934c5-0dd4-4dcb-9298-fc557ce4bb7b","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"建立晶体结构"}]}]},{"type":"listItem","attrs":{"id":"6af5d329-669c-44ab-837e-41a75a764604"},"content":[{"type":"paragraph","attrs":{"id":"0e9a4f83-97e1-41d9-b51e-5e534987d766","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"KKR自洽计算（spin-polarized）"}]}]},{"type":"listItem","attrs":{"id":"21292f8e-6155-4c95-86cb-b797a9c5e35c"},"content":[{"type":"paragraph","attrs":{"id":"458d98d0-c720-4830-bdc7-232e06227d8f","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"得到电荷密度与有效势"}]}]},{"type":"listItem","attrs":{"id":"0fe6b1d9-eecf-475d-b5ad-cd8e15618de6"},"content":[{"type":"paragraph","attrs":{"id":"328b3c92-0b85-430d-8502-33b0d375ba1d","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"得到自旋极化电子结构"}]}]},{"type":"listItem","attrs":{"id":"1d884c20-e6b1-4a73-a760-2631c0c848ac"},"content":[{"type":"paragraph","attrs":{"id":"08469046-83d8-46ac-97b5-5191648ae78e","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"计算单原子t矩阵"}]}]},{"type":"listItem","attrs":{"id":"7d2362e4-e6d2-46cf-a629-6176ac395b5f"},"content":[{"type":"paragraph","attrs":{"id":"11aeabb3-64eb-4b19-b5c1-6f346d352266","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"得到散射路径算符τij"}]}]},{"type":"listItem","attrs":{"id":"a4f8bc84-2b90-42bd-bf17-64d72ecc0f64"},"content":[{"type":"paragraph","attrs":{"id":"4a7e8676-5cfa-495b-90cf-51d0027b2184","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"构造Green函数Gij"}]}]},{"type":"listItem","attrs":{"id":"39a7e82c-616f-452f-9597-9005243ce199"},"content":[{"type":"paragraph","attrs":{"id":"01f2c527-07cd-4c3a-8633-dc4be86f7c12","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"LKAG积分计算Jij"}]}]},{"type":"listItem","attrs":{"id":"37f011a1-5173-4c3e-b4f5-b58931407321"},"content":[{"type":"paragraph","attrs":{"id":"1203d512-2d03-443c-8cbe-1608a2a4a019","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"按距离/原子对分类整理"}]}]},{"type":"listItem","attrs":{"id":"c17bdb22-3dcb-4c09-a9af-add468a1e5f9"},"content":[{"type":"paragraph","attrs":{"id":"0ddf45e9-f727-479b-86ee-1e71f9cb367c","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"得到J1, J2, J3, ..."}]}]}]},{"type":"heading","attrs":{"id":"41fa7a92-2a7c-43e3-b936-2d7aa30af6e7","textAlign":"inherit","indent":0,"level":3,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"7.1 参考磁性状态"}]},{"type":"paragraph","attrs":{"id":"1aface47-fff7-40d3-85dd-0b078a07f107","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"计算前需指定参考磁态，例如："}]},{"type":"bulletList","attrs":{"id":"f0289abb-6a68-474f-96c6-fe5bfb868fe9","isHoverDragHandle":false},"content":[{"type":"listItem","attrs":{"id":"416e2125-0ed5-4ed7-bc76-bf2598dc74a0"},"content":[{"type":"paragraph","attrs":{"id":"a612373c-a7cd-4d57-92a4-c48b7a3c87f7","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"铁磁（FM）：所有磁矩同向排列"}]}]},{"type":"listItem","attrs":{"id":"791219d2-f4ad-4c3d-82c9-89633945b3b6"},"content":[{"type":"paragraph","attrs":{"id":"96624be3-11a0-4d4e-9cc5-7637688ffa83","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"反铁磁（AFM）：磁矩交替反向排列"}]}]}]},{"type":"heading","attrs":{"id":"aac2b9c3-3eb5-42e6-88b7-d5e9e1f4611a","textAlign":"inherit","indent":0,"level":3,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"7.2 自洽计算"}]},{"type":"paragraph","attrs":{"id":"7f57ea76-cac0-4213-82ff-574ea1ed60ec","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"进行自旋极化KKR计算，分别得到有效势Veff↑("},{"type":"text","marks":[{"type":"bold"}],"text":"r"},{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":")和Veff↓("},{"type":"text","marks":[{"type":"bold"}],"text":"r"},{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":")，进而得到各原子的局域磁矩："}]},{"type":"image","attrs":{"id":"5d6e335a-7408-406b-b08e-aece60243d6f","src":"https://developer.qcloudimg.com/http-save/audit-12559234/597aa6cfa35a0fd9fa0f791a8384cfec.webp","extension":"","align":"center","alt":"","showAlt":false,"href":"","boxShadow":"","width":"","aspectRatio":0,"status":"success","showText":true,"isPercentage":false,"percentage":0,"isHoverDragHandle":false}},{"type":"heading","attrs":{"id":"394e68ad-ba6a-432c-89d2-f68241350f10","textAlign":"inherit","indent":0,"level":3,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"7.3 散射矩阵与Green函数"}]},{"type":"paragraph","attrs":{"id":"07948b88-025c-4a47-b757-8b0d0c27f282","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"每个原子对应单原子散射矩阵ti(E)。对于磁性原子，ti↑(E) ≠ ti↓(E)。通过散射路径算符τij(E)："}]},{"type":"image","attrs":{"id":"408b269b-9de9-46b0-88dc-08215e58f9c7","src":"https://developer.qcloudimg.com/http-save/audit-12559234/2f86a7ac2ab7b87dfaa9196cc93d7de6.webp","extension":"","align":"center","alt":"","showAlt":false,"href":"","boxShadow":"","width":"","aspectRatio":0,"status":"success","showText":true,"isPercentage":false,"percentage":0,"isHoverDragHandle":false}},{"type":"paragraph","attrs":{"id":"4116d01d-f23a-46d8-a147-5813c2d7bae9","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"τij包含电子从i到j的所有多重散射路径，因此可描述复杂的电子传播过程，这也是KKR能够得到长程Jij的原因。"}]},{"type":"heading","attrs":{"id":"b095fb26-d5d8-4e96-b4ec-d4a08614da50","textAlign":"inherit","indent":0,"level":3,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"7.4 LKAG积分"}]},{"type":"image","attrs":{"id":"a0ab885c-fc37-4ec7-b9c7-8ba6cb06408c","src":"https://developer.qcloudimg.com/http-save/audit-12559234/5ef327aeae996cd1e6e4720cd9a53812.webp","extension":"","align":"center","alt":"","showAlt":false,"href":"","boxShadow":"","width":"","aspectRatio":0,"status":"success","showText":true,"isPercentage":false,"percentage":0,"isHoverDragHandle":false}},{"type":"paragraph","attrs":{"id":"18d85b1f-c0eb-4faa-a781-a8fe0931570f","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"实际程序采用复能量积分或围道积分等数值方法，而非直接从−∞积到EF。该步骤为计算量较大的环节。"}]},{"type":"heading","attrs":{"id":"de682a21-632d-4758-a40d-9fa38efcd7f2","textAlign":"inherit","indent":0,"level":3,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"7.5 结果分析"}]},{"type":"paragraph","attrs":{"id":"f1ba31f3-dbbc-4574-828e-8cf810b35fdf","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"最终得到不同近邻距离的交换常数，例如："}]},{"type":"paragraph","attrs":{"id":"0ac31865-481a-45d1-abce-ab6a5f010b28","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"J1 = 8.2 meV（最近邻）"},{"type":"hardBreak","attrs":{"id":"464891b6-9d88-49e2-ac08-196c77838c57"}},{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"J2 = −1.4 meV（次近邻）"},{"type":"hardBreak","attrs":{"id":"9de18f08-139a-414b-aa4a-202c760560fa"}},{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"J3 = 0.37 meV（第三近邻）"}]},{"type":"paragraph","attrs":{"id":"afb3dde2-3779-45af-8c75-ca4d6da39f3a","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"可进一步绘制Jij随距离rij的变化关系："}]},{"type":"image","attrs":{"id":"465c80f1-da3c-4089-8e1e-fb8d61b272b2","src":"https://developer.qcloudimg.com/http-save/audit-12559234/643aac8b2e498cc4c670ac60f050d744.webp","extension":"","align":"center","alt":"","showAlt":false,"href":"","boxShadow":"","width":"","aspectRatio":0,"status":"success","showText":true,"isPercentage":false,"percentage":0,"isHoverDragHandle":false}},{"type":"paragraph","attrs":{"id":"ef09eccf-26a9-4c6c-9342-41acd24ecbcc","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"该图对于判断磁性机制具有重要价值。"}]},{"type":"heading","attrs":{"id":"4f5d677d-73ce-4868-8d40-1c3d3c2badc1","textAlign":"inherit","indent":0,"level":2,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"八、KKR-LKAG与VASP四态法的对比"}]},{"type":"heading","attrs":{"id":"6bb6797f-83db-4a2c-8116-2dd979874d92","textAlign":"inherit","indent":0,"level":3,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"8.1 VASP四态法"}]},{"type":"paragraph","attrs":{"id":"2410fb54-4c21-4355-946d-2b684b8ed40c","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"人为建立不同磁构型（如↑↑和↑↓），通过总能量差计算交换常数："}]},{"type":"image","attrs":{"id":"b11bdf12-ba23-4f59-86f2-fac618f20645","src":"https://developer.qcloudimg.com/http-save/audit-12559234/035659d905c18a31a0aa036ce29c2689.webp","extension":"","align":"center","alt":"","showAlt":false,"href":"","boxShadow":"","width":"","aspectRatio":0,"status":"success","showText":true,"isPercentage":false,"percentage":0,"isHoverDragHandle":false}},{"type":"paragraph","attrs":{"id":"501994fe-8b80-492e-8f69-1fe2e85bd9f4","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"该方法需要计算多个有限磁构型的总能量，通过能量差拟合得到J。"}]},{"type":"heading","attrs":{"id":"2f7bf30a-a519-4a77-96e1-8f3d7befb2c4","textAlign":"inherit","indent":0,"level":3,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"8.2 KKR-LKAG"}]},{"type":"paragraph","attrs":{"id":"97e208dc-27c6-40f8-b511-aa62234978fe","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"仅需一个参考磁态，通过Green函数直接计算无穷小旋转下的响应："}]},{"type":"image","attrs":{"id":"4aefef2e-bceb-4cec-91c1-5eb616c32e01","src":"https://developer.qcloudimg.com/http-save/audit-12559234/d42b75e5b2cf39ebaecf96f7ea2fa0cc.webp","extension":"","align":"center","alt":"","showAlt":false,"href":"","boxShadow":"","width":"","aspectRatio":0,"status":"success","showText":true,"isPercentage":false,"percentage":0,"isHoverDragHandle":false}},{"type":"paragraph","attrs":{"id":"7fa580a8-42eb-4efe-afe6-3b65255f8b9a","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"无需构建FM、AFM1、AFM2等多个构型，一个自洽参考态即可得到大量Jij。"}]},{"type":"heading","attrs":{"id":"cd06f63a-f9df-4261-bd3c-4234ee119cbf","textAlign":"inherit","indent":0,"level":3,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"8.3 方法特性差异"}]},{"type":"paragraph","attrs":{"id":"f2721b03-e37e-4a57-b66c-8b237ef6147e","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"LKAG本质上是δθ → 0极限下的计算，得到的是参考磁态附近的交换参数。若体系具有强非Heisenberg特性（磁矩大小随磁构型显著变化），则Jij可能不是固定不变的参数，此时需谨慎使用。"}]},{"type":"heading","attrs":{"id":"16f9d1a6-7a2e-4777-9e00-d29291b0575f","textAlign":"inherit","indent":0,"level":2,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"九、无序体系：KKR-CPA"}]},{"type":"paragraph","attrs":{"id":"62c80132-1dc8-49eb-b395-e3e40b7eceae","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"对于无序体系（如非化学计量比的NiO），若采用超胞方法建立随机构型并逐一计算Jij，工作量巨大。KKR结合相干势近似（CPA）可有效处理此类问题。"}]},{"type":"heading","attrs":{"id":"05445f40-a5d0-4fd5-be2b-59aba2f7c9ad","textAlign":"inherit","indent":0,"level":3,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"9.1 CPA基本思想"}]},{"type":"paragraph","attrs":{"id":"be9cb3fe-fdb5-437a-a9bb-5d42483dbebe","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"以Ni0.8O为例，Ni占据概率cNi = 0.8，空位概率c□ = 0.2。CPA不建立具体的随机超胞，而是构建一个有效介质，代表80% Ni 20% 空位的统计平均，在此有效介质中计算Jij。"}]},{"type":"heading","attrs":{"id":"9711f4bf-9bc4-485b-8ea6-c2b601344568","textAlign":"inherit","indent":0,"level":3,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"9.2 有序与无序的比较"}]},{"type":"paragraph","attrs":{"id":"06d93d6f-d7e5-40a2-885e-3834387986a5","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"通过KKR-LKAG（有序体系）和KKR-CPA（无序体系）分别计算，可直接比较有序与无序状态下的交换相互作用差异，从而判断无序化究竟仅破坏磁长程有序，还是从电子结构层面改变了交换作用本身。"}]},{"type":"heading","attrs":{"id":"b2700568-6db9-468e-a8ef-1777ab6cdf31","textAlign":"inherit","indent":0,"level":2,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"十、常用软件"}]},{"type":"table","attrs":{"id":"4abb3742-1c39-448a-bc4c-fc0018a1633f","isHoverDragHandle":false},"content":[{"type":"tableRow","content":[{"type":"tableHeader","attrs":{"colspan":1,"rowspan":1,"colwidth":null,"style":"-webkit-tap-highlight-color: rgba(0, 0, 0, 0); padding: 10px; outline: 0px; word-break: break-all; hyphens: auto; border-color: rgb(221, 221, 221); 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center;"},"content":[{"type":"paragraph","attrs":{"id":"b81c1ab9-f6b3-437e-b740-f02a94b329bd","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"✓"}]}]},{"type":"tableCell","attrs":{"colspan":1,"rowspan":1,"colwidth":null,"background":null,"color":null,"textAlign":null,"style":"-webkit-tap-highlight-color: rgba(0, 0, 0, 0); padding: 10px; outline: 0px; word-break: break-all; hyphens: auto; border-color: rgb(221, 221, 221); max-width: 100%; text-align: center;"},"content":[{"type":"paragraph","attrs":{"id":"8f809f68-8e14-4761-a795-da08d9c899de","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false}}]}]}]},{"type":"heading","attrs":{"id":"359af7ae-52bb-41b4-ad0f-77060dd73bfe","textAlign":"inherit","indent":0,"level":3,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"10.1 SPR-KKR"}]},{"type":"paragraph","attrs":{"id":"767b6d4a-133b-41b0-978c-ca81738f7555","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"由Hubert Ebert团队发展的自旋极化相对论KKR程序，支持Green函数、自旋极化DFT、相对论/自旋轨道耦合、CPA无序、交换参数Jij、DMI、磁矩、磁各向异性等计算。官方手册包含Exchange coupling parameters (Jij)的完整章节及Fe示例，通过TASK JXC和CLURAD控制交换参数计算。"}]},{"type":"heading","attrs":{"id":"30951065-688f-4c7c-879b-aee8f2cba3f6","textAlign":"inherit","indent":0,"level":3,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"10.2 JuKKR"}]},{"type":"paragraph","attrs":{"id":"df158b8c-5efa-4e15-b6eb-6b19f1e58063","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"德国于利希研究中心发展的全电子KKR程序，支持ASA、全势、标量相对论、SOC、非共线磁性、CPA、Jij、DMI及并行计算。其KKRhost模块适合体相及合金CPA计算，KKRnano模块针对大规模体系（数千原子）的交换耦合计算。"}]},{"type":"heading","attrs":{"id":"6bae9553-8e3c-485b-b671-3c7612aa5fa1","textAlign":"inherit","indent":0,"level":3,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"10.3 AkaiKKR"}]},{"type":"paragraph","attrs":{"id":"553bdc5a-cd27-442a-bfc4-0a801063e093","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"经典的KKR-CPA程序，KKR与CPA结合自然，支持SCF、DOS、能带、合金、空位、杂质、磁性、SOC及CPA计算，适合入门KKR-CPA方法。"}]},{"type":"heading","attrs":{"id":"0a7d9d01-1889-4042-b6d9-b005118e00ed","textAlign":"inherit","indent":0,"level":3,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"10.4 Questaal"}]},{"type":"paragraph","attrs":{"id":"faa706b4-5b33-41a8-8dee-0b900a9769bd","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"包含LMTO、Green函数、ASA、全势、CPA及磁性计算功能，提供基于Liechtenstein公式的Heisenberg交换参数计算教程。"}]},{"type":"heading","attrs":{"id":"0d47b924-fec7-4832-b8f9-c4910d64d180","textAlign":"inherit","indent":0,"level":2,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"十一、总结"}]},{"type":"paragraph","attrs":{"id":"f0be6a34-11d0-46d1-a8a6-1b637b0a4c2b","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"KKR-LKAG方法的本质是计算两个磁性原子之间电子传播的二阶磁能响应。该方法利用KKR的Green函数Gij，将电子从i到j的传播与两个原子的交换分裂Δi、Δj相结合，直接得到交换常数Jij。"}]},{"type":"paragraph","attrs":{"id":"263fddc6-a4bd-4667-9038-cc695cfd51bd","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"核心公式："}]},{"type":"image","attrs":{"id":"8bd402b3-b805-4551-9ab8-bb20ecd6b3fa","src":"https://developer.qcloudimg.com/http-save/audit-12559234/054969abaae16349c6373f968008b6ed.webp","extension":"","align":"center","alt":"","showAlt":false,"href":"","boxShadow":"","width":"","aspectRatio":0,"status":"success","showText":true,"isPercentage":false,"percentage":0,"isHoverDragHandle":false}},{"type":"paragraph","attrs":{"id":"0b330967-1887-49d5-9cfc-bff254518759","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"对于NiO等磁性体系，通过SPR-KKR或JuKKR等程序，结合LKAG方法及CPA处理无序效应，可系统研究近邻及长程交换相互作用，为理解磁性基态提供定量依据。"}]},{"type":"paragraph","attrs":{"id":null,"textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false}}]}","createTime":1786402531,"ext":{"closeTextLink":0,"comment_ban":0,"description":"","focusRead":0},"favNum":0,"html":"","isOriginal":0,"likeNum":0,